# questions

tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2013 (23 Apr Online)']
source_db: MarksBatch1_P1.db
title:
a-sonometer-wire-of-length-114-cm-is-fixed-at-both-the-ends-where-should-the-two-bridges-be-placed-so-as-to-divide-the-wire-into-three-segments-whose-

slug:
a-sonometer-wire-of-length-114-cm-is-fixed-at-both-the-ends-where-should-the-two-bridges-be-placed-so-as-to-divide-the-wire-into-three-segments-whose-25861

question:
<div class="question">A sonometer wire of length $114 \mathrm{~cm}$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1: 3: 4$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>At $36 \mathrm{~cm}$ and $84 \mathrm{~cm}$ from one end<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>At $24 \mathrm{~cm}$ and $72 \mathrm{~cm}$ from one end<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>At $48 \mathrm{~cm}$ and $96 \mathrm{~cm}$ from one end<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>At $72 \mathrm{~cm}$ and $96 \mathrm{~cm}$ from one end</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>At $72 \mathrm{~cm}$ and $96 \mathrm{~cm}$ from one end</span> </div>

answer:
<div class="solution">Total length of the wire, $\mathrm{L}=114 \mathrm{~cm}$ $\mathrm{n}_1: \mathrm{n}_2: \mathrm{n}_3=1: 3: 4$<br/>Let $\mathrm{L}_1, \mathrm{~L}_2$ and $\mathrm{L}_3$ be the lengths of the three parts<br/>As $\mathrm{n} \propto \frac{1}{\mathrm{~L}}$<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore \quad \mathrm{L}_1: \mathrm{L}_2: \mathrm{L}_3=\frac{1}{1}: \frac{1}{3}: \frac{1}{4}=12: 4: 3 \\<br/>&amp; \therefore \quad \mathrm{L}_1=72 \mathrm{~cm}\left(\frac{12}{12+4+3} \times 114\right) \\<br/>&amp; \mathrm{L}_2=24 \mathrm{~cm}\left(\frac{4}{19} \times 114\right) \\<br/>&amp; \text { and } \quad \mathrm{L}_3=18 \mathrm{~cm}\left(\frac{3}{19} \times 114\right)<br/>\end{aligned}<br/>$$<br/>Hence the bridges should be placed at $72 \mathrm{~cm}$ and $72+24=96 \mathrm{~cm}$ from one end.</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2024 (05 Apr Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">60</span> </div>
source_db: MarksBatch1_P1.db
title:
a-sonometer-wire-of-resonating-length-90-cm-has-a-fundamental-frequency-of-400-hz-when-kept-under-some-tension-the-resonating-length-of-the-wire-with-

slug:
a-sonometer-wire-of-resonating-length-90-cm-has-a-fundamental-frequency-of-400-hz-when-kept-under-some-tension-the-resonating-length-of-the-wire-with-58820

question:
<div class="question">A sonometer wire of resonating length $90 \mathrm{~cm}$ has a fundamental frequency of $400 \mathrm{~Hz}$ when kept under some tension. The resonating length of the wire with fundamental frequency of $600 \mathrm{~Hz}$ under same tension _____$\mathrm{cm}$.</div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/WITgvaiWulyK4vAa2gkoWz7Rv9yeo_R8KESXJAt3YWw.original.fullsize.png"/><br/>$\begin{aligned} &amp; \mathrm{f}_0=400 \mathrm{~Hz} ; \mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}}=\text { constant } \\ &amp; \frac{\lambda}{2}=\mathrm{L} ; \quad \mathrm{v}=\mathrm{f}_0 \lambda\end{aligned}$<br/>$\begin{aligned} &amp; \frac{\mathrm{v}}{2 \mathrm{f}_0}=\mathrm{L} \Rightarrow \mathrm{v}=2 \mathrm{Lf}_0 \\ &amp; \mathrm{~L}^{\prime}=\frac{\mathrm{v}}{2 \mathrm{f}^{\prime}}=\frac{2 \mathrm{Lf}_0}{2 \mathrm{f}^{\prime}} \\ &amp; =\frac{\mathrm{Lf}_0}{\mathrm{f}^{\prime}}=\frac{90 \times 400}{600}=60\end{aligned}$</div>


tags: ['Physics', 'Wave Optics', 'JIPMER', 'JIPMER 2017']
source_db: MarksBatch1_P1.db
title:
a-source-emits-electromagnetic-waves-of-wavelength-3-m-one-beam-reaches-the-observer-directly-and-other-after-reflection-from-a-water-surface-travelli

slug:
a-source-emits-electromagnetic-waves-of-wavelength-3-m-one-beam-reaches-the-observer-directly-and-other-after-reflection-from-a-water-surface-travelli-45669

question:
<div class="question">A source emits electromagnetic waves of wavelength 3 m . One beam reaches the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to $1 / 4$ as compared to intensity due to the direct beam alone. The resultant intensity will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">(1/4) fold</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">(3/4) fold</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">(5/4) fold</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">(9/4) fold</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(9/4) fold</span> </div>

answer:
<div class="solution">We know that a phase change of $\pi$ occurs when the reflection takes place at the boundary of denser medium. This is equivalent to a path difference of $\lambda / 2$.<br/>$\therefore$ Total phase difference $=\pi-\pi=0$<br/>Thus, the two waves superimpose in phase.<br/>$\begin{aligned}<br/>&amp; \text { Resultant amplitude }=\sqrt{I}+\sqrt{\left(\frac{I}{4}\right)}=\frac{3}{2} \sqrt{I} \\<br/>&amp; \text { Resultant intensity }=\left(\frac{3}{2} \sqrt{I}\right)^2=\frac{9}{4} I=\frac{9}{4} \text { fold. }<br/>\end{aligned}$</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-spacecraft-at-i-2-j-3-k-is-subjected-to-a-force-k-by-firing-a-rocket-the-spacecraft-is-subjected-to-a-moment-of-magnitude

slug:
a-spacecraft-at-i-2-j-3-k-is-subjected-to-a-force-k-by-firing-a-rocket-the-spacecraft-is-subjected-to-a-moment-of-magnitude-61759

question:
<div class="question">A spacecraft at $\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ is subjected to a force $\lambda \hat{\mathrm{k}}$ by firing a rocket. The spacecraft is subjected to a moment of magnitude</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\lambda$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sqrt{3} \lambda$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\sqrt{5} \lambda$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{5} \lambda$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \vec{\tau}=\vec{r} \times \overrightarrow{\mathrm{F}}=(\hat{i}+2 \hat{j}+3 \hat{k}) \times \lambda \hat{k} \\ &amp;=2 \lambda \hat{i}-\lambda \hat{j} \\ \Rightarrow &amp;|\vec{\tau}|=\sqrt{5} \lambda \end{aligned}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-special-dice-with-numbers-1-1-2-2-0-and-3-is-thrown-thrice-what-is-the-probability-that-the-sum-of-the-numbers-occurring-on-the-upper-face-is-zero

slug:
a-special-dice-with-numbers-1-1-2-2-0-and-3-is-thrown-thrice-what-is-the-probability-that-the-sum-of-the-numbers-occurring-on-the-upper-face-is-zero-94820

question:
<div class="question">A special dice with numbers $1,-1,2,-2,0$ and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 72$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 / 8$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7 / 72$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$25 / 216$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$25 / 216$</span> </div>

answer:
<div class="solution">Total no. of elementary events $=6^{3}$. Favourable no. of elementary events<br/>$=$ coefficient of $x^{0}$ in $\left[x+x^{-1}+x^{0}+x^{-2}+x^{2}+x^{3}\right]^{3}$<br/>$=$ coeff. of $x^{0}$ in $\left[\frac{1+x+x^{2}+x^{3}+x^{4}+x^{5}}{x^{2}}\right]^{3}$<br/>= coeff. of $x^{6}$ in $\left[1+x+x^{2}+x^{3}+x^{4}+x^{5}\right]^{3}$<br/>$=$ coeff. of $x^{6}$ in $\left[\frac{1-x^{6}}{1-x}\right]^{3}$<br/>$=$ coeff. of $x^{6}$ in $\left[1-x^{6}\right]^{3}[1-x]$<br/>$=$ coeff. of $x^{6}$ in $\left[1-{ }^{3} C_{1} x^{6}+\ldots .\right][1-x]^{-3}$<br/>$=$ coeff. of $x^{6}$ in $(1-x)^{-3} \cdot{ }^{3} C_{1}$ coeff. of $x^{0}$ in $(1-x)^{-3}$<br/>$={ }^{6+3-1} C_{3-1}-{ }^{3} C_{1}$<br/>$={ }^{8} C_{2}-{ }^{3} C_{1}=\frac{8 !}{6 ! 2 !}-\frac{3 !}{2 !}$<br/>$=\frac{8 \times 7}{2}-3=25$<br/>Required probability $=\frac{25}{216}$</div>


title: a-species-facing-extremely-high-risk-of-extinction-in-the-immediate-future-is-called
slug: a-species-facing-extremely-high-risk-of-extinction-in-the-immediate-future-is-called-39452
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET', 'NEET 2014']
source_db: MarksBatch1_P1.db
question:
<div class="question">A species facing extremely high risk of extinction in the immediate future is called:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Vulnerable</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Endemic</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Critically Endangered</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Extinct</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Critically Endangered</span> </div>

answer:
<div class="solution"><blockquote><p>International Union for Conservation of Nature and Natural Resources<br/>(IUCN), is now known as World Conservation Union (WCU) whose headquarters are at Morges, Switzerland looks after the species which need protection. They maintain<span style="background-color:null;"> Red Data Book, </span>which enlists the different categories of protection needed by flora and fauna.</p><p>Critically endangered organisms face an extremely high risk of extinction and hence, require a greater degree of conservation and care. Examples of such organisms include various species of mammals (rhinos), amphibians (frogs), etc.</p></blockquote></div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-sphere-of-constant-radius-r-through-the-origin-intersects-the-coordinate-axes-in-a-b-and-c-what-is-the-locus-of-the-centroid-of-the-triangle-abc

slug:
a-sphere-of-constant-radius-r-through-the-origin-intersects-the-coordinate-axes-in-a-b-and-c-what-is-the-locus-of-the-centroid-of-the-triangle-abc-16840

question:
<div class="question">A sphere of constant radius $\mathrm{r}$ through the origin intersects the coordinate axes in $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. What is the locus of the centroid of the triangle ABC?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$x^{2}+y^{2}+z^{2}=r^{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$x^{2}+y^{2}+z^{2}=4 r^{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$9\left(x^{2}+y^{2}+z^{2}\right)=4 r^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3\left(x^{2}+y^{2}+z^{2}\right)=2 r^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$9\left(x^{2}+y^{2}+z^{2}\right)=4 r^{2}$</span> </div>

answer:
<div class="solution">Let the sphere passing through points $\mathrm{A}(\mathrm{a}, 0,0), \mathrm{B}(0,$, $\mathrm{b}, 0), \mathrm{C}(0,0, \mathrm{c})$<br/>Equation of sphere is $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}-\mathrm{ax}-\mathrm{by}-\mathrm{cz}=0$<br/>radius, $\mathrm{r}=\frac{1}{2} \sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}}$<br/>$\Rightarrow a^{2}+b^{2}+c^{2}=4 r^{2}$<br/>(Squaring on both sides)<br/>Let $(\alpha, \beta, \gamma)$ be centroid of sphere. $(\alpha, \beta, \gamma)=\left(\frac{a+0+0}{3}, \frac{0+b+0}{3}, \frac{0+0+c}{3}\right)$<br/>$=\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)$<br/>$\alpha^{2}+\beta^{2}+\gamma^{2}=\frac{\mathrm{a}^{2}}{9}+\frac{\mathrm{b}^{2}}{9}+\frac{\mathrm{c}^{2}}{9}$<br/>$=\frac{a^{2}+b^{2}+c^{2}}{9}$<br/>$($ from $(1))$<br/>$\left.z^{2}\right)=4 r^{2}$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-spherical-balloon-of-radius-r-subtends-an-angle-at-the-eye-of-an-observer-while-the-angle-of-elevation-of-its-centre-is-what-is-the-height-of-the-ce

slug:
a-spherical-balloon-of-radius-r-subtends-an-angle-at-the-eye-of-an-observer-while-the-angle-of-elevation-of-its-centre-is-what-is-the-height-of-the-ce-43101

question:
<div class="question">A spherical balloon of radius $\mathrm{r}$ subtends an angle $\alpha$ at the eye of an observer, while the angle of elevation of its centre is $\beta$. What is the height of the centre of the balloon (neglecting the height of the observer)?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{r \sin \beta}{\sin \left(\frac{\alpha}{2}\right)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{r \sin \beta}{\sin \left(\frac{\alpha}{4}\right)}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{r} \sin \left(\frac{\beta}{2}\right)}{\sin \alpha}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{r \sin \alpha}{\sin \left(\frac{\beta}{2}\right)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{r \sin \beta}{\sin \left(\frac{\alpha}{2}\right)}$</span> </div>

answer:
<div class="solution">Let 'A' be the position of eye. Let ' $\mathrm{O}$ ' be the centre of spherical balloon. Let ${ }^{\circ} \mathrm{h}$ ' be the height of centre of balloon.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/TDRaK01wwbL9J9CWHKnqbVyoJt7KPStGAjsUquKU6cM.original.fullsize.png"/><br/><br/>From figure, in $\Delta \mathrm{OAD}, \sin \frac{\alpha}{2}=\frac{\mathrm{OD}}{\mathrm{OA}}=\frac{\mathrm{r}}{\mathrm{OA}}$<br/>$\Rightarrow \mathrm{OA}=\frac{\mathrm{r}}{\sin \frac{\alpha}{2}}$<br/>In $\Delta \mathrm{OAB}, \sin \beta=\frac{\mathrm{OB}}{\mathrm{OA}}=\frac{\mathrm{h}}{\mathrm{OA}}$<br/>$\Rightarrow \mathrm{h}=\mathrm{OA} \cdot \sin \beta$<br/>$=\frac{\mathrm{r} \cdot \sin \beta}{\sin \frac{\alpha}{2}} \quad(\operatorname{from}(1))$</div>


tags: ['Physics', 'Electrostatics', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-spherically-symmetric-gravitational-system-of-particles-has-a-mass-density-0-0-for-r-r-for-r-r-where-r-0-is-a-constant-a-test-mass-can-undergo-circu-1

slug:
a-spherically-symmetric-gravitational-system-of-particles-has-a-mass-density-0-0-for-r-r-for-r-r-where-r-0-is-a-constant-a-test-mass-can-undergo-circu-1-68232

question:
<div class="question">A spherically symmetric gravitational system of particles has a mass density $\rho=\left\{\begin{array}{ll}\rho_{0} &amp; \text { for } \mathrm{r} \leq \mathrm{R} \\ 0 &amp; \text { for } \mathrm{r}&gt;\mathrm{R}\end{array}\right.$
<br/> <br/>where $\mathrm{r}_{0}$ is a constant. A test mass can undergo
<br/> <br/>circular motion under the influence of the gravitational field of particles. Its speed $\mathrm{V}$ as a function of distance $r(0<r by="" centre="" from="" is="" of="" represented="" system="" the=""> <div class="tags" data-pagefind-ignore=""> <span class="tag">Physics</span><span class="tag">Electrostatics</span><span class="tag">JEE Main</span> </div> <span class="label">Options:</span>
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4_mVNkW8izvk4YpMzNKAmHSO0bin9AXBKI6-p65iKKc.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/uw-k7WgNaR6afUBiWAXADXwmrGzFD8-hxY-4VHV4RlQ.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ky9ucJjGYT4arSBcXVk96lSrhwvZIwCeMwskrxZAQLY.original.fullsize.png"/></span> </li> </ul> <!-- /Question --> <!-- Solution --> <section class="solution-container" id="accepted-answer"> <div class="solution-header"> <span class="label">Solution:</span> <div class="badges-container" data-pagefind-ignore=""> <span class="badge upvotes-count"> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.625 5.0075C14.4842 4.84795 14.3111 4.72019 14.1171 4.63269C13.9231 4.54519 13.7128 4.49996 13.5 4.5H10V3.5C10 2.83696 9.73661 2.20107 9.26777 1.73223C8.79893 1.26339 8.16304 1 7.5 1C7.40711 0.999934 7.31604 1.02574 7.237 1.07454C7.15795 1.12333 7.09407 1.19318 7.0525 1.27625L4.69125 6H2C1.73478 6 1.48043 6.10536 1.29289 6.29289C1.10536 6.48043 1 6.73478 1 7V12.5C1 12.7652 1.10536 13.0196 1.29289 13.2071C1.48043 13.3946 1.73478 13.5 2 13.5H12.75C13.1154 13.5001 13.4684 13.3668 13.7425 13.1252C14.0166 12.8835 14.1931 12.5501 14.2388 12.1875L14.9888 6.1875C15.0153 5.97626 14.9966 5.76179 14.9339 5.55833C14.8712 5.35488 14.7659 5.16711 14.625 5.0075ZM2 7H4.5V12.5H2V7Z" fill="#014A82"></path> </svg> 1262 Upvotes
</span> <span class="badge expert-verification-badge" data-pagefind-ignore=""> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.1163 6.42625C13.8806 6.18 13.6369 5.92625 13.545 5.70312C13.46 5.49875 13.455 5.16 13.45 4.83187C13.4406 4.22187 13.4306 3.53062 12.95 3.05C12.4694 2.56937 11.7781 2.55937 11.1681 2.55C10.84 2.545 10.5012 2.54 10.2969 2.455C10.0744 2.36312 9.82 2.11937 9.57375 1.88375C9.1425 1.46937 8.6525 1 8 1C7.3475 1 6.85812 1.46937 6.42625 1.88375C6.18 2.11937 5.92625 2.36312 5.70312 2.455C5.5 2.54 5.16 2.545 4.83187 2.55C4.22187 2.55937 3.53062 2.56937 3.05 3.05C2.56937 3.53062 2.5625 4.22187 2.55 4.83187C2.545 5.16 2.54 5.49875 2.455 5.70312C2.36312 5.92562 2.11937 6.18 1.88375 6.42625C1.46937 6.8575 1 7.3475 1 8C1 8.6525 1.46937 9.14187 1.88375 9.57375C2.11937 9.82 2.36312 10.0738 2.455 10.2969C2.54 10.5012 2.545 10.84 2.55 11.1681C2.55937 11.7781 2.56937 12.4694 3.05 12.95C3.53062 13.4306 4.22187 13.4406 4.83187 13.45C5.16 13.455 5.49875 13.46 5.70312 13.545C5.92562 13.6369 6.18 13.8806 6.42625 14.1163C6.8575 14.5306 7.3475 15 8 15C8.6525 15 9.14187 14.5306 9.57375 14.1163C9.82 13.8806 10.0738 13.6369 10.2969 13.545C10.5012 13.46 10.84 13.455 11.1681 13.45C11.7781 13.4406 12.4694 13.4306 12.95 12.95C13.4306 12.4694 13.4406 11.7781 13.45 11.1681C13.455 10.84 13.46 10.5012 13.545 10.2969C13.6369 10.0744 13.8806 9.82 14.1163 9.57375C14.5306 9.1425 15 8.6525 15 8C15 7.3475 14.5306 6.85812 14.1163 6.42625ZM10.8538 6.85375L7.35375 10.3538C7.30731 10.4002 7.25217 10.4371 7.19147 10.4623C7.13077 10.4874 7.06571 10.5004 7 10.5004C6.93429 10.5004 6.86923 10.4874 6.80853 10.4623C6.74783 10.4371 6.69269 10.4002 6.64625 10.3538L5.14625 8.85375C5.05243 8.75993 4.99972 8.63268 4.99972 8.5C4.99972 8.36732 5.05243 8.24007 5.14625 8.14625C5.24007 8.05243 5.36732 7.99972 5.5 7.99972C5.63268 7.99972 5.75993 8.05243 5.85375 8.14625L7 9.29313L10.1462 6.14625C10.1927 6.09979 10.2479 6.06294 10.3086 6.0378C10.3692 6.01266 10.4343 5.99972 10.5 5.99972C10.5657 5.99972 10.6308 6.01266 10.6914 6.0378C10.7521 6.06294 10.8073 6.09979 10.8538 6.14625C10.9002 6.1927 10.9371 6.24786 10.9622 6.30855C10.9873 6.36925 11.0003 6.4343 11.0003 6.5C11.0003 6.5657 10.9873 6.63075 10.9622 6.69145C10.9371 6.75214 10.9002 6.8073 10.8538 6.85375Z" fill="#00672E"></path> </svg>
Verified Answer
</span> </div> </div> <div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> </div> <div class="solution">Given mass density \(P=\left\{P_{0}\right.\) for \(r \leq R O\) for \(\left.r&gt;R\right\}\)
<br/> <br/>Since gravitational depends on mass, which is zero for \(r&gt;R\), hence it only acts for \(r \leq R\).
<br/> <br/>\(\begin{aligned}
<br/> <br/>&amp;\overrightarrow{\mathrm{F}}_{\text {graw }}=\overrightarrow{\mathrm{F}}_{\text {circular }} \\
<br/> <br/>&amp;\Rightarrow \frac{\mathrm{GM}_{\text {sphere }} \times \mathrm{M}}{\mathrm{R}^{2}}=\frac{\mathrm{M}(\mathrm{e})^{2}}{\mathrm{R}} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{M}_{\text {sphere }}}{\mathrm{R}} \text { since } \mathrm{r} \leq \mathrm{R} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{R}^{3}}{\mathrm{R}} \alpha \mathrm{R}^{2} \Rightarrow \mathrm{V} \alpha \mathrm{R} \quad \text { straight line }+\mathrm{ve} \text { slope }
<br/> <br/>\end{aligned}\)
<br/> <br/>Beyond \(\mathrm{r}=\mathrm{R}\), mass density \(=0 \Rightarrow\) acceleration due to gravity \(=0 \Rightarrow\) velocity stays constant.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/gsdhgwt463hsjhwu.png"/></div> </section> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4_mVNkW8izvk4YpMzNKAmHSO0bin9AXBKI6-p65iKKc.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/uw-k7WgNaR6afUBiWAXADXwmrGzFD8-hxY-4VHV4RlQ.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ky9ucJjGYT4arSBcXVk96lSrhwvZIwCeMwskrxZAQLY.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Given mass density \(P=\left\{P_{0}\right.\) for \(r \leq R O\) for \(\left.r&gt;R\right\}\)
<br/> <br/>Since gravitational depends on mass, which is zero for \(r&gt;R\), hence it only acts for \(r \leq R\).
<br/> <br/>\(\begin{aligned}
<br/> <br/>&amp;\overrightarrow{\mathrm{F}}_{\text {graw }}=\overrightarrow{\mathrm{F}}_{\text {circular }} \\
<br/> <br/>&amp;\Rightarrow \frac{\mathrm{GM}_{\text {sphere }} \times \mathrm{M}}{\mathrm{R}^{2}}=\frac{\mathrm{M}(\mathrm{e})^{2}}{\mathrm{R}} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{M}_{\text {sphere }}}{\mathrm{R}} \text { since } \mathrm{r} \leq \mathrm{R} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{R}^{3}}{\mathrm{R}} \alpha \mathrm{R}^{2} \Rightarrow \mathrm{V} \alpha \mathrm{R} \quad \text { straight line }+\mathrm{ve} \text { slope }
<br/> <br/>\end{aligned}\)
<br/> <br/>Beyond \(\mathrm{r}=\mathrm{R}\), mass density \(=0 \Rightarrow\) acceleration due to gravity \(=0 \Rightarrow\) velocity stays constant.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/gsdhgwt463hsjhwu.png"/></div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch1_P1.db
title:
a-spherically-symmetric-gravitational-system-of-particles-has-a-mass-density-0-0-for-r-r-for-r-r-where-r-0-is-a-constant-a-test-mass-can-undergo-circu

slug:
a-spherically-symmetric-gravitational-system-of-particles-has-a-mass-density-0-0-for-r-r-for-r-r-where-r-0-is-a-constant-a-test-mass-can-undergo-circu-74549

question:
<div class="question">A spherically symmetric gravitational system of particles has a mass density $\rho=\left\{\begin{array}{ll}\rho_{0} &amp; \text { for } \mathrm{r} \leq \mathrm{R} \\ 0 &amp; \text { for } \mathrm{r}&gt;\mathrm{R}\end{array}\right.$
<br/> <br/>where $\mathrm{r}_{0}$ is a constant. A test mass can undergo
<br/> <br/>circular motion under the influence of the gravitational field of particles. Its speed $\mathrm{V}$ as a function of distance $r(0<r by="" centre="" from="" is="" of="" represented="" system="" the=""> <div class="tags" data-pagefind-ignore=""> <span class="tag">Physics</span><span class="tag">Electrostatics</span><span class="tag">BITSAT</span><span class="tag">BITSAT 2014</span> </div> <span class="label">Options:</span>
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4_mVNkW8izvk4YpMzNKAmHSO0bin9AXBKI6-p65iKKc.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/uw-k7WgNaR6afUBiWAXADXwmrGzFD8-hxY-4VHV4RlQ.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ky9ucJjGYT4arSBcXVk96lSrhwvZIwCeMwskrxZAQLY.original.fullsize.png"/></span> </li> </ul> <!-- /Question --> <!-- Solution --> <section class="solution-container" id="accepted-answer"> <div class="solution-header"> <span class="label">Solution:</span> <div class="badges-container" data-pagefind-ignore=""> <span class="badge upvotes-count"> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.625 5.0075C14.4842 4.84795 14.3111 4.72019 14.1171 4.63269C13.9231 4.54519 13.7128 4.49996 13.5 4.5H10V3.5C10 2.83696 9.73661 2.20107 9.26777 1.73223C8.79893 1.26339 8.16304 1 7.5 1C7.40711 0.999934 7.31604 1.02574 7.237 1.07454C7.15795 1.12333 7.09407 1.19318 7.0525 1.27625L4.69125 6H2C1.73478 6 1.48043 6.10536 1.29289 6.29289C1.10536 6.48043 1 6.73478 1 7V12.5C1 12.7652 1.10536 13.0196 1.29289 13.2071C1.48043 13.3946 1.73478 13.5 2 13.5H12.75C13.1154 13.5001 13.4684 13.3668 13.7425 13.1252C14.0166 12.8835 14.1931 12.5501 14.2388 12.1875L14.9888 6.1875C15.0153 5.97626 14.9966 5.76179 14.9339 5.55833C14.8712 5.35488 14.7659 5.16711 14.625 5.0075ZM2 7H4.5V12.5H2V7Z" fill="#014A82"></path> </svg> 1141 Upvotes
</span> <span class="badge expert-verification-badge" data-pagefind-ignore=""> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.1163 6.42625C13.8806 6.18 13.6369 5.92625 13.545 5.70312C13.46 5.49875 13.455 5.16 13.45 4.83187C13.4406 4.22187 13.4306 3.53062 12.95 3.05C12.4694 2.56937 11.7781 2.55937 11.1681 2.55C10.84 2.545 10.5012 2.54 10.2969 2.455C10.0744 2.36312 9.82 2.11937 9.57375 1.88375C9.1425 1.46937 8.6525 1 8 1C7.3475 1 6.85812 1.46937 6.42625 1.88375C6.18 2.11937 5.92625 2.36312 5.70312 2.455C5.5 2.54 5.16 2.545 4.83187 2.55C4.22187 2.55937 3.53062 2.56937 3.05 3.05C2.56937 3.53062 2.5625 4.22187 2.55 4.83187C2.545 5.16 2.54 5.49875 2.455 5.70312C2.36312 5.92562 2.11937 6.18 1.88375 6.42625C1.46937 6.8575 1 7.3475 1 8C1 8.6525 1.46937 9.14187 1.88375 9.57375C2.11937 9.82 2.36312 10.0738 2.455 10.2969C2.54 10.5012 2.545 10.84 2.55 11.1681C2.55937 11.7781 2.56937 12.4694 3.05 12.95C3.53062 13.4306 4.22187 13.4406 4.83187 13.45C5.16 13.455 5.49875 13.46 5.70312 13.545C5.92562 13.6369 6.18 13.8806 6.42625 14.1163C6.8575 14.5306 7.3475 15 8 15C8.6525 15 9.14187 14.5306 9.57375 14.1163C9.82 13.8806 10.0738 13.6369 10.2969 13.545C10.5012 13.46 10.84 13.455 11.1681 13.45C11.7781 13.4406 12.4694 13.4306 12.95 12.95C13.4306 12.4694 13.4406 11.7781 13.45 11.1681C13.455 10.84 13.46 10.5012 13.545 10.2969C13.6369 10.0744 13.8806 9.82 14.1163 9.57375C14.5306 9.1425 15 8.6525 15 8C15 7.3475 14.5306 6.85812 14.1163 6.42625ZM10.8538 6.85375L7.35375 10.3538C7.30731 10.4002 7.25217 10.4371 7.19147 10.4623C7.13077 10.4874 7.06571 10.5004 7 10.5004C6.93429 10.5004 6.86923 10.4874 6.80853 10.4623C6.74783 10.4371 6.69269 10.4002 6.64625 10.3538L5.14625 8.85375C5.05243 8.75993 4.99972 8.63268 4.99972 8.5C4.99972 8.36732 5.05243 8.24007 5.14625 8.14625C5.24007 8.05243 5.36732 7.99972 5.5 7.99972C5.63268 7.99972 5.75993 8.05243 5.85375 8.14625L7 9.29313L10.1462 6.14625C10.1927 6.09979 10.2479 6.06294 10.3086 6.0378C10.3692 6.01266 10.4343 5.99972 10.5 5.99972C10.5657 5.99972 10.6308 6.01266 10.6914 6.0378C10.7521 6.06294 10.8073 6.09979 10.8538 6.14625C10.9002 6.1927 10.9371 6.24786 10.9622 6.30855C10.9873 6.36925 11.0003 6.4343 11.0003 6.5C11.0003 6.5657 10.9873 6.63075 10.9622 6.69145C10.9371 6.75214 10.9002 6.8073 10.8538 6.85375Z" fill="#00672E"></path> </svg>
Verified Answer
</span> </div> </div> <div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> </div> <div class="solution">Given mass density \(P=\left\{P_{0}\right.\) for \(r \leq R O\) for \(\left.r&gt;R\right\}\)
<br/> <br/>Since gravitational depends on mass, which is zero for \(r&gt;R\), hence it only acts for \(r \leq R\).
<br/> <br/>\(\begin{aligned}
<br/> <br/>&amp;\overrightarrow{\mathrm{F}}_{\text {graw }}=\overrightarrow{\mathrm{F}}_{\text {circular }} \\
<br/> <br/>&amp;\Rightarrow \frac{\mathrm{GM}_{\text {sphere }} \times \mathrm{M}}{\mathrm{R}^{2}}=\frac{\mathrm{M}(\mathrm{e})^{2}}{\mathrm{R}} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{M}_{\text {sphere }}}{\mathrm{R}} \text { since } \mathrm{r} \leq \mathrm{R} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{R}^{3}}{\mathrm{R}} \alpha \mathrm{R}^{2} \Rightarrow \mathrm{V} \alpha \mathrm{R} \quad \text { straight line }+\mathrm{ve} \text { slope }
<br/> <br/>\end{aligned}\)
<br/> <br/>Beyond \(\mathrm{r}=\mathrm{R}\), mass density \(=0 \Rightarrow\) acceleration due to gravity \(=0 \Rightarrow\) velocity stays constant.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/gsdhgwt463hsjhwu.png"/></div> </section> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4_mVNkW8izvk4YpMzNKAmHSO0bin9AXBKI6-p65iKKc.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/uw-k7WgNaR6afUBiWAXADXwmrGzFD8-hxY-4VHV4RlQ.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ky9ucJjGYT4arSBcXVk96lSrhwvZIwCeMwskrxZAQLY.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/zlmjtZrHwk9bZI1kJjha9uzSrXfRvbMccZpIFYZiThM.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Given mass density \(P=\left\{P_{0}\right.\) for \(r \leq R O\) for \(\left.r&gt;R\right\}\)
<br/> <br/>Since gravitational depends on mass, which is zero for \(r&gt;R\), hence it only acts for \(r \leq R\).
<br/> <br/>\(\begin{aligned}
<br/> <br/>&amp;\overrightarrow{\mathrm{F}}_{\text {graw }}=\overrightarrow{\mathrm{F}}_{\text {circular }} \\
<br/> <br/>&amp;\Rightarrow \frac{\mathrm{GM}_{\text {sphere }} \times \mathrm{M}}{\mathrm{R}^{2}}=\frac{\mathrm{M}(\mathrm{e})^{2}}{\mathrm{R}} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{M}_{\text {sphere }}}{\mathrm{R}} \text { since } \mathrm{r} \leq \mathrm{R} \\
<br/> <br/>&amp;\Rightarrow \mathrm{V}^{2} \alpha \frac{\mathrm{R}^{3}}{\mathrm{R}} \alpha \mathrm{R}^{2} \Rightarrow \mathrm{V} \alpha \mathrm{R} \quad \text { straight line }+\mathrm{ve} \text { slope }
<br/> <br/>\end{aligned}\)
<br/> <br/>Beyond \(\mathrm{r}=\mathrm{R}\), mass density \(=0 \Rightarrow\) acceleration due to gravity \(=0 \Rightarrow\) velocity stays constant.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/gsdhgwt463hsjhwu.png"/></div>


title: a-spoon-to-be-electroplated-with-gold-should-be
slug: a-spoon-to-be-electroplated-with-gold-should-be-59900
question: <div class="question">A spoon to be electroplated with gold should be</div>
tags: ['Chemistry', 'Electrochemistry', 'AIIMS', 'AIIMS 2001']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">cathode</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">anode</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">electrolyte</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">none of these.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">cathode</span> </div>

answer:
<div class="solution">Standard electrode potential for Gold is<br/>$$<br/>\mathrm{Au}^{3+}+3 e^{-} \rightleftharpoons \mathrm{Au}<br/>$$<br/>is 1.50 volt. therefore, gold get easily reduced. So to electroplate gold on the spoon, spoon should be made cathode as reduction takes place on cathode.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-square-is-drawn-by-joining-mid-points-of-the-sides-of-a-square-another-square-is-drawn-inside-the-second-square-in-the-same-way-and-the-process-is-c

slug:
a-square-is-drawn-by-joining-mid-points-of-the-sides-of-a-square-another-square-is-drawn-inside-the-second-square-in-the-same-way-and-the-process-is-c-78814

question:
<div class="question">A square is drawn by joining mid points of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued in definitely. If the side of the first square is $16 \mathrm{~cm}$, then what is the sum of the areas of all the squares?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$256 \mathrm{sq} \mathrm{cm}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$512 \mathrm{sq} \mathrm{cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1024 \mathrm{sq} \mathrm{cm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$512 / 3 \mathrm{sq} \mathrm{cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$512 \mathrm{sq} \mathrm{cm}$</span> </div>

answer:
<div class="solution">Let ABCD, EFGH and IJKL be squares. Let side of square $\mathrm{ABCD}=16$ Now, Area of $\mathrm{ABCD}=(16)^{2}$<br/>Area of EFGH $=\frac{(16)^{2}}{2}$,<br/>Area of IJKL $=\frac{(16)^{2}}{4}$ So on.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/-YXC7any67uEFRIjZy-q_3R7XypRh19R2DvnpyxjH-c.original.fullsize.png"/><br/><br/>Required sum,<br/>$=16^{2}+\frac{1}{2}(16)^{2}+\frac{1}{4}(16)^{2}+\ldots . \infty$<br/>$=(16)^{2}\left\{1+\frac{1}{2}+\frac{1}{4}+\ldots \infty\right\}$<br/>Now, $1+\frac{1}{2}+\frac{1}{4}+\ldots \ldots \infty$ is a G.P.<br/>$\therefore \quad$ Sum $=\frac{a}{1-r}$ where $a=1$ and $r=\frac{1}{2}$<br/>$\therefore \quad 1+\frac{1}{2}+\frac{1}{4}+\ldots \ldots+\infty=\frac{1}{1-\frac{1}{2}}=2$<br/>$=256 \times 2=512$ sq. $\mathrm{cm}$</div>


title: a-square-matrix-a-ij-such-that-a-ij-0-for-i-j-and-a-ij-k-where-k-is-a-constant-for-1-j-is-called
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch1_P1.db
slug:
a-square-matrix-a-ij-such-that-a-ij-0-for-i-j-and-a-ij-k-where-k-is-a-constant-for-1-j-is-called-66899

question:
<div class="question">A square matrix $\left[\mathrm{a}_{\mathrm{ij}}\right]$ such that $\mathrm{a}_{\mathrm{ij}}=0$ for $\mathrm{i} \neq \mathrm{j}$ and $\mathrm{a}_{\mathrm{ij}}=\mathrm{k}$ where<br/>$\mathrm{k}$ is a constant for $1=\mathrm{j}$ is called:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">diagonal matrix, but not scalar matrix</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">scalar matrix</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">unit matrix</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">scalar matrix</span> </div>

answer:
<div class="solution">Scalar Matrix. We know that, $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]_{\mathrm{nxn}}$ is called a scalar matrix ifa $_{\mathrm{i}}$ $=0$ for $i \neq j$ and $a_{i j}=k$ for $i=j$ [where $k$ is constant $]$</div>


title: a-square-matrix-a-is-called-orthogonal-if
slug: a-square-matrix-a-is-called-orthogonal-if-62132
question: <div class="question">A square matrix A is called orthogonal if</div>
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{A}=\mathrm{A}^{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{A}^{\prime}=\mathrm{A}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{A}=\mathrm{A}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{A}=\mathrm{A}^{\prime}$<br/>Where $A^{\prime}$ is the transpose of $A$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{A}^{\prime}=\mathrm{A}^{-1}$</span> </div>

answer:
<div class="solution">If $\mathrm{A}^{-1}=\mathrm{A}^{\mathrm{T}}$, then $\mathrm{A}$ is orthogonal matrix.</div>


tags: ['Physics', 'Experimental Physics', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch1_P1.db
title:
a-standard-cell-of-108-v-is-balanced-by-the-potential-difference-across-90-c-m-of-a-1-meter-long-wire-supplied-by-a-cell-of-emf-2-v-through-a-series-r-1

slug:
a-standard-cell-of-108-v-is-balanced-by-the-potential-difference-across-90-c-m-of-a-1-meter-long-wire-supplied-by-a-cell-of-emf-2-v-through-a-series-r-1-43488

question:
<div class="question">A standard cell of <math><mn>1.08</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math> is balanced by the potential difference across <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> of a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> meter, long wire supplied by a cell of emf <math><mn>2</mn><mi mathvariant="normal">V</mi></math> through a series resistor of resistance <math><mn>2</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Î©</mi></math>. If the internal resistance of cell in the primary circuit is zero then the resistance per unit length (in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Î©</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>) of potentiometer wire is</div>

answer:
<div class="solution"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/71558s.PNG" style="width: 300px; height: 203px;"/><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>X</mi><mo>.</mo><mi>l</mi><mo> </mo><mo> </mo><mo> </mo><mrow><mo>(</mo><mi>X</mi><mo>=</mo><mtext>Potential</mtext><mtext> </mtext><mtext>gradient</mtext><mo>)</mo></mrow></math><br/><br/><math><mi mathvariant="normal">E</mi><mi mathvariant="normal"> </mi><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>o</mi></mrow></msub></mrow><mrow><mi>L</mi></mrow></mfrac><mo>×</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mi>r</mi><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>h</mi></mrow></msub></mrow></mfrac></mrow></mfenced><mo>×</mo><mi>l</mi><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mo>∵</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">r</mi><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mn>0</mn><mo>,</mo><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mn>2</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Ω</mi></mrow></mfenced></math><br/><br/><math><mo>∴</mo><mi> </mi><mn>1.08</mn><mi> </mi><mo>=</mo><mi> </mi><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mi> </mi><mi>m</mi></mrow></mfrac><mo>×</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mn>2</mn></mrow></mfrac></mrow></mfenced><mi> </mi><mo>×</mo><mi> </mi><mn>0.90</mn><mi> </mi><mi mathvariant="normal">m</mi></math><br/><br/><math><mfrac><mrow><mn>1.08</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>0.90</mn></mrow></mfrac><mo>=</mo><mi mathvariant="normal"> </mi><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mn>2</mn></mrow></mfrac></math><br/><br/>Hence : <math><mn>0.6</mn><mi mathvariant="normal"> </mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mn>2</mn></mrow></mfrac></math><br/><br/><math><mn>0.6</mn><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mi mathvariant="normal"> </mi><mo>+</mo><mi mathvariant="normal"> </mi><mn>1.2</mn><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mo>⇒</mo><mn>1.2</mn><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mn>0.4</mn><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mi mathvariant="normal"> </mi><mo>⇒</mo><mn>3</mn><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub></math><br/><br/><math><mo>∴</mo></math> Resistance per unit length is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3 </mn><mi mathvariant="normal">Ω</mi><mi> </mi><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></div>


tags: ['Physics', 'Experimental Physics', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch1_P1.db
title:
a-standard-cell-of-108-v-is-balanced-by-the-potential-difference-across-90-c-m-of-a-1-meter-long-wire-supplied-by-a-cell-of-emf-2-v-through-a-series-r

slug:
a-standard-cell-of-108-v-is-balanced-by-the-potential-difference-across-90-c-m-of-a-1-meter-long-wire-supplied-by-a-cell-of-emf-2-v-through-a-series-r-23519

question:
<div class="question">A standard cell of <math><mn>1.08</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math> is balanced by the potential difference across <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> of a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> meter, long wire supplied by a cell of emf <math><mn>2</mn><mi mathvariant="normal">V</mi></math> through a series resistor of resistance <math><mn>2</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Î©</mi></math>. If the internal resistance of cell in the primary circuit is zero then the resistance per unit length (in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Î©</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>) of potentiometer wire is</div>

answer:
<div class="solution"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/71558s.PNG" style="max-width:100%; object-fit:contain"/><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>X</mi><mo>.</mo><mi>l</mi><mo> </mo><mo> </mo><mo> </mo><mrow><mo>(</mo><mi>X</mi><mo>=</mo><mtext>Potential</mtext><mtext> </mtext><mtext>gradient</mtext><mo>)</mo></mrow></math><br/><br/><math><mi mathvariant="normal">E</mi><mi mathvariant="normal"> </mi><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>o</mi></mrow></msub></mrow><mrow><mi>L</mi></mrow></mfrac><mo>×</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mi>r</mi><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>h</mi></mrow></msub></mrow></mfrac></mrow></mfenced><mo>×</mo><mi>l</mi><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mo>∵</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">r</mi><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mn>0</mn><mo>,</mo><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">h</mi></mrow></msub><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mn>2</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Ω</mi></mrow></mfenced></math><br/><br/><math><mo>∴</mo><mi> </mi><mn>1.08</mn><mi> </mi><mo>=</mo><mi> </mi><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>1</mn><mi> </mi><mi>m</mi></mrow></mfrac><mo>×</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mn>2</mn></mrow></mfrac></mrow></mfenced><mi> </mi><mo>×</mo><mi> </mi><mn>0.90</mn><mi> </mi><mi mathvariant="normal">m</mi></math><br/><br/><math><mfrac><mrow><mn>1.08</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>0.90</mn></mrow></mfrac><mo>=</mo><mi mathvariant="normal"> </mi><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mn>2</mn></mrow></mfrac></math><br/><br/>Hence : <math><mn>0.6</mn><mi mathvariant="normal"> </mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><mn>2</mn></mrow></mfrac></math><br/><br/><math><mn>0.6</mn><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mi mathvariant="normal"> </mi><mo>+</mo><mi mathvariant="normal"> </mi><mn>1.2</mn><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mo>⇒</mo><mn>1.2</mn><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mn>0.4</mn><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mi mathvariant="normal"> </mi><mo>⇒</mo><mn>3</mn><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">R</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub></math><br/><br/><math><mo>∴</mo></math> Resistance per unit length is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3 </mn><mi mathvariant="normal">Ω</mi><mi> </mi><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-standard-filament-lamp-consumes-100-w-when-connected-to-200-v-ac-mains-supply-the-peak-current-through-the-bulb-will-be-1

slug:
a-standard-filament-lamp-consumes-100-w-when-connected-to-200-v-ac-mains-supply-the-peak-current-through-the-bulb-will-be-1-21406

question:
<div class="question">A standard filament lamp consumes $100 \mathrm{~W}$ when connected to $200 \mathrm{~V}$ a.c. mains supply. The peak current through the bulb will be :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.707 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.414 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.707 \mathrm{~A}$</span> </div>

answer:
<div class="solution">Power,<br/>$\begin{aligned}<br/>\mathrm{P} &amp; =\mathrm{I}_{\mathrm{rms}} \mathrm{V}_{\mathrm{rms}} \\<br/>\mathrm{I}_{\mathrm{rms}} &amp; =\frac{\mathrm{P}}{\mathrm{V}_{\mathrm{rms}}}=\frac{100}{200}=\frac{1}{2} \\<br/>\mathrm{I}_0 &amp; =\sqrt{2} \mathrm{I}_{\mathrm{rms}} \\<br/>\mathrm{I}_0 &amp; =\sqrt{2} \times \frac{1}{2} \\<br/>\mathrm{I}_0 &amp; =\frac{1}{\sqrt{2}}=0.707 \mathrm{~A}<br/>\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'NEET', 'NEET 2022 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-standard-filament-lamp-consumes-100-w-when-connected-to-200-v-ac-mains-supply-the-peak-current-through-the-bulb-will-be

slug:
a-standard-filament-lamp-consumes-100-w-when-connected-to-200-v-ac-mains-supply-the-peak-current-through-the-bulb-will-be-56418

question:
<div class="question">A standard filament lamp consumes $100 \mathrm{~W}$ when connected to $200 \mathrm{~V}$ a.c. mains supply. The peak current through the bulb will be :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.707 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.414 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.707 \mathrm{~A}$</span> </div>

answer:
<div class="solution">Power,<br/>$\begin{aligned}<br/>\mathrm{P} &amp; =\mathrm{I}_{\mathrm{rms}} \mathrm{V}_{\mathrm{rms}} \\<br/>\mathrm{I}_{\mathrm{rms}} &amp; =\frac{\mathrm{P}}{\mathrm{V}_{\mathrm{rms}}}=\frac{100}{200}=\frac{1}{2} \\<br/>\mathrm{I}_0 &amp; =\sqrt{2} \mathrm{I}_{\mathrm{rms}} \\<br/>\mathrm{I}_0 &amp; =\sqrt{2} \times \frac{1}{2} \\<br/>\mathrm{I}_0 &amp; =\frac{1}{\sqrt{2}}=0.707 \mathrm{~A}<br/>\end{aligned}$</div>


title: a-standard-hydrogen-electrode-has-a-zero-potential-because
slug: a-standard-hydrogen-electrode-has-a-zero-potential-because-57781
question: <div class="question">A standard hydrogen electrode has a zero potential because</div>
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">hydrogen can be most easily oxidised</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">hydrogen has only one electron</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">the electrode potential assumed to be zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">hydrogen is the lightest element</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the electrode potential assumed to be zero</span> </div>

answer:
<div class="solution">According to convention, the standard hydrogen electrode is assigned a zero potential at all temperatures.</div>


tags: ['Physics', 'Waves and Sound', 'KVPY', 'KVPY 2012 (SB/SX)']
source_db: MarksBatch1_P1.db
title:
a-standing-wave-in-a-pipe-with-a-length-l-12-m-is-described-by-y-x-t-y-0-sin-2-l-x-sin-2-l-x-4-based-on-above-information-which-one-of-the-following-s

slug:
a-standing-wave-in-a-pipe-with-a-length-l-12-m-is-described-by-y-x-t-y-0-sin-2-l-x-sin-2-l-x-4-based-on-above-information-which-one-of-the-following-s-69177

question:
<div class="question">A standing wave in a pipe with a length $L=1.2 \mathrm{~m}$ is described by<br/>$y(x, t)=y_{0} \sin [(2 \pi / L) x] \sin [(2 \pi / \mathrm{L}) x+\pi / 4]$<br/>Based on above information, which one of the following statements is incorrect. (Speed of sound in air is $300 \mathrm{~m} \mathrm{~s}^{-1}$ )-</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The pipe is closed at hoth ends</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The wavelength of the wave could be $1.2 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">There could be a node at $\mathrm{x}=0$ and antinode at $\mathrm{x}=\mathrm{L} / 2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The frequency of the fundamental mode of vibrations is $137.5 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The frequency of the fundamental mode of vibrations is $137.5 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">$\begin{array}{l}<br/>\frac{2 \pi}{\lambda} \mathrm{x}=\frac{2 \pi}{\mathrm{L}} \mathrm{x} \\<br/>\therefore \lambda=\mathrm{L}=1.2 \mathrm{~m} \\<br/>\text { at } \mathrm{x}=0, \mathrm{x}=\mathrm{L}, \mathrm{y}=0 \\<br/>\mathrm{v}=\frac{\mathrm{v}}{\lambda}=\frac{300}{1.2}=250 \mathrm{~Hz}<br/>\end{array}$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (10 Aug Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-stationary-wave-is-represented-by-y-10-sin-4-x-cos-20-t-where-x-and-y-are-in-cm-and-t-in-second-the-distance-between-two-consecutive-nodes-is

slug:
a-stationary-wave-is-represented-by-y-10-sin-4-x-cos-20-t-where-x-and-y-are-in-cm-and-t-in-second-the-distance-between-two-consecutive-nodes-is-54525

question:
<div class="question">A stationary wave is represented by $y=10 \sin \left(\frac{\pi x}{4}\right) \cos (20 \pi t)$ where $x$ and $y$ are in $\mathrm{cm}$ and $t$ in second. The distance between two consecutive nodes is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \mathrm{~cm}$</span> </div>

answer:
<div class="solution">Given, $y=10 \sin \left(\frac{\pi x}{4}\right) \cos (\pi t)$<br/>Compare with standard equation formed after superposing<br/>$\begin{aligned} &amp; y=A \sin (k x+\omega t) \text { and } y=A \sin (k x-\omega t) \\ &amp; y=2 A \sin (k x) \cos (\omega t)\end{aligned}$<br/>Therefore, $k=\frac{\pi}{4}$<br/>We know, the propagation constant is:<br/>$k=\frac{2 \pi}{\lambda}=\frac{\pi}{4}$<br/>$\Rightarrow \lambda=8 \mathrm{~cm}$<br/>The distance between two consecutive nodes is given by half of wavelength:<br/>$\frac{\lambda}{2}=4 \mathrm{~cm}$</div>


tags: ['Physics', 'Waves and Sound']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-steel-rod-100-cm-long-is-clamped-at-its-middle-the-fundamental-frequency-of-longitudinal-vibrations-of-the-rod-are-given-to-be-253-khz-what-is-the-s

slug:
a-steel-rod-100-cm-long-is-clamped-at-its-middle-the-fundamental-frequency-of-longitudinal-vibrations-of-the-rod-are-given-to-be-253-khz-what-is-the-s-43447

question:
<div class="question">A steel rod $100 \mathrm{~cm}$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 \mathrm{kHz}$. What is the speed of sound in steel?</div>

answer:
<div class="solution">When the rod is clamped at the middle, a node is forrmed at the middle and 2 antinodes are forrmed at the two ends.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/lFc_Sd2OUhgc17VEsJhLkNowI6IC7-lEpqMRGxtSu14.original.fullsize.png"/><br/><br/>Here, $L=100 \mathrm{~cm}=1 \mathrm{~m}, v=2.53 \mathrm{kHz}=2.53 \times 10^3 \mathrm{~Hz}$<br/>$$<br/>\begin{aligned}<br/>&amp;\therefore \quad L=\frac{\lambda}{4}+\frac{\lambda}{4}=\frac{\lambda}{2} \Rightarrow \lambda=2 L=2 \mathrm{~m} \\<br/>&amp;\mathrm{v}=\mathrm{v} \lambda=2.53 \times 10^3 \times 2=5.06 \times 10^3 \mathrm{~m} / \mathrm{s}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Solids']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-steel-rod-of-length-2-l-crosssectional-area-a-and-mass-m-is-set-rotating-in-a-horizontal-plane-about-an-axis-passing-through-the-centre-if-y-is-the-

slug:
a-steel-rod-of-length-2-l-crosssectional-area-a-and-mass-m-is-set-rotating-in-a-horizontal-plane-about-an-axis-passing-through-the-centre-if-y-is-the-23263

question:
<div class="question">A steel rod of length $2 l$, cross-sectional area $A$ and mass $M$ is set rotating in a horizontal plane about an axis passing through the centre. If $Y$ is the Young's modulus for steel, find the extension in the length of the rod. (assume the rod is uniform)</div>

answer:
<div class="solution">Let an element of width $d r$ at $r$ as shown in the figure.<br/>Let $T(r)$ and $T(r+d r)$ are the tensions at $r$ and $r+d r$ respectively.<br/>Net centrifugal force due to rotation on the element = $\omega^2 r d m$<br/>(where $\omega$ is angular velocity of the rod)<br/>$=\omega^2 r \mu d r \quad(\because \mu=$ mass/length $)$<br/>Centrifugal force on element $(d r)$ due to tension difference<br/>$$<br/>\begin{aligned}<br/>=&amp; T(r+d r)-T(r)=-d T \\<br/>\Rightarrow \quad &amp; T(r+d r)-T(r)=\mu \omega^2 r d r \\<br/>&amp; \quad-d T=\mu \omega^2 r d r<br/>\end{aligned}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/b6J_mUTbzLeAfGm17SKfeyLJG-1FHkltAlDrrgOVWyM.original.fullsize.png"/><br/><br/>Integrating both sides,<br/>$$<br/>\begin{aligned}<br/>&amp;\therefore \quad-\int_{T=0}^T d T=\int_{r=r}^{r=l} \mu \omega^2 r d r=\mu \omega^2\left[\frac{r^2}{2}\right]_r^l \\<br/>&amp;{[\because T=0 \text { at } r=l]}<br/>\end{aligned}<br/>$$<br/>Tension in rod at distance $r$ from centre so, limits will varies $r$ to $l$.<br/>$$<br/>\begin{aligned}<br/>&amp;T(r)=\frac{\mu \omega^2}{2}\left(l^2-r^2\right) \\<br/>&amp;\Rightarrow T(r)=\frac{-\mu \omega^2}{2}\left(l^2-r^2\right)<br/>\end{aligned}<br/>$$<br/>Let the increase in length of the element $d r$ at distance $r$ from centre is $\delta r$ then<img src="https://cdn-question-pool.getmarks.app/modules/cbse/BX_eQql8l8hg8AdntQ50yVE11AoerNDAgh7yh2qvw2U.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>&amp;\text { So, Young's modulus } Y=\frac{\text { Stress }}{\text { Strain }}=\frac{T(r) / A}{\delta r} \\<br/>&amp;\therefore \quad \frac{\delta r}{d r}=\frac{T(r)}{A}=\frac{-\mu \omega^2}{2 Y A}\left(l^2-r^2\right) \\<br/>&amp;\therefore \quad \delta r=\frac{-1}{Y A} \frac{\mu \omega^2}{2}\left(l^2-r^2\right) d r \\<br/>&amp;\therefore \delta r=\frac{1}{Y A} \frac{\mu \omega^2}{2} \int_0^l\left(l^2-r^2\right) d r \\<br/>&amp;\int_0^\delta \delta r=\left(\frac{1}{Y A}\right) \frac{\mu \omega^2}{2}\left[l^3-\frac{l^3}{3}\right]=\frac{1}{3 Y A} \mu \omega^2 l^3<br/>\end{aligned}<br/>$$<br/>(for rod one from centre)<br/>$\therefore$ Total extension in rod both sides<br/>$$<br/>=2 \delta=\frac{2}{3 Y A} \mu \omega^2 l^3<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2018 (24 Apr Shift 2)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch1_P1.db
title:
a-steel-wire-of-length-1-m-mass-01-kg-and-uniform-area-of-cross-section-1-0-6-m-2-is-rigidly-fixed-at-both-the-ends-without-any-tension-its-temperatur

slug:
a-steel-wire-of-length-1-m-mass-01-kg-and-uniform-area-of-cross-section-1-0-6-m-2-is-rigidly-fixed-at-both-the-ends-without-any-tension-its-temperatur-16373

question:
<div class="question">A steel wire of length $1 \mathrm{~m}$, mass $0.1 \mathrm{~kg}$ and uniform area of cross section $10^{-6} \mathrm{~m}^2$ is rigidly fixed at both the ends without any tension. Its temperature is lowered by $20^{\circ} \mathrm{C}$ and transverse waves are set up by plucking the wire at the middle. The frequency of the fundamental mode is<br/>$$<br/>\left(\mathrm{Y}=200 \mathrm{GPa}, \alpha=1.21 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)<br/>$$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$21 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$42 \mathrm{~Hz}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$11 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$22 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$11 \mathrm{~Hz}$</span> </div>


tags: ['Physics', 'Mechanical Properties of Solids', 'AP EAMCET', 'AP EAMCET 2022 (07 Jul Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-steel-wire-of-length-125-m-is-stretched-between-two-rigid-supports-the-tension-in-the-wire-produces-an-elastic-strain-of-014-the-fundamental-frequen

slug:
a-steel-wire-of-length-125-m-is-stretched-between-two-rigid-supports-the-tension-in-the-wire-produces-an-elastic-strain-of-014-the-fundamental-frequen-51931

question:
<div class="question">A steel wire of length $1.25 \mathrm{~m}$ is stretched between two rigid supports. The tension in the wire produces an elastic strain of $0.14 \%$. The fundamental frequency of the wire is (Density and Young's modulus of steel are $7.7 \times 10^3 \mathrm{kgm}^{-3}$ and $2.2 \times 10^{11} \mathrm{Nm}^{-2}$ respectively)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$40 \mathrm{~Hz}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$80 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$160 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$80 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">Given, length of wire $=1.25 \mathrm{~m}$<br/>strain produced $=0.14 \%$<br/>density of wire, $d=7.7 \times 10^3 \mathrm{kgm}^{-3}$<br/>young's modulus, $Y=2.2 \times 10^{11} \mathrm{Nm}^{-2}$<br/>Fundamental frequency of vibration over a string is given by<br/>$$<br/>f=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}<br/>$$<br/><br/>Where, $T=$ Tension in string,<br/>$L=$ Length of string and<br/>$\mu=$ mass per unit length of string.<br/><br/>So, we can express frequency as<br/>$$<br/>f=\frac{1}{2 L} \sqrt{\frac{T / A}{M / l A}}<br/>$$<br/><br/>From young's modulus of elasticity we have,<br/>$$<br/>\begin{aligned}<br/>&amp; &amp; Y=\frac{T / A}{\Delta l / l} \\<br/>\Rightarrow &amp; \frac{T}{A} &amp; =2.2 \times 10^{11} \times \frac{0.14}{100} \\<br/>\Rightarrow &amp; \frac{T}{A} &amp; =0.308 \times 10^9<br/>\end{aligned}<br/>$$<br/><br/>Substituting for $L, \frac{T}{A}$ and $d$ in eq. (i) we get, Fundamental frequency,<br/>$$<br/>\begin{aligned}<br/>f &amp; =\frac{1}{2 \times 1.25} \times \sqrt{\frac{0.308 \times 10^9}{7.7 \times 10^3}} \\<br/>&amp; =\frac{1}{25} \times \sqrt{0.04 \times 10^6} \\<br/>&amp; =\frac{1}{25} \times \sqrt{4 \times 10^4}=\frac{2}{25} \times 10^2=80 \mathrm{~Hz}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Mathematics in Physics', 'KCET', 'KCET 2014']
source_db: MarksBatch1_P1.db
title:
a-step-down-transformer-has-50-turns-on-secondary-and-1000-turns-on-primary-winding-if-a-transformer-is-connected-to-220-mathrmv-1-mathrmaa-c-source-w

slug:
a-step-down-transformer-has-50-turns-on-secondary-and-1000-turns-on-primary-winding-if-a-transformer-is-connected-to-220-mathrmv-1-mathrmaa-c-source-w-28486

question:
<div class="question">A step down transformer has \( 50 \) turns on secondary and \( 1000 \) turns on primary winding. If a<br/>transformer is connected to \( 220 \mathrm{~V} 1 \mathrm{AA} \).C. source, what is output current of the transformer?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\( \frac{1}{20} A \)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\( 20 \mathrm{~A} \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( 100 \mathrm{~A} \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( 2 \mathrm{~A} \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 20 \mathrm{~A} \)</span> </div>

answer:
<div class="solution">Given, number of turns on secondary, $N_{s}=50 ;$ number of turns on primary, $N_{P}=1000 ;$ source voltage $=220 \mathrm{~V} ;$<br/>current $=1 \mathrm{~A}$.<br/>We know $\frac{N_{s}}{N_{p}}=\frac{V_{s}}{V_{p}}=\frac{I_{p}}{I_{s}}$<br/>Therefore $\frac{N_{s}}{N_{p}}=\frac{I_{p}}{I_{s}} \Rightarrow I_{s}=\frac{N_{p}}{N_{s}} I_{p}$<br/>Substituting the values, we get<br/>$I_{s}=\frac{1000}{50} \times 1=20 \mathrm{~A}$<br/>Thus, output current of transformer $=20 \mathrm{~A}$</div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2021 (22 Sep Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-step-down-transformer-is-used-to-reduce-the-main-supply-from-v-1-volt-to-v-2-volt-the-primary-coil-draws-a-current-i-1-a-and-the-secondary-coil-draw

slug:
a-step-down-transformer-is-used-to-reduce-the-main-supply-from-v-1-volt-to-v-2-volt-the-primary-coil-draws-a-current-i-1-a-and-the-secondary-coil-draw-71107

question:
<div class="question">A step down transformer is used to reduce the main supply from ' $V_1$ ' volt to ' $V_2$ ' volt. The primary coil draws a current ' $I_1$ ' A and the secondary coil draws ' $I_2$ ' A. $\left(I_1 &lt; I_2\right)$. The ratio of input power to output power is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{V}_1 \mathrm{~V}_2}{\mathrm{I}_1 \mathrm{I}_2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{I}_1 \mathrm{~V}_1}{\mathrm{I}_2 \mathrm{~V}_2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{I}_1 \mathrm{I}_2}{\mathrm{~V}_1 \mathrm{~V}_2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{V}_1 \mathrm{I}_2}{\mathrm{~V}_2 \mathrm{I}_1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{I}_1 \mathrm{~V}_1}{\mathrm{I}_2 \mathrm{~V}_2}$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \text { Input power }=\mathrm{I}_1 \mathrm{~V}_1 \\ &amp; \text { Output power }=\mathrm{I}_2 \mathrm{~V}_2\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-step-down-transformer-reduces-220-mathrmv-to-110-mathrmv-the-primary-draws-5-mathrma-of-current-and-secondary-supplies-9-a-the-efficiency-of-the-tra

slug:
a-step-down-transformer-reduces-220-mathrmv-to-110-mathrmv-the-primary-draws-5-mathrma-of-current-and-secondary-supplies-9-a-the-efficiency-of-the-tra-97168

question:
<div class="question">A step down transformer reduces \( 220 \mathrm{~V} \) to \( 110 \mathrm{~V} \). The primary draws \( 5 \mathrm{~A} \) of current and secondary supplies \( 9 \) A. The efficiency of the transformer is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\( 20 \% \)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\( 44 \% \)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\( 90 \% \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( 100 \% \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 90 \% \)</span> </div>

answer:
<div class="solution"><p>For a transformer, we all know that:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi><mo>=</mo><mfrac><msub><mi>P</mi><mi>o</mi></msub><mrow><mi>P</mi><mi>i</mi></mrow></mfrac><mo>×</mo><mn>100</mn><mo>=</mo><mo> </mo><mfrac><mrow><msub><mi>E</mi><mi>s</mi></msub><msub><mi>i</mi><mi>s</mi></msub></mrow><mrow><msub><mi>E</mi><mi>p</mi></msub><msub><mi>i</mi><mi>p</mi></msub></mrow></mfrac><mo>×</mo><mn>100</mn></math>. </p><p>This gives us:</p><p><math><mi mathvariant="normal">%</mi><mi mathvariant="normal"> </mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">y</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi></mrow></msub></mrow><mrow><msub><mrow><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow></mfrac><mo>×</mo><mn>100</mn><mo>=</mo><mfrac><mrow><mn>110</mn><mo>×</mo><mn>9</mn></mrow><mrow><mn>220</mn><mo>×</mo><mn>5</mn></mrow></mfrac><mo>×</mo><mn>100</mn></math><br/><math><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mn>90</mn><mi mathvariant="normal">%</mi></math></p></div>


tags: ['Physics', 'Alternating Current', 'NEET', 'NEET 2024 (Re-NEET)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8 mA</span> </div>
source_db: MarksBatch1_P1.db
title:
a-step-up-transformer-is-connected-to-an-ac-mains-supply-of-220-v-to-operate-at-11000-v-88-watt-the-current-in-the-secondary-circuit-ignoring-the-powe

slug:
a-step-up-transformer-is-connected-to-an-ac-mains-supply-of-220-v-to-operate-at-11000-v-88-watt-the-current-in-the-secondary-circuit-ignoring-the-powe-67456

question:
<div class="question">A step up transformer is connected to an ac mains supply of 220 V to operate at $11000 \mathrm{~V}, 88$ watt. The current in the secondary circuit, ignoring the power loss in the transformer, is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">8 mA</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4 mA</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.4 A</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4 A</span> </li> </ul>

answer:
<div class="solution">In secondary circuit, $P=V i$<br/>$\Rightarrow 88=11000 i$<br/>$\Rightarrow \quad i=\frac{88}{11 \times 10^3}=8 \times 10^{-3} \mathrm{~A}$<br/>$\Rightarrow \quad i=8 \mathrm{~mA}$</div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2022 (06 Aug Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-stepdown-transformer-has-n-s-to-n-p-ratio-of-20-1-if-8-v-are-developed-across-04-secondary-the-primary-current-will-be

slug:
a-stepdown-transformer-has-n-s-to-n-p-ratio-of-20-1-if-8-v-are-developed-across-04-secondary-the-primary-current-will-be-46637

question:
<div class="question">A step-down transformer has $N_{\mathrm{S}}$ to $N_{\mathrm{p}}$ ratio of $20: 1$. If $8 \mathrm{~V}$ are developed across $0.4 \Omega$ secondary, the primary current will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \mathrm{~A}$</span> </div>

answer:
<div class="solution">For a step-down transformer:<br/>$\frac{N_{\mathrm{P}}}{N_{\mathrm{S}}}=\frac{20}{1}=\frac{V_p}{V_{\mathrm{s}}}=\frac{I_s}{I_p}$<br/>$\begin{aligned} &amp; \therefore I_s=\frac{8 \mathrm{~V}}{0.4 \mathrm{~A}}=20 \mathrm{~A} \\ &amp; \Rightarrow I_p=I_s \times \frac{1}{20}=1 \mathrm{~A}\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2021 (22 Sep Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1 A</span> </div>
source_db: MarksBatch1_P1.db
title:
a-stepdown-transformer-has-turns-ratio-20-1-if-8-v-is-applied-across-04-ohm-secondary-coil-then-the-primary-current-will

slug:
a-stepdown-transformer-has-turns-ratio-20-1-if-8-v-is-applied-across-04-ohm-secondary-coil-then-the-primary-current-will-96722

question:
<div class="question">A step-down transformer has turns ratio 20: 1 . If $8 \mathrm{~V}$ is applied across 0.4 ohm secondary coil, then the primary current will</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2 A</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1 A</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.5 A</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4 A</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} &amp; \mathrm{V}_{\mathrm{s}}=8 \mathrm{~V}, \mathrm{R}_{\mathrm{s}}=0.4 \Omega \\ &amp; \mathrm{I}_{\mathrm{s}}=\frac{\mathrm{V}_{\mathrm{s}}}{\mathrm{R}_{\mathrm{s}}}=\frac{8}{0.4}=20 \mathrm{~A} \\ &amp; \frac{\mathrm{I}_{\mathrm{p}}}{\mathrm{I}_{\mathrm{s}}}=\frac{\mathrm{N}_{\mathrm{s}}}{\mathrm{N}_{\mathrm{p}}}=\frac{1}{20} \\ &amp; \therefore \mathrm{I}_{\mathrm{p}}=\frac{\mathrm{I}_{\mathrm{s}}}{20}=\frac{20}{20}=1 \mathrm{~A}\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-stepdown-transformer-is-used-on-a-1000-v-line-to-deliver-20-a-at-120-v-at-the-secondary-coil-if-the-efficiency-of-the-transformer-is-80-the-current--1

slug:
a-stepdown-transformer-is-used-on-a-1000-v-line-to-deliver-20-a-at-120-v-at-the-secondary-coil-if-the-efficiency-of-the-transformer-is-80-the-current-1-43462

question:
<div class="question">A step-down transformer is used on a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo> </mo><mi mathvariant="normal">V</mi></math> line to deliver <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">A</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo> </mo><mi mathvariant="normal">V</mi></math> at the secondary coil. If the efficiency of the transformer is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn><mo>%</mo></math>, the current drawn from the line is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: -33px; top: -6px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>4</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: -33px; top: -6px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution"><math><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mfrac><mrow><mn>80</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>120</mn><mo>Ã</mo><mn>20</mn></mrow><mrow><mn>1000</mn><mo>Ã</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac></math><br/><br/><math><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>120</mn><mo>Ã</mo><mn>20</mn></mrow><mrow><mn>1000</mn><mo>Ã</mo><mn>0.8</mn></mrow></mfrac><mo>=</mo><mn>3</mn><mi> </mi><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-stepdown-transformer-is-used-on-a-1000-v-line-to-deliver-20-a-at-120-v-at-the-secondary-coil-if-the-efficiency-of-the-transformer-is-80-the-current-

slug:
a-stepdown-transformer-is-used-on-a-1000-v-line-to-deliver-20-a-at-120-v-at-the-secondary-coil-if-the-efficiency-of-the-transformer-is-80-the-current-61952

question:
<div class="question">A step-down transformer is used on a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo> </mo><mi mathvariant="normal">V</mi></math> line to deliver <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">A</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo> </mo><mi mathvariant="normal">V</mi></math> at the secondary coil. If the efficiency of the transformer is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn><mo>%</mo></math>, the current drawn from the line is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: -33px; top: -6px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>4</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: -33px; top: -6px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi><mo>%</mo><mo>=</mo><mfrac><mn>80</mn><mn>100</mn></mfrac><mo>=</mo><mfrac><mrow><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">s</mi></msub><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">s</mi></msub></mrow><mrow><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">p</mi></msub><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">p</mi></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>120</mn><mo>×</mo><mn>20</mn></mrow><mrow><mn>1000</mn><mo>×</mo><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">p</mi></msub></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mfrac><mrow><mn>120</mn><mo>×</mo><mn>20</mn></mrow><mrow><mn>1000</mn><mo>×</mo><mn>0.8</mn></mrow></mfrac><mo>=</mo><mn>3</mn><mi> </mi><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2020 (16 Oct Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-stepup-transformer-has-300-turns-of-primary-winding-and-450-turns-of-secondary-winding-a-primary-is-connected-to-150-volt-and-the-current-flowing-th

slug:
a-stepup-transformer-has-300-turns-of-primary-winding-and-450-turns-of-secondary-winding-a-primary-is-connected-to-150-volt-and-the-current-flowing-th-72200

question:
<div class="question">A step-up transformer has 300 turns of primary winding and 450 turns of secondary winding. A primary is connected to 150 volt and the current flowing through it is $9 \mathrm{~A}$. The current and voltage in the secondary are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$13.5 \mathrm{~A}, 225 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$13.5 \mathrm{~A}, \quad 100 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4.5 \mathrm{~A}, \quad 100 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$6.0 \mathrm{~A}, \quad 225 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6.0 \mathrm{~A}, \quad 225 \mathrm{~V}$</span> </div>

answer:
<div class="solution">$6.0 A, 225 V$<br/>Given that, number of turns in primary winding, $N_{p}=300$<br/>Number of turns in secondary winding, $N_{S}=450$<br/>Primary voltage, $\mathrm{V}_{\mathrm{p}}=150 \mathrm{~V}$<br/>Primary current, $I_{p}=9 \mathrm{~A}$<br/>For step-up transformer,<br/>$\begin{array}{l}<br/>\frac{V_{S}}{V_{P}}=\frac{N_{S}}{N_{P}} \\<br/>\frac{V_{S}}{150}=\frac{450}{300} \\<br/>\Rightarrow V_{S}=\frac{450}{300} \times 150 \\<br/>\Rightarrow V_{S}=225 \mathrm{~V}<br/>\end{array}$<br/>$\begin{array}{l}<br/>\text { Again, } \mathrm{V}_{\mathrm{p}} \mathrm{I}_{\mathrm{p}}=\mathrm{V}_{\mathrm{s}} \mathrm{I}_{\mathrm{S}} \\<br/>150 \times 9=225 \times \mathrm{I}_{\mathrm{S}} \\<br/>\mathrm{I}_{\mathrm{s}}=\frac{1350}{225}=6.0 \mathrm{~A}<br/>\end{array}$</div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-stepup-transformer-is-used-on-120-v-line-to-provide-a-potential-difference-of-2400-v-if-the-number-of-turns-in-the-primary-is-75-then-the-number-of-

slug:
a-stepup-transformer-is-used-on-120-v-line-to-provide-a-potential-difference-of-2400-v-if-the-number-of-turns-in-the-primary-is-75-then-the-number-of-56260

question:
<div class="question">A step-up transformer is used on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo> </mo><mi mathvariant="normal">V</mi></math> line to provide a potential difference of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2400</mn><mo> </mo><mi mathvariant="normal">V</mi></math>. If the number of turns in the primary is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn></math>, then the number of turns in the secondary shall be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1500</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1500</mn></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mtext mathvariant="italic">N</mtext><mtext mathvariant="italic">s</mtext></msub><msub><mtext mathvariant="italic">N</mtext><mtext mathvariant="italic">p</mtext></msub></mfrac><mo>=</mo><mfrac><msub><mtext mathvariant="italic">V</mtext><mtext mathvariant="italic">s</mtext></msub><msub><mtext mathvariant="italic">V</mtext><mtext mathvariant="italic">p</mtext></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>N</mi><mi>s</mi></msub><mn>75</mn></mfrac><mo>=</mo><mfrac><mn>2400</mn><mn>120</mn></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext mathvariant="italic">N</mtext><mtext mathvariant="italic">s</mtext></msub><mo>=</mo><mn>1</mn><mn>5</mn><mn>0</mn><mn>0</mn></math></p></div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2021 (23 Sep Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$40 A$</span> </div>
source_db: MarksBatch1_P1.db
title:
a-stepup-transformer-operates-on-220-v-and-supplies-current-of-2-a-the-ratio-of-primary-and-secondary-windings-is-1-20-the-current-in-the-primary-is

slug:
a-stepup-transformer-operates-on-220-v-and-supplies-current-of-2-a-the-ratio-of-primary-and-secondary-windings-is-1-20-the-current-in-the-primary-is-43901

question:
<div class="question">A step-up transformer operates on $220 \mathrm{~V}$ and supplies current of $2 \mathrm{~A}$. The ratio of primary and secondary windings is $1: 20$. The current in the primary is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 A$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 A$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$40 A$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20 A$</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} &amp; \frac{N_{\mathrm{s}}}{N_p}=20=\frac{I_p}{I_s} \\ &amp; \therefore I_p=20 I_S \\ &amp; =20 \times 2=40 \mathrm{~A}\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'KCET', 'KCET 2018']
source_db: MarksBatch1_P1.db
title:
a-stepup-transformer-operates-on-a-230-mathrmv-line-and-a-load-current-of-2-mathrma-the-ratio-of-primary-and-secondary-windings-is-1-25-then-the-curre

slug:
a-stepup-transformer-operates-on-a-230-mathrmv-line-and-a-load-current-of-2-mathrma-the-ratio-of-primary-and-secondary-windings-is-1-25-then-the-curre-55763

question:
<div class="question">A step-up transformer operates on a \( 230 \mathrm{~V} \) line and a load current of \( 2 \mathrm{~A} \). The ratio of primary<br/>and secondary windings is \( 1: 25 \). Then the current in the primary is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\( 25 \) A</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\( 50 \mathrm{~A} \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( 15 \mathrm{~A} \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( 12.5 \mathrm{~A} \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 50 \mathrm{~A} \)</span> </div>

answer:
<div class="solution">Transformer operates on \( 230 \mathrm{~V} \) line; load current \( =2 \mathrm{~A} \)<br/>Ratio of primary and secondary windings, \( \frac{N_{P}}{N_{S}}=\frac{1}{25} \)<br/>Since, \( \frac{N_{s}}{N_{p}}=\frac{I_{p}}{I_{s}} \)<br/>\( \Rightarrow I_{p}=\frac{N_{s}}{N_{p}} \times I_{s} \) \( \Rightarrow I_{p}=\frac{25}{1} \times 2=50 \)<br/>Therefore, current in primary \( =50 \mathrm{~A} \)</div>


tags: ['Physics', 'Alternating Current', 'VITEEE', 'VITEEE 2021']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P1.db
title:
a-stepup-transformer-operates-on-a-230-v-line-and-supplies-a-load-of-2-ampere-the-ratio-of-the-primary-and-secondary-windings-is-1-25-the-current-in-t

slug:
a-stepup-transformer-operates-on-a-230-v-line-and-supplies-a-load-of-2-ampere-the-ratio-of-the-primary-and-secondary-windings-is-1-25-the-current-in-t-83511

question:
<div class="question">A step-up transformer operates on a $230 \mathrm{~V}$ line and supplies a load of 2 ampere. The ratio of the primary and secondary windings is $1: 25$. The current in the primary is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15 \mathrm{~A}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$50 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$25 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$12.5 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$50 \mathrm{~A}$</span> </div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-stone-thrown-vertically-upward-satisfies-the-equation-s-64-t-16-t-2-where-s-is-in-meter-and-t-is-in-second-what-is-the-time-required-toreach-the-max

slug:
a-stone-thrown-vertically-upward-satisfies-the-equation-s-64-t-16-t-2-where-s-is-in-meter-and-t-is-in-second-what-is-the-time-required-toreach-the-max-39102

question:
<div class="question">A stone thrown vertically upward satisfies the equation $\mathrm{s}=64 \mathrm{t}-16 \mathrm{t}^{2}$, where s is in meter and $\mathrm{t}$ is in second. What is the time required toreach the maximumheight?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~s}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \mathrm{~s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \mathrm{~s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \mathrm{~s}$</span> </div>

answer:
<div class="solution">Given equation is $s=64 t-16 t^{2}$ $\therefore$ On differentiating w.r.t. $t$, we get $\frac{d s}{d t}=64-32 t$<br/>Put $\frac{d s}{d t}=0$ for maximumheight $\Rightarrow 64-32 t=0 \quad \Rightarrow t=2$<br/>Now, $\frac{d^{2} s}{d t^{2}}=-32$<br/>At $t=2, \frac{d^{2} s}{d t^{2}}=-32$<br/>Since, $\left(\frac{d^{2} s}{d t^{2}}\right)_{t=2}   &lt; 0$<br/>- Required time $=2$ second</div>


tags: ['Mathematics', 'Straight Lines', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-straight-line-cuts-off-an-intercept-of-2-units-on-the-positive-direction-of-x-axis-and-passes-through-the-point-3-5-what-is-the-foot-of-the-perpendi-1

slug:
a-straight-line-cuts-off-an-intercept-of-2-units-on-the-positive-direction-of-x-axis-and-passes-through-the-point-3-5-what-is-the-foot-of-the-perpendi-1-55798

question:
<div class="question">A straight line cuts off an intercept of 2 units on the positive direction of $\mathrm{x}$ -axis and passes through the point $(-3,5)$. What is the foot of the perpendicular drawn from the point $(3,3)$ on this line?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(1,3)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(2,0)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(0,2)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$(1,1)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(1,1)$</span> </div>

answer:
<div class="solution">The given line passes through $(-3,5)$ and $(2,0)$. Its equation is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/s-_MlSnytWGR5xHfrhQ5lnKKPvsaEQM7N75mHDP7L7g.original.fullsize.png"/><br/><br/>$y-y_{1}=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)\left(x-x_{1}\right)$<br/>$\Rightarrow(y-5)=\left(\frac{0-5}{2+3}\right)(x+3)$<br/>$\Rightarrow y=-x+2$ ...(1)<br/>Slope $=m=-1$<br/>and slope of perpendicular line $=-\frac{1}{m}=1$<br/>Equation of this line passing through $(3,3)$ is:<br/>$(y-3)=1(x-3)$<br/>$\Rightarrow \quad y=x .$<br/>From eq. (1) we get, $x=-x+2$<br/>$\Rightarrow x=1$ and $y=1 .$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-straight-line-cuts-off-an-intercept-of-2-units-on-the-positive-direction-of-x-axis-and-passes-through-the-point-3-5-what-is-the-foot-of-the-perpendi

slug:
a-straight-line-cuts-off-an-intercept-of-2-units-on-the-positive-direction-of-x-axis-and-passes-through-the-point-3-5-what-is-the-foot-of-the-perpendi-71341

question:
<div class="question">A straight line cuts off an intercept of 2 units on the positive direction of $\mathrm{x}$ -axis and passes through the point $(-3,5)$. What is the foot of the perpendicular drawn from the point $(3,3)$ on this line?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(1,3)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(2,0)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(0,2)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$(1,1)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(1,1)$</span> </div>

answer:
<div class="solution">The given line passes through $(-3,5)$ and $(2,0)$. Its equation is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/s-_MlSnytWGR5xHfrhQ5lnKKPvsaEQM7N75mHDP7L7g.original.fullsize.png"/><br/><br/>$y-y_{1}=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)\left(x-x_{1}\right)$<br/>$\Rightarrow(y-5)=\left(\frac{0-5}{2+3}\right)(x+3)$<br/>$\Rightarrow y=-x+2$ ...(1)<br/>Slope $=m=-1$<br/>and slope of perpendicular line $=-\frac{1}{m}=1$<br/>Equation of this line passing through $(3,3)$ is:<br/>$(y-3)=1(x-3)$<br/>$\Rightarrow \quad y=x .$<br/>From eq. (1) we get, $x=-x+2$<br/>$\Rightarrow x=1$ and $y=1 .$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-straight-line-intersects-x-and-y-axes-at-p-and-qrespectively-if-3-5-is-the-middle-point-of-pq-then-what-is-the-area-of-the-triangle-opq

slug:
a-straight-line-intersects-x-and-y-axes-at-p-and-qrespectively-if-3-5-is-the-middle-point-of-pq-then-what-is-the-area-of-the-triangle-opq-25362

question:
<div class="question">A straight line intersects $\mathrm{x}$ and $\mathrm{y}$ axes at $\mathrm{P}$ and Qrespectively. If $(3,5)$ is the middle point of $\mathrm{PQ}$, then what is the area of the triangle OPQ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">12 square units</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">15 square units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">20 square units</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">30 square units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">30 square units</span> </div>

answer:
<div class="solution">As we know that line $P Q$ intersects $x$ -axis and $y$ -axis at $P$ and $Q$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/FbMd8T_6Xvk1eAJXGSEctJOlXvMhOQhhf--bZs0Ap2w.original.fullsize.png"/><br/><br/>$\because \mathrm{M}$ is the mid point of $\mathrm{PQ}$<br/>$\therefore \frac{x+0}{2}=3$ and $\frac{0+y}{2}=5$<br/>$\Rightarrow x=6$ and $y=10$<br/>Hence area of triangle $O P Q=\frac{1}{2} \times 6 \times 10=30$ sq. unit</div>


tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-straight-line-is-passing-through-the-points-represented-by-the-complex-numbers-a-ib-and-a-ib-1-where-a-b-0-0-which-one-of-the-following-is-correct

slug:
a-straight-line-is-passing-through-the-points-represented-by-the-complex-numbers-a-ib-and-a-ib-1-where-a-b-0-0-which-one-of-the-following-is-correct-89517

question:
<div class="question">A straight line is passing through the points represented by<br/>the complex numbers a $+\mathrm{ib}$ and $\frac{1}{-\mathrm{a}+\mathrm{ib}}$, where $(\mathrm{a}, \mathrm{b}) \neq$ $(0,0)$<br/>Which one of the following is correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">It passes through the origin</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">It is parallel to the $\mathrm{x}$ -axis</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">It is parallel to the y-axis</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">It passes through $(0, b)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It passes through the origin</span> </div>

answer:
<div class="solution">Complex numbers are : $(\mathrm{a}+\mathrm{ib})$ and $\frac{1}{-\mathrm{a}+\mathrm{ib}}$<br/>Second number is rationalized as,<br/>$\frac{-a-i b}{(-a+i b)(-a-i b)}=\frac{-a-i b}{a^{2}+b^{2}}$<br/>These two complex numbers represent two points,<br/>$(\mathrm{a}, \mathrm{b})$ and $\left(\frac{-\mathrm{a}}{\mathrm{a}^{2}+\mathrm{b}^{2}}, \frac{-\mathrm{b}}{\mathrm{a}^{2}+\mathrm{b}^{2}}\right)$<br/>Eq. of line passing through these point is<br/>$(\mathrm{y}-\mathrm{b})=\frac{-\frac{\mathrm{b}}{\mathrm{a}^{2}+\mathrm{b}^{2}}-\mathrm{b}}{\frac{-\mathrm{a}}{\mathrm{a}^{2}+\mathrm{b}^{2}}-\mathrm{a}}(\mathrm{x}-\mathrm{a})$<br/>$\Rightarrow \mathrm{y}-\mathrm{b}=\frac{\mathrm{b}}{\mathrm{a}}(\mathrm{x}-\mathrm{a}) \Rightarrow \mathrm{ay}-\mathrm{ab}=\mathrm{bx}-\mathrm{ab}$<br/>$\Rightarrow \mathrm{y}=\frac{\mathrm{b}}{\mathrm{a}} \mathrm{x}$<br/>So, line passes through the origin.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-straight-line-passes-through-1-2-3-and-perpendicular-to-the-plane-2-x-3-y-z-7-what-are-the-direction-ratios-of-normal-to-plane

slug:
a-straight-line-passes-through-1-2-3-and-perpendicular-to-the-plane-2-x-3-y-z-7-what-are-the-direction-ratios-of-normal-to-plane-11104

question:
<div class="question">A straight line passes through $(1,-2,3)$ and perpendicular to the plane $2 x+3 y-z=7$<br/>What are the direction ratios of normal to plane?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$   &lt; 2,3,-1&gt;$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$   &lt; 2,3,1&gt;$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$   &lt; -1,2,3&gt;$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$   &lt; 2,3,-1&gt;$</span> </div>

answer:
<div class="solution">Direction ratios of normal to plane $2 \mathrm{x}+3 \mathrm{y}-\mathrm{z}=7$ is $   &lt; 2,3,-1&gt;$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-straight-line-passes-through-1-2-3-and-perpendicular-to-the-plane-2-x-3-y-z-7-what-is-the-image-of-the-point-1-2-3-in-the-plane

slug:
a-straight-line-passes-through-1-2-3-and-perpendicular-to-the-plane-2-x-3-y-z-7-what-is-the-image-of-the-point-1-2-3-in-the-plane-92409

question:
<div class="question">A straight line passes through $(1,-2,3)$ and perpendicular to the plane $2 x+3 y-z=7$<br/>What is the image of the point $(1,-2,3)$ in the plane?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(2,-1,5)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(-1,2,-3)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$(5,4,1)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(5,4,1)$</span> </div>

answer:
<div class="solution">Let $\mathrm{Q}(\mathrm{x}, \mathrm{y}, \mathrm{z})$ is the image of $(1,-2,3)$ in the plane<br/>$\frac{x+1}{2}=3 \Rightarrow x=5$<br/>$\frac{y-2}{2}=1 \Rightarrow y=4$<br/>$\frac{\mathrm{z}+3}{2}=2 \Rightarrow \mathrm{z}=1$<br/>Image of $(1,-2,3)$ are $(5,4,1)$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-straight-line-passes-through-1-2-3-and-perpendicular-to-the-plane-2-x-3-y-z-7-where-does-the-line-meet-the-plane

slug:
a-straight-line-passes-through-1-2-3-and-perpendicular-to-the-plane-2-x-3-y-z-7-where-does-the-line-meet-the-plane-49709

question:
<div class="question">A straight line passes through $(1,-2,3)$ and perpendicular to the plane $2 x+3 y-z=7$<br/>Where does the line meet the plane?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(2,3,-1)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(1,2,3)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(2,1,3)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$(3,1,2)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(3,1,2)$</span> </div>

answer:
<div class="solution">Equation of line, $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{-1}$ Let $\mathrm{P}(2 \mathrm{r}+1,3 \mathrm{r}-2,-\mathrm{r}+3)$ of the line meets the plane. Then, $2(2 \mathrm{r}+1)+3(3 \mathrm{r}-2)-(-\mathrm{r}+3)=0$<br/>$4 r+2+9 r-6+r-3=7$<br/>$14 r=14$<br/>$\mathbf{r}=1$<br/>$\mathrm{P}(3,1,2)$ meets the plane.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-straight-line-passes-through-the-points-5-0-and-0-3-the-length-of-the-perpendicular-from-the-point-4-4-on-the-line-is

slug:
a-straight-line-passes-through-the-points-5-0-and-0-3-the-length-of-the-perpendicular-from-the-point-4-4-on-the-line-is-78193

question:
<div class="question">A straight line passes through the points $(5,0)$ and $(0,3)$. The length of the perpendicular from the point $(4,4)$ on the line is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{17}}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{\frac{17}{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{15}{\sqrt{34}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{17}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{\frac{17}{2}}$</span> </div>

answer:
<div class="solution">Suppose equation of line is<br/>$\frac{x}{5}+\frac{y}{3}=1$<br/>$\Rightarrow \quad 3 x+5 y-15=0$<br/>Now, length of perpendicular from $(4,4)$ on $3 \mathrm{x}+5 \mathrm{y}-15$ $=0$ is<br/>$P=\left|\frac{3.4+5.4-15}{\sqrt{34}}\right|=\left|\frac{17}{\sqrt{34}}\right|=\frac{\sqrt{17} \cdot \sqrt{17}}{\sqrt{17} \cdot \sqrt{2}}$<br/>$P=\sqrt{\frac{17}{2}}$</div>


title: a-straight-line-with-direction-cosines-0-1-0-is
slug: a-straight-line-with-direction-cosines-0-1-0-is-77630
question: <div class="question">A straight line with direction cosines $(0,1,0)$ is</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">parallel to $\mathrm{x}$ -axis</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">parallel to $y$ -axis</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">parallel to z-axis</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">equally inclined to all the axes</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">parallel to $y$ -axis</span> </div>

answer:
<div class="solution">$\mathrm{D} \cdot \mathrm{C}^{\prime} \mathrm{s}(0,1,0)$<br/>Since $x$ and $z$ are zero, the straight line is parallel to $\mathrm{y}-$ axis</div>


title: a-straight-line-x-y-2-touches-the-circle-4-x-2-y-2-r-2-the-value-of-r-is-2015-ii
slug: a-straight-line-x-y-2-touches-the-circle-4-x-2-y-2-r-2-the-value-of-r-is-2015-ii-98049
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P1.db
question:
<div class="question">A straight line $\mathrm{x}=\mathrm{y}+2$ touches the circle $4\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)=\mathrm{r}^{2}$. The value of r is $\quad[2015-I I]$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \sqrt{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \sqrt{2}$</span> </div>

answer:
<div class="solution">$\because 4\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)=\mathrm{r}^{2}$<br/>$\Rightarrow x^{2}+y^{2}=\left(\frac{r}{2}\right)^{2}$<br/>Center $(0,0)$ and radius $\frac{\mathrm{r}}{2}$ Eq. of line is $; \mathrm{x}-\mathrm{y}-2=0$ $\because$ Line touches the circle.<br/>$$<br/>\therefore \frac{\mathrm{r}}{2}=\frac{|0-0-2|}{\sqrt{(1)^{2}+(-1)^{2}}}<br/>$$<br/>$\mathrm{r}=2 \sqrt{2}$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2020 (20 Oct Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-stretched-uniform-wire-of-length-l-under-tension-t-is-vibrating-with-frequency-n-a-closed-pipe-of-same-length-is-also-vibrating-with-same-fundamenta

slug:
a-stretched-uniform-wire-of-length-l-under-tension-t-is-vibrating-with-frequency-n-a-closed-pipe-of-same-length-is-also-vibrating-with-same-fundamenta-14015

question:
<div class="question">A stretched uniform wire of length L under tension $\mathrm{T}$ is vibrating with frequency<br/>'n'. A closed pipe of same length is also vibrating with same fundamental frequency<br/>'n'. If $\mathrm{T}$ is increased by $16 \mathrm{~N}$, it is in resonance with $2^{\text {nd }}$ harmonic of same closed<br/>pipe. The initial tension in the wire is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~N}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 \cdot 5 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0 \cdot 5 \mathrm{~N}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \mathrm{~N}$</span> </div>

answer:
<div class="solution">$\mathrm{n}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}=\frac{\mathrm{v}}{4 \ell}=\frac{1}{2 \ell} \sqrt{\frac{\mathrm{T}+16}{\mathrm{n}}}=\frac{3 \mathrm{v}}{4 \ell}$<br/>$\sqrt{\frac{T}{T+16}}=\frac{1}{3}$<br/>$\frac{T}{T+16}=\frac{1}{9}$<br/>$9 \mathrm{T}=\mathrm{T}+16 \quad \therefore 8 \mathrm{T}=16 \quad \therefore \mathrm{T}=2 \mathrm{~N}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2019 (09 Apr Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-string-20-m-long-and-fixed-at-its-ends-is-driven-by-a-240-h-z-vibrator-the-string-vibrates-in-its-third-harmonic-mode-the-speed-of-the-wave-and-its--1

slug:
a-string-20-m-long-and-fixed-at-its-ends-is-driven-by-a-240-h-z-vibrator-the-string-vibrates-in-its-third-harmonic-mode-the-speed-of-the-wave-and-its-1-26693

question:
<div class="question">A string <math><mn>2.0</mn><mi> </mi><mi mathvariant="normal">m</mi></math> long and fixed at its ends is driven by a <math><mn>240</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math> vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>320</mn><mtext>  </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>  </mtext><mn>120</mn><mo> </mo><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>320</mn><mtext>â </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>ââ</mtext><mn>80</mn><mo> </mo><mtext>â</mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mtext>  </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>  </mtext><mn>80</mn><mo> </mo><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mtext>  </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>  </mtext><mn>120</mn><mo> </mo><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>320</mn><mtext>â </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>ââ</mtext><mn>80</mn><mo> </mo><mtext>â</mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </div>

answer:
<div class="solution">For a string fixed at both the ends,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mi>v</mi></math><br/>For third harmonic, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo>=</mo><mfrac><mn>3</mn><mrow><mn>2</mn><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mi>v</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>v</mi><mo>=</mo><mfrac><mrow><mn>240</mn><mo>×</mo><mn>4</mn></mrow><mn>3</mn></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>320</mn><mtext>  </mtext><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/>Fundamental frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>0</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mi>v</mi></math><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>×</mo><mn>320</mn><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>80</mn><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-string-20-m-long-and-fixed-at-its-ends-is-driven-by-a-240-h-z-vibrator-the-string-vibrates-in-its-third-harmonic-mode-the-speed-of-the-wave-and-its-

slug:
a-string-20-m-long-and-fixed-at-its-ends-is-driven-by-a-240-h-z-vibrator-the-string-vibrates-in-its-third-harmonic-mode-the-speed-of-the-wave-and-its-43679

question:
<div class="question">A string <math><mn>2.0</mn><mi> </mi><mi mathvariant="normal">m</mi></math> long and fixed at its ends is driven by a <math><mn>240</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math> vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>320</mn><mtext>  </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>  </mtext><mn>120</mn><mo> </mo><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>320</mn><mtext>â </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>ââ</mtext><mn>80</mn><mo> </mo><mtext>â</mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mtext>  </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>  </mtext><mn>80</mn><mo> </mo><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn><mtext>  </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>  </mtext><mn>120</mn><mo> </mo><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>320</mn><mtext>â </mtext><msup><mi>m s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mtext>ââ</mtext><mn>80</mn><mo> </mo><mtext>â</mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></span> </div>

answer:
<div class="solution">For a string fixed at both the ends,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mi>v</mi></math><br/>For third harmonic, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo>=</mo><mfrac><mn>3</mn><mrow><mn>2</mn><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mi>v</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>v</mi><mo>=</mo><mfrac><mrow><mn>240</mn><mo>×</mo><mn>4</mn></mrow><mn>3</mn></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>320</mn><mtext>  </mtext><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/>Fundamental frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>0</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mi>v</mi></math><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>×</mo><mn>320</mn><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>80</mn><mtext> </mtext><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-string-has-a-length-of-5-cm-between-fixed-points-and-has-a-fundamental-frequency-of-20-hz-what-is-the-frequency-of-the-second-overtone

slug:
a-string-has-a-length-of-5-cm-between-fixed-points-and-has-a-fundamental-frequency-of-20-hz-what-is-the-frequency-of-the-second-overtone-51858

question:
<div class="question">A string has a length of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi>cm</mi></math> between fixed points and has a fundamental frequency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi>Hz</mi></math>. What is the frequency of the second overtone?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo> </mo><mi>Hz</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mi>Hz</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mi>Hz</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mi>Hz</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mi>Hz</mi></math></span> </div>

answer:
<div class="solution">Given,<br/><br/>Length of string between fixed ends <math><mo>=</mo><mn>5</mn><mi> </mi><mi mathvariant="normal">m</mi></math><br/><br/>Fundamental frequency <math><mfenced separators="|"><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mfenced><mo>=</mo><mn>20</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math><br/><br/>For second overtone, <math><mi>n</mi><mo>=</mo><mn>3</mn></math><br/><br/><math><mo>â´</mo><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mi> </mi><msub><mrow><mi>f</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>3</mn><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub></math><br/><br/><math><mo>=</mo><mn>3</mn><mo>Ã</mo><mn>20</mn></math><br/><br/><math><mo>=</mo><mn>60</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></div>


tags: ['Physics', 'Waves and Sound', 'AIIMS', 'AIIMS 2002']
source_db: MarksBatch1_P1.db
title:
a-string-in-a-musical-instrument-is-50-cm-long-and-its-fundamental-frequency-is-800-hz-if-a-frequency-of-1000-hz-is-to-be-produced-then-required-lengt

slug:
a-string-in-a-musical-instrument-is-50-cm-long-and-its-fundamental-frequency-is-800-hz-if-a-frequency-of-1000-hz-is-to-be-produced-then-required-lengt-47259

question:
<div class="question">A string in a musical instrument is $50 \mathrm{~cm}$ long and its fundamental frequency is $800 \mathrm{~Hz}$. If a frequency of $1000 \mathrm{~Hz}$ is to be produced, then required length of string is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$62.5 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$40 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$50 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$37.5 \mathrm{~cm}$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40 \mathrm{~cm}$</span> </div>

answer:
<div class="solution">Initial length of string $\left(l_1\right)=50 \mathrm{~cm}=0.5 \mathrm{~m}$ Initial fundamental frequency $\left(n_1\right)=800 \mathrm{~Hz}$ and final frequency $\left(n_2\right)=1000 \mathrm{~Hz}$.<br/>Frequency of vibration of the string, $n=\frac{1}{2 l} \sqrt{\frac{T}{m}} \propto \frac{1}{l}$<br/>$$<br/>\therefore \quad \frac{n_1}{n_2}=\frac{l_2}{l_1} \quad \text { or } \quad l_2=\frac{n_1 \times l_1}{n_2}=\frac{800 \times 50}{1000}=40 \mathrm{~cm} \text {. }<br/>$$<br/>(where $l_2=$ final length of the string).</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (07 Aug Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-string-in-a-musical-instrument-is-50-cm-long-and-its-fundamental-frequency-is-800-hz-keeping-the-tension-applied-to-the-string-same-the-change-in-th

slug:
a-string-in-a-musical-instrument-is-50-cm-long-and-its-fundamental-frequency-is-800-hz-keeping-the-tension-applied-to-the-string-same-the-change-in-th-42867

question:
<div class="question">A string in a musical instrument is $50 \mathrm{~cm}$ long and its fundamental frequency is $800 \mathrm{~Hz}$. Keeping the tension applied to the string same, the change in the length to produce sound note of fundamental frequency $1000 \mathrm{~Hz}$ will be.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$20 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$60 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$40 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40 \mathrm{~cm}$</span> </div>

answer:
<div class="solution">For stretched string $\mathrm{v} \propto \frac{1}{l}$<br/>$\therefore \frac{\mathrm{v}_1}{\mathrm{v}_2}=\frac{l_2}{l_1} \Rightarrow l_2=\frac{800}{1000} \times 50=40 \mathrm{~cm}$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2021 (23 Aug Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-string-is-divided-into-three-segments-so-that-the-segment-possesses-fundamental-frequencies-in-the-ratio-1-2-3-then-the-length-of-the-segments-are-i

slug:
a-string-is-divided-into-three-segments-so-that-the-segment-possesses-fundamental-frequencies-in-the-ratio-1-2-3-then-the-length-of-the-segments-are-i-96641

question:
<div class="question">A string is divided into three segments, so that the segment possesses fundamental frequencies in the ratio $1: 2: 3$. Then, the length of the segments are in the ratio</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$6: 3: 2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4: 3: 2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4: 2: 1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3: 2: 1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6: 3: 2$</span> </div>

answer:
<div class="solution">Given, ratio of fundamental frequencies be $f_1: f_2: f_3=1: 2: 3$<br/>Let ratio of length be $l_1: l_2: l_3$.<br/>Since, $\quad f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$<br/>where, $f$ is frequency,<br/>$l$ is length of string,<br/>$T$ is tension<br/>and $\mu$ is mass per unit length.<br/>$\therefore \quad l \propto \frac{1}{f}$<br/>So, $l_1: l_2: l_3=\frac{1}{f_1}: \frac{1}{f_2}: \frac{1}{f_3}$<br/>$=\frac{1}{1}: \frac{1}{2}: \frac{1}{3}$<br/>$=\frac{6}{6}: \frac{3}{6}: \frac{2}{6}$<br/>$=6: 3: 2$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (05 Aug Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-string-is-vibrating-in-its-fifth-overtone-between-two-rigid-supports-24-m-apart-the-distance-between-successive-node-and-antinode-is-2

slug:
a-string-is-vibrating-in-its-fifth-overtone-between-two-rigid-supports-24-m-apart-the-distance-between-successive-node-and-antinode-is-2-81371

question:
<div class="question">A string is vibrating in its fifth overtone between two rigid supports $2.4 \mathrm{~m}$ apart. The distance between successive node and antinode is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.8 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.2 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.1 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.6 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.2 \mathrm{~m}$</span> </div>

answer:
<div class="solution">The correct option is (B).<br/>If the string is clamped between two supports separated by L.<br/>For the fundamental overtone separation between successive nodes is $\mathrm{L}$.<br/>For the first overtone separation between successive nodes is $\frac{L}{2}$.<br/>For the second overtone the separation between successive nodes will be $\frac{L}{3}$.<br/>So, for nth overtone the separation between successive nodes will be $\frac{\mathrm{L}}{(\mathrm{n}+1)}$.<br/>Therefore, for the fifth over separation between successive nodes will be $\frac{\mathrm{L}}{6}$.<br/>In the separation between successive node and antinode is half of the separation between two successive nodes.<br/>So, $\frac{\mathrm{L}}{12}=\frac{2.4 \mathrm{~m}}{12}=0.2 \mathrm{~m}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-string-of-length-1-5-m-with-its-two-ends-clamped-is-vibrating-in-the-fundamental-mode-the-amplitude-at-the-centre-of-the-string-is-4-mm-the-minimum--1

slug:
a-string-of-length-1-5-m-with-its-two-ends-clamped-is-vibrating-in-the-fundamental-mode-the-amplitude-at-the-centre-of-the-string-is-4-mm-the-minimum-1-74233

question:
<div class="question">A string of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> with its two ends clamped is vibrating in the fundamental mode. The amplitude at the centre of the string is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>mm</mi></math>. The minimum distance between the two points having amplitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>mm</mi></math> is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div><div id="gtx-trans" style="position: absolute; left: 88px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">λ</mi><mo>=</mo><mn>2</mn><mi>l</mi><mo>=</mo><mn>3</mn><mo> </mo><mi mathvariant="normal">m</mi></math><br/><br/>Equation of standing wave<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mi>A</mi><mi>sin</mi><mo>⁡</mo><mi>k</mi><mi>x</mi><mi>cos</mi><mo>⁡</mo><mi>ω</mi><mi>t</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi></math> as amplitude is 2A.<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>2</mn><mi>A</mi><mi>sin</mi><mo>⁡</mo><mi>k</mi><mi>x</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi mathvariant="normal">λ</mi></mfrac><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac><mo>⇒</mo><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo> </mo><mi mathvariant="normal">m</mi></math><br/><br/>And <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi mathvariant="normal">λ</mi></mfrac><mo>.</mo><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mn>5</mn><mi mathvariant="normal">π</mi></mrow><mn>6</mn></mfrac><mo>⇒</mo><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mn>1.25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi><mo>⇒</mo><msub><mi>x</mi><mn>2</mn></msub><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mn>1</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi></math></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch1_P1.db
title:
a-string-of-length-1-5-m-with-its-two-ends-clamped-is-vibrating-in-the-fundamental-mode-the-amplitude-at-the-centre-of-the-string-is-4-mm-the-minimum-

slug:
a-string-of-length-1-5-m-with-its-two-ends-clamped-is-vibrating-in-the-fundamental-mode-the-amplitude-at-the-centre-of-the-string-is-4-mm-the-minimum-27863

question:
<div class="question">A string of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> with its two ends clamped is vibrating in the fundamental mode. The amplitude at the centre of the string is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>mm</mi></math>. The minimum distance between the two points having amplitude of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>mm</mi></math> is:</div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>2</mn><mi>L</mi><mo>=</mo><mn>3</mn><mo> </mo><mi mathvariant="normal">m</mi></math><br/><br/>Equation of standing wave<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>2</mn><mi>A</mi><mi>sin</mi><mi>k</mi><mi>x</mi><mi>cos</mi><mi>ω</mi><mi>t</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi></math> as amplitude is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>A</mi></math>.<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>2</mn><mi>A</mi><mi>sin</mi><mi>k</mi><mi>x</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi>λ</mi></mfrac><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfrac><mi mathvariant="normal">π</mi><mn>6</mn></mfrac><mo>⇒</mo><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo> </mo><mi mathvariant="normal">m</mi></math><br/><br/>And <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi>λ</mi></mfrac><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mn>5</mn><mi mathvariant="normal">π</mi></mrow><mn>6</mn></mfrac><mo>⇒</mo><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mn>1.25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi><mo>⇒</mo><msub><mi>x</mi><mn>2</mn></msub><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mn>1</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi></math></div>


tags: ['Physics', 'Waves and Sound', 'TS EAMCET', 'TS EAMCET 2019 (04 May Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-string-of-length-100-cm-has-three-resonant-frequencies-120-hz-200-hz-and-280-hz-if-a-node-is-formed-at-the-end-of-the-string-the-speed-of-the-transv

slug:
a-string-of-length-100-cm-has-three-resonant-frequencies-120-hz-200-hz-and-280-hz-if-a-node-is-formed-at-the-end-of-the-string-the-speed-of-the-transv-28645

question:
<div class="question">A string of length $100 \mathrm{~cm}$ has three resonant frequencies, $120 \mathrm{~Hz}, 200 \mathrm{~Hz}$ and $280 \mathrm{~Hz}$. If a node is formed at the end of the string, the speed of the transverse wave on this string is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$60 \mathrm{~m} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$80 \mathrm{~m} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$100 \mathrm{~m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$120 \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$80 \mathrm{~m} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Given, length of string, $l=100 \mathrm{~cm}=1 \mathrm{~m}$<br/>Three resonant frequencies are given as $f_1=120 \mathrm{~Hz}, f_2=200 \mathrm{~Hz}, f_3=280 \mathrm{~Hz}$<br/>$\because$ Fundamental frequency $\left(f_0\right)$ is equal to the greatest common factor of $f_1, f_2$ and $f_3$.<br/><br/>$\therefore f_0=$ greatest common factor of $120 \mathrm{~Hz}, 200 \mathrm{~Hz}$ and $280 \mathrm{~Hz}$ i.e., $f_0=40 \mathrm{~Hz}$<br/>Now, we know that, speed of transverse wave is given by $v=2 l f_0=2 \times 1 \times 40=80 \mathrm{~m} / \mathrm{s}$.</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-string-of-mass-per-unit-length-is-clamped-at-both-ends-such-that-one-end-of-the-string-is-at-x-0-and-the-other-is-at-x-l-when-the-string-vibrates-in

slug:
a-string-of-mass-per-unit-length-is-clamped-at-both-ends-such-that-one-end-of-the-string-is-at-x-0-and-the-other-is-at-x-l-when-the-string-vibrates-in-90087

question:
<div class="question">A string of mass per unit length <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Î¼</mi></math> is clamped at both ends such that one end of the string is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn></math> and the other is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">L</mi></math>. When the string vibrates in fundamental mode, the amplitude of the mid-point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">O</mi></math> of the string is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi></math>, and tension in the string is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math>, Find the total oscillation energy stored in the string.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math> <mrow> <mfrac> <mrow> <msup> <mi>Ï</mi> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn>2</mn> </msup> <mtext>T</mtext> </mrow> <mrow> <mn>4</mn> <mtext>L</mtext> </mrow> </mfrac> </mrow> </math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math> <mrow> <mfrac> <mrow> <msup> <mi>π</mi> <mn></mn> </msup> <msup> <mi>a</mi> <mn></mn> </msup> <mtext>T</mtext> </mrow> <mrow> <mn>2</mn> <mtext>L</mtext> </mrow> </mfrac> </mrow> </math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math> <mrow> <mo>-</mo> <mfrac> <mrow> <msub> <mi>π</mi> <mn>2</mn> </msub> <msub> <mi>a</mi> <mn>2</mn> </msub> <mtext>T</mtext> </mrow> <mrow> <mn>3</mn> <mtext>L</mtext> </mrow> </mfrac> </mrow> </math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math> <mrow> <mfrac> <mrow> <msup> <mi>π</mi> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn></mn> </msup> <mtext>T</mtext> </mrow> <mrow> <mn>6</mn> <mtext>L</mtext> </mrow> </mfrac> </mrow> </math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math> <mrow> <mfrac> <mrow> <msup> <mi>Ï</mi> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn>2</mn> </msup> <mtext>T</mtext> </mrow> <mrow> <mn>4</mn> <mtext>L</mtext> </mrow> </mfrac> </mrow> </math></span> </div>

answer:
<div class="solution"><math><mfrac><mrow><mi>Î»</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mi>L</mi></math><br/><br/><math><mi>Î»</mi><mo>=</mo><mn>2</mn><mi>L</mi></math><br/><br/><math><mi>Ï</mi><mo>=</mo><mi>Î¼</mi><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></math><br/><br/>The amplitude at a distance x from the origin is given by<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo> </mo><mo>=</mo><mo> </mo><mi mathvariant="normal">a</mi><mi>sinkx</mi></math><br/>consider an element of mass dm and length dx of string at a distance x from the origin<br/>The total energy of this element = its maximum KE<br/><br/><math> <mrow> <mo>=</mo> <mfrac> <mrow> <mtext>1</mtext> </mrow> <mrow> <mtext>2</mtext> </mrow> </mfrac> <mfenced close=")" open="(" separators=","> <mrow> <mtext>d</mtext> <mtext>m</mtext> </mrow> </mfenced> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> <msup> <mtext>A</mtext> <mn>2</mn> </msup> </mrow> </math><br/><br/><math> <mrow> <mo>=</mo> <mfrac> <mrow> <mtext>1</mtext> </mrow> <mrow> <mtext>2</mtext> </mrow> </mfrac> <mtext>Î¼</mtext> <mtext>d</mtext> <mi></mi><mi></mi><mi>x</mi><mo>â¡</mo> <mspace width="0.5em"></mspace> <mn>4</mn> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> <msup> <mtext>f</mtext> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn>2</mn> </msup> <mspace width="0.5em"></mspace> <msup> <mtext>sin</mtext> <mn>2</mn> </msup> <mi></mi><mi></mi><mi>k</mi><mo>â¡</mo> <mi>x</mi> </mrow> </math><br/><br/>(Because <math><mrow><mtext>Î¼</mtext><mo>=</mo><mfrac> <mrow> <mtext>dm</mtext> </mrow> <mrow> <mtext>dx</mtext> </mrow> </mfrac> </mrow></math> and  <math><mrow><mtext>Ï</mtext><mo>=</mo><mtext>2Ïf</mtext></mrow></math>  and it is given that  <math> <mrow><mtext> A </mtext> <mo>=</mo> <mtext> a sinkx   )</mtext></mrow></math><br/><br/><math> <mrow> <mtext>total energy of string</mtext> <mo>=</mo> <msubsup> <mo>â«</mo> <mn>0</mn> <mtext>L</mtext> </msubsup> <mn>2</mn> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> <msup> <mrow> <mtext>Î¼</mtext> <mtext>f</mtext> </mrow> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn>2</mn> </msup> <mspace width="0.5em"></mspace> <msup> <mtext>sin</mtext> <mn>2</mn> </msup> <mi></mi><mi></mi><mi>k</mi><mo>â¡</mo> <mi>x</mi> <mspace width="0.5em"></mspace> <mtext>d</mtext> <mi>x</mi> </mrow> </math><br/><br/><math> <mrow> <mo>=</mo> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> <msup> <mrow> <mtext>Î¼</mtext> <mtext>f</mtext> </mrow> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>[</mo> <mi>x</mi> <mo>-</mo> <mfrac> <mrow> <mtext>sin</mtext> <mn>2</mn> <mi></mi><mi>k</mi><mo>â¡</mo> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <msubsup> <mo>]</mo> <mn>0</mn> <mn>L</mn> </msubsup> </mrow> </math><br/><br/><math> <mrow> <mo>=</mo> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> <msup> <mrow> <mtext>Î¼</mtext> <mtext>f</mtext> </mrow> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn>2</mn> </msup> <mtext>L</mtext> </mrow> </math><br/><br/><math> <mrow> <mo>=</mo> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> <mtext>Î¼</mtext> <mfrac> <mrow> <msup> <mtext>V</mtext> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mtext>Î»</mtext> <mn>2</mn> </msup> </mrow> </mfrac> <msup> <mi>a</mi> <mn>2</mn> </msup> <mtext>L</mtext> <mo>=</mo> <mfrac> <mrow> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> </mrow> <mrow> <mn>4</mn> <msup> <mtext>L</mtext> <mn>2</mn> </msup> </mrow> </mfrac> <mspace></mspace> <mtext>T</mtext> <msup> <mi>a</mi> <mn>2</mn> </msup> <mtext>L</mtext> <mo>=</mo> <mfrac> <mrow> <msup> <mtext>Ï</mtext> <mn>2</mn> </msup> <msup> <mi>a</mi> <mn>2</mn> </msup> <mtext>T</mtext> </mrow> <mrow> <mn>4</mn> <mtext>L</mtext> </mrow> </mfrac> </mrow> </math></div>


tags: ['Biology', 'Biomolecules (B)', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-structure-that-forms-when-the-secondary-coiled-polypeptides-are-folded-to-produce-a-hollow-wollenlike-structure-is-called-structure-of-proteins

slug:
a-structure-that-forms-when-the-secondary-coiled-polypeptides-are-folded-to-produce-a-hollow-wollenlike-structure-is-called-structure-of-proteins-71343

question:
<div class="question">A structure that forms when the secondary coiled polypeptides are folded to produce a hollow, wollen-like structure is called___ structure of proteins.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Secondary</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Tertiary</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Quaternary</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Tertiary</span> </div>

answer:
<div class="solution">A structure that forms when the secondary coiled polypeptides are folded to produce a hollow, wollen-like structure is called tertiary structure of proteins.</div>


tags: ['Biology', 'Cell - The Unit of Life', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-structure-that-is-traversing-the-middle-lamella-and-connecting-the-cytoplasm-of-neighbouring-cells-is-called

slug:
a-structure-that-is-traversing-the-middle-lamella-and-connecting-the-cytoplasm-of-neighbouring-cells-is-called-20138

question:
<div class="question">A structure that is traversing the middle lamella and connecting the cytoplasm of neighbouring cells is called</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary wall junction</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Plasmodesmata</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Desmosomes</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Secondary wall</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Plasmodesmata</span> </div>

answer:
<div class="solution">The middle lamella is the layer mainly of calcium pectate which holds or glues the different neighbouring cells together. The cell wall and Middle lamellae may be traversed by cytoplasmic channel called plasmodesmata which connects the cytoplasm of neighbouring cells.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-student-appears-for-tests-i-ii-and-iii-the-student-is-considered-successful-if-he-passes-in-tests-i-ii-or-iii-or-all-the-three-the-probabilities-of-

slug:
a-student-appears-for-tests-i-ii-and-iii-the-student-is-considered-successful-if-he-passes-in-tests-i-ii-or-iii-or-all-the-three-the-probabilities-of-24789

question:
<div class="question">A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or III or all the three. The probabilities of the student passing in tests I, II and III are $\mathrm{m}, \mathrm{n}$ and $1 / 2$ respectively. If the probability of the student to be successful is $1 / 2$, then which one of the following is correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\quad \mathrm{m}(1+\mathrm{n})=1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{n}(1+\mathrm{m})=1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{m}=1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{mn}=1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \mathrm{m}(1+\mathrm{n})=1$</span> </div>

answer:
<div class="solution">$\frac{1}{2}=\mathrm{m} \times \mathrm{n} \times \frac{1}{2}+\mathrm{m} \times \frac{1}{2} \times(1-\mathrm{n})+\mathrm{m} \times \mathrm{n} \times 1-\frac{1}{2}$<br/>$\Rightarrow 1=\mathrm{m}(\mathrm{n}+1)$</div>


tags: ['Mathematics', 'Statistics', 'JEE Main', 'JEE Main 2019 (08 Apr Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-student-scores-the-following-marks-in-five-tests-4554415743-his-score-is-not-known-for-the-sixth-test-if-the-mean-score-is-48-in-the-six-tests-then-

slug:
a-student-scores-the-following-marks-in-five-tests-4554415743-his-score-is-not-known-for-the-sixth-test-if-the-mean-score-is-48-in-the-six-tests-then-37155

question:
<div class="question">A student scores the following marks in five tests: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45,54,41,57,43</mn></math>. His score is not known for the sixth test. If the mean score is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn></math> in the six tests, then the standard deviation of the marks in six tests is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>3</mn></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>100</mn><mn>3</mn></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><msqrt><mn>3</mn></msqrt></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>100</mn><msqrt><mn>3</mn></msqrt></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><msqrt><mn>3</mn></msqrt></mfrac></math></span> </div>

answer:
<div class="solution">Given mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> observations is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn></math><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mfrac><mrow><mn>41</mn><mo>+</mo><mn>45</mn><mo>+</mo><mn>54</mn><mo>+</mo><mn>57</mn><mo>+</mo><mn>43</mn><mo>+</mo><mi>x</mi></mrow><mn>6</mn></mfrac><mo>=</mo><mn>48</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>x</mi><mo>=</mo><mn>48</mn></math><br/>Now variance <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>σ</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mo>∑</mo><msup><mfenced separators="|"><mrow><mi>x</mi><mo>-</mo><menclose notation="top"><mi>x</mi></menclose></mrow></mfenced><mn>2</mn></msup></mrow><mi>n</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><msup><mn>7</mn><mn>2</mn></msup><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup><mo>+</mo><msup><mn>6</mn><mn>2</mn></msup><mo>+</mo><msup><mn>9</mn><mn>2</mn></msup><mo>+</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><msup><mn>0</mn><mn>2</mn></msup></mrow><mn>6</mn></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>100</mn><mn>3</mn></mfrac></math><br/>Hence standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>10</mn><msqrt><mn>3</mn></msqrt></mfrac></math>.</p></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">45</span> </div>
source_db: MarksBatch1_P1.db
title:
a-survey-of-850-students-in-a-university-yields-that-680-students-like-music-and-215-like-dance-what-is-the-least-number-of-students-who-like-both-mus

slug:
a-survey-of-850-students-in-a-university-yields-that-680-students-like-music-and-215-like-dance-what-is-the-least-number-of-students-who-like-both-mus-87793

question:
<div class="question">A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">40</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">45</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">50</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">55</span> </li> </ul>

answer:
<div class="solution">Number of students who like music, $\mathrm{n}(\mathrm{m})=680$ Number of students who like dance, $n(d)=215$ Total number of students, $n(m \cup \mathrm{d})=850$<br/>$n(m \cup d)=n(m)+n(d)-n(m \cap d)$<br/>$\Rightarrow 850=680+215-\mathrm{n}(\mathrm{m} \cap \mathrm{d})$<br/>$\Rightarrow n(m \cap d)=895-850=45$<br/>$0   &lt; a &lt; 1$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2018 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">254</span> </div>
source_db: MarksBatch1_P1.db
title:
a-survey-was-conducted-among-300-students-if-was-found-that-125-students-like-to-play-cricket-145-students-like-to-play-football-and-90-students-like--1

slug:
a-survey-was-conducted-among-300-students-if-was-found-that-125-students-like-to-play-cricket-145-students-like-to-play-football-and-90-students-like-1-59600

question:
<div class="question">A survey was conducted among 300 students. If was found that 125 students like to play cricket, 145 students like to play football and 90 students like to play tennis, 32 students like to play exactly two games out of the three games. <br/>How many students like to play exactly only one game?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">196</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">228</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">254</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">268</span> </li> </ul>

answer:
<div class="solution">Exactly one $=|\mathrm{A}|+|\mathrm{B}|+|\mathrm{C}|-$<br/>$2[[\mathrm{~A} \cap \mathrm{B}|+| \mathrm{B} \cap \mathrm{C}|+| \mathrm{A} \cap \mathrm{C} \mid]+3|\mathrm{~A} \cap \mathrm{B} \cap \mathrm{C}|$<br/>$=125+145+90-2[32+3 \times 14]+3 \times 14$<br/>$=360-106=254$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2018 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">14</span> </div>
source_db: MarksBatch1_P1.db
title:
a-survey-was-conducted-among-300-students-if-was-found-that-125-students-like-to-play-cricket-145-students-like-to-play-football-and-90-students-like-

slug:
a-survey-was-conducted-among-300-students-if-was-found-that-125-students-like-to-play-cricket-145-students-like-to-play-football-and-90-students-like-88375

question:
<div class="question">A survey was conducted among 300 students. If was found that 125 students like to play cricket, 145 students like to play football and 90 students like to play tennis, 32 students like to play exactly two games out of the three games. How many students like to play all the three games?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">14</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">21</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">28</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">35</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} 300=125+145+90-\\ &amp;(|A \cap B|+|B \cap C|+|A \cap C|)+|A \cap B \cap C| \\ &amp;|A \cap B|+|B \cap C|+|A \cap C| \\ &amp;=60+|A \cap B \cap C|...(i) \end{aligned}$<br/>Again, $|A \cap B|+|B \cap C|+|A \cap C|-3|A \cap B \cap C|=32$<br/>$\begin{aligned} \Rightarrow|A \cap B|+\mid B &amp; \cap C|+| A \cap C \mid \\ &amp;=32+3|A \cap B \cap C|...(ii) \end{aligned}$<br/>From (i) and (ii) $|A \cap B \cap C|=14$</div>


tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-taxon-which-is-facing-an-extremely-high-risk-of-extinction-in-the-wild-in-immediate-future-is-known-as

slug:
a-taxon-which-is-facing-an-extremely-high-risk-of-extinction-in-the-wild-in-immediate-future-is-known-as-56330

question:
<div class="question">A taxon, which is facing an extremely high risk of extinction in the wild in immediate future is known as</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Exotic</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Vulnerable</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Endangered</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Critically endangered</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Critically endangered</span> </div>

answer:
<div class="solution">A taxon is critically endangered when it is facing an extremely high risk of extinction in the wild in the near future.</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-tea-party-is-arranged-for-16-people-along-two-sides-of-a-long-table-with-eight-chairs-on-each-side-four-particular-men-wish-to-sit-on-one-particular

slug:
a-tea-party-is-arranged-for-16-people-along-two-sides-of-a-long-table-with-eight-chairs-on-each-side-four-particular-men-wish-to-sit-on-one-particular-50872

question:
<div class="question">A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$24 \times 8 ! \times 8 !$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(81)^{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$210 \times 8 ! \times 8 !$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$16 !$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$210 \times 8 ! \times 8 !$</span> </div>

answer:
<div class="solution">Number of ways $=\frac{8 ! 8 !}{4 ! 6 !} \times 10 !$<br/>$=(8 !)^{2} \times \frac{10 !}{4 ! 6 !}$<br/>$=(8 !)^{2} \times \frac{10 \times 9 \times 8 \times 7}{4 !}$<br/>$=(8 !)^{2} \times \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1}$<br/>$=(210) \times(8 !)^{2}$</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">27720</span> </div>
source_db: MarksBatch1_P1.db
title:
a-team-of-8-players-is-to-be-chosen-from-a-group-of-12-players-out-of-the-eight-players-one-is-to-be-elected-as-captain-and-another-vicecaptain-in-how

slug:
a-team-of-8-players-is-to-be-chosen-from-a-group-of-12-players-out-of-the-eight-players-one-is-to-be-elected-as-captain-and-another-vicecaptain-in-how-68357

question:
<div class="question">A team of 8 players is to be chosen from a group of 12 players. Out of the eight players one is to be elected as captain and another vice-captain. In how many ways can this be done?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">27720</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">13860</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6930</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">495</span> </li> </ul>

answer:
<div class="solution">Total no. of players $=12$ No. of chosen players $=8$ Number of ways to choose 8 players from 12 players<br/>$={ }^{12} C_{8}=\frac{12 !}{8 ! 4 !}=\frac{12 \times 11 \times 10 \times 9 \times 8 !}{8 ! 4 !}=495$<br/>Since, out of the 8 players 1 is to be elected as captain and another vice-captain Therefore number of ways to choose a captain and a vice-captain<br/>$={ }^{8} C_{1} \times{ }^{7} C_{1}=8 \times 7=56 \quad\left(\because{ }^{n} C_{1}=n\right)$<br/>Hence, required number of ways $=495 \times 56=27720$</div>


tags: ['Biology', 'Reproductive Health', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-temporary-family-planning-method-based-on-the-natural-effect-of-breastfeeding-on-fertility-is-due-to-the-high-level-of

slug:
a-temporary-family-planning-method-based-on-the-natural-effect-of-breastfeeding-on-fertility-is-due-to-the-high-level-of-84898

question:
<div class="question">A temporary family planning method based on the natural effect of breastfeeding on fertility is due to the high level of:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Progesterone</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Prolactin</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Estrogen</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">FSH</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Prolactin</span> </div>

answer:
<div class="solution">Progesterone is a female sex hormone. It's produced mainly in the ovaries and it helps in maintenance of pregnancy.<br/><br/>Prolactin causes the breasts to grow and make milk during pregnancy and after birth. Prolactin levels are normally high for pregnant women and new mothers.<br/><br/>Estrogen also helps regulate the menstrual cycle, controlling the growth of the uterine lining during the first part of the cycle and also control secondary sexual characters in female.<br/><br/>FSH helps control the menstrual cycle and stimulates the growth of eggs in the ovaries</div>


title: a-tertiary-alcohol-is-obtained-when-grignard-reagent-reacts-with
slug: a-tertiary-alcohol-is-obtained-when-grignard-reagent-reacts-with-97859
question: <div class="question">A tertiary alcohol is obtained when Grignard reagent reacts with</div>
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">pentan \( -2- \) one</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">butanone</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">propanone</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">all of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">all of these</span> </div>

answer:
<div class="solution"><blockquote><p>Grignard reagent reacts with carbonyl compound to form alcohol. Formaldehyde give primary alcohol, other aldehydes give secondary aldehyde whereas ketone give tertiary alcohol. </p></blockquote></div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-tertiary-butyl-carbocation-is-more-stable-than-a-secondary-butyl-carbocation-because-of-which-of-the-following-1

slug:
a-tertiary-butyl-carbocation-is-more-stable-than-a-secondary-butyl-carbocation-because-of-which-of-the-following-1-93310

question:
<div class="question">A tertiary butyl carbocation is more stable than a secondary butyl carbocation because of which of the following?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mi mathvariant="normal">R</mi></math> effect of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><msub><mi>CH</mi><mn>3</mn></msub></math> groups</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><mi mathvariant="normal">R</mi></math> effect of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><msub><mi>CH</mi><mn>3</mn></msub></math> groups</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Hyperconjugation</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><mi mathvariant="normal">I</mi></math> effect of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><msub><mi>CH</mi><mn>3</mn></msub></math> groups</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Hyperconjugation</span> </div>

answer:
<div class="solution"><p>The stability of given carbocations can be explained based on the hyperconjugation effect. The more the number of alpha hydrogen, the more is the stability of carbocations.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/neet/70e24ceb-2acf-43f1-b8c7-969b62a20b26-image.png" style="width: 292px; height: 185px;"/></p></div>


tags: ['Chemistry', 'General Organic Chemistry', 'NEET', 'NEET 2020 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-tertiary-butyl-carbocation-is-more-stable-than-a-secondary-butyl-carbocation-because-of-which-of-the-following

slug:
a-tertiary-butyl-carbocation-is-more-stable-than-a-secondary-butyl-carbocation-because-of-which-of-the-following-80134

question:
<div class="question">A tertiary butyl carbocation is more stable than a secondary butyl carbocation because of which of the following?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mi mathvariant="normal">R</mi></math> effect of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><msub><mi>CH</mi><mn>3</mn></msub></math> groups</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><mi mathvariant="normal">R</mi></math> effect of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><msub><mi>CH</mi><mn>3</mn></msub></math> groups</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Hyperconjugation</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><mi mathvariant="normal">I</mi></math> effect of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><msub><mi>CH</mi><mn>3</mn></msub></math> groups</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Hyperconjugation</span> </div>

answer:
<div class="solution"><p>The stability of given carbocations can be explained based on the hyperconjugation effect. The more the number of alpha hydrogen, the more is the stability of carbocations.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/neet/70e24ceb-2acf-43f1-b8c7-969b62a20b26-image.png" style="width: 292px; height: 185px;"/></p></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Main', 'JEE Main 2013 (23 Apr Online)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P1.db
title:
a-thin-tube-sealed-at-both-ends-is-100-cm-long-it-lies-horizontally-the-middle-20-cm-containing-mercury-and-two-equal-ends-containing-air-at-standard-

slug:
a-thin-tube-sealed-at-both-ends-is-100-cm-long-it-lies-horizontally-the-middle-20-cm-containing-mercury-and-two-equal-ends-containing-air-at-standard-44605

question:
<div class="question">A thin tube sealed at both ends is $100 \mathrm{~cm}$ long. It lies horizontally, the middle $20 \mathrm{~cm}$ containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced ?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/jK1qgtz-Akd8_MbX7lkau5G1v4UI2UFEDxE28nLbRLc.original.fullsize.png"/><br/><br/>(Given : cross-section of the tube can be assumed to be uniform)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2.95 \mathrm{~cm}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$5.18 \mathrm{~cm}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$8.65 \mathrm{~cm}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$0.0 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$5.18 \mathrm{~cm}$<br/></span> </div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-thin-wire-of-length-of-99-cm-is-fixed-at-both-ends-as-shown-in-the-figure-the-wire-is-kept-under-a-tension-and-is-divided-into-three-segments-of-len-1

slug:
a-thin-wire-of-length-of-99-cm-is-fixed-at-both-ends-as-shown-in-the-figure-the-wire-is-kept-under-a-tension-and-is-divided-into-three-segments-of-len-1-95180

question:
<div class="question">A thin wire of length of $99 \mathrm{~cm}$ is fixed at both ends as shown in the figure. The wire is kept under a tension and is divided into three segments of lengths $l_1, l_2$ and $l_3$ as shown in figure. When the wire is made to vibrate, the segments vibrate respectively with their fundamental frequencies in the ratio $1: 2: 3$. Then, the lengths $l_1, l_2$ and $l_3$ of the segments respectively are (in cm)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/zwXLuq-jras3z_4vgaZRU1L4BNoF7hzFw_v9O8ih2A8.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$27,54,18$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$18,27,54$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$54,27,18$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$27,9,14$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$54,27,18$</span> </div>

answer:
<div class="solution">Ratio of fundamental frequency<br/>$$<br/>\left(n_1: n_2: n_3\right)=1: 2: 3<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/LmNIYFx_qc_lDO18i0XdipEgIYptS3rggjO3QEFBMGc.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>l_1: l_2: l_3 &amp; =\frac{1}{n_1}: \frac{1}{n_2}: \frac{1}{n_3} \\<br/>&amp; =\frac{1}{1}: \frac{1}{2}: \frac{1}{3}=6: 3: 2 \\<br/>l_1 &amp; =\frac{6 \times 99}{11}=54 \\<br/>l_2 &amp; =\frac{3 \times 99}{11}=27 \\<br/>l_3 &amp; =\frac{2 \times 99}{11}=18<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'TS EAMCET', 'TS EAMCET 2015']
source_db: MarksBatch1_P1.db
title:
a-thin-wire-of-length-of-99-cm-is-fixed-at-both-ends-as-shown-in-the-figure-the-wire-is-kept-under-a-tension-and-is-divided-into-three-segments-of-len

slug:
a-thin-wire-of-length-of-99-cm-is-fixed-at-both-ends-as-shown-in-the-figure-the-wire-is-kept-under-a-tension-and-is-divided-into-three-segments-of-len-78898

question:
<div class="question">A thin wire of length of $99 \mathrm{~cm}$ is fixed at both ends as shown in the figure. The wire is kept under a tension and is divided into three segments of lengths $l_1, l_2$ and $l_3$ as shown in figure. When the wire is made to vibrate, the segments vibrate respectively with their fundamental frequencies in the ratio $1: 2: 3$. Then, the lengths $l_1, l_2$ and $l_3$ of the segments respectively are (in cm)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/zwXLuq-jras3z_4vgaZRU1L4BNoF7hzFw_v9O8ih2A8.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$27,54,18$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$18,27,54$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$54,27,18$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$27,9,14$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$54,27,18$</span> </div>

answer:
<div class="solution">Ratio of fundamental frequency<br/>$$<br/>\left(n_1: n_2: n_3\right)=1: 2: 3<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/LmNIYFx_qc_lDO18i0XdipEgIYptS3rggjO3QEFBMGc.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>l_1: l_2: l_3 &amp; =\frac{1}{n_1}: \frac{1}{n_2}: \frac{1}{n_3} \\<br/>&amp; =\frac{1}{1}: \frac{1}{2}: \frac{1}{3}=6: 3: 2 \\<br/>l_1 &amp; =\frac{6 \times 99}{11}=54 \\<br/>l_2 &amp; =\frac{3 \times 99}{11}=27 \\<br/>l_3 &amp; =\frac{2 \times 99}{11}=18<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Mathematics in Physics', 'JEE Main', 'JEE Main 2022 (27 Jul Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-torque-meter-is-calibrated-to-reference-standards-of-mass-length-and-time-each-with-5-accuracy-after-calibration-the-measured-torque-with-this-torqu

slug:
a-torque-meter-is-calibrated-to-reference-standards-of-mass-length-and-time-each-with-5-accuracy-after-calibration-the-measured-torque-with-this-torqu-87611

question:
<div class="question">A torque meter is calibrated to reference standards of mass, length and time each with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math> accuracy. After calibration, the measured torque with this torque meter will have net accuracy of </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>%</mo></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn><mo>%</mo></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>%</mo></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math></span> </div>

answer:
<div class="solution"><blockquote><p>Dimensional formula for Torque</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mi>τ</mi></mfenced><mo>=</mo><mfenced close="]" open="["><mrow><msup><mi>ML</mi><mn>2</mn></msup><msup><mrow><mo> </mo><mi mathvariant="normal">T</mi></mrow><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced></math></p><p>Now the percentage error in torque can be calculated by</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>%</mo><mo>=</mo><mfenced><mrow><mn>1</mn><mo>×</mo><mfrac><mrow><mo>∆</mo><mi>M</mi></mrow><mi>M</mi></mfrac><mo>+</mo><mn>2</mn><mo>×</mo><mfrac><mrow><mo>∆</mo><mi>L</mi></mrow><mi>L</mi></mfrac><mo>+</mo><mn>2</mn><mo>×</mo><mfrac><mrow><mo>∆</mo><mi>T</mi></mrow><mi>T</mi></mfrac></mrow></mfenced><mo>×</mo><mn>100</mn><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>τ</mi><mo>%</mo><mo>=</mo><mn>25</mn><mo>%</mo></math></p></blockquote></div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-tower-of-height-15-m-stands-vertically-on-the-ground-from-a-point-on-the-ground-the-angle-of-elevation-of-the-top-of-the-tower-is-found-to-be-3-0-wh

slug:
a-tower-of-height-15-m-stands-vertically-on-the-ground-from-a-point-on-the-ground-the-angle-of-elevation-of-the-top-of-the-tower-is-found-to-be-3-0-wh-30173

question:
<div class="question">A tower of height $15 \mathrm{~m}$ stands vertically on the ground. From a point on the ground the angle of elevation of the top of the tower is found to be $30^{\circ}$. What is the distance of the point from the foot of the tower? $\quad$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$15 \sqrt{3} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \sqrt{3} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$5 \sqrt{3} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$30 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$15 \sqrt{3} \mathrm{~m}$</span> </div>

answer:
<div class="solution">Let $\mathrm{AB}$ be a tower of height $15 \mathrm{~m}$. Let $\mathrm{B}$ be the point on the ground. Let $\angle \mathrm{ACB}=30^{\circ}$ be the angle of elevation. To find $\mathrm{BC}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Mc_xxSiuJ73_qp64-vll8LYfVHu79KHrxSJIf9k3kN0.original.fullsize.png"/><br/><br/>Let $\mathrm{BC}=x m$<br/>$\operatorname{In} \Delta \mathrm{ABC}, \tan 30^{\circ}=\frac{\mathrm{AB}}{\mathrm{BC}}=\frac{15}{x}$<br/>$\Rightarrow \frac{1}{\sqrt{3}}=\frac{15}{x} \Rightarrow x=15 \sqrt{3} \mathrm{~m}$</div>


tags: ['Mathematics', 'Heights and Distances', 'JEE Main', 'JEE Main 2007']
source_db: MarksBatch1_P1.db
title:
a-tower-stands-at-the-centre-of-a-circular-park-a-and-b-are-two-points-on-the-boundary-of-the-park-such-that-a-b-a-subtends-an-angle-of-6-0-at-the-foo

slug:
a-tower-stands-at-the-centre-of-a-circular-park-a-and-b-are-two-points-on-the-boundary-of-the-park-such-that-a-b-a-subtends-an-angle-of-6-0-at-the-foo-67773

question:
<div class="question">A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $A B(=a)$ subtends an angle of $60^{\circ}$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is $30^{\circ}$. The height of the tower is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{2 a}{\sqrt{3}}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$2 a \sqrt{3}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{a}{\sqrt{3}}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$a \sqrt{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{a}{\sqrt{3}}$<br/></span> </div>

answer:
<div class="solution">$\triangle \mathrm{O A B}$ is equilateral<br/>$\therefore \mathrm{OA}=\mathrm{OB}=\mathrm{AB}=\mathrm{a}$<br/>Now $\tan 30^{\circ}=\frac{h}{a}$<br/>$\therefore h=\frac{a}{\sqrt{3}} \text {. }$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/IR1Oldz_f51bmUBbNx7bW1jyaoIVgv2SQsPGml3z6Vg.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-train-covers-the-first-5-km-of-its-journey-at-a-speed-of-30-km-hr-and-the-next-15-km-at-a-speed-of-45-km-hr-what-is-the-average-speed-of-the-train

slug:
a-train-covers-the-first-5-km-of-its-journey-at-a-speed-of-30-km-hr-and-the-next-15-km-at-a-speed-of-45-km-hr-what-is-the-average-speed-of-the-train-93543

question:
<div class="question">A train covers the first $5 \mathrm{~km}$ of its journey at a speed of 30 $\mathrm{km} / \mathrm{hr}$ and the next $15 \mathrm{~km}$ at a speed of $45 \mathrm{~km} / \mathrm{hr}$. What is the average speed of the train?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$35 \mathrm{~km} / \mathrm{hr}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$37.5 \mathrm{~km} / \mathrm{hr}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$39.5 \mathrm{~km} / \mathrm{hr}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$40 \mathrm{~km} / \mathrm{hr}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40 \mathrm{~km} / \mathrm{hr}$</span> </div>

answer:
<div class="solution">Time taken by train to cover first $5 \mathrm{~km}=\frac{\text { Distance }}{\text { Speed }}$<br/>$=\frac{5}{30}=\frac{1}{6} \mathrm{hr}$<br/>Time taken by train to cover next $15 \mathrm{~km}=\frac{15}{45}=\frac{1}{3} \mathrm{hr}$.<br/>Average speed $=\frac{5+15}{\frac{1}{6}+\frac{1}{3}}$<br/>$=\frac{20}{\frac{1+2}{6}}=\frac{120}{3}=40 \mathrm{~km} / \mathrm{h}$</div>


tags: ['Physics', 'Waves and Sound', 'KCET', 'KCET 2020']
source_db: MarksBatch1_P1.db
title:
a-train-whistling-at-constant-frequency-n-is-moving-towards-a-station-at-a-constant-speed-v-the-train-goes-past-a-stationary-observer-on-the-station-t

slug:
a-train-whistling-at-constant-frequency-n-is-moving-towards-a-station-at-a-constant-speed-v-the-train-goes-past-a-stationary-observer-on-the-station-t-96776

question:
<div class="question">A train whistling at constant frequency $n$ is moving towards a station at a constant speed $v$. The train goes past a stationary observer on the station. The frequency $n$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the correct curve.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/XToz8RdHxkW3Lob4qD_aquADv7-7Ap8WrIsLy1i8Oyw.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/ci-3SnAH2KaWZJ9E76WEvYAEi_NdAj4FV-av28Z53UY.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/4FjoW8jZ-ML4xlAIbHWxSt6oJzNIURWDlh7gaZl_mYw.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/NxdAn_argpqS6MVRnd9d-TDjLOZfZ45GuPC7CuopCVs.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/NxdAn_argpqS6MVRnd9d-TDjLOZfZ45GuPC7CuopCVs.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">Since, the observer is stationary, so when train is approaching towards the observer or moving towards the observer, apparent frequency is given as,<br/>$n^{\prime}=n\left(\frac{v}{v-v_{s}}\right)$<br/>where, $v_{s}$ is the speed of sound.<br/>It is clear from the above expression that $n^{\prime}&gt;n$. However, when the train is going away from the observer, then apparent frequency,<br/>$\begin{array}{ll} <br/>&amp; n^{\prime}=n\left(\frac{v}{v+v_{s}}\right) \\<br/>\therefore \quad &amp; n^{\prime} &lt; n<br/>\end{array}$<br/>Hence, graph represented in option (d) is correct.</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transformer-consisting-of-300-turns-in-the-primary-and-150-turns-in-the-secondary-gives-output-power-of-22-k-w-if-the-current-in-the-secondary-coil--1

slug:
a-transformer-consisting-of-300-turns-in-the-primary-and-150-turns-in-the-secondary-gives-output-power-of-22-k-w-if-the-current-in-the-secondary-coil-1-42924

question:
<div class="question">A transformer consisting of <math><mn>300</mn></math> turns in the primary and <math><mn>150</mn></math> turns in the secondary gives output power of <math><mi> </mi><mn>2.2</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">W</mi></math> . If the current in the secondary coil is <math><mi> </mi><mn>10</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> , then the input voltage and current in the primary coil are:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>440</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>20</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>220</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>20</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mn>440</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>220</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>10</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>440</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution"><p>Assuming 100% efficiency,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>V</mi><mn>2</mn></msub><msub><mi>V</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>i</mi><mn>1</mn></msub><msub><mi>i</mi><mn>2</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>N</mi><mn>2</mn></msub><msub><mi>N</mi><mn>1</mn></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>i</mi><mn>1</mn></msub><msub><mi>i</mi><mn>2</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>N</mi><mn>2</mn></msub><msub><mi>N</mi><mn>1</mn></msub></mfrac><mspace linebreak="newline"></mspace><mfrac><msub><mi>i</mi><mn>1</mn></msub><mn>10</mn></mfrac><mo>=</mo><mfrac><mn>150</mn><mn>300</mn></mfrac><mspace linebreak="newline"></mspace><msub><mi>i</mi><mn>1</mn></msub><mo>=</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">A</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>V</mi><mi>I</mi><mspace linebreak="newline"></mspace><mn>2200</mn><mo>=</mo><mn>5</mn><mo>×</mo><msub><mi>V</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><msub><mi>V</mi><mn>1</mn></msub><mo>=</mo><mn>440</mn><mo> </mo><mi mathvariant="normal">V</mi></math></p></div>


tags: ['Physics', 'Alternating Current', 'JEE Main', 'JEE Main 2019 (10 Apr Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-transformer-consisting-of-300-turns-in-the-primary-and-150-turns-in-the-secondary-gives-output-power-of-22-k-w-if-the-current-in-the-secondary-coil-

slug:
a-transformer-consisting-of-300-turns-in-the-primary-and-150-turns-in-the-secondary-gives-output-power-of-22-k-w-if-the-current-in-the-secondary-coil-66639

question:
<div class="question">A transformer consisting of <math><mn>300</mn></math> turns in the primary and <math><mn>150</mn></math> turns in the secondary gives output power of <math><mi> </mi><mn>2.2</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">W</mi></math> . If the current in the secondary coil is <math><mi> </mi><mn>10</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> , then the input voltage and current in the primary coil are:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>440</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>20</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>220</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>20</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mn>440</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>220</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>10</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>440</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">V</mi></math> and <math><mn>5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution"><p>Assuming 100% efficiency,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>V</mi><mn>2</mn></msub><msub><mi>V</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>i</mi><mn>1</mn></msub><msub><mi>i</mi><mn>2</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>N</mi><mn>2</mn></msub><msub><mi>N</mi><mn>1</mn></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>i</mi><mn>1</mn></msub><msub><mi>i</mi><mn>2</mn></msub></mfrac><mo>=</mo><mfrac><msub><mi>N</mi><mn>2</mn></msub><msub><mi>N</mi><mn>1</mn></msub></mfrac><mspace linebreak="newline"></mspace><mfrac><msub><mi>i</mi><mn>1</mn></msub><mn>10</mn></mfrac><mo>=</mo><mfrac><mn>150</mn><mn>300</mn></mfrac><mspace linebreak="newline"></mspace><msub><mi>i</mi><mn>1</mn></msub><mo>=</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">A</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>V</mi><mi>I</mi><mspace linebreak="newline"></mspace><mn>2200</mn><mo>=</mo><mn>5</mn><mo>×</mo><msub><mi>V</mi><mn>1</mn></msub><mspace linebreak="newline"></mspace><msub><mi>V</mi><mn>1</mn></msub><mo>=</mo><mn>440</mn><mo> </mo><mi mathvariant="normal">V</mi></math></p></div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2023 (13 May Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3000</span> </div>
source_db: MarksBatch1_P1.db
title:
a-transformer-has-20-turns-in-the-primary-and-100-turns-in-the-secondary-coil-an-ac-voltage-of-v-in-600-sin-314-t-is-applied-to-primary-terminal-of-tr

slug:
a-transformer-has-20-turns-in-the-primary-and-100-turns-in-the-secondary-coil-an-ac-voltage-of-v-in-600-sin-314-t-is-applied-to-primary-terminal-of-tr-49572

question:
<div class="question">A transformer has 20 turns in the primary and 100 turns in the secondary coil. An ac voltage of $\mathrm{V}_{\text {in }}=600 \sin 314 \mathrm{t}$ is applied to primary terminal of transformer. Then maximum value of secondary output voltage obtained in volt is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">600</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">300</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">3000</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6000</span> </li> </ul>

answer:
<div class="solution">We know,<br/>$$<br/>\frac{V_s}{V_p}=\frac{N_s}{N_p}<br/>$$<br/>$\therefore \quad$ The maximum value of secondary output voltage is:<br/>$$<br/>\begin{aligned}<br/>V_s &amp; =\frac{N_s}{N_p} \times V_p=\frac{100}{20} \times 600 \\<br/>V_s &amp; =3000 V<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transformer-has-100-turns-in-the-primary-coil-and-carries-8-a-current-if-the-input-power-is-1-kw-the-number-of-turns-in-secondary-coil-to-have-500-v-1

slug:
a-transformer-has-100-turns-in-the-primary-coil-and-carries-8-a-current-if-the-input-power-is-1-kw-the-number-of-turns-in-secondary-coil-to-have-500-v-1-41254

question:
<div class="question">A transformer has <math><mn>100</mn></math> turns in the primary coil and carries <math><mn>8</mn><mi> A</mi></math> current. If the input power is <math><mn>1</mn><mi> kW</mi><mo>,</mo></math> the number of turns in secondary coil to have <math><mn>500</mn><mi> V</mi></math> of output will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>100</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>200</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mn>400</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>300</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>400</mn></math></span> </div>

answer:
<div class="solution">Given that,<br/><br/><math><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>100</mn><mo>,</mo><mi> </mi><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>8</mn><mi> A</mi></math><br/><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>500</mn><mi> V</mi><mo>,</mo><mi> </mi><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn><mi> k</mi><mn>W</mn><mo>=</mo><mn>100</mn><mi> W</mi></math><br/><br/>Input power, <math><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub><msub><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msub></math><br/><br/><math><mn>1000</mn><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>Ã</mo><mn>8</mn></math><br/><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>=</mo><mn>125</mn><mi> V</mi></math><br/><br/>Again, we know that<br/><br/><math><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac></math><br/><br/><math><mo>â</mo><mi> </mi><mi> </mi><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>500</mn></mrow><mrow><mn>125</mn></mrow></mfrac></math><br/><br/><math><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>500</mn><mo>Ã</mo><mn>100</mn></mrow><mrow><mn>125</mn></mrow></mfrac></math><br/><br/><math><mo>=</mo><mn>400</mn></math></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-transformer-has-100-turns-in-the-primary-coil-and-carries-8-a-current-if-the-input-power-is-1-kw-the-number-of-turns-in-secondary-coil-to-have-500-v

slug:
a-transformer-has-100-turns-in-the-primary-coil-and-carries-8-a-current-if-the-input-power-is-1-kw-the-number-of-turns-in-secondary-coil-to-have-500-v-68245

question:
<div class="question">A transformer has <math><mn>100</mn></math> turns in the primary coil and carries <math><mn>8</mn><mi> A</mi></math> current. If the input power is <math><mn>1</mn><mi> kW</mi><mo>,</mo></math> the number of turns in secondary coil to have <math><mn>500</mn><mi> V</mi></math> of output will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>100</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>200</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mn>400</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>300</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>400</mn></math></span> </div>

answer:
<div class="solution">Given that,<br/><br/><math><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>100</mn><mo>,</mo><mi> </mi><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>8</mn><mi> A</mi></math><br/><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>500</mn><mi> V</mi><mo>,</mo><mi> </mi><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn><mi> k</mi><mn>W</mn><mo>=</mo><mn>100</mn><mi> W</mi></math><br/><br/>Input power, <math><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub><msub><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msub></math><br/><br/><math><mn>1000</mn><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>Ã</mo><mn>8</mn></math><br/><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>=</mo><mn>125</mn><mi> V</mi></math><br/><br/>Again, we know that<br/><br/><math><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac></math><br/><br/><math><mo>â</mo><mi> </mi><mi> </mi><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>500</mn></mrow><mrow><mn>125</mn></mrow></mfrac></math><br/><br/><math><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>500</mn><mo>Ã</mo><mn>100</mn></mrow><mrow><mn>125</mn></mrow></mfrac></math><br/><br/><math><mo>=</mo><mn>400</mn></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main', 'JEE Main 2024 (01 Feb Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-transformer-has-an-efficiency-of-80-and-works-at-10-v-and-4-kw-if-the-secondary-voltage-is-240-v-then-the-current-in-the-secondary-coil-is

slug:
a-transformer-has-an-efficiency-of-80-and-works-at-10-v-and-4-kw-if-the-secondary-voltage-is-240-v-then-the-current-in-the-secondary-coil-is-78791

question:
<div class="question">A transformer has an efficiency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn><mo>%</mo></math> and works at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>Â </mo><mi mathvariant="normal">V</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>Â </mo><mi>kW</mi><mo>.</mo></math> If the secondary voltage is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo>Â </mo><mi mathvariant="normal">V</mi><mo>,</mo></math> then the current in the secondary coil is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>59</mn><mo>Â </mo><mi mathvariant="normal">A</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>33</mn><mo>Â </mo><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>33</mn><mo>Â </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>1</mn><mo>Â </mo><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>33</mn><mo>Â </mo><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution"><p>EfficiencyÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Î·</mi><mo>=</mo><mfrac><msub><mi>P</mi><mrow><mi>o</mi><mi>u</mi><mi>t</mi><mi>p</mi><mi>u</mi><mi>t</mi></mrow></msub><msub><mi>P</mi><mrow><mi>i</mi><mi>n</mi><mi>p</mi><mi>u</mi><mi>t</mi></mrow></msub></mfrac><mo>=</mo><mfrac><mrow><msub><mi>E</mi><mi>S</mi></msub><msub><mi>I</mi><mi>S</mi></msub></mrow><mrow><msub><mi>E</mi><mi>P</mi></msub><msub><mi>I</mi><mi>P</mi></msub></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>=</mo><mfrac><mrow><mn>240</mn><msub><mi>I</mi><mi>S</mi></msub></mrow><mn>4000</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><msub><mi>I</mi><mi>S</mi></msub><mo>=</mo><mfrac><mn>3200</mn><mn>240</mn></mfrac><mo>=</mo><mn>13</mn><mo>.</mo><mn>33</mn><mo>Â </mo><mi mathvariant="normal">A</mi></math></p></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-the-voltage-across-the-seco-1

slug:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-the-voltage-across-the-seco-1-60310

question:
<div class="question">A transformer having an efficiency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> is working on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi mathvariant="normal"> </mi><mi>kW</mi></math> power supply. If the current in the secondary coil is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math>, the voltage across the secondary coil and the current in the primary coil  respectively, are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13.5</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Power output <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo> </mo><mi>kW</mi><mo>×</mo><mfrac><mn>90</mn><mn>100</mn></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo> </mo><mi>kW</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>s</mi></msub><mo>=</mo><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mfrac><mrow><mn>2.7</mn><mo> </mo><mi>kW</mi></mrow><mrow><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></mrow></mfrac><mo>=</mo><mn>450</mn><mo> </mo><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>I</mi><mi>p</mi></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mo> </mo><mi>kW</mi></mrow><mrow><mn>200</mn><mo> </mo><mi mathvariant="normal">V</mi></mrow></mfrac><mo>=</mo><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-the-voltage-across-the-seco

slug:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-the-voltage-across-the-seco-84173

question:
<div class="question">A transformer having an efficiency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> is working on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi mathvariant="normal"> </mi><mi>kW</mi></math> power supply. If the current in the secondary coil is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math>, the voltage across the secondary coil and the current in the primary coil, respectively, are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13.5</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Power output <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo> </mo><mi>kW</mi><mo>×</mo><mfrac><mn>90</mn><mn>100</mn></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo> </mo><mi>kW</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>s</mi></msub><mo>=</mo><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mfrac><mrow><mn>2.7</mn><mo> </mo><mi>kW</mi></mrow><mrow><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></mrow></mfrac><mo>=</mo><mn>450</mn><mo> </mo><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>I</mi><mi>p</mi></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mo> </mo><mi>kW</mi></mrow><mrow><mn>200</mn><mo> </mo><mi mathvariant="normal">V</mi></mrow></mfrac><mo>=</mo><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-then-the-voltage-across-the-1

slug:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-then-the-voltage-across-the-1-85801

question:
<div class="question">A transformer having an efficiency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> is working on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi mathvariant="normal"> </mi><mi>kW</mi></math> power supply. If the current in the secondary coil is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math>, then the voltage across the secondary coil and the current in the primary coil  respectively, are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13.5</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Power output <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo> </mo><mi>kW</mi><mo>×</mo><mfrac><mn>90</mn><mn>100</mn></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>7</mn><mo> </mo><mi>kW</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>s</mi></msub><mo>=</mo><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mfrac><mrow><mn>2.7</mn><mo> </mo><mi>kW</mi></mrow><mrow><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></mrow></mfrac><mo>=</mo><mn>450</mn><mo> </mo><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>I</mi><mi>p</mi></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mo> </mo><mi>kW</mi></mrow><mrow><mn>200</mn><mo> </mo><mi mathvariant="normal">V</mi></mrow></mfrac><mo>=</mo><mn>15</mn><mo> </mo><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-then-the-voltage-across-the

slug:
a-transformer-having-an-efficiency-of-90-is-working-on-200-v-3-kw-power-supply-if-the-current-in-the-secondary-coil-is-6-a-then-the-voltage-across-the-59083

question:
<div class="question">A transformer having an efficiency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> is working on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi mathvariant="normal"> </mi><mi>kW</mi></math> power supply. If the current in the secondary coil is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math>, then the voltage across the secondary coil and the current in the primary coil  respectively, are</div>


tags: ['Physics', 'Alternating Current', 'JIPMER', 'JIPMER 2016']
source_db: MarksBatch1_P1.db
title:
a-transformer-having-efficiency-of-75-is-working-on-220-v-and-44-kw-power-supply-if-the-current-in-the-secondary-coil-is-5-a-what-will-be-the-voltage-

slug:
a-transformer-having-efficiency-of-75-is-working-on-220-v-and-44-kw-power-supply-if-the-current-in-the-secondary-coil-is-5-a-what-will-be-the-voltage-89028

question:
<div class="question">A transformer having efficiency of $75 \%$ is working on 220 V and 4.4 kW power supply. If the current in the secondary coil is 5 A . What will be the voltage across secondary coil and the current in primary coil?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$V_S=220 \mathrm{~V}, i_P=20 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$V_S=660 \mathrm{~V}, i_P=15 \mathrm{~A}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$V_S=660 \mathrm{~V}, i_P=20 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$V_S=220 \mathrm{~V}, i_P=15 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$V_S=660 \mathrm{~V}, i_P=20 \mathrm{~A}$</span> </div>

answer:
<div class="solution">Given, $P_{\text {in }}=4.4 \mathrm{~kW}, V_p=220 \mathrm{~V}, i_s=5 \mathrm{~A}, V_s=$ ?<br/>We know that, $\quad i_P=\frac{P_{\text {in }}}{V_P}=\frac{4.4 \times 10^3}{220}=20 \mathrm{~A}$<br/>$\therefore$ Efficiency, $\eta=\frac{\text { Output power }}{\text { Input power }}$<br/>Percentage efficiency $\eta=\frac{P_{\text {out }}}{P_{\text {in }}} \times 100$<br/>$\begin{aligned} 75 \% &amp; =100 \times \frac{P_{\text {out }}}{4.4 \times 10^3} \\ \therefore \quad P_{\text {out }} &amp; =\frac{75 \times 4.4 \times 10^3}{100} \\ &amp; =3300 \mathrm{~W} \\ \therefore \quad P_{\text {out }} &amp; =V_S \cdot i_S \\ \Rightarrow \quad V_S &amp; =\frac{3300}{5}=660 \mathrm{~V}\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'NEET', 'NEET 2014']
source_db: MarksBatch1_P1.db
title:
a-transformer-having-efficiency-of-90-is-working-on-200-v-and-3-k-w-power-supply-if-the-current-in-the-secondary-coil-is-6-a-the-voltage-across-the-se

slug:
a-transformer-having-efficiency-of-90-is-working-on-200-v-and-3-k-w-power-supply-if-the-current-in-the-secondary-coil-is-6-a-the-voltage-across-the-se-67688

question:
<div class="question">A transformer having efficiency of <math><mn>90</mn><mi>%</mi></math> is working on <math><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math> and <math><mn>3</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">W</mi></math> power supply. If the current in the secondary coil is <math><mn>6</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> the voltage across the secondary coil and the current in the primary coil respectively are:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>300</mn><mi>Â </mi><mi mathvariant="normal">V</mi><mo>,</mo><mi mathvariant="normal">Â </mi><mn>15</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math><mn>450</mn><mi> </mi><mi mathvariant="normal">V</mi><mo>,</mo><mi mathvariant="normal"> </mi><mn>15</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>450</mn><mi>Â </mi><mi mathvariant="normal">V</mi><mo>,</mo><mi mathvariant="normal">Â </mi><mn>13.5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>600</mn><mi>Â </mi><mi mathvariant="normal">V</mi><mo>,</mo><mi mathvariant="normal">Â </mi><mn>15</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>450</mn><mi> </mi><mi mathvariant="normal">V</mi><mo>,</mo><mi mathvariant="normal"> </mi><mn>15</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Current in primary coil <math><mo>=</mo><mfrac><mrow><mi>P</mi></mrow><mrow><mi>V</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3000</mn></mrow><mrow><mn>200</mn></mrow></mfrac><mo>=</mo><mn>15</mn><mi>A</mi></math><br/><math><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>=</mo><mi>Î·</mi><mi>%</mi><mi> </mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal"> </mi><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>90</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>Ã</mo><mfenced separators="|"><mrow><mn>3000</mn></mrow></mfenced></math><br/><math><mfenced separators="|"><mrow><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><mn>6</mn></mrow></mfenced><mo>=</mo><mn>2700</mn></math><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>450</mn><mi> </mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">t</mi></math></div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2022 (11 Aug Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-transformer-having-efficiency-of-90-is-working-on-200-v-and-3-kw-power-supply-if-the-current-is-the-secondary-coil-is-6-a-the-voltage-across-the-sec

slug:
a-transformer-having-efficiency-of-90-is-working-on-200-v-and-3-kw-power-supply-if-the-current-is-the-secondary-coil-is-6-a-the-voltage-across-the-sec-29096

question:
<div class="question">A transformer having efficiency of $90 \%$ is working on $200 \mathrm{~V}$ and $3 \mathrm{~kW}$ power supply. If the current is the secondary coil is $6 \mathrm{~A}$, the voltage across the secondary coil and the current in the primary coil respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">450 V , 12 A</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">600 V , 15 A</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">300 V , 15 V</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">450 V , 15 A</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">450 V , 15 A</span> </div>

answer:
<div class="solution">Primary current, $I_{\mathrm{P}}=\frac{P}{V}=\frac{3000}{200}=15 \mathrm{~A}$<br/>Output power $=90 \%$ of $3000 \mathrm{~W}=2700 \mathrm{~W}$<br/>Therefore, voltage across the secondary coil, $V_{\mathrm{s}}=\frac{2700}{6}=450 \mathrm{~V}$</div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-transformer-is-having-2100-turns-in-primary-and-4200-turns-in-secondary-an-ac-source-of-120-v-10-a-is-connected-to-its-primary-the-secondary-voltage

slug:
a-transformer-is-having-2100-turns-in-primary-and-4200-turns-in-secondary-an-ac-source-of-120-v-10-a-is-connected-to-its-primary-the-secondary-voltage-77514

question:
<div class="question">A transformer is having <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2100</mn></math> turns in primary and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4200</mn></math> turns in secondary. An AC source of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo> </mo><mi mathvariant="normal">V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mi mathvariant="normal">A</mi></math> is connected to its primary. The secondary voltage and current are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>5</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 77px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>10</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 77px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>10</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 77px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>120</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>20</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 77px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>5</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 77px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>s</mi></msub><mo>=</mo><mfrac><msub><mi>n</mi><mi>s</mi></msub><msub><mi>n</mi><mi>P</mi></msub></mfrac><mi> </mi><msub><mi>E</mi><mi>P</mi></msub><mo>=</mo><mfrac><mn>4200</mn><mn>2100</mn></mfrac><mo>×</mo><mn>120</mn><mo>=</mo><mn>240</mn><mo> </mo><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>i</mi><mi>s</mi></msub><mi> </mi><mo>=</mo><mfrac><msub><mi>n</mi><mi>s</mi></msub><msub><mi>n</mi><mi>P</mi></msub></mfrac><mi> </mi><msub><mi>i</mi><mi>P</mi></msub><mo>=</mo><mfrac><mn>2100</mn><mn>4200</mn></mfrac><mo>×</mo><mn>10</mn><mo>=</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2008']
source_db: MarksBatch1_P1.db
title:
a-transformer-is-used-to-light-a-100-w-and-110-v-lamp-from-a-220-v-mains-if-the-main-current-is-05-a-the-efficiency-of-the-transformer-is-approximatel-1

slug:
a-transformer-is-used-to-light-a-100-w-and-110-v-lamp-from-a-220-v-mains-if-the-main-current-is-05-a-the-efficiency-of-the-transformer-is-approximatel-1-90470

question:
<div class="question">A transformer is used to light a $100 \mathrm{~W}$ and $110 \mathrm{~V}$ lamp from a $220 \mathrm{~V}$ mains. If the main current is $0.5 \mathrm{~A}$, the efficiency of the transformer is approximately</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$30 \%$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$50 \%$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$90 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$90 \%$</span> </div>

answer:
<div class="solution">The efficiency of transformer $=\frac{\text { Energy obtained from the secondary coil }}{\text { Energy given to the primary coil }}$<br/>Or $\eta=\frac{\text { Output power }}{\text { Input power }}$<br/>or<br/>$$<br/>\eta=\frac{V_{s} I_{s}}{V_{p} I_{p}}<br/>$$<br/>Given, $\quad V_{s} I_{s}=100 \mathrm{~W}, V_{p}=220 \mathrm{~V}, I_{p}=0.5 \mathrm{~A}$<br/>$$<br/>\text { Hence, } \quad \eta=\frac{100}{220 \times 0.5}=0.90=90 \%<br/>$$<br/>Note The efficiency of an ideal transformer is 1 (or $100 \%$ ). But in practice due to loss in energy, the efficiency of transformer is always less than 1 (or less than $100 \%$ ).</div>


tags: ['Physics', 'Alternating Current', 'JIPMER', 'JIPMER 2009']
source_db: MarksBatch1_P1.db
title:
a-transformer-is-used-to-light-a-100-w-and-110-v-lamp-from-a-220-v-mains-if-the-main-current-is-05-a-the-efficiency-of-the-transformer-is-approximatel-2

slug:
a-transformer-is-used-to-light-a-100-w-and-110-v-lamp-from-a-220-v-mains-if-the-main-current-is-05-a-the-efficiency-of-the-transformer-is-approximatel-2-31107

question:
<div class="question">A transformer is used to light a 100 W and 110 V lamp from a 220 V mains. If the main current is 0.5 A , the efficiency of the transformer is approximately</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$30 \%$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$50 \%$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$90 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$90 \%$</span> </div>

answer:
<div class="solution">The efficiency of transformer<br/>$=\frac{\text { Energy obtained from the secondary coil }}{\text { Energy given to the primary coil }}$<br/>or<br/>$\begin{array}{lrl}<br/>\text { or } &amp; \eta &amp; =\frac{\text { Output power }}{\text { Input power }} \\<br/>\text { or } &amp; \eta &amp; =\frac{V_s I_s}{V_p I_p} \\<br/>\text { Given, } &amp; V_s I_s &amp; =100 \mathrm{~W}, V_p=220 \mathrm{~V}, I_p=0.5 \mathrm{~A} \\<br/>\text { Hence, } &amp; \eta &amp; =\frac{100}{220 \times 0.5}=0.90=90 \%<br/>\end{array}$</div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-transformer-of-efficiency-90-has-turns-ratio-10-1-if-the-voltage-across-the-primary-is-220-v-and-current-in-the-primary-is-05-a-then-the-current-in--1

slug:
a-transformer-of-efficiency-90-has-turns-ratio-10-1-if-the-voltage-across-the-primary-is-220-v-and-current-in-the-primary-is-05-a-then-the-current-in-1-26902

question:
<div class="question">A transformer of efficiency <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> has turns ratio <math><mn>10</mn><mo>:</mo><mn>1</mn><mo>.</mo></math> If the voltage across the primary is <math><mn>220 V</mn></math> and current in the primary is <math><mn>0.5</mn><mi> </mi><mn>A</mn><mo>,</mo></math> then the current in secondary is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>5.5</mn><mi> </mi><mn>A</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>5</mn><mi>Â </mi><mn>A</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>4</mn><mi>Â </mi><mn>A</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mn>4.5</mn><mi> </mi><mn>A</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>4.5</mn><mi> </mi><mn>A</mn></math></span> </div>

answer:
<div class="solution">Given, <math><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>10</mn></mrow><mrow><mn>1</mn></mrow></mfrac></math><br/><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>=</mo><mn>220</mn><mi> V</mi><mo>,</mo><mtext>â</mtext><msub><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>=</mo><mn>0.5</mn><mi> A</mi></math><br/><br/>We know that, <math><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac></math><br/><br/>Efficiency, <math><mi>Î·</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">O</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mtext>â</mtext><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">w</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mtext>â</mtext><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">w</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>S</mi></mrow></msub><msub><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msub><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow></mfrac></math><br/><br/><math><mfrac><mrow><mn>90</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow><mrow><mn>0.5</mn></mrow></mfrac></math><math> <mrow> <mo>Ã</mo><mfrac> <mn>1</mn> <mrow> <mn>10</mn></mrow> </mfrac> </mrow> </math><br/><br/><math><mo>â</mo><mi> </mi><mi> </mi><msub><mrow><mi>I</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>=</mo><mn>4.5</mn><mtext>â</mtext><mn>A</mn></math></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-transformer-of-efficiency-90-has-turns-ratio-10-1-if-the-voltage-across-the-primary-is-220-v-and-current-in-the-primary-is-05-a-then-the-current-in-

slug:
a-transformer-of-efficiency-90-has-turns-ratio-10-1-if-the-voltage-across-the-primary-is-220-v-and-current-in-the-primary-is-05-a-then-the-current-in-26776

question:
<div class="question">A transformer of efficiency <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>%</mo></math> has turns ratio <math><mn>10</mn><mo>:</mo><mn>1</mn><mo>.</mo></math> If the voltage across the primary is <math><mn>220 V</mn></math> and current in the primary is <math><mn>0.5</mn><mi> </mi><mn>A</mn><mo>,</mo></math> then the current in secondary is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>5.5</mn><mi> </mi><mn>A</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>5</mn><mi>Â </mi><mn>A</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>4</mn><mi>Â </mi><mn>A</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mn>4.5</mn><mi> </mi><mn>A</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>4.5</mn><mi> </mi><mn>A</mn></math></span> </div>

answer:
<div class="solution">Given, <math><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>10</mn></mrow><mrow><mn>1</mn></mrow></mfrac></math><br/><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>=</mo><mn>220</mn><mi> V</mi><mo>,</mo><mtext>â</mtext><msub><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msub><mo>=</mo><mn>0.5</mn><mi> A</mi></math><br/><br/>We know that, <math><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></mfrac></math><br/><br/>Efficiency, <math><mi>Î·</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">O</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mtext>â</mtext><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">w</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi><mtext>â</mtext><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">w</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>S</mi></mrow></msub><msub><mrow><mi>V</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>P</mi></mrow></msub><msub><mrow><mi>V</mi></mrow><mrow><mi>P</mi></mrow></msub></mrow></mfrac></math><br/><br/><math><mfrac><mrow><mn>90</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow><mrow><mn>0.5</mn></mrow></mfrac></math><math> <mrow> <mo>Ã</mo><mfrac> <mn>1</mn> <mrow> <mn>10</mn></mrow> </mfrac> </mrow> </math><br/><br/><math><mo>â</mo><mi> </mi><mi> </mi><msub><mrow><mi>I</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>=</mo><mn>4.5</mn><mtext>â</mtext><mn>A</mn></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main', 'JEE Main 2022 (28 Jul Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-transformer-operating-at-primary-voltage-8-kv-and-secondary-voltage-160-v-serves-a-load-of-80-kw-assuming-the-transformer-to-be-ideal-with-purely-re

slug:
a-transformer-operating-at-primary-voltage-8-kv-and-secondary-voltage-160-v-serves-a-load-of-80-kw-assuming-the-transformer-to-be-ideal-with-purely-re-35398

question:
<div class="question">A transformer operating at primary voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mi>kV</mi></math> and secondary voltage <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn><mo> </mo><mi mathvariant="normal">V</mi></math> serves a load of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn><mo> </mo><mi>kW</mi></math>. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>06</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>32</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>06</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>32</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>Since the transformer is assumed to be purely resistive, the power of the transformer can be calculated with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfrac><msup><mi>V</mi><mn>2</mn></msup><mi>R</mi></mfrac></math>. Therefore,</p><p>For the primary coil,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfrac><msup><mfenced><mrow><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfenced><mn>2</mn></msup><msub><mi>R</mi><mi>P</mi></msub></mfrac><mo>=</mo><mn>80</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi mathvariant="normal">W</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>R</mi><mi>P</mi></msub><mo>=</mo><mn>800</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p>For the secondary coil,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfrac><msup><mfenced><mn>160</mn></mfenced><mn>2</mn></msup><msub><mi>R</mi><mi mathvariant="normal">S</mi></msub></mfrac><mo>=</mo><mn>80</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi mathvariant="normal">W</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>R</mi><mi>S</mi></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mi mathvariant="normal">Ω</mi></math></p></blockquote></div>


tags: ['Physics', 'Alternating Current', 'AIIMS', 'AIIMS 2017']
source_db: MarksBatch1_P1.db
title:
a-transformer-with-efficiency-80-works-at-4-kw-and-100-v-if-the-secondary-voltage-is-200-v-then-the-primary-and-secondary-currents-are-respectively-1

slug:
a-transformer-with-efficiency-80-works-at-4-kw-and-100-v-if-the-secondary-voltage-is-200-v-then-the-primary-and-secondary-currents-are-respectively-1-30501

question:
<div class="question">A transformer with efficiency $80 \%$ works at $4 \mathrm{~kW}$ and $100 \mathrm{~V}$. If the secondary voltage is $200 \mathrm{~V}$, then the primary and secondary currents are respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$40 \mathrm{~A}$ and $16 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$16 \mathrm{~A}$ and $40 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{~A}$ and $40 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$40 \mathrm{~A}$ and $20 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40 \mathrm{~A}$ and $16 \mathrm{~A}$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \text { (a) : Here, } \eta=80 \% \\ &amp; P_i=4 \mathrm{~kW}=4000 \mathrm{~W} \\ &amp; V_p=100 \mathrm{~V}, V_s=200 \mathrm{~V} \\ &amp; I_p=\frac{P_i}{V_p}=\frac{4000}{100}=40 \mathrm{~A} \\ &amp; \eta=\frac{V_s I_s}{V_p I_p} ; \frac{80}{100}=\frac{200 I_s}{4000}=\frac{I_s}{20} \\ &amp; \text { or } I_s=\frac{20 \times 80}{100}=16 \mathrm{~A}\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transformer-with-efficiency-80-works-at-4-kw-and-100-v-if-the-secondary-voltage-is-200-v-then-the-primary-and-secondary-currents-are-respectively-2

slug:
a-transformer-with-efficiency-80-works-at-4-kw-and-100-v-if-the-secondary-voltage-is-200-v-then-the-primary-and-secondary-currents-are-respectively-2-17159

question:
<div class="question">A transformer with efficiency <math><mn>80</mn><mi>%</mi></math> works at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi mathvariant="normal"> </mi><mi>kW</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>. If the secondary voltage is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi><mo>,</mo></math> then the primary and secondary currents are respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Here, <math><mi>η</mi><mo>=</mo><mn>80</mn><mi>%</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi>i</mi></msub><mo>=</mo><mn>4</mn><mo> </mo><mi>kW</mi><mo>=</mo><mn>4000</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">W</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>p</mi></msub><mo>=</mo><mn>100</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi><mo>,</mo><mi> </mi><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>p</mi></msub><mo>=</mo><mfrac><msub><mi>P</mi><mi>i</mi></msub><msub><mi>V</mi><mi>p</mi></msub></mfrac><mo>=</mo><mfrac><mn>4000</mn><mn>100</mn></mfrac><mo>=</mo><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math><br/><br/><math><mi>η</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mo>;</mo><mfrac><mrow><mn>80</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>200</mn><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mn>4000</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mn>20</mn></mrow></mfrac></math><br/><br/>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>s</mi></msub><mo>=</mo><mfrac><mrow><mn>20</mn><mo>×</mo><mn>80</mn></mrow><mn>100</mn></mfrac><mo>=</mo><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transformer-with-efficiency-80-works-at-4-kw-and-100-v-if-the-secondary-voltage-is-200-v-then-the-primary-and-secondary-currents-are-respectively

slug:
a-transformer-with-efficiency-80-works-at-4-kw-and-100-v-if-the-secondary-voltage-is-200-v-then-the-primary-and-secondary-currents-are-respectively-49513

question:
<div class="question">A transformer with efficiency <math><mn>80</mn><mi>%</mi></math> works at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi mathvariant="normal"> </mi><mi>kW</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math>. If the secondary voltage is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi><mo>,</mo></math> then the primary and secondary currents are respectively</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Here, <math><mi>η</mi><mo>=</mo><mn>80</mn><mi>%</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi>i</mi></msub><mo>=</mo><mn>4</mn><mo> </mo><mi>kW</mi><mo>=</mo><mn>4000</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">W</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>p</mi></msub><mo>=</mo><mn>100</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi><mo>,</mo><mi> </mi><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mn>200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>p</mi></msub><mo>=</mo><mfrac><msub><mi>P</mi><mi>i</mi></msub><msub><mi>V</mi><mi>p</mi></msub></mfrac><mo>=</mo><mfrac><mn>4000</mn><mn>100</mn></mfrac><mo>=</mo><mn>40</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math><br/><br/><math><mi>η</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mo>;</mo><mfrac><mrow><mn>80</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>200</mn><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mn>4000</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mn>20</mn></mrow></mfrac></math><br/><br/>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>s</mi></msub><mo>=</mo><mfrac><mrow><mn>20</mn><mo>×</mo><mn>80</mn></mrow><mn>100</mn></mfrac><mo>=</mo><mn>16</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></div>


