# questions

tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'KVPY', 'KVPY 2016 (SB/SX)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3,6</span> </div>
source_db: MarksBatch1_P1.db
title:
233-g-of-compound-x-empirical-formula-coh-12-n-4-cl-3-upon-treatment-with-excess-agno-3-solution-produces-1435-g-of-a-white-precipitate-the-primary-an

slug:
233-g-of-compound-x-empirical-formula-coh-12-n-4-cl-3-upon-treatment-with-excess-agno-3-solution-produces-1435-g-of-a-white-precipitate-the-primary-an-24922

question:
<div class="question">$2.33 \mathrm{~g}$ of compound $\mathrm{X}$ (empirical formula $\left.\mathrm{CoH}_{12} \mathrm{~N}_{4} \mathrm{Cl}_{3}\right)$ upon treatment with excess $\mathrm{AgNO}_{3}$ solution produces $1.435 \mathrm{~g}$ of a white precipitate. The primary and secondary valences of cobalt in compound $\mathrm{X}$, respectively, are<br/>[Given : Atomic mass : $\mathrm{Co}=59, \mathrm{Cl}=35.5, \mathrm{Ag}=108$ ]</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">3,6</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">3,4</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2,4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4,3</span> </li> </ul>

answer:
<div class="solution">$$<br/>\begin{array}{l}<br/>\text { M.wt }=59+12+14 \times 4+35.5 \times 3=233.5 \\<br/>\mathrm{C}_{0} \mathrm{H}_{12} \mathrm{~N}_{4} \mathrm{Cl}_{3} \stackrel{\mathrm{AgNO}_{3}}{\longrightarrow} 1.435 \mathrm{~g} \mathrm{AgCl} \\<br/>\frac{2.33}{233.5} \mathrm{~g}=0.01 \text { mole } \quad(0.01 \mathrm{~mole})<br/>\end{array}<br/>$$<br/>(i) $0.01$ mole molecule produce $0.01$ mole $\mathrm{AgCl}$ $\therefore$ one replaceable $\mathrm{Cl}^{\underline{\Theta}}$ ion so formula of complex is<br/>$$<br/>\left[\mathrm{CO}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}<br/>$$<br/>(ii) Oxidation no. of Co is $+3$ so primary valency is 3 .<br/>(iii) Coordination no. is 6 so sec. valency is 6 so ans. is 3,6</div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-1-2-1-3-and-b-2-1-3-2-then-which-of-the-following-isare-correct-1-ab-a-1-b-1-is-a-unit-matrix-2-ab-1-a-1-b-1-select-the-correct-answer-using-the-cod

slug:
a-1-2-1-3-and-b-2-1-3-2-then-which-of-the-following-isare-correct-1-ab-a-1-b-1-is-a-unit-matrix-2-ab-1-a-1-b-1-select-the-correct-answer-using-the-cod-49172

question:
<div class="question">$\mathrm{A}=\left[\begin{array}{cc}1 &amp; -1 \\ 2 &amp; 3\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{rr}2 &amp; 3 \\ -1 &amp; -2\end{array}\right]$, then which of the following is/are correct? <br/>$1.$ $\mathrm{AB}\left(\mathrm{A}^{-1} \mathrm{~B}^{-1}\right)$ is a unit matrix.<br/>$2.$ $(\mathrm{AB})^{-1}=\mathrm{A}^{-1} \mathrm{~B}^{-1}$<br/>Select the correct answer using the code given below.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2 only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both 1 only 2</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Neither 1 nor 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">Neither 1 nor 2</span> </div>

answer:
<div class="solution">Here, $A=\left[\begin{array}{cc}1 &amp; -1 \\ 2 &amp; 3\end{array}\right]$ and $B=\left[\begin{array}{cc}2 &amp; 3 \\ -1 &amp; -2\end{array}\right]$<br/>$|A|=3-(-2)=5$ and $|B|=-4-(-3)=-1$<br/>$\Rightarrow A^{-1}=\frac{1}{5}\left[\begin{array}{cc}3 &amp; 1 \\ -2 &amp; 1\end{array}\right]$ and $B^{-1}=-1\left[\begin{array}{cc}-2 &amp; -3 \\ 1 &amp; 2\end{array}\right]$<br/>$A B=\left[\begin{array}{ll}3 &amp; 5 \\ 1 &amp; 0\end{array}\right]$ and $A^{-1} B^{-1}=\frac{1}{5}\left[\begin{array}{cc}5 &amp; 7 \\ -5 &amp; 8\end{array}\right]$<br/>$\Rightarrow A B\left(A^{-1} B^{-1}\right)=\frac{1}{5}\left[\begin{array}{cc}-10 &amp; -61 \\ 5 &amp; 7\end{array}\right] \neq 1 .$<br/>$|A B|=0-5=-5$<br/>$\therefore(A B)^{-1}=\frac{-1}{5}\left[\begin{array}{cc}0 &amp; -5 \\ -1 &amp; 3\end{array}\right] \neq A^{-1} B^{-1}$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch1_P1.db
title:
a-2-b-is-the-midpoint-of-the-line-segment-joining-the-points-10-6-and-k-4-if-a-2-b-7-then-what-is-the-value-of-k

slug:
a-2-b-is-the-midpoint-of-the-line-segment-joining-the-points-10-6-and-k-4-if-a-2-b-7-then-what-is-the-value-of-k-29191

question:
<div class="question">(a, $2 \mathrm{~b}$ ) is the mid-point of the line segment joining the points $(10,-6)$ and $(\mathrm{k}, 4)$. If $\mathrm{a}-2 \mathrm{~b}=7$, then what is the value of $\mathrm{k}$ ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">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">3</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution">$M \equiv$ mid point of line segment $P Q$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/4eS-Lm4AMjrATqEMDn8KKzNen8rxUuQN0fPOu15uCSU.original.fullsize.png"/><br/><br/>$\frac{K+10}{2}=a \Rightarrow K=(2 a-10)$<br/>$2 b=\frac{4-6}{2}=-1$<br/>given $a-2 b=7$...(1)<br/>Put the values of $a$ \&amp; $b$ in $e q(1)$, we get<br/>$\frac{K+10}{2}+1=7$<br/>$\frac{K+10}{2}=6 \Rightarrow K=12-10$<br/>$K=2$</div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-3-0-1-4-and-b-1-0-1-2-then-which-of-the-following-isare-correct-i-a-b-is-defined-ii-b-a-is-defined-iii-a-b-b-a-select-the-correct-answer-using-the-c

slug:
a-3-0-1-4-and-b-1-0-1-2-then-which-of-the-following-isare-correct-i-a-b-is-defined-ii-b-a-is-defined-iii-a-b-b-a-select-the-correct-answer-using-the-c-32918

question:
<div class="question">$A=\left[\begin{array}{ll}3 &amp; 1 \\ 0 &amp; 4\end{array}\right]$ and $B=\left[\begin{array}{ll}1 &amp; 1 \\ 0 &amp; 2\end{array}\right]$, then which of the following is/are correct? <br/>I. $A B$ is defined<br/>II. $B A$ is defined<br/>III. $A B=B A$<br/>Select the correct answer using the codes given below.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Only I</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Only II</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both I and II</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">I, II and III</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">I, II and III</span> </div>

answer:
<div class="solution">Let $\mathrm{A}=\left[\begin{array}{ll}3 &amp; 1 \\ 0 &amp; 4\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}1 &amp; 1 \\ 0 &amp; 2\end{array}\right]$<br/>Now, $\mathrm{AB}=\left[\begin{array}{ll}3 &amp; 1 \\ 0 &amp; 4\end{array}\right]\left[\begin{array}{ll}1 &amp; 1 \\ 0 &amp; 2\end{array}\right]=\left[\begin{array}{ll}3 &amp; 5 \\ 0 &amp; 8\end{array}\right]$<br/>and $\mathrm{BA}=\left[\begin{array}{ll}1 &amp; 1 \\ 0 &amp; 2\end{array}\right]\left[\begin{array}{ll}3 &amp; 1 \\ 0 &amp; 4\end{array}\right]=\left[\begin{array}{ll}3 &amp; 5 \\ 0 &amp; 8\end{array}\right]$<br/>$\Rightarrow \quad \mathrm{AB}=\mathrm{BA}$<br/>Hence, all the three statements are correct.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-3-4-and-b-5-2-are-two-points-and-p-is-a-point-such-that-pa-pb-if-the-area-of-triangle-pab-is-10-square-unit-what-are-the-coordinates-of-p

slug:
a-3-4-and-b-5-2-are-two-points-and-p-is-a-point-such-that-pa-pb-if-the-area-of-triangle-pab-is-10-square-unit-what-are-the-coordinates-of-p-34815

question:
<div class="question">$\mathrm{A}(3,4)$ and $\mathrm{B}(5,-2)$ are two points and $\mathrm{P}$ is a point such that $\mathrm{PA}=\mathrm{PB}$. If the area of triangle $\mathrm{PAB}$ is 10 square unit, what are the coordinates of P ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(1,0)$ only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(7,2)$ only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$(1,0)$ or $(7,2)$</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">Neither $(1,0)$ nor $(7,2)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(1,0)$ or $(7,2)$</span> </div>

answer:
<div class="solution">Given $\mathrm{A}(3,4)$ and $\mathrm{B}(5,-2)$ Let, $\mathrm{P}(\mathrm{x}, \mathrm{y})$<br/>Given that, $\mathrm{PA}=\mathrm{PB}$ $\Rightarrow \mathrm{PA}^{2}=\mathrm{PB}^{2}$<br/>$\Rightarrow(x-3)^{2}+(y-4)^{2}=(x-5)^{2}+(y+2)^{2}$<br/>$\Rightarrow x^{2}-6 x+9+y^{2}-8 y+16$<br/>$=x^{2}-10 x+25+y^{2}+4 y+4$<br/>$\Rightarrow 4 x-12 y=4$<br/>$\Rightarrow x-3 y=1$ ...(i)<br/>$\therefore$ Area of $\Delta \mathrm{PAB}=10$<br/>$\frac{1}{2}\left|\begin{array}{lll}x &amp; y &amp; 1 \\ 3 &amp; 4 &amp; 1 \\ 5 &amp; -2 &amp; 1\end{array}\right|=\pm 10$<br/>$\Rightarrow x(4+2)-y(3-5)+1(-6-20)=\pm 20$<br/>$\Rightarrow 6 \mathrm{x}+2 \mathrm{y}-26=\pm 20$<br/>$\Rightarrow 6 \mathrm{x}+2 \mathrm{y}-26=20$<br/>or, $6 x+2 y-26=-20$<br/>$\Rightarrow 6 x+2 y=46$...(ii)<br/>or $6 x+2 y=6$...(iii)<br/>From eqs. (i) and (ii), we get $x=7, y=2$<br/>Similarly, from eqs. (i) and (iii), we get $\mathrm{x}=1, \mathrm{y}=0$<br/>Hence, coordinates of $\mathrm{P}$ are $(7,2)$ or $(1,0)$</div>


tags: ['Physics', 'Alternating Current', 'NEET', 'NEET 2023 (All India)']
source_db: MarksBatch1_P1.db
title:
a-12-v-60-w-lamp-is-connected-to-the-secondary-of-a-step-down-transformer-whose-primary-is-connected-to-ac-mains-of-220-v-assuming-the-transformer-to-

slug:
a-12-v-60-w-lamp-is-connected-to-the-secondary-of-a-step-down-transformer-whose-primary-is-connected-to-ac-mains-of-220-v-assuming-the-transformer-to-44172

question:
<div class="question">A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>60</mn><mo> </mo><mi mathvariant="normal">W</mi></math> lamp is connected to the secondary of a step down transformer, whose primary is connected to ac mains of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>220</mn><mo> </mo><mi mathvariant="normal">V</mi></math>. Assuming the transformer to be ideal, what is the current in the primary winding?</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>0</mn><mo>.</mo><mn>37</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>0</mn><mo>.</mo><mn>27</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>2</mn><mo>.</mo><mn>7</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>3</mn><mo>.</mo><mn>7</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>0</mn><mo>.</mo><mn>27</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>For an ideal transformer,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><mrow><mi>P</mi><mi>o</mi><mi>w</mi><mi>e</mi><mi>r</mi></mrow></mfenced><mrow><mi>i</mi><mi>n</mi><mi>p</mi><mi>u</mi><mi>t</mi></mrow></msub><mo>=</mo><msub><mfenced><mrow><mi>P</mi><mi>o</mi><mi>w</mi><mi>e</mi><mi>r</mi></mrow></mfenced><mrow><mi>o</mi><mi>u</mi><mi>t</mi><mi>p</mi><mi>u</mi><mi>t</mi></mrow></msub><mspace linebreak="newline"></mspace><mo>⇒</mo><msub><mi>V</mi><mi>P</mi></msub><msub><mi>I</mi><mi>P</mi></msub><mo>=</mo><msub><mfenced><mrow><mi>P</mi><mi>o</mi><mi>w</mi><mi>e</mi><mi>r</mi></mrow></mfenced><mrow><mi>o</mi><mi>u</mi><mi>t</mi><mi>p</mi><mi>u</mi><mi>t</mi></mrow></msub><mspace linebreak="newline"></mspace><mo>⇒</mo><msub><mi>I</mi><mi>P</mi></msub><mo>=</mo><mfrac><mn>60</mn><mn>220</mn></mfrac><mo>≈</mo><mn>0</mn><mo>.</mo><mn>27</mn><mo> </mo><mi mathvariant="normal">A</mi></math></p></blockquote></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">59.29</span> </div>
source_db: MarksBatch1_P1.db
title:
a-25-cm-long-string-is-fixed-at-both-ends-it-has-a-mass-of-2-5-g-and-vibrates-in-its-first-overtone-under-tension-also-given-is-a-closed-pipe-which-is

slug:
a-25-cm-long-string-is-fixed-at-both-ends-it-has-a-mass-of-2-5-g-and-vibrates-in-its-first-overtone-under-tension-also-given-is-a-closed-pipe-which-is-75970

question:
<div class="question">A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo> </mo><mi>cm</mi></math> long string is fixed at both ends. It has a mass of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math> and vibrates in its first overtone under tension. Also given is a closed pipe which is  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mi>cm</mi></math> long which vibrates in its fundamental frequency. When both of these are sounded simultaneously, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> beats per second are heard. It is also observed that decreasing the tension in the string also decreases the beat frequency. What is the tension (in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math>) in the string? [Given, speed of sound in air is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn><mo> </mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>]</div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>5</mn></mrow><mn>25</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mi mathvariant="normal">g</mi><mo>/</mo><mi>cm</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mi>kg</mi><mo>/</mo><mi mathvariant="normal">m</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>1</mn><mtext>st </mtext></msup></math> overtone,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mi mathvariant="normal">s</mi></msub><mo>=</mo><mn>25</mn><mo> </mo><mi>cm</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">m</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi mathvariant="normal">f</mi><mi mathvariant="normal">s</mi></msub><mo>=</mo><mfrac><mn>1</mn><msub><mi>λ</mi><mi mathvariant="normal">s</mi></msub></mfrac><msqrt><mfrac><mi mathvariant="normal">T</mi><mi>μ</mi></mfrac></msqrt></math></p><p><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/abs/bd3625fe-696c-4fdf-868b-f043979c5d38-10.JPG" style="width: 147px; height: 94px;"/><br/>Pipe in fundamental frequency, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>λ</mi><mi>p</mi></msub><mn>4</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mi>p</mi></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mi mathvariant="normal">m</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi mathvariant="normal">f</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mfrac><msub><mi mathvariant="normal">v</mi><mi mathvariant="normal">s</mi></msub><msub><mi>λ</mi><mi mathvariant="normal">p</mi></msub></mfrac><mo>=</mo><mfrac><mn>360</mn><mrow><mn>1</mn><mo>.</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>300</mn><mo> </mo><mi>Hz</mi></math></p><p><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/abs/1e111a34-03a4-4668-b7b5-c5ba39013803-11.JPG" style="width: 112px; height: 181px;"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo></math> By decreasing the tension, beat<br/>frequency is decreased.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo>  </mo><msub><mi>f</mi><mi>s</mi></msub><mo>&gt;</mo><msub><mi>f</mi><mi>p</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi mathvariant="normal">f</mi><mi mathvariant="normal">s</mi></msub><mo>-</mo><msub><mi mathvariant="normal">f</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mn>8</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mn>1</mn><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac><msqrt><mfrac><mi>T</mi><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mfrac></msqrt><mo>-</mo><mfrac><mn>360</mn><mrow><mn>1</mn><mo>.</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>8</mn></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mn>10</mn><mo>×</mo><mn>100</mn></mrow><mn>25</mn></mfrac><msqrt><mi mathvariant="normal">T</mi></msqrt><mo>-</mo><mn>300</mn><mo>=</mo><mn>8</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msqrt><mi mathvariant="normal">T</mi></msqrt><mo>=</mo><mfrac><mrow><mn>308</mn><mo>×</mo><mn>25</mn></mrow><mn>1000</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">T</mi><mo>=</mo><mn>59</mn><mo>.</mo><mn>29</mn><mo> </mo><mi mathvariant="normal">N</mi></math></p></div>


tags: ['Chemistry', 'Alternating Current', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.27 A</span> </div>
answer: <div class="solution">Correct Option is : (B)<br/>0.27 A</div>
source_db: MarksBatch1_P1.db
title:
a-60-w-load-is-connected-to-the-secondary-of-a-transformer-whose-primary-draws-line-voltage-if-a-current-of-054-a-flows-in-the-load-what-is-the-curren-1

slug:
a-60-w-load-is-connected-to-the-secondary-of-a-transformer-whose-primary-draws-line-voltage-if-a-current-of-054-a-flows-in-the-load-what-is-the-curren-1-50284

question:
<div class="question">A 60 W load is connected to the secondary of a transformer whose primary draws line voltage. If a current of 0.54 A flows in the load, what is the current in the primary coil?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.54 A</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">0.27 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">1.08 A</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2.16 A</span> </li> </ul>


tags: ['Physics', 'Alternating Current']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-60-w-load-is-connected-to-the-secondary-of-a-transformer-whose-primary-draws-line-voltage-if-a-current-of-054-a-flows-in-the-load-what-is-the-curren

slug:
a-60-w-load-is-connected-to-the-secondary-of-a-transformer-whose-primary-draws-line-voltage-if-a-current-of-054-a-flows-in-the-load-what-is-the-curren-94291

question:
<div class="question">A $60 \mathrm{~W}$ load is connected to the secondary of a transformer whose primary draws line voltage. If a current of $0.54 \mathrm{~A}$ flows in the load, what is the current in the primary coil? Comment on the type of tansformer being used.</div>

answer:
<div class="solution">As given that,<br/>$$<br/>\begin{aligned}<br/>&amp;\mathrm{P}_{\mathrm{S}}=60 \mathrm{~W} \\<br/>&amp;\mathrm{I}_{\mathrm{S}}=0.54 \mathrm{~A}<br/>\end{aligned}<br/>$$<br/>Primary current $\mathrm{I}_{\mathrm{p}}=$ ?<br/>Taking line voltage as $220 \mathrm{~V}\left(\mathrm{~V}_{\mathrm{P}}=220 \mathrm{~V}\right)$<br/>$$<br/>\begin{aligned}<br/>&amp;\mathrm{P}_{\mathrm{S}}=\mathrm{V}_{\mathrm{S}} \mathrm{I}_{\mathrm{S}} \\<br/>&amp;\mathrm{P}_{\mathrm{S}}=60 \mathrm{~W}, \mathrm{I}_{\mathrm{S}}=0.54 \mathrm{~A} \\<br/>&amp;\mathrm{~V}_{\mathrm{S}}=\frac{60}{0.54}=110 \mathrm{Volt} .<br/>\end{aligned}<br/>$$<br/>Voltage in the secondary $\left(\mathrm{V}_{\mathrm{S}}\right)$ is less than voltage in the primary $\left(\mathrm{V}_{\mathrm{p}}\right)$.<br/>So, the transformer is step down transformer.<br/>since, the transformation ratio factor is<br/>$$<br/>\begin{aligned}<br/>&amp;r=\frac{\text { Secondary voltage }}{\text { Primary voltage }} \\<br/>&amp;r=\frac{V_S}{V_P}<br/>\end{aligned}<br/>$$<br/>$\therefore$ For transformer $\frac{V_S}{V_{\mathrm{p}}}=\frac{I_P}{I_s}$<br/>Substituting the values,<br/>$$<br/>\begin{aligned}<br/>\frac{110 \mathrm{~V}}{220 \mathrm{~V}} &amp;=\frac{\mathrm{I}_{\mathrm{P}}}{0.54 \mathrm{~A}} \\<br/>\Rightarrow \quad \quad \mathrm{I}_{\mathrm{P}} &amp;=0.27 \text { Ampere }<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'TS EAMCET', 'TS EAMCET 2021 (05 Aug Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-90-g-of-ethyl-amine-on-reaction-with-methyl-chloride-produced-a-tertiary-amine-as-an-exclusive-product-the-amount-of-methyl-chloride-required-is-giv

slug:
a-90-g-of-ethyl-amine-on-reaction-with-methyl-chloride-produced-a-tertiary-amine-as-an-exclusive-product-the-amount-of-methyl-chloride-required-is-giv-50613

question:
<div class="question">A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of ethyl amine on reaction with methyl chloride produced a tertiary amine as an exclusive product. The amount of methyl chloride required is<br/>[Given mass in amu : <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mi mathvariant="normal">C</mi><mo>=</mo><mn>12</mn><mo>,</mo><mo> </mo><mi mathvariant="normal">N</mi><mo>=</mo><mn>14</mn><mo>,</mo><mo> </mo><mi>Cl</mi><mo>=</mo><mn>35</mn><mo>.</mo><mn>5</mn></math>]</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>50</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</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>101</mn><mo> </mo><mi mathvariant="normal">g</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>202</mn><mo> </mo><mi mathvariant="normal">g</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>303</mn><mo> </mo><mi mathvariant="normal">g</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>202</mn><mo> </mo><mi mathvariant="normal">g</mi></math></span> </div>

answer:
<div class="solution"><p>The Standard Reaction is:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msub><mi>NH</mi><mn>2</mn></msub><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msub><mi>CH</mi><mn>3</mn></msub><mi>Cl</mi><mo> </mo><mo>→</mo><mo> </mo><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>3</mn></msub><mi mathvariant="normal">N</mi><mo> </mo><mo>+</mo><mo> </mo><mi>HCl</mi></math></p><p>Molar mass of ethyl amine <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mn>45</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p><p>The molar mass of methyl chloride <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mn>50</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p><p>Given Moles ethyl amine<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mfrac><mn>90</mn><mn>45</mn></mfrac><mo>=</mo><mn>2</mn></math> </p><p>As per the Standard reaction,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> mole of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msub><mi>NH</mi><mn>2</mn></msub></math> react with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> mole of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><mi>Cl</mi></math>, </p><p>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> moles of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msub><mi>NH</mi><mn>2</mn></msub></math> react with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> moles of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><mi>Cl</mi></math></p><p>Hence, the amount methyl chloride obtained is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>×</mo><mn>50</mn><mo>.</mo><mn>5</mn><mo> </mo><mo>=</mo><mo> </mo><mn>202</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p></div>


tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-200-resistance-has-a-certain-colour-code-as-per-standard-colour-coding-if-one-replaces-the-red-colour-by-green-in-the-code-the-new-resistance-will-b

slug:
a-200-resistance-has-a-certain-colour-code-as-per-standard-colour-coding-if-one-replaces-the-red-colour-by-green-in-the-code-the-new-resistance-will-b-20401

question:
<div class="question">A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200 </mn><mi mathvariant="normal">Ω</mi></math> resistance has a certain colour code as per standard colour coding. If one replaces the red colour by green in the code, the new resistance will be</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>500</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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo> </mo><mi mathvariant="normal">Ω</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>300</mn><mo> </mo><mi mathvariant="normal">Ω</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>100</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>500</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </div>

answer:
<div class="solution">When red is replaced by green, then the first significant figure in the value of resistance changes from 2 to 5. So the new resistance is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-and-b-are-two-events-such-that-a-and-b-are-mutually-exclusive-if-p-a-05-and-p-b-06-then-what-is-the-value-of-p-a-b

slug:
a-and-b-are-two-events-such-that-a-and-b-are-mutually-exclusive-if-p-a-05-and-p-b-06-then-what-is-the-value-of-p-a-b-89373

question:
<div class="question">A and B are two events such that $\bar{A}$ and $\bar{B}$ are mutually exclusive. If $\mathrm{P}(\mathrm{A})=0.5$ and $\mathrm{P}(\mathrm{B})=0.6$, then what is the value of $\mathrm{P}(\mathrm{A} \mid \mathrm{B})$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{5}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{6}$</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">$\frac{2}{5}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{6}$</span> </div>

answer:
<div class="solution">$\bar{A}$ and $\bar{B}$ are mutually exclusive $\therefore P(\bar{A} \cap \bar{B})=0$<br/>Given, $\mathrm{P}(\mathrm{A})=0.5 \Rightarrow P(\bar{A})=1-0.5=0.5$<br/>$\mathrm{P}(\mathrm{B})=0.6 \Rightarrow P(\bar{B})=1-0.6=0.4$<br/>$P(A \mid B)=\frac{P(A \cap B)}{P(B)}=\frac{1-P(\bar{A} \cup \bar{B})}{P(B)}$<br/>$=\frac{1-(P(\bar{A})+P(\bar{B}))}{P(B)}=\frac{1-(0.5+0.4)}{0.6}$<br/>$=\frac{1-0.9}{0.6}=\frac{0.1}{0.6}=\frac{1}{6}$</div>


tags: ['Chemistry', 'Electrochemistry', 'TS EAMCET', 'TS EAMCET 2023 (13 May Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-and-b-are-two-metals-the-standard-reduction-potential-of-a-aq-a-s-and-b-aq-b-s-are-05-v-and-05-v-respectively-what-is-the-lo-g-k-c-value-for-the-fol

slug:
a-and-b-are-two-metals-the-standard-reduction-potential-of-a-aq-a-s-and-b-aq-b-s-are-05-v-and-05-v-respectively-what-is-the-lo-g-k-c-value-for-the-fol-54265

question:
<div class="question">A and B are two metals. The standard reduction potential of $\mathrm{A}^{+}(\mathrm{aq}) / \mathrm{A}(\mathrm{s})$ and $\mathrm{B}^{+}(\mathrm{aq}) / \mathrm{B}(\mathrm{s})$ are $-0.5 \mathrm{~V}$ and $+0.5 \mathrm{~V}$ respectively. What is the $\log K_C$ value for the following reaction at $298 \mathrm{~K}$ ?<br/>$$<br/>\mathrm{A}(\mathrm{s})+\mathrm{B}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{A}^{+}(\mathrm{aq})+\mathrm{B}(\mathrm{s})<br/>$$<br/>$\left(\right.$ Given : $\left.\frac{2.303 R T}{F}=0.06 \mathrm{~V}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{6}{100}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{100}{6}$</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">$\frac{}{200}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{200}{6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{100}{6}$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \text { } \Delta \mathrm{G}^{\circ}=\mathrm{nFE}_{\text {cell }}^{\circ} \\ &amp; \Delta \mathrm{G}^{\circ}=-\mathrm{RT} \ln \mathrm{K}_{\mathrm{c}} \\ &amp; \therefore \quad \mathrm{nFE}_{\text {cell }}^{\circ}=-\mathrm{RT} \ln \mathrm{K}_{\mathrm{c}}=\frac{-2.303 \mathrm{RT}}{\mathrm{nF}} \log \mathrm{K}_{\mathrm{c}} \\ &amp; \mathrm{n}=\text { no. of electrons involved }=1 \\ &amp; \mathrm{E}_{\text {cell }}^{\circ}=\mathrm{E}_{\text {cathode }}^{\circ}-\mathrm{E}_{\text {Anode }}^{\circ}=0.5-(-0.5)=1 \text {. } \\ &amp; \therefore \quad \mathrm{E}_{\text {cell }}^{\circ}=\frac{-2.303 \mathrm{RT} \log \mathrm{K}_{\mathrm{c}}}{\mathrm{nF}} \\ &amp; 1=0.06 \log \mathrm{K}_{\mathrm{c}} \text {. } \\ &amp; \therefore \log \mathrm{K}_{\mathrm{c}}=\frac{100}{6} \\ &amp; \end{aligned}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-b-are-two-events-and-a-denotes-the-complements-of-a-consider-the-following-statements-1-p-a-b-p-b-p-a-2-p-a-p-a-b-1-p-b-which-of-the-above-statement

slug:
a-b-are-two-events-and-a-denotes-the-complements-of-a-consider-the-following-statements-1-p-a-b-p-b-p-a-2-p-a-p-a-b-1-p-b-which-of-the-above-statement-32455

question:
<div class="question">A, B are two events and $\bar{A}$ denotes the complements of A. Consider the following statements <br/>$1 \quad P(A \cup B) \leq P(B)+P(A)$<br/>$2 \quad \mathrm{P}(\mathrm{A})+\mathrm{P}(\overline{\mathrm{A}} \cup \mathrm{B}) \leq 1+\mathrm{P}(\mathrm{B})$<br/>Which of the above statements is/are correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2 only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Both 1 and 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">Neither 1 nor 2</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both 1 and 2</span> </div>

answer:
<div class="solution">(1) $\mathrm{P}(\mathrm{A} \cup \mathrm{B}) \leq \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})$ is correct<br/>and (2) $\mathrm{P}(\mathrm{A})+\mathrm{P}(\overline{\mathrm{A}} \cup \mathrm{B}) \leq 1+\mathrm{P}(\mathrm{B})$ is also correct<br/>$\Rightarrow$ Both the given statement are correct.</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2 only</span> </div>
source_db: MarksBatch1_P1.db
title:
a-b-c-and-d-are-four-sets-such-that-a-b-c-d-consider-the-following-1-a-c-and-b-d-are-always-disjoint-2-a-c-and-b-d-are-always-disjoint-which-of-the-ab

slug:
a-b-c-and-d-are-four-sets-such-that-a-b-c-d-consider-the-following-1-a-c-and-b-d-are-always-disjoint-2-a-c-and-b-d-are-always-disjoint-which-of-the-ab-75418

question:
<div class="question">$\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are four sets such that $\mathrm{A} \cap \mathrm{B}=\mathrm{C} \cap \mathrm{D}=\phi$.<br/>Consider the following: <br/>1.$\mathrm{A} \cup \mathrm{C}$ and $\mathrm{B} \cup \mathrm{D}$ are always disjoint.<br/>2.$\mathrm{A} \cap \mathrm{C}$ and $\mathrm{B} \cap \mathrm{D}$ are always disjoint Which of the above statements is/are correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 only</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">2 only</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">Both 1 and 2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither 1 nor 2</span> </li> </ul>

answer:
<div class="solution">$\quad$ Let $\mathrm{A}=\{1,2\}$<br/>$\mathrm{B}=\{3,4,0\}$<br/>$\mathrm{C}=\{5,6,0\}$<br/>$\mathrm{D}=\{7,8\}$<br/>Such that $(\mathrm{A} \cap \mathrm{B})=(\mathrm{C} \cap \mathrm{D})=\phi$<br/>$\Rightarrow(\mathrm{A} \cup \mathrm{C})=\{1,2,5,6,0\}$<br/>$\Rightarrow(\mathrm{B} \cup \mathrm{D})=\{3,4,7,8,0\}$<br/>$\Rightarrow(\mathrm{A} \cup \mathrm{C}) \cap(\mathrm{B} \cup \mathrm{D})=\{0\}$<br/>So $(\mathrm{A} \cup \mathrm{C})$ and $(\mathrm{B} \cup \mathrm{D})$ are not always dispoint $\Rightarrow(\mathrm{A} \cap \mathrm{C})=\phi$ and $(\mathrm{B} \cap \mathrm{D})=\phi$<br/>So $(\mathrm{A} \cap \mathrm{C})$ and $(\mathrm{B} \cap \mathrm{D})$ are always disjoint.</div>


tags: ['Biology', 'The Living World', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-b-c-and-d-are-respectively-common-name-man-housefly-c-wheat-biological-name-a-musca-domestica-mangifera-indica-triticum-aestivum-genus-homo-musca-ma

slug:
a-b-c-and-d-are-respectively-common-name-man-housefly-c-wheat-biological-name-a-musca-domestica-mangifera-indica-triticum-aestivum-genus-homo-musca-ma-62388

question:
<div class="question">A, B, C and D are respectively :-<br/>
 
<table border="1"> <tbody> <tr> <td> Common Name</td> <td> Man</td> <td> Housefly</td> <td> C</td> <td> Wheat</td> </tr> <tr> <td> Biological Name</td> <td> A</td> <td> <em>Musca domestica</em></td> <td> <em>Mangifera indica</em></td> <td> <em>Triticum aestivum</em></td> </tr> <tr> <td> Genus</td> <td> Homo</td> <td> <em>Musca</em></td> <td> <em>Mangifera</em></td> <td> <em>Triticum</em></td> </tr> <tr> <td> Family</td> <td> Hominidae</td> <td> B</td> <td> Anacardiaceae</td> <td> D</td> </tr> </tbody> </table> </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A - Homo,<br/>B - Muscidae,<br/>C - Neem,<br/>D - Poaceae</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">A - Homo sapiens,<br/>B - Muscidae,<br/>C - Mango,<br/>D - Poaceae</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">A - Primata,<br/>B - Insecta,<br/>C - Mango,<br/>D - Poales</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">A - Primata,<br/>B - Muscidae,<br/>C - Mango,<br/>D - Sapindales</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A - Homo sapiens,<br/>B - Muscidae,<br/>C - Mango,<br/>D - Poaceae</span> </div>

answer:
<div class="solution"><table border="1" cellpadding="1" cellspacing="1" style="width: 100%;"> <tbody> <tr> <td> CommonName</td> <td> Man</td> <td> Housefl<strong>y</strong></td> <td><strong> Mango</strong></td> <td> Wheat</td> </tr> <tr> <td> BiologicalName</td> <td> <strong><em>Homo  sapien</em></strong></td> <td> <em>Musca domestica</em></td> <td> <em>Mangifera indica </em></td> <td> <em>Triticum aestivum</em></td> </tr> <tr> <td> Genus</td> <td> Homo</td> <td> Musca</td> <td> Mangifera</td> <td> Triticum</td> </tr> <tr> <td> Family</td> <td> Hominidae</td> <td> <strong>Muscidae</strong></td> <td><strong> </strong>Anacardiaceae</td> <td><strong> Poaceae</strong></td> </tr> </tbody></table></div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-b-c-are-in-gp-with-1-a-b-n-and-n-1-is-an-integer-lo-g-an-n-lo-g-b-n-lo-g-c-n-form-a-sequence-this-sequence-is-which-one-of-the-following

slug:
a-b-c-are-in-gp-with-1-a-b-n-and-n-1-is-an-integer-lo-g-an-n-lo-g-b-n-lo-g-c-n-form-a-sequence-this-sequence-is-which-one-of-the-following-89140

question:
<div class="question">$\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in G.P. with $1   &lt; \mathrm{a} &lt; \mathrm{b} &lt; \mathrm{n}$, and $\mathrm{n}&gt;1$ is an integer. $\log _{\text {an }}$ $\mathrm{n}, \log _{\mathrm{b}} \mathrm{n}, \log _{\mathrm{c}} \mathrm{n}$ form a sequence. This sequence is which<br/>one of the following ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Harmonic progression</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">Arithmetic progression</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Geometric progression</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">Harmonic progression</span> </div>

answer:
<div class="solution">If a, b, c are in G.P. then, $\mathrm{b}^{2}=\mathrm{ac} \Rightarrow \mathrm{b}=(\mathrm{ac})^{1 / 2} \quad \ldots .(1)$<br/>Taking $\log _{\mathrm{n}}$ on both the sides of eq. (1).<br/>$\log _{\mathrm{n}} \mathrm{b}=\frac{1}{2}\left[\left(\log _{\mathrm{n}}(\mathrm{ac})\right]=\frac{\log _{\mathrm{n}} \mathrm{a}+\log _{\mathrm{n}} \mathrm{c}}{2}\right.$<br/>or, $\frac{\log _{n} a+\log _{n} c}{2}=\log _{n} b$<br/>So, $\log _{\mathrm{n}} \mathrm{a}, \log _{\mathrm{n}} \mathrm{b}$ and $\log _{\mathrm{n}} \mathrm{c}$ are in $\mathrm{AP}$.<br/>Hence, $\frac{1}{\log _{n} a}, \frac{1}{\log _{n} b}, \frac{1}{\log _{n} c}$ are in H.P.<br/>$\log _{\mathrm{a}} \mathrm{n}=\frac{1}{\log _{\mathrm{n}} \mathrm{a}}$<br/>$\log _{\mathrm{b}} \mathrm{n}=\frac{1}{\log _{\mathrm{n}} \mathrm{b}}$<br/>$\log _{\mathrm{c}} \mathrm{n}=\frac{1}{\log _{\mathrm{n}} \mathrm{c}}$<br/>i.e. $\log _{\mathrm{a}} \mathrm{n}, \log _{\mathrm{b}} \mathrm{n}$, and $\log _{\mathrm{c}} \mathrm{n}$ are in $\mathrm{HP}$.</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2011 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch1_P1.db
title:
a-b-c-d-and-e-are-coplanar-points-and-three-of-them-lie-in-a-straight-line-what-is-the-maximum-number-of-triangles-that-can-be-drawn-with-these-points

slug:
a-b-c-d-and-e-are-coplanar-points-and-three-of-them-lie-in-a-straight-line-what-is-the-maximum-number-of-triangles-that-can-be-drawn-with-these-points-19648

question:
<div class="question">$A, B, C, D$ and $E$ are coplanar points and three of them lie in a straight line. What is the maximum number of triangles that can be drawn with these points as their vertices?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">9</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">10</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">12</span> </li> </ul>

answer:
<div class="solution">Number of triangles using 5 points out of three are on a straight line $={ }^{5} C_{3}-{ }^{3} C_{3}=\frac{5 !}{3 ! 2 !}-1=\frac{5 \times 4}{2}-1$<br/>$=10-1=9$</div>


tags: ['Physics', 'Current Electricity']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-b-is-a-potentiometer-wire-figure-if-the-value-of-r-is-increased-in-which-direction-will-the-balance-point-j-shift

slug:
a-b-is-a-potentiometer-wire-figure-if-the-value-of-r-is-increased-in-which-direction-will-the-balance-point-j-shift-69723

question:
<div class="question">$\quad A B$ is a potentiometer wire (figure). If the value of $R$ is increased, in which direction will the balance point $\mathrm{J}$ shift?<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/ZUra6zegeUhWhzbHbkYM0yWKdXiFoREUcgTfaVVudX4.original.fullsize.png"/><br/></div>

answer:
<div class="solution">If $\mathrm{R}$ increases then, the current in main circuit decreases which in turn, decreases the potential difference across $\mathrm{AB}$ and hence potential gradient $(\mathrm{K})$ across $\mathrm{AB}$ decreases. Since, at neutral point, for given emf of cell, I increases as potential gradient $(\mathrm{K})$ across $\mathrm{AB}$ has decreased because.<br/>$$<br/>\mathrm{E}=\mathrm{kI} \quad\left[\because \mathrm{K}=\frac{\mathrm{V}}{(\mathrm{AB})}\right]<br/>$$<br/>So balance potential accross $\mathrm{AB}$ equal to potential of secondary circuit the length $(\mathrm{AJ})$ must be longer then earlier.<br/>Thus, with increase of 1 , the balance point neutral point will shift towards B.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-bag-contains-4-white-and-2-black-balls-and-another-bag-contains-3-white-and-5-black-balls-if-one-ball-is-drawn-from-each-bag-then-the-probability-th

slug:
a-bag-contains-4-white-and-2-black-balls-and-another-bag-contains-3-white-and-5-black-balls-if-one-ball-is-drawn-from-each-bag-then-the-probability-th-84620

question:
<div class="question">A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5}{24}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{13}{24}$</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">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{13}{24}$</span> </div>

answer:
<div class="solution">$\mathrm{P}$ (one white ball \&amp; one black ball) $=\mathrm{P}\{[$ black from 1 st bag $\&amp;$ white from $2 \mathrm{nd}]$ or [white from 1 st $\&amp;$ black from $2 \mathrm{nd}]\}$ $=\mathrm{P}\left(\left[\mathrm{B}_{1} \cap \mathrm{W}_{2}\right) \cup\left(\mathrm{W}_{1} \cap \mathrm{B}_{2}\right)\right]$<br/>$=\mathrm{P}\left(\mathrm{B}_{1} \cap \mathrm{W}_{2}\right)+\mathrm{P}\left(\mathrm{W}_{1} \cap \mathrm{B}_{2}\right)$<br/>(By addition theorem for mutually<br/>exclusive events) $=\mathrm{P}\left(\mathrm{B}_{1}\right) \mathrm{P}\left(\mathrm{W}_{2}\right)+\mathrm{P}\left(\mathrm{W}_{1}\right) \mathrm{P}\left(\mathrm{B}_{2}\right)$<br/>$\left(\therefore \mathrm{B}_{2} \&amp; \mathrm{~W}_{2} ; \mathrm{B}_{2} \&amp; \mathrm{~W}_{1}\right.$ are pairs of<br/>independent events) $=\left[\frac{2}{6} \times \frac{3}{8}\right]+\left[\frac{4}{6} \times \frac{5}{8}\right]$<br/>$=\frac{13}{24}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-bag-contains-5-black-and-3-white-balls-two-balls-are-drawn-at-random-one-after-the-other-without-replacement-what-is-the-probability-that-both-are-w

slug:
a-bag-contains-5-black-and-3-white-balls-two-balls-are-drawn-at-random-one-after-the-other-without-replacement-what-is-the-probability-that-both-are-w-98389

question:
<div class="question">A bag contains 5 black and 3 white balls. Two balls are drawn at random one after the other without replacement. What is the probability that both are white?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{28}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{14}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{3}{28}$</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 above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{28}$</span> </div>

answer:
<div class="solution">Total number of balls $=5+3=8$. Prob (both ball are white)<br/>$=\frac{3}{8} \times \frac{2}{7}(\because$ No. of white ball $=3)$<br/>$=\frac{3}{28}$</div>


tags: ['Mathematics', 'Probability', 'JEE Main', 'JEE Main 2019 (11 Jan Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-bag-contains-30-white-balls-and-10-red-balls-16-balls-are-drawn-one-by-one-randomly-from-the-bag-with-replacement-if-x-be-the-number-of-white-balls-

slug:
a-bag-contains-30-white-balls-and-10-red-balls-16-balls-are-drawn-one-by-one-randomly-from-the-bag-with-replacement-if-x-be-the-number-of-white-balls-13468

question:
<div class="question">A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If $X$ be the number of white balls drawn, then
<br/> <br/>$\left(\frac{\text { mean of } \mathrm{X}}{\text { standard deviation of } \mathrm{X}}\right)$ is equal to:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$4 \sqrt{3}$</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">$3 \sqrt{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{4 \sqrt{3}}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \sqrt{3}$</span> </div>

answer:
<div class="solution">$P($ white ball $)=\frac{30}{40}=\frac{3}{4}, Q$ (red ball) $=\frac{10}{40}=\frac{1}{4}, n=16$
<br/> <br/>$\frac{\text { Mean of } X}{\text { standard deviation of } X}=\frac{n P}{\sqrt{n P Q}}=\frac{\sqrt{n P}}{\sqrt{Q}}$ $=\sqrt{\frac{16 \times \frac{3}{4}}{\frac{1}{4}}}=\sqrt{48}=4 \sqrt{3}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch1_P1.db
title:
a-bag-contains-balls-of-two-colours-3-black-and-3-white-what-is-the-smallest-number-of-balls-which-must-be-drawn-from-the-bag-without-looking-so-that-

slug:
a-bag-contains-balls-of-two-colours-3-black-and-3-white-what-is-the-smallest-number-of-balls-which-must-be-drawn-from-the-bag-without-looking-so-that-32521

question:
<div class="question">A bag contains balls of two colours, 3 black and 3 white. What is the smallest number of balls which must be drawn from the bag, without looking, so that among these three are two of the same colour?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">3</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">4</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">5</span> </li> </ul>

answer:
<div class="solution">Minimum 4 balls have to be drawn so that among these there are two of the same colour</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-balloon-is-directly-above-one-end-of-a-bridge-the-angle-of-depression-of-the-other-end-of-the-bridge-from-the-balloon-is-4-8-if-the-height-of-the-ba

slug:
a-balloon-is-directly-above-one-end-of-a-bridge-the-angle-of-depression-of-the-other-end-of-the-bridge-from-the-balloon-is-4-8-if-the-height-of-the-ba-80233

question:
<div class="question">A balloon is directly above one end of a bridge. The angle of depression of the other end of the bridge from the balloon is $48^{\circ} .$ If the height of the balloon above the bridge is $122 \mathrm{~m}$, then what is the length of the bridge?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$122 \sin 48^{\circ} \mathrm{m}$</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">$122 \tan 42^{\circ} \mathrm{m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$122 \cos 48^{\circ} \mathrm{m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$122 \tan 48^{\circ} \mathrm{m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$122 \sin 48^{\circ} \mathrm{m}$</span> </div>

answer:
<div class="solution">Let the bridge is $\mathrm{BC}$ and height above the bridge $\mathrm{AB}=122 \mathrm{~m}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/kzw3_7M5y8SN4f4OnyPx-2Elr5e2vUcBQTCP4Qr0zro.original.fullsize.png"/><br/><br/>From DABC,<br/>$\begin{aligned} \cot 48^{\circ}=\frac{\mathrm{BC}}{\mathrm{AB}}=\frac{\mathrm{BC}}{122} \\ \mathrm{BC}=122 \cdot \cot \left(48^{\circ}\right) \\=122 \cdot \cot \left(90^{\circ}-42^{\circ}\right) \\=&amp; 122 \cdot \tan 42^{\circ} \end{aligned}$</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-balloon-is-pumped-at-the-rate-of-4-cm-3-per-second-what-is-the-rate-at-which-its-surface-area-increases-and-radius-is-4-cm

slug:
a-balloon-is-pumped-at-the-rate-of-4-cm-3-per-second-what-is-the-rate-at-which-its-surface-area-increases-and-radius-is-4-cm-94880

question:
<div class="question">A balloon is pumped at the rate of $4 \mathrm{~cm}^{3}$ per second. What is the rate at which its surface area increases and radius is $4 \mathrm{~cm} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~cm}^{2} / \mathrm{s}$ ?</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~cm}^{2} / \mathrm{s}$</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">$3 \mathrm{~cm}^{2} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \mathrm{~cm}^{2} / \mathrm{s}$</span> </li> </ul>

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

answer:
<div class="solution">Let $r$ be the radius of balloon.<br/>Balloon is like a sphere and volume of sphere $=\frac{4}{3} \pi r^{3}$<br/>$\therefore \quad V=\frac{4}{3} \pi r^{3}$<br/>Differentiate both side w.r.t ' $\mathrm{t}^{\prime}$<br/>$\Rightarrow \frac{d V}{d t}=\frac{4}{3} \pi \cdot 3 r^{2} \frac{d r}{d t}$<br/>$\Rightarrow 4=\frac{4}{3} \pi .3(4)^{2} \frac{d r}{d t} \quad\left(\because \frac{d V}{d t}=4 \mathrm{~cm}^{3} / \mathrm{s}\right)$<br/>$\Rightarrow \frac{d r}{d t}=\frac{1}{16 \pi}$<br/>Now, surface area of balloon $=S=4 \pi r^{2}$<br/>$$<br/>\begin{aligned}<br/>\frac{d S}{d t} &amp;=4 \pi \cdot 2 r \frac{d r}{d t} \\<br/>&amp;=4 \pi \cdot 2 \times 4 \frac{1}{16 \pi}(\text { from }(1))=2 \mathrm{~cm}^{2} / \mathrm{s}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Laws of Motion', 'AP EAMCET', 'AP EAMCET 2020 (18 Sep Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-balloon-of-mass-m-descends-with-an-acceleration-a-g-what-mass-need-to-be-removed-from-the-balloon-so-that-it-starts-ascending-with-acceleration-a

slug:
a-balloon-of-mass-m-descends-with-an-acceleration-a-g-what-mass-need-to-be-removed-from-the-balloon-so-that-it-starts-ascending-with-acceleration-a-83316

question:
<div class="question">A balloon of mass \(M\) descends with an acceleration \(a( &lt; g)\). What mass need to be removed from the balloon, so that it starts ascending with acceleration, \(a\) ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\frac{2 M}{(a+g)}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(\frac{2 M a}{(a+g)}\)</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">\(\frac{2 M a}{(a-g)}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\frac{2 M a}{(g-a)}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{2 M a}{(a+g)}\)</span> </div>

answer:
<div class="solution">The given situation is shown in the figure<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/_pkzq6rjZmg5oF6-jLY5QcdNDASBnZaxwTaREMNmL1Y.original.fullsize.png"/><br/><br/>In above figures, \(M\) is the mass of balloon and \(M^{\prime}\) is the mass remove from the ballon.<br/>According to Newton's law of motion in first case,<br/>\(M g-F=M a \Rightarrow F=M g-M a\) ...(i)<br/>According to Newton's second law of motion, for second case,<br/>\(\begin{aligned}<br/>&amp; F-\left(M-M^{\prime}\right) g=\left(M-M^{\prime}\right) a \\<br/>&amp; \Rightarrow F-M g+M^{\prime} g=M a-M^{\prime} a \\<br/>&amp; \Rightarrow M g-M a-M g+M^{\prime} g=M a-M^{\prime} a \text { [from Eq. (i)] } \\<br/>&amp; \Rightarrow M^{\prime} g+M^{\prime} a=M a+M a \\<br/>&amp; \Rightarrow M^{\prime}(g+a)=2 M a \\<br/>&amp; \Rightarrow M^{\prime}=\frac{2 M a}{g+a} \\<br/>\end{aligned}\)</div>


tags: ['Physics', 'Current Electricity', 'AP EAMCET', 'AP EAMCET 2018 (22 Apr Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">52 cm</span> </div>
source_db: MarksBatch1_P1.db
title:
a-battery-of-emf-10-v-is-connected-to-a-uniform-wire-a-b-of-1-m-length-and-having-a-resistance-of-10-in-series-with-a-10-resistor-as-shown-in-the-figu

slug:
a-battery-of-emf-10-v-is-connected-to-a-uniform-wire-a-b-of-1-m-length-and-having-a-resistance-of-10-in-series-with-a-10-resistor-as-shown-in-the-figu-74939

question:
<div class="question">A battery of emf $10 \mathrm{~V}$ is connected to a uniform wire $A B$ of $1 \mathrm{~m}$ length and having a resistance of $10 \Omega$ in series with a $10 \Omega$ resistor as shown in the figure. Two cells of emf $2 \mathrm{~V}$ and $3 \mathrm{~V}$ having internal resistance $2 \Omega$ and $3 \Omega$, respectively are connected as shown in the figure. If the galvanometer shows null deflection at point $J$ on the wire, then the distance of point $J$ from the point $B$ is.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/B57eDYWstbt5s9VoSvoYHiRHUj7HdqmDeTlxZEgxTQg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">48 cm</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">50 cm</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">52 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">54 cm</span> </li> </ul>

answer:
<div class="solution">Given $r=10 \Omega, R=10 \Omega, E=10 \mathrm{~V}$ and $L=100 \mathrm{~cm}$.<br/>Now, voltage drop on the wire, $E^{\prime}=\frac{E}{(r+R)} \times R$<br/>$$<br/>\Rightarrow \quad E^{\prime}=\frac{10}{20} \times 10=5 R<br/>$$<br/>So, potential gradient on wire,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/zdMB-s7PaFiW8uExjzllj1nBXTTQHpW5yDCBlCXX4hU.original.fullsize.png"/><br/><br/>Effective emf of combination in secondary circuit,<br/>$$<br/>\begin{array}{rlrl} <br/>&amp; &amp; \frac{V}{r_{\text {eff }}} &amp; =\frac{\varepsilon_1}{r_1}+\frac{\varepsilon_2}{r_2} \\<br/>\Rightarrow \text { Here, } \quad &amp; \frac{1}{r_{\text {eff }}} &amp; =\frac{1}{2}+\frac{1}{3}=\frac{5}{6} \\<br/>\Rightarrow \quad &amp; V &amp; =\frac{6}{5}(1+1)=\frac{12}{5}<br/>\end{array}<br/>$$<br/>Now, at balancing point (from point $A$ ) is<br/>$$<br/>\begin{aligned}<br/>&amp; l=V / x=\frac{12}{5} \times \frac{100}{5} \\<br/>&amp; l=48 \mathrm{~cm}<br/>\end{aligned}<br/>$$<br/>So, length from point $B$ is<br/>$$<br/>100-48=52 \mathrm{~cm}<br/>$$</div>


title: a-bc-is-a-triangle-in-which-bc-10-cm-c-a-6-cm-and-a-b-8-cm-which-one-of-the-following-is-correct
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch1_P1.db
slug:
a-bc-is-a-triangle-in-which-bc-10-cm-c-a-6-cm-and-a-b-8-cm-which-one-of-the-following-is-correct-17811

question:
<div class="question">$A B C$ is a triangle in which $B C=10 \mathrm{~cm}, C A=6 \mathrm{~cm}$ and $A B=8 \mathrm{~cm} .$ Which one of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$A B C$ is an acute angled triangle</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$A B C$ is an obtuse angled triangle</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$A B C$ is a right angled triangle</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">$A B C$ is a right angled triangle</span> </div>

answer:
<div class="solution">Given a $\triangle \mathrm{ABC}$ in which $\mathrm{BC}=10 \mathrm{~cm}$, $\mathrm{CA}=6 \mathrm{~cm}$ and $\mathrm{AB}=8 \mathrm{~cm} .$<br/>Since, $\mathrm{CA}^{2}+\mathrm{AB}^{2}=36+64=100=\mathrm{BC}^{2}$<br/>$\therefore \Delta \mathrm{ABC}$ is a right angled triangle.</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-a-d-d-c-what-is-on

slug:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-a-d-d-c-what-is-on-60079

question:
<div class="question">$A B C$ is a triangle right-angled at $B$. The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $A D   &lt; D C$.<br/>What is one of the acute angle of the triangle?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$15^{\circ}$</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">$30^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$45^{\circ}$</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">$15^{\circ}$</span> </div>

answer:
<div class="solution">Let $\mathrm{BD}=\mathrm{P}$ and $\mathrm{DE}=x$ <br/>$\Rightarrow <br/>\quad A C=4 P$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Zzx-LY9gIT819g0yc0XqPk9noHDWI5ll19PNrz0-NjA.original.fullsize.png"/><br/><br/>Let $\mathrm{E}$ be mid-point of $\mathrm{AC}$. Then, $\mathrm{AE}=\mathrm{EC}=\mathrm{BE}=2 \mathrm{P}$<br/>In $\Delta \mathrm{BDE},(\mathrm{BE})^{2}=(\mathrm{BD})^{2}+(\mathrm{ED})^{2}$<br/>$\Rightarrow(2 P)^{2}=(P)^{2}+x^{2}$<br/>$\Rightarrow \quad 4 \mathrm{P}^{2}=\mathrm{P}^{2}+\mathrm{x}^{2}$<br/>$\Rightarrow \quad 3 \mathrm{P}^{2}=\mathrm{x}^{2} \Rightarrow x=\sqrt{3} \mathrm{P}$<br/>Now, $\mathrm{AD}=2 \mathrm{P}-x=2 \mathrm{P}-\sqrt{3} \mathrm{P}=\mathrm{P}(2-\sqrt{3})$<br/>$\mathrm{DC}=2 \mathrm{P}+x=2 \mathrm{P}+\sqrt{3} \mathrm{P}=\mathrm{P}(2+\sqrt{3})$<br/>In $\Delta \mathrm{BAD}, \tan \mathrm{A}=\frac{\mathrm{BD}}{\mathrm{AD}}=\frac{\mathrm{P}}{\mathrm{P}(2-\sqrt{3})}$<br/>$=\frac{1}{2-\sqrt{3}} \times \frac{2+\sqrt{3}}{2-\sqrt{3}}=2+\sqrt{3}=\tan 75^{\circ}$<br/>$\tan \alpha=\frac{\mathrm{AD}}{\mathrm{BD}}=\frac{\mathrm{P}(2-\sqrt{3})}{\mathrm{P}}=2-\sqrt{3}=\tan 15^{\circ}$<br/>$\Rightarrow \quad \alpha=15^{\circ}$<br/>As, $\Delta \mathrm{ABC}$ is right angled at $\mathrm{B}$, from figure $\alpha+\beta=90^{\circ}$ $\Rightarrow \quad 15+\beta=90^{\circ} \Rightarrow \beta=75^{\circ}$<br/>In $\triangle \mathrm{ABC}, \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ}$<br/>$\Rightarrow \quad 75^{\circ}+90^{\circ}+\angle \mathrm{C}=180^{\circ}$<br/>$\Rightarrow \quad \angle \mathrm{C}=180^{\circ}-165^{\circ}=15^{\circ}$<br/>One of the a cute angle is $15^{\circ}$</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2011 (Phase 1)']
answer: <div class="solution">$\angle \mathrm{ABD}=\alpha=15^{\circ}$</div>
source_db: MarksBatch1_P1.db
title:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-ad-dc-what-is-a-b-

slug:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-ad-dc-what-is-a-b-95450

question:
<div class="question">$A B C$ is a triangle right-angled at $B$. The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $\mathrm{AD}   &lt; \mathrm{DC}$.<br/>What is $\angle A B D_{?}$</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-ad-dc-what-is-a-d-

slug:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-ad-dc-what-is-a-d-42754

question:
<div class="question">$A B C$ is a triangle right-angled at $B$. The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $\mathrm{AD}   &lt; \mathrm{DC}$.<br/>What is $A D: D C$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(7-2 \sqrt{3}): 1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(7-4 \sqrt{3}): 1$</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">$1: 2$</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">$(7-4 \sqrt{3}): 1$</span> </div>

answer:
<div class="solution">$\mathrm{AD}: \mathrm{DC}=\frac{\mathrm{AD}}{\mathrm{DC}}=\frac{\mathrm{P}(2-\sqrt{3})}{\mathrm{P}(2+\sqrt{3})}=\frac{2-\sqrt{3}}{2+\sqrt{3}} \times \frac{2-\sqrt{3}}{2-\sqrt{3}}$<br/>$=\frac{4+3-4 \sqrt{3}}{1}=\frac{7-4 \sqrt{3}}{1}$<br/>$\mathrm{AD}: \mathrm{DC}=7-4 \sqrt{3}: 1$</div>


tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-ad-dc-what-is-tan-

slug:
a-bc-is-a-triangle-rightangled-at-b-the-hypotenuse-a-c-is-four-times-the-perpendicular-b-d-drawn-to-it-from-the-opposite-vertex-and-ad-dc-what-is-tan-14650

question:
<div class="question">$A B C$ is a triangle right-angled at $B$. The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $\mathrm{AD}   &lt; \mathrm{DC}$.<br/>What is tan $(A-C)$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None 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">None of these</span> </div>

answer:
<div class="solution">$\tan (A-C)=\tan \left(75^{\circ}-15^{\circ}\right)=\tan 60^{\circ}=\sqrt{3}$</div>


tags: ['Mathematics', 'Circle', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-bc-is-an-equilateral-triangle-inscribed-in-a-circle-of-centre-o-and-radius-5-cm-let-the-diameter-through-c-meet-the-circle-again-at-d-assertion-a-a--1

slug:
a-bc-is-an-equilateral-triangle-inscribed-in-a-circle-of-centre-o-and-radius-5-cm-let-the-diameter-through-c-meet-the-circle-again-at-d-assertion-a-a-1-49513

question:
<div class="question">$A B C$ is an equilateral triangle inscribed in a circle of centre $O$ and radius $5 \mathrm{~cm}$. Let the diameter through $C$ meet the circle again at $\mathrm{D}$. <br/>Assertion (A): $A D \cdot B D   &lt; O B \cdot O C$<br/>Reason (R): $2\left(A D^{2}+B D^{2}\right)=C D^{2}=100$ sq cm</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Both A and R are individually true and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Both $\mathrm{A}$ and $\mathrm{R}$ are individually true but $\mathrm{R}$ is not the correct explanation of $\mathrm{A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{A}$ is true but $\mathrm{R}$ is false</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">A is false but $\mathrm{R}$ is true</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">A is false but $\mathrm{R}$ is true</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/JaogXx5q3BI9d6hOZ1NgOpS6oT4gJ7w1tzoVkYUI77g.original.fullsize.png"/><br/><br/>(A) : Consider $A D \cdot B D &lt; O B \cdot O C$<br/>Now, $\mathrm{OA}=5 \mathrm{~cm}$ (Radius), $\mathrm{OB}=5 \mathrm{~cm}$ (Radius) and $\mathrm{OC}=5 \mathrm{~cm}($ Radius $)$<br/>Since, $\Delta O A D$ and $\triangle O B D$<br/>are congruent by SAS therefore<br/>$$<br/>A D=O A=5 \mathrm{~cm}<br/>$$<br/>and $B D=O B=5 \mathrm{~cm}$<br/>Thus, $A D \cdot B D=5 \times 5=25$<br/>and $\quad O B \cdot O C=5 \times 5=25$<br/>Thus, we have<br/>$A D \cdot B D=25=O B \cdot O C$<br/>$$<br/>\begin{aligned}<br/>\operatorname{Now}(\mathrm{R}): &amp; 2\left(A D^{2}+B D^{2}\right) \\<br/>&amp;=2[25+25]=100 \\<br/>\text { and } \quad &amp; C D^{2}=(10)^{2}=100<br/>\end{aligned}<br/>$$<br/>Thus, $2\left(A D^{2}+B D^{2}\right)=C D^{2}=100$ sq. $\mathrm{cm}$.<br/>Hence, (A) is false and (R) is true.</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-bc-is-an-equilateral-triangle-inscribed-in-a-circle-of-centre-o-and-radius-5-cm-let-the-diameter-through-c-meet-the-circle-again-at-d-assertion-a-a-

slug:
a-bc-is-an-equilateral-triangle-inscribed-in-a-circle-of-centre-o-and-radius-5-cm-let-the-diameter-through-c-meet-the-circle-again-at-d-assertion-a-a-42226


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2022 (04 Jul Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-body-is-suspended-from-a-string-of-length-1-m-and-mass-2-g-the-mass-of-the-body-to-produce-a-fundamental-mode-of-100-hz-frequency-in-the-string-is-a

slug:
a-body-is-suspended-from-a-string-of-length-1-m-and-mass-2-g-the-mass-of-the-body-to-produce-a-fundamental-mode-of-100-hz-frequency-in-the-string-is-a-13176

question:
<div class="question">A body is suspended from a string of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math> and mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi mathvariant="normal">g</mi></math>. The mass of the body to produce a fundamental mode of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi>Hz</mi></math> frequency in the string is<br/>(Acceleration due to gravity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>)</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>80</mn><mo> </mo><mi mathvariant="normal">g</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>4</mn><mo> </mo><mi>kg</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>400</mn><mo> </mo><mi mathvariant="normal">g</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mi>kg</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> </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>8</mn><mo> </mo><mi>kg</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>Mass per unit length of the given string is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mfrac><mi>m</mi><mi>l</mi></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mn>1</mn></mfrac><mo>=</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Speed of transverse waves on a string is given by,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mi>T</mi><mi>μ</mi></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>μ</mi></mfrac></msqrt></math></p><p>Fundamental frequency on a string fixed at both ends is given by,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>0</mn></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mfrac><msqrt><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mi>μ</mi></mfrac></msqrt><mrow><mn>2</mn><mi>l</mi></mrow></mfrac><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>m</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi>l</mi><mn>2</mn></msup><msup><msub><mi>f</mi><mn>0</mn></msub><mn>2</mn></msup><mi>μ</mi></mrow><mi>g</mi></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>×</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup><mo>×</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mn>10</mn></mfrac><mo>=</mo><mn>8</mn><mo> </mo><mi>kg</mi></math></p></blockquote></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-body-of-density-d-1-is-counterpoised-by-m-g-of-weights-of-density-d-2-in-the-air-of-density-d-then-the-true-mass-of-the-body-is

slug:
a-body-of-density-d-1-is-counterpoised-by-m-g-of-weights-of-density-d-2-in-the-air-of-density-d-then-the-true-mass-of-the-body-is-45923

question:
<div class="question">A body of density<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msub><mi>d</mi><mn>1</mn></msub></math><sub> </sub>is counterpoised by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>g</mi></math> of weights of density <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>d</mi><mn>2</mn></msub></math> in the air of density <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>. Then the true mass of the body 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"><mi>M</mi></math><div id="gtx-trans" style="position: absolute; left: 86px; 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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mi>d</mi><msub><mi>d</mi><mn>2</mn></msub></mfrac></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mi>d</mi><msub><mi>d</mi><mn>1</mn></msub></mfrac></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>M</mi><mfenced><mrow><mn>1</mn><mo>-</mo><mi>d</mi><mo>/</mo><msub><mi>d</mi><mn>2</mn></msub></mrow></mfenced></mrow><mfenced><mrow><mn>1</mn><mo>-</mo><mi>d</mi><mo>/</mo><msub><mi>d</mi><mn>1</mn></msub></mrow></mfenced></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> </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><mrow><mi>M</mi><mfenced><mrow><mn>1</mn><mo>-</mo><mi>d</mi><mo>/</mo><msub><mi>d</mi><mn>2</mn></msub></mrow></mfenced></mrow><mfenced><mrow><mn>1</mn><mo>-</mo><mi>d</mi><mo>/</mo><msub><mi>d</mi><mn>1</mn></msub></mrow></mfenced></mfrac></math></span> </div>

answer:
<div class="solution">Let M<sub>0</sub> = mass of body in vacuum.<br/>Apparent weight of the body in air=Apparent weight of standard weights in air <br/>â Actual weight - upthrust due to displaced air = Actual weight - upthrust due to displaced air<br/><br/><math><mrow><mo> â</mo> <mspace width="0.5em"></mspace> <msub> <mtext>M</mtext> <mn>0</mn> </msub> <mtext>g</mtext> <mo>-</mo> <mfenced close=")" open="(" separators=","> <mrow> <mfrac> <mrow> <msub> <mtext>M</mtext> <mn>0</mn> </msub> </mrow> <mrow> <msub> <mtext>d</mtext> <mn>1</mn> </msub> </mrow> </mfrac> </mrow> </mfenced> <mtext>d</mtext> <mtext>g</mtext> <mo>=</mo> <mtext>M</mtext> <mtext>g</mtext> <mo>-</mo> <mfenced close=")" open="(" separators=","> <mrow> <mfrac> <mrow> <mtext>M</mtext> </mrow> <mrow> <msub> <mtext>d</mtext> <mn>2</mn> </msub> </mrow> </mfrac> </mrow> </mfenced> <mtext>dg</mtext> <mspace width="0.5em"></mspace> <mo>â</mo> <msub> <mtext>M</mtext> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mtext>M</mtext> <mfenced close="]" open="[" separators=","> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mtext>d</mtext> </mrow> <mrow> <msub> <mtext>d</mtext> <mn>2</mn> </msub> </mrow> </mfrac> </mrow> </mfenced> </mrow> <mrow> <mfenced close="]" open="[" separators=","> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mtext>d</mtext> </mrow> <mrow> <msub> <mtext>d</mtext> <mn>1</mn> </msub> </mrow> </mfrac> </mrow> </mfenced> </mrow> </mfrac> </mrow> </math></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-body-of-density-d-is-counterpoised-by-m-g-of-weight-of-density-d-2-in-air-of-density-d-then-the-true-mass-of-the-body-is

slug:
a-body-of-density-d-is-counterpoised-by-m-g-of-weight-of-density-d-2-in-air-of-density-d-then-the-true-mass-of-the-body-is-87358

question:
<div class="question">A body of density <math><mi>d</mi></math>, is counterpoised by <math><mi>M</mi><mi>g</mi></math> of weight of density <math><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></math> in air of density <math><mi>d</mi></math> . Then, the true mass of the body is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mi>M</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mi>M</mi><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mi>M</mi><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mi>M</mi><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></mrow></mfrac></mrow></mfenced></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><mi>M</mi><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></mrow></mfrac></mrow></mfenced></math></span> </div>

answer:
<div class="solution">Let the <math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math>  is the mass of the body. Apparent weight of the body in air<br/><br/> <math><mo>=</mo></math>  Apparent weight of standard weight in air <br/><br/> <math><mo>â´</mo></math>  Actual weight - Upthrust due to displaced air <br/><br/> <math><mo>â</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>g</mi><mo>-</mo><mfrac><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mi>d</mi><mi>g</mi><mo>=</mo><mi>M</mi><mi>g</mi><mo>-</mo><mfrac><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mi>d</mi><mi>g</mi></math> <br/><br/> <math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>g</mi><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mo>=</mo><mi>M</mi><mi>g</mi><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></mfenced></math> <br/><br/> <math><mo>â´</mo><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>M</mi><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfrac></math></div>


tags: ['Physics', 'Oscillations', 'TS EAMCET', 'TS EAMCET 2019 (04 May Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-body-of-mass-03-kg-hangs-by-a-spring-with-a-force-constant-of-50-n-m-the-amplitude-of-oscillations-is-damped-and-reaches-e-1-of-its-original-value-i

slug:
a-body-of-mass-03-kg-hangs-by-a-spring-with-a-force-constant-of-50-n-m-the-amplitude-of-oscillations-is-damped-and-reaches-e-1-of-its-original-value-i-35443

question:
<div class="question">A body of mass $0.3 \mathrm{~kg}$ hangs by a spring with a force constant of $50 \mathrm{~N} / \mathrm{m}$. The amplitude of oscillations is damped and reaches $\frac{1}{e}$ of its original value in about 100 oscillations. If $\omega$ and $\omega^{\prime}$ are the angular frequencies of undamped and damped oscillations respectively, then percentage of $\left(\frac{\omega-\omega}{\omega}\right)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(\frac{1}{800 \pi}\right)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\frac{\pi^2}{600}\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(\frac{1}{800 \pi^2}\right)$</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">D</span> <span class="option-data">$\left(\frac{\pi}{400}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{1}{800 \pi^2}\right)$</span> </div>

answer:
<div class="solution">Hint The displacement of a spring mass oscillator, $X=A e^{-b t / 2 m} \cos \left(\omega^{\prime} t+\phi\right)$ where, $\omega^{\prime}=$ angular frequency of damped oscillation and $\omega^{\prime}=\omega_0 \sqrt{1-\frac{b^2}{4 m^2 \omega_0^2}}$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-body-of-mass-m-hits-normally-a-rigid-wall-with-velocity-v-and-bounce-s-back-with-the-same-velocity-the-impulse-experienced-by-the-body-is

slug:
a-body-of-mass-m-hits-normally-a-rigid-wall-with-velocity-v-and-bounce-s-back-with-the-same-velocity-the-impulse-experienced-by-the-body-is-65277

question:
<div class="question"><div> <p align="left" style="text-align:left;"><span>A body of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> hits normally a rigid wall with velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> and bounce</span><span>s</span><span> back with the same velocity. The impulse experienced by the body is :</span></p> </div> </div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><div><p align="left" style="text-align:left;"><i><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>V</mi></math></span></i></p></div></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>M</mi><mi>V</mi></math></span></p></div><div id="gtx-trans" style="position: absolute; left: 89px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><div><p align="left" style="text-align:left;"><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>M</mi><mi>V</mi></math></span></p></div><div id="gtx-trans" style="position: absolute; left: 51px; 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">D</span> <span class="option-data">Zero</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><div><p align="left" style="text-align:left;"><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>M</mi><mi>V</mi></math></span></p></div><div id="gtx-trans" style="position: absolute; left: 51px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution"><div><p align="left" style="text-align:left;"><span>Impulse,  <math> <mrow> <mover accent="true"> <mi>J</mi> <mo>→</mo> </mover> <mo>=</mo><mstyle displaystyle="true"> <mrow> <msubsup> <mo>∫</mo> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>t</mi> <mn>2</mn> </msub> </mrow> </msubsup> <mrow> <mover accent="true"> <mi>F</mi> <mo>→</mo> </mover> <mo>.</mo><mi>d</mi><mi>t</mi> </mrow> </mrow> </mstyle> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>or            <math> <mrow> <mi>J</mi><mo>=</mo><msub> <mi>F</mi> <mrow> <mi>avg</mi> </mrow> </msub> <mo>.</mo><mtext> </mtext><mi>Δ</mi><mi>t</mi> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span>Now, according to Newton’s Second Law</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mover accent="true"> <mi>F</mi> <mo>→</mo> </mover> <mo>=</mo><mfrac> <mrow> <mi>d</mi><mover accent="true"> <mi>P</mi> <mo>→</mo> </mover> </mrow> <mrow> <mi>d</mi><mi>t</mi> </mrow> </mfrac> <mtext> </mtext><mtext> </mtext><mi>or</mi><mtext> </mtext><mtext> </mtext><mstyle displaystyle="true"> <mrow> <msubsup> <mo>∫</mo> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>t</mi> <mn>2</mn> </msub> </mrow> </msubsup> <mrow> <mover accent="true"> <mi>F</mi> <mo>→</mo> </mover> <mo>.</mo><mtext> </mtext><mi>d</mi><mi>t</mi> </mrow> </mrow> </mstyle><mo>=</mo><mstyle displaystyle="true"> <mrow> <msubsup> <mo>∫</mo> <mrow> <msub> <mover accent="true"> <mi>P</mi> <mo>→</mo> </mover> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mover accent="true"> <mi>P</mi> <mo>→</mo> </mover> <mn>2</mn> </msub> </mrow> </msubsup> <mrow> <mi>d</mi><mover accent="true"> <mi>P</mi> <mo>→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math> <mrow> <mo>∴</mo><mtext> </mtext><mtext> </mtext><mover accent="true"> <mi>J</mi> <mo>→</mo> </mover> <mo>=</mo><msub> <mover accent="true"> <mi>P</mi> <mo>→</mo> </mover> <mn>2</mn> </msub> <mo>−</mo><msub> <mover accent="true"> <mi>P</mi> <mo>→</mo> </mover> <mn>1</mn> </msub> <mo>=</mo><mi>Δ</mi><mover accent="true"> <mi>P</mi> <mo>→</mo> </mover> </mrow> </math> </span><span>  </span></p><p align="left" style="text-align:left;"><span>[<i>i.e.</i>, the action of impulse is to change  the momentum of a body and the impulse of force is equal to the change in momentum. This is also known as impulse-momentum theorem]</span></p><p align="left" style="text-align:left;"><span>In the given case,</span></p><p align="left" style="text-align:left;"><span><img alt="" height="133" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/IL0001908_AnsExp3_1.png" width="132"/></span></p><p align="left" style="text-align:left;"><span>Impulse  <math> <mrow> <mo>=</mo><msub> <mover accent="true"> <mi>p</mi> <mo>→</mo> </mover> <mn>2</mn> </msub> <mo>−</mo><msub> <mover accent="true"> <mi>p</mi> <mo>→</mo> </mover> <mn>1</mn> </msub> </mrow> </math>  <br/> (<i>i.e.</i>, impulse  <math> <mo>=</mo> </math> change in momentum)</span></p><p align="left" style="text-align:left;"><span>or Impulse,  <math> <mrow> <mi>J</mi><mo>=</mo><mi>M</mi><mtext> </mtext><msub> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> <mn>2</mn> </msub> <mo>−</mo><mi>M</mi><mtext> </mtext><msub> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> <mn>1</mn> </msub> </mrow> </math> </span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mo>⇒</mo><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>=</mo><mi>M</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>v</mi><mo>)</mo><mo>−</mo><mo>(</mo><mo>−</mo><mi>v</mi><mo>)</mo></mrow><mo>]</mo></mrow></mtd></mtr><mtr><mtd><mo>⇒</mo><mtext> </mtext><mtext> </mtext><mi>J</mi><mo>=</mo><mn>2</mn><mi>M</mi><mi>v</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">N</mi><mo> </mo><mi mathvariant="normal">s</mi></mtd></mtr></mtable></math> </span></p></div> <!-- /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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tags: ['Physics', 'Oscillations']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-body-of-mass-m-is-situated-in-a-potential-field-u-x-u-0-1-cos-x-when-u-0-and-are-constants-find-the-time-period-of-small-oscillations

slug:
a-body-of-mass-m-is-situated-in-a-potential-field-u-x-u-0-1-cos-x-when-u-0-and-are-constants-find-the-time-period-of-small-oscillations-68979

question:
<div class="question">A body of mass $m$ is situated in a potential field $U(x)=U_0(1-\cos \alpha x)$ when, $U_0$ and $\alpha$ are constants. Find the time period of small oscillations.</div>

answer:
<div class="solution">As given that, the potential energy (associated with the field) for a body of mass $m$.<br/>$$<br/>U(x)=U_0(1-\cos \alpha x)<br/>$$<br/>$\because$ for conservative force $f$, we can write $f=\frac{-d u}{d x}$<br/>We have assumed the field to be conservative<br/>$$<br/>\begin{aligned}<br/>F &amp;=-\frac{d}{d x}\left(U_0-U_0 \cos \alpha x\right) \\<br/>&amp;=-U_0 \alpha \sin \alpha x<br/>\end{aligned}<br/>$$<br/>For SHM, $\alpha x$ is small so $\sin \alpha x$ i.e. $\sin \alpha x=\alpha x$ so,<br/>$$<br/>\begin{aligned}<br/>&amp;F=-U_0 \alpha^2 x \\<br/>&amp;\therefore F \propto(-x)<br/>\end{aligned}<br/>$$<br/>As, $U_0, \alpha$ being constant.<br/>$\therefore$ So motion is SHM for small oscillations.<br/>Standard equation for SHM,<br/>$$<br/>F=-m \omega^2 x<br/>$$<br/>Comparing Eqs. (ii) and (iii), then<br/>$$<br/>\begin{aligned}<br/>&amp;-m \omega^2 x=-U_0 \alpha^2 x \\<br/>&amp;m \omega^2=U_0 \alpha^2 \\<br/>&amp;\omega^2=\frac{U_0 \alpha^2}{m} \text { or } \omega=\sqrt{\frac{U_0 \alpha^2}{m}} \\<br/>&amp;\therefore \text { Time period } T=\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{m}{U_0 \alpha^2}}<br/>\end{aligned}<br/>$$<br/>From (i) this period is valid for small angle $\alpha x$.<br/>$$<br/>T=\frac{2 \pi}{\alpha} \sqrt{\frac{m}{U_0}}<br/>$$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-box-contains-3-white-and-2-black-balls-two-balls-are-drawn-at-random-one-after-the-other-if-the-balls-are-not-replaced-what-is-the-probability-that-

slug:
a-box-contains-3-white-and-2-black-balls-two-balls-are-drawn-at-random-one-after-the-other-if-the-balls-are-not-replaced-what-is-the-probability-that-80102

question:
<div class="question">A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 / 5$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 / 5$</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">$1 / 10$</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">$1 / 5$</span> </div>

answer:
<div class="solution">Total number of balls $=5$ Number of black balls $=2$ Required probability $=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{{ }^{2} \mathrm{C}_{1} \times{ }^{1} \mathrm{C}_{1}}{{ }^{5} \mathrm{C}_{2}}=\frac{2}{5} \times \frac{1}{2}=\frac{1}{5}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-box-contains-6-distinct-dolls-from-this-box-3-dolls-are-randomly-selected-one-by-one-with-replacement-what-is-the-probability-of-selecting-3-distinc

slug:
a-box-contains-6-distinct-dolls-from-this-box-3-dolls-are-randomly-selected-one-by-one-with-replacement-what-is-the-probability-of-selecting-3-distinc-51086

question:
<div class="question">A box contains 6 distinct dolls. From this box, 3 dolls are randomly selected one by one with replacement. What is the probability of selecting 3 distinct dolls?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 / 54$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$12 / 25$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 20$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$5 / 9$</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">$5 / 9$</span> </div>

answer:
<div class="solution">Required probability $=\frac{{ }^{6} \mathrm{C}_{1} \times{ }^{5} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{1}}{{ }^{6} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{1}}$<br/>$=\frac{6 \times 5 \times 4}{6 \times 6 \times 6}=\frac{5}{9}$</div>


tags: ['Mathematics', 'Probability', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-box-contains-6-pens-2-of-which-are-defective-two-pens-are-taken-randomly-from-the-box-if-random-variable-x-number-of-defective-pens-obtained-then-st-1

slug:
a-box-contains-6-pens-2-of-which-are-defective-two-pens-are-taken-randomly-from-the-box-if-random-variable-x-number-of-defective-pens-obtained-then-st-1-75877

question:
<div class="question">A box contains <math> <mn>6</mn> </math> pens, <math> <mn>2</mn> </math> of which are defective. Two pens are taken randomly from the box. If random variable <math><mi>x</mi><mo>:</mo></math> Number of defective pens obtained, then standard deviation of <math><mi>x</mi><mo>=</mo></math></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mo>Â±</mo><mi>Â </mi><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn><mo>â</mo><mn>5</mn></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mfrac><mrow><mn>8</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mfrac><mrow><mn>16</mn></mrow><mrow><mn>45</mn></mrow></mfrac></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt></mrow></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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt></mrow></mfrac></math></span> </div>

answer:
<div class="solution"><math><mi>x</mi></math> : no. of defective pens<br/>Two pens are taken from box<br/><math><mo>â´</mo><mi> </mi><mi> </mi><mi>x</mi></math> can taken values 0, 1, 2<br/><math><mi>p</mi><mfenced separators="|"><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>=</mo><mfrac><mrow><msup><mrow><mi> </mi></mrow><mrow><mn>4</mn></mrow></msup><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msup><mrow><mi> </mi></mrow><mrow><mn>6</mn></mrow></msup><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mo>Ã</mo><mn>3</mn></mrow><mrow><mn>6</mn><mo>Ã</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>6</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math><br/><math><mi>p</mi><mi> </mi><mfenced separators="|"><mrow><mi>x</mi><mo>=</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mfrac><mrow><msup><mrow><mi> </mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>Ã</mo><msup><mrow><mi> </mi></mrow><mrow><mn>4</mn></mrow></msup><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msup><mrow><mi> </mi></mrow><mrow><mn>6</mn></mrow></msup><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>Ã</mo><mn>4</mn><mo>Ã</mo><mn>2</mn><mo>Ã</mo><mn>1</mn></mrow><mrow><mn>6</mn><mo>Ã</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math><br/><math><mi>p</mi><mfenced separators="|"><mrow><mi>x</mi><mo>=</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mfrac><mrow><msup><mrow><mi> </mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mrow><msup><mrow><mi> </mi></mrow><mrow><mn>6</mn></mrow></msup><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>Ã</mo><mn>2</mn><mo>Ã</mo><mn>1</mn></mrow><mrow><mn>6</mn><mo>Ã</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math><table border="1"> <tbody> <tr> <td>x</td> <td>P</td> <td><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></td> <td><math><msubsup><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></td> </tr> <tr> <td>0</td> <td><math><mfrac><mrow><mn>6</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math></td> <td>0</td> <td>0</td> </tr> <tr> <td>1</td> <td><math><mfrac><mrow><mn>8</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math></td> <td><math><mfrac><mrow><mn>8</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math></td> <td><math><mfrac><mrow><mn>8</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math></td> </tr> <tr> <td>2</td> <td><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math></td> <td><math><mfrac><mrow><mn>2</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math></td> <td><math><mfrac><mrow><mn>4</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math></td> </tr> </tbody></table><math><mi>E</mi><mfenced separators="|"><mrow><mi>x</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mn>10</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math><br/><math><mo>=</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math><br/><math><mi>E</mi><mfenced separators="|"><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced><mo>=</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>15</mn></mrow></mfrac></math><br/><math><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math><br/>Standard deviation <math><mo>=</mo><msqrt><mi>E</mi><mfenced separators="|"><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced><mo>-</mo><msup><mrow><mfenced close="]" open="[" separators="|"><mrow><mi>E</mi><mfenced separators="|"><mrow><mi>x</mi></mrow></mfenced></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup></msqrt></math><br/>Standard deviation <math><mo>=</mo><msqrt><mfenced separators="|"><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow></mfenced><mo>-</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup></msqrt></math><br/><math><mo>=</mo><msqrt><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>9</mn></mrow></mfrac></msqrt></math><br/><math><mo>=</mo><msqrt><mfrac><mrow><mn>4</mn><mo>Ã</mo><mn>4</mn></mrow><mrow><mn>45</mn></mrow></mfrac></msqrt></math><br/><math><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn><mo>â</mo><mn>5</mn></mrow></mfrac></math></div>


tags: ['Mathematics', 'Probability', 'MHT CET', 'MHT CET 2017']
source_db: MarksBatch1_P1.db
title:
a-box-contains-6-pens-2-of-which-are-defective-two-pens-are-taken-randomly-from-the-box-if-random-variable-x-number-of-defective-pens-obtained-then-st

slug:
a-box-contains-6-pens-2-of-which-are-defective-two-pens-are-taken-randomly-from-the-box-if-random-variable-x-number-of-defective-pens-obtained-then-st-25853


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-box-contains-10-identical-electronic-components-of-which-4-are-defective-if-3-components-are-selected-at-random-from-the-box-in-succession-without-r

slug:
a-box-contains-10-identical-electronic-components-of-which-4-are-defective-if-3-components-are-selected-at-random-from-the-box-in-succession-without-r-36887

question:
<div class="question">A box contains 10 identical electronic components of which 4 are defective. If 3 components are selected at random from the box in succession, without replacing the units already drawn, what is the probability that two of the selected components are defective?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 5$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 / 24$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3 / 10$</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">$1 / 40$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 10$</span> </div>

answer:
<div class="solution">Total number of selecting 3 components out of $10=$ ${ }^{10} \mathrm{C}_{3}$. Out of 3 selected components two defective pieces can be selected in ${ }^{4} \mathrm{C}_{2}$ ways and one non-defective piece will be selected in ${ }^{6} \mathrm{C}_{1}$ ways, hence.<br/>Required probability $=\frac{{ }^{6} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{2}}{{ }^{10} \mathrm{C}_{3}}=\frac{6 \times 6 \times 6}{10 \times 9 \times 8}=\frac{3}{10}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-box-has-ten-chits-numbered-0-1-2-3-9-first-one-chit-is-drawn-at-random-and-kept-aside-from-the-remaining-a-second-chit-is-drawn-at-random-what-is-th

slug:
a-box-has-ten-chits-numbered-0-1-2-3-9-first-one-chit-is-drawn-at-random-and-kept-aside-from-the-remaining-a-second-chit-is-drawn-at-random-what-is-th-38054

question:
<div class="question">A box has ten chits numbered $0,1,2,3, \ldots$, 9. First, one chit is drawn at random and kept aside. From the remaining, a second chit is drawn at random. What is the probability that the second chit drawn is " 9 "?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{10}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{9}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{90}$</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">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{90}$</span> </div>

answer:
<div class="solution">First chit can be drawn in 10 ways. Second chit can be drawn in 9 ways. Total number of events, $\mathrm{n}(\mathrm{S})=10 \times 9=90$. Number of events of drawing chit numbered $9=\mathrm{n}(\mathrm{E})=1$<br/>Probability $=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{1}{90}$</div>


tags: ['Physics', 'Laws of Motion', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-boy-throws-a-cricket-ball-from-the-boundary-to-the-wicket-keeper-if-the-frictional-force-due-to-air-f-a-cannot-be-ignored-the-forces-acting-on-the-b-1

slug:
a-boy-throws-a-cricket-ball-from-the-boundary-to-the-wicket-keeper-if-the-frictional-force-due-to-air-f-a-cannot-be-ignored-the-forces-acting-on-the-b-1-41578

question:
<div class="question"><p>A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>f</mi><mi>a</mi></msub></mfenced></math> cannot be ignored, the forces acting on the ball at the position <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> are represented by</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/7ab689cd-874c-4388-a542-b56846632b47-image.png" style="width: 400px; height: 174px;"/></p></div>

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/ap_eamcet/c66823f5-adf8-4f74-99a8-556f3aaa63b4-image.png" style="width: 109px; height: 192px;"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/064c67ce-578d-4bd5-a4fa-89946e7b72a5-image.png" style="width: 89px; height: 194px;"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/48c6e526-6611-412e-bf3d-f3e9b7b5f704-image.png" style="width: 171px; height: 148px;"/></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/ap_eamcet/3cc3c37f-e23f-493f-abdf-ca24ee379ccf-image.png" style="width: 145px; height: 175px;"/></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/ap_eamcet/48c6e526-6611-412e-bf3d-f3e9b7b5f704-image.png" style="width: 171px; height: 148px;"/></span> </div>

answer:
<div class="solution"><p>The fiction force due to air on the ball <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>a</mi></msub><mo> </mo></math>will always act in the opposite direction of the velocity of the ball, and the velocity of the ball at any point on the path is always in the tangential direction of the path of the projectile.</p><p>The weight of the body always acts downward perpendicular to the surface of the earth and along the centre of the earth.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/f9524d4c-db9e-4fbf-bf30-3a3e75472261-image.png" style="width: 240px; height: 96px;"/></p></div>


tags: ['Physics', 'Laws of Motion', 'AP EAMCET', 'AP EAMCET 2021 (20 Aug Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-boy-throws-a-cricket-ball-from-the-boundary-to-the-wicket-keeper-if-the-frictional-force-due-to-air-f-a-cannot-be-ignored-the-forces-acting-on-the-b

slug:
a-boy-throws-a-cricket-ball-from-the-boundary-to-the-wicket-keeper-if-the-frictional-force-due-to-air-f-a-cannot-be-ignored-the-forces-acting-on-the-b-55741


tags: ['Physics', 'Laws of Motion', 'KCET', 'KCET 2010']
source_db: MarksBatch1_P1.db
title:
a-boy-throws-a-cricket-ball-from-the-boundary-to-the-wicketkeeper-if-the-frictional-force-due-to-air-cannot-be-ignored-the-forces-acting-on-the-ball-a

slug:
a-boy-throws-a-cricket-ball-from-the-boundary-to-the-wicketkeeper-if-the-frictional-force-due-to-air-cannot-be-ignored-the-forces-acting-on-the-ball-a-65817

question:
<div class="question">A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position $X$ are respected by<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/iEKJYAsnSzU5bLNZ3GA4xGDR5vyBYQdXH-hGZdGYc_M.original.fullsize.png"/><br/></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/SEWsQrPmKAeJfxBtTj6VUNYqv3qjA6CnVD6iZ0LQBcs.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/rFQUgdCSqy5XzNGgGiv7_lFSY7kjhNhOb-XeK2tM53s.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/K0vBgrKXAHfhKxa-HcmWnejBZJongLFXWPwpeqf3yaE.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><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/bkluIkBSR7ZwsFY-hHRX5a6ZLZhG_rmV17GgIurQO8Q.original.fullsize.png"/><br/></span> </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/K0vBgrKXAHfhKxa-HcmWnejBZJongLFXWPwpeqf3yaE.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">The forces acting on the ball will be (i) in the direction opposite to its motion ie, frictional force and (ii) weight mg.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-can-hit-a-target-4-times-in-5-shots-b-can-hit-a-target-3-times-in-4-shots-c-can-hit-a-target-2-times-in-3-shots-all-the-three-fire-a-shot-each-what-

slug:
a-can-hit-a-target-4-times-in-5-shots-b-can-hit-a-target-3-times-in-4-shots-c-can-hit-a-target-2-times-in-3-shots-all-the-three-fire-a-shot-each-what-86521

question:
<div class="question">A can hit a target 4 times in 5 shots; $\mathrm{B}$ can hit a target 3 times in 4 shots:<br/>$\mathrm{C}$ can hit a target 2 times in 3 shots All the three fire a shot each. What is the probability that two shots are at least hit?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 / 6$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 / 5$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$5 / 6$</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">$1 / 3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 / 6$</span> </div>

answer:
<div class="solution">Probability of no one hitting the target<br/>$=\frac{1}{5 \times 4 \times 3}=\frac{1}{60}$<br/>Probability of one hitting the target<br/>$=\frac{4+3+2}{60}=\frac{9}{60}$<br/>$\therefore$ Probability of maximum one hit<br/>$=\frac{1}{60}+\frac{9}{60}=\frac{10}{60}=\frac{1}{6}$<br/>Probability that two shots are hit at least is the required<br/>probability $=1-\frac{1}{6}=\frac{5}{6}$</div>


tags: ['Mathematics', 'Probability', 'KCET', 'KCET 2021']
source_db: MarksBatch1_P1.db
title:
a-car-manufacturing-factory-has-two-plants-x-and-y-plant-x-manufactures-70-of-cars-and-plant-y-manufactures-30-of-cars-80-of-cars-at-plant-x-and-90-of

slug:
a-car-manufacturing-factory-has-two-plants-x-and-y-plant-x-manufactures-70-of-cars-and-plant-y-manufactures-30-of-cars-80-of-cars-at-plant-x-and-90-of-68595

question:
<div class="question">A car manufacturing factory has two plants $X$ and $Y$. Plant $X$ manufactures $70 \%$ of cars and plant $Y$ manufactures $30 \%$ of cars. $80 \%$ of cars at plant $X$ and $90 \%$ of cars at plant $Y$ are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant $X$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{56}{73}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{56}{84}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{56}{83}$</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">$\frac{56}{79}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{56}{83}$</span> </div>

answer:
<div class="solution">Let $E=$ the event that the car is of standard quáº£lity.<br/>Let $A_{1}=$ the event that the car is manufactured in plant $X$.<br/>and $A_{2}=$ the event that the car is manufactured in plant $Y$.<br/>Now, $P\left(A_{1}\right)=\frac{70}{100}=\frac{7}{10}, P\left(A_{2}\right)=\frac{30}{100}=\frac{3}{10}$ $P\left(\frac{E}{A_{1}}\right)=$ Probability that a standard quality car is manufactured in plant $X=\frac{80}{100}=\frac{8}{10}$ $P\left(\frac{E}{A_{2}}\right)=$ Probability that a standard quality car is manu factured in blant $Y=\frac{90}{100}=\frac{9}{10}$ $P\left(\frac{A_{1}}{E}\right)=$ Probability that a standard quality car has come from plant $X$<br/>$\begin{aligned}<br/>=&amp; \frac{P\left(A_{1}\right) \times P\left(\frac{E}{A_{1}}\right)}{P\left(A_{1}\right) \cdot P\left(\frac{E}{A_{1}}\right)+P\left(A_{2}\right) \cdot P\left(\frac{E}{A_{2}}\right)} \\<br/>=&amp; \frac{\frac{7}{10} \times \frac{8}{10}}{\frac{7}{10} \times \frac{8}{10}+\frac{3}{10} \times \frac{9}{10}} \\<br/>=&amp; \frac{7 \times 8}{7 \times 8+3 \times 9} \\<br/>=&amp; \frac{56}{56+27}=\frac{56}{83}<br/>\end{aligned}$<br/>Hence, the required probability is $\frac{56}{83}$.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9 to 4</span> </div>
source_db: MarksBatch1_P1.db
title:
a-card-is-drawn-from-a-pack-of-52-cards-and-a-gambler-bets-that-it-is-a-spade-or-an-ace-which-one-of-the-following-are-the-odds-against-his-winning-th

slug:
a-card-is-drawn-from-a-pack-of-52-cards-and-a-gambler-bets-that-it-is-a-spade-or-an-ace-which-one-of-the-following-are-the-odds-against-his-winning-th-44345

question:
<div class="question">A card is drawn from a pack of 52 cards and a gambler bets that it is a spade or an ace. Which one of the following are the odds against his winning this bet?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">13 to 4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4 to 13</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">9 to 4</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">4 to 9</span> </li> </ul>

answer:
<div class="solution">Probability of getting a spade $=\frac{13}{52}$<br/>Probability of an ace $=\frac{4}{52}$<br/>and probability of getting a spade ace $=\frac{1}{52}$<br/>$\therefore \quad$ Required probability $=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$<br/>Odds against his winning $=\frac{1-\frac{4}{13}}{\frac{4}{13}}=\frac{\frac{9}{13}}{\frac{4}{13}}=\frac{9}{4}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-card-is-drawn-from-a-wellshuffled-ordinary-deck-of-52-cards-what-is-the-probability-that-it-is-an-ace

slug:
a-card-is-drawn-from-a-wellshuffled-ordinary-deck-of-52-cards-what-is-the-probability-that-it-is-an-ace-70710

question:
<div class="question">A card is drawn from a well-shuffled ordinary deck of 52 cards. What is the probability that it is an ace?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{13}$</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">$\frac{2}{13}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{13}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{52}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{13}$</span> </div>

answer:
<div class="solution">$\quad$ Number of ace cards $=4$<br/>So, probability $=\frac{4}{52}=\frac{1}{13}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-card-is-drawn-from-a-welshuffled-deck-of-52-cards-what-is-the-probability-that-it-is-queen-of-spade

slug:
a-card-is-drawn-from-a-welshuffled-deck-of-52-cards-what-is-the-probability-that-it-is-queen-of-spade-90057

question:
<div class="question">A card is drawn from a wel-shuffled deck of 52 cards. What is the probability that it is queen of spade?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{52}$</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">$\frac{1}{13}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{8}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{52}$</span> </div>

answer:
<div class="solution">Prob. of getting queen of spade $=\frac{{ }^{1} C_{1}}{{ }^{52} C_{1}}=\frac{1}{52}$</div>


tags: ['Physics', 'Ray Optics']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-cassegrain-telescope-uses-two-mirrors-as-shown-in-figure-such-a-telescope-is-built-with-the-mirrors-20-mm-apart-if-the-radius-of-curvature-of-the-la

slug:
a-cassegrain-telescope-uses-two-mirrors-as-shown-in-figure-such-a-telescope-is-built-with-the-mirrors-20-mm-apart-if-the-radius-of-curvature-of-the-la-43231

question:
<div class="question">A Cassegrain telescope uses two mirrors as shown in figure. Such a telescope is built with the mirrors 20 $\mathrm{mm}$ apart. If the radius of curvature of the large mirror is $220 \mathrm{~mm}$ and the small mirror is $140 \mathrm{~mm}$, where will the final image of an object at infinity be?<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/slX6sPSbwIG_CWFT-sX9_XI5Hrrz3X67yHVlCu19ISY.original.fullsize.png"/><br/></div>

answer:
<div class="solution">For objective mirror (concave), $u=-\infty$<br/>Radius of curvature $R=-220 \mathrm{~mm}=-22 \mathrm{~cm}$<br/>Focal length $f=\frac{R}{2}=-11 \mathrm{~cm}$<br/>Image will be obtained at focus.<br/>$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ or $\frac{1}{v}+\frac{1}{-\infty}=\frac{1}{-11}$ or $v=-11 \mathrm{~cm}$<br/>Image formed by objective mirror act as a virtual object<br/>for secondary mirror.<br/>Distance of virtual object for secondary mirror.<br/>$u_0=(11-2) \mathrm{cm}=+9 \mathrm{~cm}$<br/>Focal length of convex mirror used $=14 \mathrm{~cm}$<br/>So, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ or $\frac{1}{v}=\frac{1}{14}-\frac{1}{9}$ or $v=-25.5 \mathrm{~cm}$</div>


tags: ['Physics', 'Current Electricity', 'TS EAMCET', 'TS EAMCET 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3.5 m</span> </div>
source_db: MarksBatch1_P1.db
title:
a-cell-in-secondary-circuit-gives-null-deflection-for-25-m-length-of-potentiometer-having-10-m-length-of-wire-if-the-length-of-the-potentiometer-wire--1

slug:
a-cell-in-secondary-circuit-gives-null-deflection-for-25-m-length-of-potentiometer-having-10-m-length-of-wire-if-the-length-of-the-potentiometer-wire-1-71428

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">3.5 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">3 m</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2.75 m</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2.0 m</span> </li> </ul>

answer:
<div class="solution">Resistance of potentiometer wire<br/>$R=\rho \times \frac{l}{A}$<br/>or $\quad R=\left(\rho \times \frac{10}{A}\right)$<br/>The value of $2.5 \mathrm{~m}$ length wire<br/>$R^{\prime}=\frac{\rho \times 10}{A \times 10} \times 2.5$<br/>or $\quad R^{\prime}=\left(\frac{2.5 \rho}{A \times 10}\right)$<br/>Potential<br/>$\begin{aligned}<br/>V^{\prime} &amp; =I \times R^{\prime} \\<br/>&amp; =I\left(\frac{2.5 \rho}{A \times 10}\right)<br/>\end{aligned}$<br/>Now, again the length of potentiometer wire is increased by $1 \mathrm{~m}$, then resistance of null position wire.<br/>$\begin{aligned}<br/>R^{\prime \prime} &amp; =\left(\frac{\rho \times l}{11 \times A}\right) \\<br/>V^{\prime \prime} &amp; =I R^{\prime \prime} \\<br/>and \quad V &amp; =V^{\prime}<br/>\end{aligned}$<br/>$\begin{aligned} \frac{I \times 2.5 \rho}{A \times 10} &amp; =\frac{\rho \times l}{11 \times A} \times I \\ \text { or } \quad \frac{2.5 \times 11}{10} &amp; =l=2.75 \mathrm{~m}\end{aligned}$</div>


tags: ['Physics', 'Current Electricity', 'AP EAMCET', 'AP EAMCET 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3.5 m</span> </div>
source_db: MarksBatch1_P1.db
title:
a-cell-in-secondary-circuit-gives-null-deflection-for-25-m-length-of-potentiometer-having-10-m-length-of-wire-if-the-length-of-the-potentiometer-wire--2

slug:
a-cell-in-secondary-circuit-gives-null-deflection-for-25-m-length-of-potentiometer-having-10-m-length-of-wire-if-the-length-of-the-potentiometer-wire-2-71662


tags: ['Physics', 'Current Electricity', 'VITEEE', 'VITEEE 2009']
source_db: MarksBatch1_P1.db
title:
a-cell-in-secondary-circuit-gives-null-deflection-for-25-m-length-of-potentiometer-having-10-m-length-of-wire-if-the-length-of-the-potentiometer-wire-

slug:
a-cell-in-secondary-circuit-gives-null-deflection-for-25-m-length-of-potentiometer-having-10-m-length-of-wire-if-the-length-of-the-potentiometer-wire-66960

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3.5 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2.75 \mathrm{~m}$</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">D</span> <span class="option-data">$2.0 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2.75 \mathrm{~m}$</span> </div>

answer:
<div class="solution">Here length of potentiometer wire, $l=10 \mathrm{~m}$ Resistance of potentiometer wire<br/>$R=\rho \times \frac{l}{A}$ or $R=\left(\rho \times \frac{10}{A}\right)$<br/>The value of $2.5 \mathrm{~m}$ length wire<br/>$$<br/>R^{\prime}=\frac{\rho \times 10}{A \times 10} \times 2.5 \Rightarrow R^{\prime}=\left(\frac{2.5 \rho}{A \times 10}\right)<br/>$$<br/>Potential, $V^{\prime}=I \times R^{\prime}=I\left(\frac{2.5 \rho}{A \times 10}\right)$<br/>Again the length of potentiometer wire is increased by $1 \mathrm{~m}$.<br/>Resistance of null position<br/>$$<br/>R^{n}=\left(\frac{\rho \times l}{11 \times A}\right)<br/>$$<br/>$\therefore V^{\prime \prime}=I R^{\prime \prime}$ and $V=V^{\prime}$<br/>$$<br/>\begin{array}{l}<br/>\Rightarrow \frac{I \times 2.5 \rho}{A \times 10}=\frac{\rho \times I}{11 \times A} \times I \\<br/>\text { or } \frac{2.5 \times 11}{10}=I=2.75 \mathrm{~m}<br/>\end{array}<br/>$$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch1_P1.db
title:
a-certain-type-of-missile-hits-the-target-with-probability-p-03-what-is-the-least-number-of-missiles-should-be-fired-so-that-there-is-at-least-an-80-p

slug:
a-certain-type-of-missile-hits-the-target-with-probability-p-03-what-is-the-least-number-of-missiles-should-be-fired-so-that-there-is-at-least-an-80-p-46299

question:
<div class="question">A certain type of missile hits the target with probability $\mathrm{p}=0.3$. What is the least number of missiles should be fired so that there is at least an $80 \%$ probability that the target is hit?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">5</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">6</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

answer:
<div class="solution">Probability of hitting the target $=0.3$ If'n' is the no. of times that the Missile is fired. $\therefore$ Probability ofhitting at least once $=1-[1-0.3]^{\mathrm{n}}=0.8$ $0.7^{\mathrm{n}}=0.2$<br/>$n \log 0.7=\log 0.2$<br/>$\Rightarrow \mathrm{n}=4.512$<br/>for $\mathrm{n}=4 ; \mathrm{p}   &lt; 0.8$<br/>take $\mathrm{n}=5$<br/>$n=5$<br/>Hence 5 missiles should be fired so that there is at least $80 \%$ prob. that the target is hit.</div>


tags: ['Biology', 'Evolution', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-change-in-the-relative-abundance-of-an-allele-the-allelic-frequency-within-a-population-over-a-succession-of-generations-is-called

slug:
a-change-in-the-relative-abundance-of-an-allele-the-allelic-frequency-within-a-population-over-a-succession-of-generations-is-called-96817

question:
<div class="question">A change in the relative abundance of an allele (the allelic frequency) within a population, over a succession of generations, is called</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Micro-evolution</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">Macro-evolution</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Co-evolution</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Phylogenetic evolution</span> </li> </ul>

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

answer:
<div class="solution">Microevolution involves changes in allelic frequency within a gene pool for a given species in a relatively short period of geologic time by the alterations of successfully reproducing individuals within a population. The macroevolution involves large scale changes among groups of species. Co-evolution occurs when two or more species reciprocally affect each other's evolution through the process of natural selection. Phylogenetic evolution represents evolutionary relationships among organisms and reflects how species or other groups evolved from a series of common ancestors.</div>


title: a-child-took-sugar-cane-and-sucked-its-juice-regarding-this-which-of-the-following-match-is-correct
tags: ['Chemistry', 'Biomolecules', 'AIIMS', 'AIIMS 2007']
source_db: MarksBatch1_P1.db
slug:
a-child-took-sugar-cane-and-sucked-its-juice-regarding-this-which-of-the-following-match-is-correct-61644

question:
<div class="question">A child took sugar cane and sucked its juice. Regarding this which of the following match is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\begin{array}{|c|c|c|c|} \hline \text{Substrate} &amp; \text{Enzyme} &amp; \text{Site of secretion of enzyme} &amp; \text{Products formed} \\ \hline \text{Proteins} &amp; \text{Pepsin} &amp; \text{Duodenum} &amp; \text{Polypeptides} \\ \hline \end{array}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\begin{array}{|c|c|c|c|} \hline \text{Substrate} &amp; \text{Enzyme} &amp; \text{Site of secretion of enzyme} &amp; \text{Products formed} \\ \hline \text{Starch} &amp; \text{Amylase} &amp; \text{Salivary glands} &amp; \text{Glucose} \\ \hline \end{array}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\begin{array}{|c|c|c|c|} \hline \text{Substrate} &amp; \text{Enzyme} &amp; \text{Site of secretion of enzyme} &amp; \text{Products formed} \\ \hline \text{Lipids} &amp; \text{Lipase} &amp; \text{Pancreas} &amp; \text{Fat globules} \\ \hline \end{array}\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(\begin{array}{|c|c|c|c|} \hline \text{Substrate} &amp; \text{Enzyme} &amp; \text{Site of secretion of enzyme} &amp; \text{Products formed} \\ \hline \text{Sucrose} &amp; \text{Invertase} &amp; \text{Duodenum} &amp; \text{Glucose + Fructose} \\ \hline \end{array}\)</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">\(\begin{array}{|c|c|c|c|} \hline \text{Substrate} &amp; \text{Enzyme} &amp; \text{Site of secretion of enzyme} &amp; \text{Products formed} \\ \hline \text{Sucrose} &amp; \text{Invertase} &amp; \text{Duodenum} &amp; \text{Glucose + Fructose} \\ \hline \end{array}\)</span> </div>

answer:
<div class="solution">Sucrose (cane sugar; beet sugar; saccharose) is a sugar comprising one molecule of glucose linked to a fructose molecule. It occurs widely in plants and is particularly abundant in sugar cane and sugar beet \((15-20 \%)\), from which it is extracted and refined for table sugar. If heated to \(200^{\circ} \mathrm{C}\), sucrose becomes caramel. Sucrose is broken down into the monosaccharides glucose and fructose with the help of carbohydrate digesting enzyme, invertase, produced in the small intestine (duodenum).</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-circle-is-drawn-on-the-chord-of-a-circle-x-2-y-2-a-2-as-diameter-the-chord-lies-on-the-line-x-y-a-what-is-the-equation-of-the-circle

slug:
a-circle-is-drawn-on-the-chord-of-a-circle-x-2-y-2-a-2-as-diameter-the-chord-lies-on-the-line-x-y-a-what-is-the-equation-of-the-circle-91086

question:
<div class="question">A circle is drawn on the chord of a circle $x^{2}+y^{2}=a^{2}$ as diameter. The chord lies on the line $x+y=a$. What is the equation of the circle?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$x^{2}+y^{2}-a x-a y+a^{2}=0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$x^{2}+y^{2}-a x-a y=0$</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">$x^{2}+y^{2}+a x+a y=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$x^{2}+y^{2}+a x+a y-2 a^{2}=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x^{2}+y^{2}-a x-a y=0$</span> </div>

answer:
<div class="solution">Given, equation of circle $\Rightarrow x^{2}+y^{2}=a^{2}$ Equation of chord $\Rightarrow x+y=a$ (1) $\Rightarrow x^{2}+(a-x)^{2}=a^{2}$<br/>$\Rightarrow x^{2}+a^{2}+x^{2}-2 a x=a^{2}$<br/>$\Rightarrow 2 x^{2}=2 a x$<br/>$\Rightarrow \mathrm{x}=0, \mathrm{a}$<br/>When, $x=0, y=a$ and when $x=a, y=0$. $\therefore$ Points of intersection are $(0, \mathrm{a})$ and $(\mathrm{a}, 0)$ $\therefore$ Equation of circle with chord as diameter is $(x-0)(x-a)+(y-a)(y-0)=0$<br/>$\Rightarrow x(x-a)+y(y-a)=0$<br/>$\Rightarrow x^{2}-a x+y^{2}-a y=0$<br/>$\Rightarrow x^{2}+y^{2}-a x-a y=0$</div>


tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-circle-is-drawn-with-the-two-foci-of-an-ellipse-a-2-x-2-b-2-y-2-1-at-the-end-of-the-diameter-what-is-the-equation-of-the-circle

slug:
a-circle-is-drawn-with-the-two-foci-of-an-ellipse-a-2-x-2-b-2-y-2-1-at-the-end-of-the-diameter-what-is-the-equation-of-the-circle-28151

question:
<div class="question">A circle is drawn with the two foci of an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$<br/>at the end of the diameter. What is the equation of the circle?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$x^{2}+y^{2}=a^{2}+b^{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$x^{2}+y^{2}=a^{2}-b^{2}$ (20) 10-I]</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">$x^{2}+y^{2}=2\left(a^{2}+b^{2}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$x^{2}+y^{2}=2\left(a^{2}-b^{2}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x^{2}+y^{2}=a^{2}-b^{2}$ (20) 10-I]</span> </div>

answer:
<div class="solution">Foci of an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ are given as $(a e, 0)$ and $(-a, 0)$.<br/>Since, two foci are at the end of the diameter $\therefore$ Equation of circle, is<br/>$(x-a e)(x+a e)+(y-0)(y-0)=0$<br/>$\Rightarrow x^{2}-a^{2} e^{2}+y^{2}=0$<br/>$\Rightarrow x^{2}+y^{2}-a^{2}\left(1-\frac{b^{2}}{a^{2}}\right)=0\left(\because e=\sqrt{1-\frac{b^{2}}{a^{2}}}\right)$<br/>$\Rightarrow x^{2}+y^{2}-a^{2}+b^{2}=0$<br/>$\Rightarrow x^{2}+y^{2}=a^{2}-b^{2}$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-class-consists-of-3-sections-a-b-and-c-with-3535-and-30-students-respectively-the-arithmetic-means-of-the-marks-secured-by-students-of-sections-a-an

slug:
a-class-consists-of-3-sections-a-b-and-c-with-3535-and-30-students-respectively-the-arithmetic-means-of-the-marks-secured-by-students-of-sections-a-an-44252

question:
<div class="question">A class consists of 3 sections $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ with 35,35 and 30 students respectively. The arithmetic means of the marks secured by students of sections $\mathrm{A}$ and $\mathrm{B}$, who appeared fol a test of 100 marks are 74 and 70 respectively. The arithmetic mean of the marks secured by students of section $\mathrm{C}$, who appeared for a test in the same subject which carried marks is 51 . What is the averagc perocntage of marks socuros by all the 100 student of the three sections? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad 70.0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$70 . \mathrm{E}$</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">65</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">67</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$70 . \mathrm{E}$</span> </div>

answer:
<div class="solution">Total no. of students in section A $=74 \times 35=2590$<br/>Total no. of students in section $\mathrm{B}$ $=70 \times 35=2450$<br/>Now, total no. of students in section $\mathrm{C}$<br/>$=\frac{51}{75} \times 100 \times 30=2040$<br/>Thus, total students in all $=2590+2450+2040$ $\begin{aligned} &amp;=7080 \\ \text { Thus, Required percentage } &amp;=7080 \div 100 \\ &amp;=70.8 \end{aligned}$</div>


tags: ['Mathematics', 'Probability']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-class-has-15-students-whose-ages-are-14-17-15-14-21-17-19-20-16-18-20-17-16-19-and-20-years-one-student-is-selected-in-such-a-manner-that-each-has-t

slug:
a-class-has-15-students-whose-ages-are-14-17-15-14-21-17-19-20-16-18-20-17-16-19-and-20-years-one-student-is-selected-in-such-a-manner-that-each-has-t-35209

question:
<div class="question">A class has 15 students whose ages are $14,17,15,14,21$,<br/>$17,19,20,16,18,20,17,16,19$ and 20 years. One student<br/>is selected in such a manner that each has the same chance<br/>of being chosen and the age $\mathrm{X}$ of the selected student is<br/>recorded.What is the probability distribution of the random<br/>variable $\mathrm{X}$ ? Find mean, variance and standard deviation<br/>of X?</div>

answer:
<div class="solution">There are 15 students in a class. Each has the same chance<br/>of being choosen.<br/>The probability of each student to be selected $=\frac{1}{15}$<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/KRQ8ZRJsGBalGq7MRuKcibEHDTZdiXMtNSLDYt5NkPQ.original.fullsize.png"/><br/><br/>First and third columns from the probability distribution Mean $=\mathrm{E}(\mathrm{X})=\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}=\frac{293}{15}=17.53333$<br/>Varience $=E\left(X^2\right)-[E(X)]^2=\sum p_i x_i{ }^2-\left(\sum p_i x_i\right)^2$<br/>$$<br/>\begin{aligned}<br/>&amp;=\frac{4683}{15}-(17.53333)^2 \\<br/>&amp;=312.20-307.41766=4.78<br/>\end{aligned}<br/>$$<br/>Standard deviation<br/>$$<br/>=\sqrt{\text { Variance }}=\sqrt{4 \cdot 78}=2 \cdot 19<br/>$$<br/>probability distribution is<img src="https://cdn-question-pool.getmarks.app/modules/cbse/h2DiXn2FndvK3yZPmOz10FiKPZwH9TVQpnC4r6iCXj4.original.fullsize.png"/><br/><br/>Mean $=17 \cdot 53$, variance $=4 \cdot 78$, S.D. $(X)=2 \cdot 19$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-closed-and-an-open-organ-pipe-have-the-same-length-when-they-are-vibrating-simultaneously-in-their-first-overtone-they-produce-three-beats-the-lengt

slug:
a-closed-and-an-open-organ-pipe-have-the-same-length-when-they-are-vibrating-simultaneously-in-their-first-overtone-they-produce-three-beats-the-lengt-62297

question:
<div class="question">A closed and an open organ pipe have the same length. When they are vibrating simultaneously in their first overtone, they produce three beats. The length of the open pipe is now made one third the original length and one of its ends is closed. On the other hand, the length of the closed pipe is made three times the original length. The number of beats produced when they vibrate with fundamental frequencies will be</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>8</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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></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>17</mn></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>8</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>8</mn></math></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">V</mi><mo>=</mo></math> speed of sound and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">L</mi><mo>=</mo></math> lenght of pipes<br/><br/>For open pipe first overtone <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">f</mi><mn>1</mn></msub><mo>=</mo><mfrac><mi mathvariant="normal">V</mi><mi mathvariant="normal">L</mi></mfrac></math><br/><br/>For closed pipe first overtone <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><msub><mo>'</mo><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">V</mi></mrow><mrow><mn>4</mn><mi mathvariant="normal">L</mi></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â´</mo><mtext>âââ</mtext><msub><mi mathvariant="normal">f</mi><mn>1</mn></msub><mo>â</mo><mi mathvariant="normal">f</mi><msub><mo>'</mo><mn>1</mn></msub><mo>=</mo><mfrac><mi mathvariant="normal">V</mi><mi mathvariant="normal">L</mi></mfrac><mo>â</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">V</mi></mrow><mrow><mn>4</mn><mi mathvariant="normal">L</mi></mrow></mfrac><mo>=</mo><mn>3</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â´</mo><mo>  </mo><mi mathvariant="normal"> </mi><mfrac><mi mathvariant="normal">V</mi><mrow><mn>4</mn><mi mathvariant="normal">L</mi></mrow></mfrac><mo>=</mo><mn>3</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â´</mo><mo>  </mo><mo> </mo><mfrac><mi mathvariant="normal">V</mi><mi mathvariant="normal">L</mi></mfrac><mo>=</mo><mn>12</mn><mi mathvariant="normal"> </mi></math><br/><br/>When we close one end of the open pipe and make its length one-third of the original length, then its fundamental frequency is<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><mfrac><mi mathvariant="normal">V</mi><mrow><mn>4</mn><mrow><mo>(</mo><mstyle displaystyle="true"><mfrac><mi mathvariant="normal">L</mi><mn>3</mn></mfrac></mstyle><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">V</mi></mrow><mrow><mn>4</mn><mi mathvariant="normal">L</mi></mrow></mfrac></math><br/><br/>When the length of closed pipe is made <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> times, the fundamental frequency is<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>'</mo><mo>=</mo><mfrac><mi mathvariant="normal">V</mi><mrow><mn>4</mn><mrow><mo>(</mo><mn>3</mn><mi mathvariant="normal">L</mi><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mi mathvariant="normal">V</mi><mrow><mn>12</mn><mi mathvariant="normal">L</mi></mrow></mfrac></math><br/><br/>Beats produced <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi mathvariant="normal">f</mi><mo>-</mo><mi mathvariant="normal">f</mi><mo>'</mo></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">V</mi></mrow><mrow><mn>4</mn><mi mathvariant="normal">L</mi></mrow></mfrac><mo>-</mo><mfrac><mi mathvariant="normal">V</mi><mrow><mn>12</mn><mi mathvariant="normal">L</mi></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>8</mn><mn>12</mn></mfrac><mo>.</mo><mfrac><mi mathvariant="normal">V</mi><mi mathvariant="normal">L</mi></mfrac><mo>=</mo><mfrac><mn>8</mn><mn>12</mn></mfrac><mo>Ã</mo><mn>12</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn></math></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2024 (27 Jan Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">294</span> </div>
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-150-cm-long-gives-7-beats-per-second-with-an-open-organ-pipe-of-length-350-cm-both-vibrating-in-fundamental-mode-the-velocity-of-s

slug:
a-closed-organ-pipe-150-cm-long-gives-7-beats-per-second-with-an-open-organ-pipe-of-length-350-cm-both-vibrating-in-fundamental-mode-the-velocity-of-s-38480

question:
<div class="question"><p>A closed organ pipe <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn><mo>Â </mo><mi>cm</mi></math> long gives <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> beats per second with an open organ pipe of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn><mo>Â </mo><mi>cm</mi></math>, both vibrating in fundamental mode. The velocity of sound is ______Â <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mo>Â </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p></div>

answer:
<div class="solution"><p>The formula to calculate the fundamental frequency in a closed pipe is given by</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>c</mi></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>4</mn><msub><mi>l</mi><mn>1</mn></msub></mrow></mfrac><mo>Â </mo><mo>Â </mo><mo>Â </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>1</mn></mfenced></math></p><p>And, that in an open pipe is given by</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>o</mi></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><msub><mi>l</mi><mn>2</mn></msub></mrow></mfrac><mo>Â </mo><mo>Â </mo><mo>Â </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>2</mn></mfenced></math></p><p>Given that</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mrow><msub><mi>f</mi><mi>c</mi></msub><mo>-</mo><msub><mi>f</mi><mi>o</mi></msub></mrow></mfenced><mo>=</mo><mn>7</mn><mo>Â </mo><mo>Â </mo><mo>Â </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>3</mn></mfenced></math></p><p>From equations (1), (2) and (3), it follows that</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>v</mi><mrow><mn>4</mn><mo>Ã</mo><mn>150</mn></mrow></mfrac><mo>-</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mo>Ã</mo><mn>350</mn></mrow></mfrac><mo>=</mo><mn>7</mn><mspace linebreak="newline"></mspace><mo>â</mo><mfrac><mi>v</mi><mrow><mn>600</mn><mo>Â </mo><mi>cm</mi></mrow></mfrac><mo>-</mo><mfrac><mi>v</mi><mrow><mn>700</mn><mo>Â </mo><mi>cm</mi></mrow></mfrac><mo>=</mo><mn>7</mn><mspace linebreak="newline"></mspace><mo>â</mo><mfrac><mi>v</mi><mrow><mn>6</mn><mi>m</mi></mrow></mfrac><mo>-</mo><mfrac><mi>v</mi><mrow><mn>7</mn><mi>m</mi></mrow></mfrac><mo>=</mo><mn>7</mn><mspace linebreak="newline"></mspace><mo>â</mo><mi>v</mi><mfenced><mfrac><mn>1</mn><mn>42</mn></mfrac></mfenced><mo>=</mo><mn>7</mn><mspace linebreak="newline"></mspace><mo>â</mo><mi>v</mi><mo>=</mo><mn>42</mn><mo>Ã</mo><mn>7</mn><mspace linebreak="newline"></mspace><mo>=</mo><mn>294</mn><mo>Â </mo><mi mathvariant="normal">m</mi><mo>Â </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-and-an-open-organ-pipe-are-tuned-to-the-same-fundamental-frequency-the-ratio-of-their-lengths-is

slug:
a-closed-organ-pipe-and-an-open-organ-pipe-are-tuned-to-the-same-fundamental-frequency-the-ratio-of-their-lengths-is-40014

question:
<div class="question">A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths 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>1</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>2</mn><mo>:</mo><mn>1</mn></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>1</mn><mo>:</mo><mn>4</mn></math></span> </li><li class="correct"> <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>2</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 xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>2</mn></math></span> </div>

answer:
<div class="solution">Fundamental frequency of close pipe,<br/><br/><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>4</mn><msub><mrow><mi>l</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac></math><br/><br/>Fundamental frequency of open pipe,<br/><br/><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>2</mn><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></math><br/><br/>But <math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math><br/><br/><math><mo>â´</mo><mfrac><mrow><msub><mrow><mi>l</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2021 (24 Sep Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-and-an-open-organ-pipe-of-same-length-produce-2-beats-per-second-when-they-are-set-into-vibrations-together-in-fundamental-mode-th

slug:
a-closed-organ-pipe-and-an-open-organ-pipe-of-same-length-produce-2-beats-per-second-when-they-are-set-into-vibrations-together-in-fundamental-mode-th-78795

question:
<div class="question">A closed organ pipe and an open organ pipe of same length produce 2 beats per second when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced per second will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">7</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>

answer:
<div class="solution">Fundamental frequency of closed pipe, $\mathrm{n}_{\mathrm{c}}=\frac{\mathrm{V}}{4 \mathrm{~L}}$ Fundamental frequency of open pipe, $\mathrm{n}_0=\frac{\mathrm{v}}{2 \mathrm{~L}}$ They produce 2 beats per second<br/>$\begin{aligned} &amp; \therefore \mathrm{n}_{\mathrm{o}}-\mathrm{n}_{\mathrm{c}}=2, \\ &amp; \frac{\mathrm{V}}{2 \mathrm{~L}}-\frac{\mathrm{V}}{4 \mathrm{~L}}=2 \\ &amp; \frac{\mathrm{V}}{4 \mathrm{~L}}=2 \text { or } \frac{\mathrm{v}}{\mathrm{L}}=8\end{aligned}$<br/>When length of open pipe is halved<br/>$\mathrm{n}_{\mathrm{o}}^{\prime}=\frac{\mathrm{v}}{2\left(\frac{\mathrm{L}}{2}\right)}=\frac{\mathrm{v}}{\mathrm{L}}$<br/>When length of closed pipe is doubled<br/>$\mathrm{n}_{\mathrm{c}}^{\prime}=\frac{\mathrm{v}}{4 \times 2 \mathrm{~L}}=\frac{\mathrm{v}}{8 \mathrm{~L}}$<br/>New beat frequency $=\mathrm{n}_{\mathrm{o}}^{\prime}-\mathrm{n}_{\mathrm{c}}^{\prime}=\frac{\mathrm{v}}{\mathrm{L}}-\frac{\mathrm{v}}{8 \mathrm{~L}}=\frac{7 \mathrm{v}}{8 \mathrm{~L}}=\frac{7}{8} \times 8=7$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2020 (23 Sep Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-and-an-open-organ-pipe-of-same-length-produce-2-beats-sec-1-when-they-are-set-into-vibrations-together-in-fundamental-mode-the-len

slug:
a-closed-organ-pipe-and-an-open-organ-pipe-of-same-length-produce-2-beats-sec-1-when-they-are-set-into-vibrations-together-in-fundamental-mode-the-len-18550

question:
<div class="question">A closed organ pipe and an open organ pipe of same length produce <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>beats</mi><mo> </mo><msup><mi>sec</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be</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>7</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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></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>8</mn></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></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>7</mn></math></span> </div>

answer:
<div class="solution"><p>Fundamental frequency of closed organ pipe <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>c</mi></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>4</mn><mi>l</mi></mrow></mfrac></math> </p><p>Fundamental frequency of open organ pipe <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>o</mi></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mi>l</mi></mrow></mfrac></math></p><p>Initial beats frequency </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>o</mi></msub><mo>-</mo><msub><mi>f</mi><mi>c</mi></msub><mo>=</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mi>l</mi></mrow></mfrac><mo>-</mo><mfrac><mi>v</mi><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mi>v</mi><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mi>v</mi><mi>l</mi></mfrac><mo>=</mo><mn>8</mn></math></p><p>After changing of length </p><p> Fundamental frequency of closed organ pipe <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>f</mi><mi>c</mi><mo>'</mo></msubsup><mo>=</mo><mfrac><mi>v</mi><mrow><mn>4</mn><mfenced><mstyle displaystyle="true"><mn>2</mn><mi>l</mi></mstyle></mfenced></mrow></mfrac><mo>=</mo><mfrac><mi>v</mi><mrow><mn>8</mn><mi>l</mi></mrow></mfrac></math></p><p>Fundamental frequency of open organ pipe <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>f</mi><mi>o</mi><mo>'</mo></msubsup><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mfenced><mstyle displaystyle="true"><mfrac><mstyle displaystyle="true"><mi>l</mi></mstyle><mn>2</mn></mfrac></mstyle></mfenced></mrow></mfrac><mo>=</mo><mfrac><mi>v</mi><mi>l</mi></mfrac></math></p><p>New beats frequency </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>f</mi><mi>o</mi><mo>'</mo></msubsup><mo>-</mo><msubsup><mi>f</mi><mi>c</mi><mo>'</mo></msubsup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mi>v</mi><mi>l</mi></mfrac><mo>-</mo><mfrac><mi>v</mi><mrow><mn>8</mn><mi>l</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>7</mn><mi>v</mi></mrow><mrow><mn>8</mn><mi>l</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>7</mn><mo>×</mo><mn>8</mn></mrow><mn>8</mn></mfrac><mo>=</mo><mn>7</mn></math></p></div>


tags: ['Physics', 'Waves and Sound', 'KCET', 'KCET 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-and-an-open-organ-pipe-of-same-length-produce-2-beatssecond-while-vibrating-in-their-fundamental-modes-the-length-of-the-open-orga

slug:
a-closed-organ-pipe-and-an-open-organ-pipe-of-same-length-produce-2-beatssecond-while-vibrating-in-their-fundamental-modes-the-length-of-the-open-orga-26383

question:
<div class="question">A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">7</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>

answer:
<div class="solution">Given, $\quad \mathrm{f}_{\mathrm{o}}-\mathrm{f}_{\mathrm{c}}=2 \quad \text{...(i)}$ <br/>Frequency of fundamental mode for a closed Frequency of fundar organ pipe, $f_{c}=\frac{v}{4 L_{c}}$<br/>Similarly frequency of fundamental mode for an open organ pipe, $\mathrm{f}_{\mathrm{o}}=\frac{\mathrm{V}}{2 \mathrm{~L}_{\mathrm{o}}}$<br/>Given $\quad \mathrm{L}_{\mathrm{c}}=\mathrm{L}_{\mathrm{o}}$ <br/>$\Rightarrow$ $f_{0}=2 f_{c} \quad \text{...(ii)}$<br/>From Eqs. (i) and (ii), we get <br/>$\mathrm{f}_{\mathrm{o}}=2 \mathrm{f}_{\mathrm{c}}$ $\mathrm{f}_{\mathrm{o}}=4 \mathrm{~Hz}$ and $\mathrm{f}_{\mathrm{c}}=2 \mathrm{~Hz}$ <br/>When the length of the open pipe is halved, frequency of fundamental mode is $$ \mathrm{f}_{\mathrm{o}}^{\prime}=\frac{\mathrm{v}}{2\left[\frac{\mathrm{L}_{\mathrm{o}}}{2}\right]}=2 \mathrm{f}_{\mathrm{o}}=2 \times 4 \mathrm{~Hz}=8 \mathrm{~Hz} $$<br/>When the length of the closed pipe is doubled, its frequency of fundamental mode is<br/>$$<br/>\mathrm{f}_{\mathrm{o}}^{\prime}=\frac{\mathrm{v}}{4\left(2 \mathrm{~L}_{\mathrm{c}}\right)}=\frac{1}{2} \mathrm{f}_{\mathrm{c}}=\frac{1}{2} \times 2=1 \mathrm{~Hz}<br/>$$<br/>Hence, number of beats produced per second is<br/>$$<br/>\mathrm{f}_{\mathrm{o}}^{\prime}-\mathrm{f}_{\mathrm{c}}^{\prime}=8-1=7<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-and-an-open-pipe-of-same-length-produce-2-beats-s-1-when-they-are-set-into-vibrations-together-in-fundamental-mode-the-length-of-o

slug:
a-closed-organ-pipe-and-an-open-pipe-of-same-length-produce-2-beats-s-1-when-they-are-set-into-vibrations-together-in-fundamental-mode-the-length-of-o-35737

question:
<div class="question">A closed organ pipe and an open pipe of same length produce 2 beats <math><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">7</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</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution"><math><msub><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>,</mo><mi> </mi><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>2</mn><mi>l</mi></mrow></mfrac></math><br/><br/>As <math><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mn>2</mn></math><br/><br/><math><mo>â´</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>2</mn><mi>l</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>2</mn><mi> </mi><mi>o</mi><mi>r </mi><mfrac><mrow><mi>v</mi></mrow><mrow><mi>l</mi></mrow></mfrac><mo>=</mo><mn>8</mn></math><br/><br/>Now<br/><br/>Number of beats <math><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msubsup><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>â²</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow><mrow><mi>â²</mi></mrow></msubsup></math><br/><br/><math><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mi>l</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>8</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>7</mn><mi>v</mi></mrow><mrow><mn>8</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac><mo>Ã</mo><mn>8</mn><mo>=</mo><mn>7</mn></math></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2019 (10 Jan Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-has-a-fundamental-frequency-of-15-khz-the-number-of-overtones-that-can-be-distinctly-heard-by-a-person-with-this-organ-pipe-will-b

slug:
a-closed-organ-pipe-has-a-fundamental-frequency-of-15-khz-the-number-of-overtones-that-can-be-distinctly-heard-by-a-person-with-this-organ-pipe-will-b-64135

question:
<div class="question">A closed organ pipe has a fundamental frequency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.5</mn><mtext> </mtext><mi>kHz</mi></math>. The number of overtones that can be distinctly heard by a person with this organ pipe will be <math><mo>(</mo></math>Assume that the highest frequency a person can hear is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20,000</mn><mtext> </mtext><mi>Hz</mi></math>).</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>7</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>4</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>6</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>5</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>6</mn></math></span> </div>

answer:
<div class="solution"><blockquote><p>For a closed organ pipe, the resonate frequency(harmonics) is an odd multiple of the fundamental frequency.</p><p>Therefore, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><msub><mi>f</mi><mn>0</mn></msub><mo>≤</mo><mn>20000</mn><mo> </mo><mi>Hz</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>.</mo><mo>.</mo><mo>.</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>0</mn></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>kHz</mi><mo>⇒</mo></math> fundamental frequency</p><p>Then, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>7</mn></math></p><p>The total number of overtones that can be heard is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math>. (<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mi>nd</mi></msup></math> harmonic to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>7</mn><mi>th</mi></msup></math> harmonic. )</p></blockquote></div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2021 (21 Sep Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-closed-organ-pipe-of-length-l-c-and-an-open-organ-pipe-of-length-l-0-contain-different-gases-of-densities-1-and-2-respectively-the-compressibility-o

slug:
a-closed-organ-pipe-of-length-l-c-and-an-open-organ-pipe-of-length-l-0-contain-different-gases-of-densities-1-and-2-respectively-the-compressibility-o-18481

question:
<div class="question">A closed organ pipe of length ' $L_c$ ' and an open organ pipe of length ' $L_0$ ' contain different gases of densities ' $\rho_1$ ' and ' $\rho_2$ ' respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of open organ pipe?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{4 L_c}{3} \sqrt{\frac{\rho_1}{\rho_2}}$</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">$\frac{3 L_c}{4} \sqrt{\frac{\rho_2}{\rho_1}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{4 L_c}{3} \sqrt{\frac{\rho_2}{\rho_1}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2 L_c}{3} \sqrt{\frac{\rho_2}{\rho_1}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4 L_c}{3} \sqrt{\frac{\rho_1}{\rho_2}}$</span> </div>

answer:
<div class="solution">For open organ pipe:<br/>Fundamental frequency $\mathrm{n}=\frac{\mathrm{V}}{2 \mathrm{~L}_{\text {o }}}$<br/>First overtone $\mathrm{n}_1=2 \mathrm{n}=\frac{\mathrm{V}}{\mathrm{L}_{\text {ã }}}$<br/>For closed organ pipe<br/>Fundamental frequency $n^{\prime}=\frac{V^{\prime}}{4 L_c}$<br/>First overtone $n_1{ }^{\prime}=3 n^{\prime}=\frac{3 \mathrm{~V}^{\prime}}{4 \mathrm{~L}_{\mathrm{c}}}$<br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \because \mathrm{n}_1=\mathrm{n}_1^{\prime} \\<br/>&amp; \therefore \frac{\mathrm{V}}{\mathrm{L}_{\mathrm{o}}}=\frac{3 \mathrm{~V}^{\prime}}{4 \mathrm{~L}_{\mathrm{c}}} \\<br/>&amp; \therefore \frac{\mathrm{L}_{\mathrm{o}}}{\mathrm{L}_{\mathrm{c}}}=\frac{4}{3} \frac{\mathrm{V}}{\mathrm{V}^{\prime}} \\<br/>&amp; \mathrm{V}=\sqrt{\frac{\mathrm{k}}{\rho_2}}, \mathrm{~V}^{\prime}=\sqrt{\frac{\mathrm{k}}{\rho_1}}<br/>\end{aligned}<br/>$$<br/>where $\mathrm{k}$ is the adiabatic bulk modulus, which is reciprocal of compressibility.<br/>$$<br/>\frac{L_0}{L_c}=\frac{4}{3} \sqrt{\frac{\rho_1}{\rho_2}}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'JIPMER', 'JIPMER 2005']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1: 2$</span> </div>
source_db: MarksBatch1_P1.db
title:
a-closed-orgon-pipe-and-an-open-orgon-pipe-are-tuned-to-the-same-fundamental-frequency-what-is-the-ratio-of-their-lengths

slug:
a-closed-orgon-pipe-and-an-open-orgon-pipe-are-tuned-to-the-same-fundamental-frequency-what-is-the-ratio-of-their-lengths-15218

question:
<div class="question">A closed orgon pipe and an open orgon pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1: 2$</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><li class=""> <span class="option-label">B</span> <span class="option-data">$2: 1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2: 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4: 3$</span> </li> </ul>

answer:
<div class="solution">Avoiding end correction, the length of the closed organ pipe is<br/>$l_1=\frac{\lambda_1}{4}$ or $\lambda_1=4 l_1$<br/>The length of open organ pipe is<br/>$l_2=\frac{\lambda_2}{2}$ or $\lambda_2=2 l_2$<br/>Here, $n_1=n_2$<br/>So, $\frac{v}{\lambda_1}=\frac{v}{\lambda_2}$ or $\frac{v}{4 l_1}=\frac{v}{2 l_2}$<br/>Therefore, $l_1: l_2=1: 2$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2014']
source_db: MarksBatch1_P1.db
title:
a-closed-pipe-is-suddenly-opened-and-changed-to-an-open-pipe-of-same-length-the-fundamental-frequency-of-the-resulting-open-pipe-is-less-than-that-of--1

slug:
a-closed-pipe-is-suddenly-opened-and-changed-to-an-open-pipe-of-same-length-the-fundamental-frequency-of-the-resulting-open-pipe-is-less-than-that-of-1-61385


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-closed-pipe-is-suddenly-opened-and-changed-to-an-open-pipe-of-same-length-the-fundamental-frequency-of-the-resulting-open-pipe-is-less-than-that-of--2

slug:
a-closed-pipe-is-suddenly-opened-and-changed-to-an-open-pipe-of-same-length-the-fundamental-frequency-of-the-resulting-open-pipe-is-less-than-that-of-2-63964


tags: ['Physics', 'Waves and Sound', 'TS EAMCET', 'TS EAMCET 2014']
source_db: MarksBatch1_P1.db
title:
a-closed-pipe-is-suddenly-opened-and-changed-to-an-open-pipe-of-same-length-the-fundamental-frequency-of-the-resulting-open-pipe-is-less-than-that-of-

slug:
a-closed-pipe-is-suddenly-opened-and-changed-to-an-open-pipe-of-same-length-the-fundamental-frequency-of-the-resulting-open-pipe-is-less-than-that-of-82309


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-closed-pipe-of-length-22-c-m-when-excited-by-a-1875-h-z-source-forms-standing-waves-the-number-of-pressure-nodes-formed-in-the-pipe-are-velocity-of-

slug:
a-closed-pipe-of-length-22-c-m-when-excited-by-a-1875-h-z-source-forms-standing-waves-the-number-of-pressure-nodes-formed-in-the-pipe-are-velocity-of-41527

question:
<div class="question">A closed pipe of length <math><mn>22</mn><mi> </mi><mn>c</mn><mn>m</mn></math>, when excited by a <math><mn>1875</mn><mi> </mi><mn>H</mn><mn>z</mn></math> source forms standing waves. The number of pressure nodes formed in the pipe are [velocity of sound in air <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>330</mn><mi> </mi><mn>m</mn><mo> </mo><msup><mn>s</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>]</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>1</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>2</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>4</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mn>3</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>3</mn></math></span> </div>

answer:
<div class="solution">Velocity of sound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>330</mn><mi> </mi><mn>m</mn><mo> </mo><msup><mn>s</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/><br/>Length of closed pipe <math><mo>=</mo><mn>22</mn><mi> </mi><mi>cm</mi><mo>=</mo><mn>22</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>2 </mn></mrow></msup><mn>m</mn></math><br/><br/>The fundamental frequency of the stationary wave,<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ν</mi><mn>0</mn></msub><mo>=</mo><mfrac><mi>v</mi><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mfrac><mn>330</mn><mrow><mn>4</mn><mo>×</mo><mn>22</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfrac></math><br/><br/><math><mo>=</mo><mfrac><mrow><mn>330</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</mn><mo>×</mo><mn>22</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3000</mn></mrow><mrow><mn>8</mn></mrow></mfrac></math><br/><br/><math><msub><mrow><mi>ν</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>375</mn><mi> </mi><mi>Hz</mi></math><br/><br/><math><mn>3</mn><msub><mrow><mi>ν</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>375</mn><mo>×</mo><mn>3</mn><mo>=</mo><mn>1125</mn><mi> </mi><mi>Hz</mi></math><br/><br/><math><mn>5</mn><msub><mrow><mi>ν</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>5</mn><mo>×</mo><mn>375</mn><mo>=</mo><mn>1875</mn><mi> </mi><mi>Hz</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>5</mn><mi>th</mi></msup></math> harmonic<br/><br/>Number of nodes <math><mo>=</mo><mn>3</mn></math><br/><br/>Note: In a closed pipe, odd harmonics are produced.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2009 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">11</span> </div>
source_db: MarksBatch1_P1.db
title:
a-coin-is-tossed-10-times-the-number-of-heads-minus-the-number-of-tails-in-10-tosses-is-considered-as-the-outcome-of-the-experiment-what-is-the-number

slug:
a-coin-is-tossed-10-times-the-number-of-heads-minus-the-number-of-tails-in-10-tosses-is-considered-as-the-outcome-of-the-experiment-what-is-the-number-37967

question:
<div class="question">A coin is tossed 10 times. The number of heads minus the number of tails in 10 tosses is considered as the outcome of the experiment. What is the number of points in the sample space</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">10</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">11</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">21</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">99</span> </li> </ul>

answer:
<div class="solution">\begin{array}{c|c} <br/>Head &amp; Tail \\<br/>10 &amp; 0 \\<br/>9 &amp; 1 \\<br/>8 &amp; 2 \\<br/>7 &amp; 3 \\<br/>6 &amp; 4 \\<br/>5 &amp; 5 \\<br/>4 &amp; 6 \\<br/>3 &amp; 7 \\<br/>2 &amp; 8 \\<br/>1 &amp; 9 \\<br/>0 &amp; 10<br/>\end{array}<br/>Hence, total number of points in the sample space is<br/>$11 .$</div>


title: a-coin-is-tossed-five-times-what-is-the-probability-that-heads-are-observed-more-than-three-times
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P1.db
slug:
a-coin-is-tossed-five-times-what-is-the-probability-that-heads-are-observed-more-than-three-times-58079

question:
<div class="question">A coin is tossed five times. What is the probability that heads are observed more than three times?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{3}{16}$</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">$\frac{5}{16}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{3}{32}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{16}$</span> </div>

answer:
<div class="solution">Let P denote the probability of getting head in a single toss of a coin.<br/>$\mathrm{p}=\frac{1}{2} \Rightarrow \mathrm{q}=\frac{1}{2}$<br/>Let $X$ denote the no. of heads in 5 tosses of a coin. then, $\mathrm{X}$ is a binomial variate with parameters; $\mathrm{n}=5 \&amp;$<br/>$\mathrm{p}=\frac{1}{2}$.<br/>$\therefore$ Req. probability $=\mathrm{P}(\mathrm{x}&gt;3)$<br/>$=1-\mathrm{P}(\mathrm{x} \leq 3)$<br/>$=1-[\mathrm{P}(\mathrm{x}=0)+\mathrm{P}(\mathrm{x}=1)+\mathrm{P}(\mathrm{x}=2)+\mathrm{P}(\mathrm{x}=3)]$<br/>$=1-\left[{ }^{5} \mathrm{C}_{0}+{ }^{5} \mathrm{C}_{1}+{ }^{5} \mathrm{C}_{2}+{ }^{5} \mathrm{C}_{3}\right] \frac{1}{2^{5}}$<br/>$=1-[1+5+10+10] \frac{1}{32}$<br/>$=\frac{32}{32}-\frac{26}{32}=\frac{6}{32}=\frac{3}{16}$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-coin-is-tossed-three-times-consider-the-following-events-a-no-head-appears-b-exactly-one-head-appears-c-at-least-two-heads-appear-which-one-of-the-f

slug:
a-coin-is-tossed-three-times-consider-the-following-events-a-no-head-appears-b-exactly-one-head-appears-c-at-least-two-heads-appear-which-one-of-the-f-54501

question:
<div class="question">A coin is tossed three times. Consider the following events:<br/>A: No head appears<br/>B: Exactly one head appears<br/>C: At least two heads appear Which one of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(\mathrm{A} \cup \mathrm{B}) \cap(\mathrm{A} \cup \mathrm{C})=\mathrm{B} \cup \mathrm{C}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\mathrm{A} \cap \mathrm{B}^{\prime}\right) \cup\left(\mathrm{A} \cap \mathrm{C}^{\prime}\right)=\mathrm{B}^{\prime} \cup \mathrm{C}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{A} \cap\left(\mathrm{B}^{\prime} \cup \mathrm{C}^{\prime}\right)=\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$A \cap\left(B^{\prime} \cup C^{\prime}\right)=B^{\prime} \cap C$</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">$A \cap\left(B^{\prime} \cup C^{\prime}\right)=B^{\prime} \cap C$</span> </div>

answer:
<div class="solution">$\quad U=\{(H H H)(H H T)(H T H)(H T T)(T H H)(T H T)(T T H)(T T T)\}$<br/>$A=\{(T T T)\}$<br/>$B=\{(H T T)(T H T)(T T H)\}$<br/>$C=\{(H H H)(H H T)(H T H)(T H H)\}$<br/>By checking the options<br/>(d) $A \cap\left(B^{\prime} \cup C^{\prime}\right)=B^{\prime} \cap C^{\prime}$ is correct.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-coin-is-tossed-three-times-what-is-the-probability-of-getting-head-and-tail-hth-or-tail-and-head-tht-alternatively

slug:
a-coin-is-tossed-three-times-what-is-the-probability-of-getting-head-and-tail-hth-or-tail-and-head-tht-alternatively-82821

question:
<div class="question">A coin is tossed three times. What is the probability of getting head and tail (HTH) or tail and head (THT) alternatively?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1 / 4$</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">$1 / 5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 6$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 8$</span> </li> </ul>

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

answer:
<div class="solution">Total possible outcomes, $\mathrm{S}=\{\mathrm{HHH}, \mathrm{HHT}, \mathrm{HTH}, \mathrm{THT}$.<br/>TTH. THH, TTT, HTT $\}$ and desired outcomes E $=\{\mathrm{HTH}, \mathrm{THT}\}$<br/>$\Rightarrow \mathrm{n}(\mathrm{E})=2$ and $\mathrm{n}(\mathrm{S})=8$<br/>Hence, required probability $=\mathrm{P}(\mathrm{E})=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{2}{8}=\frac{1}{4}$</div>


tags: ['Chemistry', 'Surface Chemistry', 'AIIMS', 'AIIMS 2015']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P1.db
title:
a-colloidal-solution-is-kept-in-dark-and-is-illuminated-by-a-beam-of-light-then-brightness-appears-at-the-right-angle-of-direction-of-light-this-effec-1

slug:
a-colloidal-solution-is-kept-in-dark-and-is-illuminated-by-a-beam-of-light-then-brightness-appears-at-the-right-angle-of-direction-of-light-this-effec-1-21043

question:
<div class="question">A colloidal solution is kept in dark and is illuminated by a beam of light then, brightness appears at the right angle of direction of light. This effect is called</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Tyndall effect</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">Brownian effect</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Hardy-Schulze effect</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">Tyndall effect</span> </div>


tags: ['Chemistry', 'Surface Chemistry', 'AIIMS', 'AIIMS 2012']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P1.db
title:
a-colloidal-solution-is-kept-in-dark-and-is-illuminated-by-a-beam-of-light-then-brightness-appears-at-the-right-angle-of-direction-of-light-this-effec

slug:
a-colloidal-solution-is-kept-in-dark-and-is-illuminated-by-a-beam-of-light-then-brightness-appears-at-the-right-angle-of-direction-of-light-this-effec-74410

question:
<div class="question">A colloidal solution is kept in dark and is illuminated by a beam of light then brightness appears at the right angle of direction of light. This effect is called</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Tyndall effect</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">Brownian effect</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Hardy-Schulze effect</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-committee-of-three-has-to-be-chosen-from-a-group-of-4-men-and-5-women-if-the-selection-is-made-at-random-what-is-the-probability-that-exactly-two-me

slug:
a-committee-of-three-has-to-be-chosen-from-a-group-of-4-men-and-5-women-if-the-selection-is-made-at-random-what-is-the-probability-that-exactly-two-me-10272

question:
<div class="question">A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made at random, what is the probability that exactly two members are men?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{5}{14}$</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">$\frac{1}{21}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{14}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{8}{21}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{14}$</span> </div>

answer:
<div class="solution">$\mathrm{n}(\mathrm{E})={ }^{4} \mathrm{C}_{2} \times{ }^{5} \mathrm{C}_{1}=6 \times 5=30$.<br/>$\mathrm{n}(\mathrm{S})={ }^{9} \mathrm{C}_{3}=84$<br/>$\therefore$ Probability, $\mathrm{P}(\mathrm{E})=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{30}{84}=\frac{5}{14}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-committee-of-two-persons-is-contituted-from-two-men-and-two-women-what-is-the-probability-that-the-committee-will-have-only-women

slug:
a-committee-of-two-persons-is-contituted-from-two-men-and-two-women-what-is-the-probability-that-the-committee-will-have-only-women-44201

question:
<div class="question">A committee of two persons is contituted from two men and two women. What is the probability that the committee will have only women?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{6}$</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">$\frac{1}{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2}{3}$</span> </li> </ul>

answer:
<div class="solution">$2 \mathrm{Men}+2$ Women Required probability $=\frac{{ }^{2} \mathrm{C}_{0} \times{ }^{2} \mathrm{C}_{2}}{{ }^{4} \mathrm{C}_{2}}=\frac{1 \times 1}{6}=\frac{1}{6}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch1_P1.db
title:
a-committee-of-two-persons-is-selected-from-two-men-and-two-women-the-probability-that-the-committee-will-have-exactly-one-woman-is

slug:
a-committee-of-two-persons-is-selected-from-two-men-and-two-women-the-probability-that-the-committee-will-have-exactly-one-woman-is-80641

question:
<div class="question">A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{6}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2}{3}$</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">$\frac{1}{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}$</span> </li> </ul>

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

answer:
<div class="solution">We know, $\mathrm{P}(\mathrm{E})=\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}$<br/>Number of possible outcomes $={ }^{4} \mathrm{C}_{2}=\frac{4 \times 3}{2 \times 1}=6$<br/>(selecting 2 people from 4 people $)$ Number of favourable outcomes<br/>$={ }^{2} \mathrm{C}_{1} \times{ }^{2} \mathrm{C}_{1}=2 \times 2=4$<br/>(selecting 1 from 2 men, 1 from 2 women)<br/>$\mathrm{P}(\mathrm{E})=\frac{4}{6}=\frac{2}{3}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main', 'JEE Main 2021 (24 Feb Shift 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">440</span> </div>
source_db: MarksBatch1_P1.db
title:
a-common-transistor-radio-set-requires-12-v-d-c-for-its-operation-the-d-c-source-is-constructed-by-using-a-transformer-and-a-rectifier-circuit-which-a

slug:
a-common-transistor-radio-set-requires-12-v-d-c-for-its-operation-the-d-c-source-is-constructed-by-using-a-transformer-and-a-rectifier-circuit-which-a-85215

question:
<div class="question">A common transistor radio set requires <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo> </mo><mi mathvariant="normal">V</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi mathvariant="normal">D</mi><mo>.</mo><mi mathvariant="normal">C</mi><mo>.</mo></mrow></mfenced></math> for its operation. The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">D</mi><mo>.</mo><mi mathvariant="normal">C</mi><mo>.</mo></math> source is constructed by using a transformer and a rectifier circuit, which are operated at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>220</mn><mo> </mo><mi mathvariant="normal">V</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi mathvariant="normal">A</mi><mo>.</mo><mi mathvariant="normal">C</mi><mo>.</mo></mrow></mfenced></math> on standard domestic <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>.</mo><mi mathvariant="normal">C</mi><mo>.</mo></math> supply. The number of turns of secondary coil are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>,</mo></math> then the number of turns of primary are</div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>N</mi><mi>P</mi></msub><msub><mi>N</mi><mi>S</mi></msub></mfrac><mo>=</mo><mfrac><msub><mi>V</mi><mi>P</mi></msub><msub><mi>V</mi><mi>S</mi></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>N</mi><mi>P</mi></msub><mn>24</mn></mfrac><mo>=</mo><mfrac><mn>220</mn><mn>12</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msub><mi>N</mi><mi>P</mi></msub><mo>=</mo><mfrac><mrow><mn>220</mn><mo>×</mo><mn>24</mn></mrow><mn>12</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msub><mi>N</mi><mi>P</mi></msub><mo>=</mo><mn>440</mn></math></p></div>


tags: ['Chemistry', 'Coordination Compounds', 'AP EAMCET', 'AP EAMCET 2005']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch1_P1.db
title:
a-complex-compound-of-co-3-with-molecular-formula-cocl-x-ynh-3-gives-a-total-of-3-ions-when-dissolved-in-water-how-many-cl-ions-satisfy-both-primary-a-1

slug:
a-complex-compound-of-co-3-with-molecular-formula-cocl-x-ynh-3-gives-a-total-of-3-ions-when-dissolved-in-water-how-many-cl-ions-satisfy-both-primary-a-1-44463


tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch1_P1.db
title:
a-complex-compound-of-co-3-with-molecular-formula-cocl-x-ynh-3-gives-a-total-of-3-ions-when-dissolved-in-water-how-many-cl-ions-satisfy-both-primary-a-2

slug:
a-complex-compound-of-co-3-with-molecular-formula-cocl-x-ynh-3-gives-a-total-of-3-ions-when-dissolved-in-water-how-many-cl-ions-satisfy-both-primary-a-2-23808


tags: ['Chemistry', 'Coordination Compounds', 'TS EAMCET', 'TS EAMCET 2005']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch1_P1.db
title:
a-complex-compound-of-co-3-with-molecular-formula-cocl-x-ynh-3-gives-a-total-of-3-ions-when-dissolved-in-water-how-many-cl-ions-satisfy-both-primary-a

slug:
a-complex-compound-of-co-3-with-molecular-formula-cocl-x-ynh-3-gives-a-total-of-3-ions-when-dissolved-in-water-how-many-cl-ions-satisfy-both-primary-a-44104


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-complex-of-cobalt-with-ammonia-is-analyzed-for-determining-its-formula-by-titrating-it-against-a-strandarized-acid-as-follows-co-nh-3-x-cl-y-aq-hcl-

slug:
a-complex-of-cobalt-with-ammonia-is-analyzed-for-determining-its-formula-by-titrating-it-against-a-strandarized-acid-as-follows-co-nh-3-x-cl-y-aq-hcl-80284

question:
<div class="question">A complex of cobalt with ammonia is analyzed for determining its formula, by titrating it against a strandarized acid as follows :<br/>
 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Co</mi><msub><mfenced><msub><mi>NH</mi><mn>3</mn></msub></mfenced><mi mathvariant="normal">x</mi></msub><msub><mi>Cl</mi><mi mathvariant="normal">y</mi></msub><mfenced><mi>aq</mi></mfenced><mo>+</mo><mi>HCl</mi><mo>â</mo><msubsup><mi>NH</mi><mn>4</mn><mo>+</mo></msubsup><mfenced><mi>aq</mi></mfenced><mo>+</mo><msup><mi>Co</mi><mrow><mi mathvariant="normal">y</mi><mo>+</mo></mrow></msup><mo>+</mo><mfenced><mi>aq</mi></mfenced><mo>+</mo><msup><mi>Cl</mi><mo>â</mo></msup><mfenced><mi>aq</mi></mfenced></math>  A 1.8 g complex required 20.00 mL 1.54 M HCl to reach the equivalence point. Also, if the reaction mixture at equivalence point is treated with excess of AgNO<sub>3</sub>  solution, 7.735 g of AgCl precipitate was produced. What is the formula of this complex?<br/>
[Given: atomic weight of CO = 59 gmol<sup>-1</sup>]</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math> <mrow> <mtext>Co</mtext> <msub> <mrow> <mfenced close=")" open="(" separators=","> <mrow> <msub> <mtext>NH</mtext> <mn>3</mn> </msub> </mrow> </mfenced> </mrow> <mn>4</mn> </msub> <msub> <mtext>Cl</mtext> <mn>3</mn> </msub> </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> <mtext>Co</mtext> <msub> <mrow> <mfenced close=")" open="(" separators=","> <mrow> <msub> <mtext>NH</mtext> <mn>4</mn> </msub> </mrow> </mfenced> </mrow> <mn>4</mn> </msub> <msub> <mtext>Cl</mtext> <mn>3</mn> </msub> </mrow> </math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math> <mrow> <mtext>Co</mtext> <msub> <mrow> <mfenced close=")" open="(" separators=","> <mrow> <msub> <mtext>NH</mtext> <mn>3</mn> </msub> </mrow> </mfenced> </mrow> <mn>3</mn> </msub> <msub> <mtext>Cl</mtext> <mn>4</mn> </msub> </mrow> </math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math> <mrow> <mtext>Co</mtext> <msub> <mrow> <mfenced close=")" open="(" separators=","> <mrow> <msub> <mtext>NH</mtext> <mn>4</mn> </msub> </mrow> </mfenced> </mrow> <mn>3</mn> </msub> <msub> <mtext>Cl</mtext> <mn>4</mn> </msub> </mrow> </math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math> <mrow> <mtext>Co</mtext> <msub> <mrow> <mfenced close=")" open="(" separators=","> <mrow> <msub> <mtext>NH</mtext> <mn>3</mn> </msub> </mrow> </mfenced> </mrow> <mn>4</mn> </msub> <msub> <mtext>Cl</mtext> <mn>3</mn> </msub> </mrow> </math></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><mi>Co</mi><msub><mrow><mo>(</mo><msub><mi>NH</mi><mn>3</mn></msub><mo>)</mo></mrow><mi mathvariant="normal">x</mi></msub><msub><mi>Cl</mi><mi mathvariant="normal">y</mi></msub></mrow><mfrac><mrow><mn>1</mn><mo>.8</mo></mrow><mi mathvariant="normal">M</mi></mfrac></munder><mo>+</mo><munder><mi>xHCL</mi><mfrac><mrow><mn>1</mn><mo>.8</mo></mrow><mi mathvariant="normal">M</mi></mfrac></munder><mo>â</mo><mi mathvariant="normal">x</mi><munder><msubsup><mi>NH</mi><mn>4</mn><mo>+</mo></msubsup><mi>aq</mi></munder><mo>+</mo><msup><mi>Co</mi><mrow><mi mathvariant="normal">y</mi><mo>+</mo></mrow></msup><mo>+</mo><munder><mrow><mo>(</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>)</mo><msup><mi>Cl</mi><mo>-</mo></msup></mrow><mfrac><mrow><mn>1</mn><mo>.8</mo><mo>(</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">r</mi><mo>)</mo></mrow><mi mathvariant="normal">M</mi></mfrac></munder></math><br/><br/><math> <mrow> <mfrac> <mrow> <mn>1</mn> <mtext>.</mtext> <mn>8</mn> <mtext>x</mtext> </mrow> <mrow> <mtext>M</mtext> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mn>0</mn> <mo>Ã</mo> <mn>1</mn> <mtext>.</mtext> <mn>5</mn> <mn>4</mn> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>3</mn> <mn>0</mn> <mtext>.</mtext> <mn>8</mn> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>       ........(I)<br/><br/><math> <mrow> <mfrac> <mrow> <mn>1</mn> <mo>Â·</mo> <mn>8</mn> <mfenced close=")" open="(" separators=","> <mrow> <mtext>x</mtext> <mo>+</mo> <mtext>y</mtext> </mrow> </mfenced> </mrow> <mrow> <mtext>M</mtext> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>7</mn> <mtext>.</mtext> <mn>7</mn> <mn>3</mn> <mn>5</mn> </mrow> <mrow> <mn>1</mn> <mn>4</mn> <mn>3</mn> <mtext>.</mtext> <mn>5</mn> </mrow> </mfrac> <mo>=</mo> <mn>5</mn> <mn>3</mn> <mtext>.</mtext> <mn>9</mn> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>           ........(II)<br/><br/><math> <mrow> <mfrac> <mrow> <mtext>II</mtext> </mrow> <mrow> <mtext>I</mtext>  </mrow> </mfrac> <mo>â </mo> <mfrac> <mrow> <mn>5</mn> <mn>3</mn> <mtext>.</mtext> <mn>9</mn> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mn>3</mn> <mn>0</mn> <mtext>.</mtext> <mn>8</mn> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mtext>.</mtext> <mn>7</mn> <mn>5</mn> <mo>=</mo> <mfrac> <mrow> <mtext>x</mtext> <mo>+</mo> <mtext>y</mtext> </mrow> <mrow> <mtext>x</mtext> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <mtext>y</mtext> </mrow> <mrow> <mtext>x</mtext> </mrow> </mfrac> </mrow> </math><br/><br/><math> <mrow> <mfrac> <mrow> <mtext>y</mtext> </mrow> <mrow> <mtext>x</mtext> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mtext>.</mtext> <mn>7</mn> <mn>5</mn> </mrow> </math><br/><br/>Substituting in (I) <math> <mrow> <mo>â</mo> </mrow> </math><br/><br/><math> <mrow> <mfrac> <mrow> <mn>1</mn> <mtext>.</mtext> <mn>8</mn> <mtext>x</mtext> </mrow> <mrow> <mn>5</mn> <mn>9</mn> <mo>+</mo> <mn>1</mn> <mn>7</mn> <mtext>x</mtext> <mo>+</mo> <mn>3</mn> <mn>5</mn> <mtext>.</mtext> <mn>5</mn> <mo>Ã</mo> <mtext>0</mtext> <mtext>.</mtext> <mn>7</mn> <mn>5</mn> <mtext>x</mtext> </mrow> </mfrac> <mo>=</mo> <mn>3</mn> <mn>0</mn> <mtext>.</mtext> <mn>8</mn> <mo>Ã</mo> <mn>1</mn> <msup> <mn>0</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math><br/><br/><math> <mrow> <mo>â´</mo> </mrow> </math>     x = 3.98 = 4        <math> <mrow> <mo>â´</mo> </mrow> </math>    y = 3</div>


tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-compound-x-with-molecular-formula-c-3-h-9-n-reacts-with-c-6-h-5-s-o-2-c-l-to-give-a-solid-which-is-insoluble-in-alkali-x-is

slug:
a-compound-x-with-molecular-formula-c-3-h-9-n-reacts-with-c-6-h-5-s-o-2-c-l-to-give-a-solid-which-is-insoluble-in-alkali-x-is-72916

question:
<div class="question">A compound (X) with molecular formula <math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>9</mn></mrow></msub><mi mathvariant="normal">N</mi></math> reacts with <math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">S</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi></math> to give a solid which is insoluble in alkali (X) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/eda1790e-bd40-4b85-b0ef-1b53624777c1.png" style="width:0.79125in;height:0.91913in"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></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"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/e1d6cb43-54f3-4630-996c-8bea4990cd94.png" style="width:1.08681in;height:0.64653in"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> </div>

answer:
<div class="solution">Since the compound reacts with benzenesulphonyl chloride to give a product which is insoluble in alkali, it shows there is no H attached to N in the product. <br/>Hence, the compound X is a secondary amine. <br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/41c8e5c6-46d2-4c8f-901e-7a4bd79b61ed.png" style="width:3.82708in;height:0.95347in"/></div>


tags: ['Chemistry', 'Amines']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-compound-z-with-molecular-formula-c-3-h-9-n-reacts-with-c-6-h-5-so-2-cl-to-give-a-solid-insoluble-in-alkali-idenfity-z

slug:
a-compound-z-with-molecular-formula-c-3-h-9-n-reacts-with-c-6-h-5-so-2-cl-to-give-a-solid-insoluble-in-alkali-idenfity-z-28543

question:
<div class="question">A compound $\mathrm{Z}$ with molecular formula $\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}$ reacts with $\mathrm{C}_6 \mathrm{H}_5 \mathrm{SO}_2 \mathrm{Cl}$ to give a solid, insoluble in alkali. Idenfity $\mathrm{Z}$.</div>

answer:
<div class="solution">Since, $\mathrm{Z}$ on reaction with $\mathrm{C}_6 \mathrm{H}_5 \mathrm{SO}_2 \mathrm{Cl}$ gives a product insoluble in alkali. Therefore, the product does not have a replaceable shows that $\mathrm{Z}$ is a secondary amine.<br/><br/>![rendered image](https://cdn.mathpix.com/snip/images/kY6f1uLbfmvn5fXFwz0vZHkPniN4tEBwFKmyZNHPX5g.rendered.fullsize.png)</div>


title: a-condition-where-the-protoxylem-lies-towards-periphery-and-metaxylem-lies-towards-the-center-is
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Exarch</span> </div>
source_db: MarksBatch1_P1.db
slug:
a-condition-where-the-protoxylem-lies-towards-periphery-and-metaxylem-lies-towards-the-center-is-96584

question:
<div class="question">A condition where the protoxylem lies towards periphery and metaxylem lies towards the center is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Exarch</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">Endarch</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Mesarch</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Diarch</span> </li> </ul>

answer:
<div class="solution">In exarch, the development of protoxylem occurs from the outermost part of the procambium, i.e., the development is from outside to inside. The protoxylem is found outside of the metaxylem (centripetal pattern). It is found in roots.</div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch1_P1.db
title:
a-convex-lens-shown-in-the-figure-is-made-up-of-two-types-of-transparent-materials-a-point-sources-of-light-is-placed-on-its-principal-axis-if-reflect

slug:
a-convex-lens-shown-in-the-figure-is-made-up-of-two-types-of-transparent-materials-a-point-sources-of-light-is-placed-on-its-principal-axis-if-reflect-91699

question:
<div class="question">A convex lens shown in the figure is made up of two types of transparent materials. A point sources of light is placed on its principal axis. If reflections from the boundaries between layers are ignored, the lens will form<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9d490464-232a-4a92-a368-eb213a0feddd-image.png" style="width: 90px; height: 261px;"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">only one image</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">two images</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">infinite images</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">no image at all</span> </li> </ul>

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

answer:
<div class="solution">Since, the lens is made up of two kinds of transparent material, it has two refractive indices for the incident beam of light. Hence, there will be two focal lengths of the lens and therefore two images will be observed.</div>


tags: ['Chemistry', 'Coordination Compounds', 'AP EAMCET', 'AP EAMCET 2018 (23 Apr Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-coordination-compound-is-made-of-co-3-nh-3-and-cl-01-m-solution-of-this-complex-when-treated-with-excess-silver-nitrate-gave-no-precipitate-the-form

slug:
a-coordination-compound-is-made-of-co-3-nh-3-and-cl-01-m-solution-of-this-complex-when-treated-with-excess-silver-nitrate-gave-no-precipitate-the-form-48414

question:
<div class="question">A coordination compound is made of $\mathrm{Co}^{3+}$, $\mathrm{NH}_3$, and $\mathrm{Cl}^{-}, 0.1 \mathrm{M}$ solution of this complex when treated with excess silver nitrate gave no precipitate. The formula of the complex and secondary valency of metal are respectively.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right], 6$</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">$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}_3 \mathrm{Cl}_2, 6\right.$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right], 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right] \mathrm{Cl}, 6$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right], 6$</span> </div>

answer:
<div class="solution">Since, no precipitate of $\mathrm{AgCl}$ is obtained on treating the compound with silver nitrate that means no $\mathrm{Cl}^{-}$ions are available outside the coordination sphere. So, correct formula of coordination compound is $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right.$. Since, central metal $\mathrm{Co}$ forms six coordination bonds thus the secondary valency is 6 .</div>


title: a-corner-point-of-a-feasible-region-is-a-point-in-the-region-which-is-the-of-two-boundary-lines
tags: ['Mathematics', 'Linear Programming']
options: None
correct_option: None
answer: <div class="solution">Intersection</div>
source_db: MarksBatch1_P1.db
slug:
a-corner-point-of-a-feasible-region-is-a-point-in-the-region-which-is-the-of-two-boundary-lines-79083

question:
<div class="question">A corner point of a feasible region is a point in the region which is the of two boundary lines.</div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-1

slug:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-1-94620

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>0</mn><mo>.25</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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.5</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>.5</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>5</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>0</mn><mo>.25</mo><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Given, power output<br/><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>Ã</mo></math> power input (or <math><mn>50</mn><mi>%</mi></math> of input power)<br/><br/><math><mo>â´</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>â</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub></math> <math><mfenced close="]" open="[" separators="|"><mrow><mo>âµ</mo><mi>P</mi><mo>=</mo><mi>V</mi><mi>I</mi></mrow></mfenced></math><br/><br/>Here, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>p</mi></msub><mo>=</mo><mn>5</mn><mi> </mi><mi mathvariant="normal">A</mi><mo>,</mo><mi> </mi><msub><mi>V</mi><mi>p</mi></msub><mo>=</mo><mn>220</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math><br/><br/>and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mn>2200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â´</mo><msub><mi>I</mi><mi>s</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>I</mi><mi>p</mi></msub><mo>â</mo><msub><mi>V</mi><mi>p</mi></msub></mrow><mrow><mn>2</mn><msub><mi>V</mi><mi>s</mi></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn><mo>Ã</mo><mn>220</mn></mrow><mrow><mn>2</mn><mo>Ã</mo><mn>2200</mn></mrow></mfrac><mo>=</mo><mn>0.</mn><mn>25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'COMEDK', 'COMEDK 2018']
source_db: MarksBatch1_P1.db
title:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-2

slug:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-2-38820

question:
<div class="question">A current of $5 \mathrm{~A}$ is flowing at $220 \mathrm{~V}$ in the primary coil of a transformer. If the voltage produced in the secondary coil is $2200 \mathrm{~V}$ and $50 \%$ of power is lost, then the current in the secondary will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.5 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 \mathrm{~A}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.25 \mathrm{~A}$</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">$0.5 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.25 \mathrm{~A}$</span> </div>

answer:
<div class="solution">For a transformer,<br/>$\begin{aligned} I_{P}=5 \mathrm{~A}, V_{P} &amp;=220 \mathrm{~V} \\ V_{S}=2200 \mathrm{~V} \end{aligned}$<br/>Since, $50 \%$ power is lost, hence power at secondary side,<br/>$$<br/>\begin{array}{cl} <br/>&amp; P_{0}=50 \% \text { of } P_{i}=\frac{50}{100} \times 1100 \\<br/>\Rightarrow &amp; P_{0}=550 \mathrm{~W} \\<br/>\Rightarrow &amp; V_{S} I_{S}=550 \\<br/>\Rightarrow &amp; 2200 \times I_{S}=550 \\<br/>\Rightarrow &amp; I_{S}=\frac{550}{2200}=\frac{1}{4}=0.25 \mathrm{~A}<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'KCET', 'KCET 2008']
source_db: MarksBatch1_P1.db
title:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-3

slug:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-3-86535

question:
<div class="question">A current of $5 \mathrm{~A}$ is flowing at $220 \mathrm{~V}$ in the primary coil of a transformer. If the voltage produced in the secondary coil is $2200 \mathrm{~V}$ and $50 \%$ of power is lost, then the current in secondary will be</div>

answer:
<div class="solution">$\mathrm{V}_{\mathrm{p}}=220 \mathrm{~V}, \mathrm{~V}_{\mathrm{s}}=2200 \mathrm{~V}, \mathrm{I}_{\mathrm{p}}=5 \mathrm{~A}, \mathrm{I}_{\mathrm{s}}=$ ?<br/>Power loss $=50 \%$<br/>Efficiency of transformer ( $\eta$ ) is defined as the ratio of output power and input power<br/>$$<br/>\eta \%=\frac{\mathrm{P}_{\mathrm{out}}}{\mathrm{P}_{\mathrm{in}}} \times 100=\frac{\mathrm{V}_{\mathrm{s}} \mathrm{I}_{\mathrm{s}}}{\mathrm{V}_{\mathrm{p}} \mathrm{I}_{\mathrm{p}}} \times 100<br/>$$<br/>$$<br/>\begin{aligned}<br/>50 &amp;=\frac{2200 \times \mathrm{I}_{\mathrm{s}}}{220 \times 5} \times 100 \\<br/>\mathrm{I}_{\mathrm{s}} &amp;=0.25 \mathrm{~A}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-4

slug:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-4-56050

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>0</mn><mo>.25</mo><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>2</mn><mo>.5</mo><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>0</mn><mo>.5</mo><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>5</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>0</mn><mo>.25</mo><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution">Given, power output<br/><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo></math> power input (or <math><mn>50</mn><mi>%</mi></math> of input power)<br/><br/><math><mo>∴</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub></math> <math><mfenced close="]" open="[" separators="|"><mrow><mo>∵</mo><mi>P</mi><mo>=</mo><mi>V</mi><mi>I</mi></mrow></mfenced></math><br/><br/>Here, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>p</mi></msub><mo>=</mo><mn>5</mn><mi> </mi><mi mathvariant="normal">A</mi><mo>,</mo><mi> </mi><msub><mi>V</mi><mi>p</mi></msub><mo>=</mo><mn>220</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math><br/><br/>and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mn>2200</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><msub><mi>I</mi><mi>s</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>I</mi><mi>p</mi></msub><mo>⋅</mo><msub><mi>V</mi><mi>p</mi></msub></mrow><mrow><mn>2</mn><msub><mi>V</mi><mi>s</mi></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn><mo>×</mo><mn>220</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>2200</mn></mrow></mfrac><mo>=</mo><mn>0.</mn><mn>25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l

slug:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-l-59032


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2022 (08 Aug Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.25 A</span> </div>
source_db: MarksBatch1_P1.db
title:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-los

slug:
a-current-of-5-a-is-flowing-at-220-v-in-the-primary-coil-of-transformer-if-the-voltage-produced-in-the-secondary-coil-is-2200-v-and-50-of-power-is-los-95366

question:
<div class="question">A current of $5 \mathrm{~A}$ is flowing at $220 \mathrm{~V}$ in the primary coil of transformer. If the voltage produced in the secondary coil is $2200 \mathrm{~V}$ and $50 \%$ of power is lost, then the current in secondary will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2.5 A</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.5 A</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">0.25 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">5 A</span> </li> </ul>

answer:
<div class="solution">Let $I$ be the current flowing through secondary coil.<br/>Current on primary (input) coil $i=5 \mathrm{~A}$<br/>Voltage in primary coil $V=220 \mathrm{~V}$<br/>Voltage in secondary coil $V^{\prime}=2200 \mathrm{~V}$<br/>Considering only $50 \%$ power is transmitted:<br/>$\begin{aligned}<br/>&amp; 0.5(\mathrm{Vi})=V^{\prime} I \\<br/>&amp; \therefore 0.5 \times 220 \times 5=2200 \times I \\<br/>&amp; \Rightarrow I=0.25 \mathrm{~A}<br/>\end{aligned}$</div>


tags: ['Physics', 'Dual Nature of Matter', 'TS EAMCET', 'TS EAMCET 2020 (09 Sep Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-current-of-6-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-1100-v-and-40-of-power-is-l

slug:
a-current-of-6-a-is-flowing-at-220-v-in-the-primary-coil-of-a-transformer-if-the-voltage-produced-in-the-secondary-coil-is-1100-v-and-40-of-power-is-l-30708

question:
<div class="question">A current of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></math> is flowing at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>220</mn><mo> </mo><mi mathvariant="normal">V</mi></math> in the primary coil of a transformer. If the voltage produced in the secondary coil is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1100</mn><mo> </mo><mi mathvariant="normal">V</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>%</mo></math> of power is lost, then the current in the secondary coil will 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>0</mn><mo>.</mo><mn>28</mn><mo> </mo><mi mathvariant="normal">A</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>0</mn><mo>.</mo><mn>36</mn><mo> </mo><mi mathvariant="normal">A</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>0</mn><mo>.</mo><mn>48</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">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>42</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>0</mn><mo>.</mo><mn>48</mn><mo> </mo><mi mathvariant="normal">A</mi></math></span> </div>

answer:
<div class="solution"><p>Given: Voltage in the primary coil <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>i</mi></msub><mo>=</mo><mn>220</mn><mo> </mo><mi mathvariant="normal">V</mi></math>, voltage in the secondary coil <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>O</mi></msub><mo>=</mo><mn>1100</mn><mo> </mo><mi mathvariant="normal">V</mi></math>, current in the primary coil, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>i</mi></msub><mo>=</mo><mn>6</mn><mo> </mo><mi mathvariant="normal">A</mi></math>, Power lost<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>40</mn><mo>%</mo></math></p><p>Let the current in the secondary coil be <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>O</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi></math> be the efficiency of the transformer.</p><p>Efficiency <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi><mo>=</mo><mfrac><msub><mi>P</mi><mi>OUT</mi></msub><msub><mi>P</mi><mi>IN</mi></msub></mfrac></math></p><p>Then, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi>OUT</mi></msub><mo>=</mo><msub><mi>P</mi><mi>IN</mi></msub><mo>×</mo><mi>η</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>O</mi></msub><mo>×</mo><msub><mi>I</mi><mi>O</mi></msub><mo>=</mo><msub><mi>V</mi><mi>i</mi></msub><mo>×</mo><msub><mi>I</mi><mi>i</mi></msub><mo>×</mo><mi>η</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>O</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>V</mi><mi>i</mi></msub><mo>×</mo><msub><mi>I</mi><mi>i</mi></msub><mo>×</mo><mi>η</mi></mrow><msub><mi>V</mi><mi>O</mi></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mi>O</mi></msub><mo>=</mo><mfrac><mrow><mn>220</mn><mo>×</mo><mn>6</mn><mo>×</mo><mn>40</mn></mrow><mrow><mn>110</mn><mo>×</mo><mn>100</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>48</mn><mo> </mo><mi mathvariant="normal">A</mi></math></p></div>


tags: ['Physics', 'Electromagnetic Induction', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-current-of-10-a-in-the-primary-coil-of-a-circuit-is-reduced-to-zero-if-the-coefficient-of-mutual-inductance-is-3-h-and-emf-induced-in-the-secondary-

slug:
a-current-of-10-a-in-the-primary-coil-of-a-circuit-is-reduced-to-zero-if-the-coefficient-of-mutual-inductance-is-3-h-and-emf-induced-in-the-secondary-32292

question:
<div class="question">A current of <math> <mrow> <mn>10</mn><mtext>â</mtext><mtext>A</mtext></mrow> </math> in the primary coil of a circuit is reduced to zero. If the coefficient of mutual inductance is <math> <mrow> <mn>3</mn><mtext>â</mtext><mtext>H</mtext></mrow> </math> and emf induced in the secondary coil is <math> <mrow> <mn>30</mn><mtext>â</mtext><mtext>kV,</mtext></mrow> </math> time taken for the change of current is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><msup><mrow><mn>10</mn></mrow><mrow><mn>3</mn></mrow></msup><mi> s</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><msup><mrow><mn>10</mn></mrow><mrow><mn>2</mn></mrow></msup><mn> s</mn></math> </span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></msup><mn> s</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><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>2</mn></mrow></msup><mn> s</mn></math> </span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></msup><mn> s</mn></math></span> </div>

answer:
<div class="solution">As <math><mi>e</mi><mo>=</mo><mi>M</mi><mfrac><mrow><mn>d</mn><mi>i</mi></mrow><mrow><mn>d</mn><mi>t</mi></mrow></mfrac></math><br/><br/><math><mo>â´</mo><mi> </mi><mn>30</mn><mo>Ã</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mn>3</mn><mo>Ã</mo><mfrac><mrow><mn>10</mn></mrow><mrow><mn>d</mn><mi>t</mi></mrow></mfrac><mo>,</mo></math><br/><br/><math><mn>d</mn><mi>t</mi><mo>=</mo><mi> </mi><mfrac><mrow><mn>30</mn></mrow><mrow><mn>30</mn><mo>Ã</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>3</mn></mrow></msup></mrow></mfrac><mo>=</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></msup><mi> s</mi></math></div>


tags: ['Physics', 'Thermodynamics']
options: None
correct_option: None
source_db: MarksBatch1_P1.db
title:
a-cylinder-with-a-movable-piston-contains-3-moles-of-hydrogen-at-standard-temperature-and-pressure-the-walls-of-the-cylinder-are-made-of-a-heat-insula

slug:
a-cylinder-with-a-movable-piston-contains-3-moles-of-hydrogen-at-standard-temperature-and-pressure-the-walls-of-the-cylinder-are-made-of-a-heat-insula-19565

question:
<div class="question">A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase, if the gas is compressed to half its original volume?</div>

answer:
<div class="solution">The process is adiabatic, as no heat in exchanged<br/>$$<br/>\therefore \quad P_2 V_2^\gamma=P_1 V_1^\gamma \quad \therefore \frac{P_2}{P_1}=\left(\frac{V_1}{V_2}\right)^\gamma<br/>$$<br/>Given $V_2=1 / 2 V_1$<br/>$$<br/>\therefore \quad \frac{P_2}{P_1}=\left(\frac{V_1}{V_1 / 2}\right)^{1.4}=2.64<br/>$$</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2017 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch1_P1.db
title:
a-cylindrical-jar-without-a-lid-has-to-be-constructed-using-a-given-surface-area-of-a-metal-sheet-if-the-capacity-of-the-jar-is-to-be-maximum-then-the

slug:
a-cylindrical-jar-without-a-lid-has-to-be-constructed-using-a-given-surface-area-of-a-metal-sheet-if-the-capacity-of-the-jar-is-to-be-maximum-then-the-13983

question:
<div class="question">A cylindrical jar without a lid has to be constructed using a given surface area of a metal sheet. If the capacity of the jar is to be maximum, then the diameter of the jar must be $\mathrm{k}$ times the height of the jar. The value of k is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">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">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution">The capacity of the jar will be maximum if height and radius of the cylinder are equal. $\therefore$ height $=$ radius<br/>(1) Given diameter is $\mathrm{k}$ times the height of the jar. Diameter $=2 \times$ radius $=2 \times$ height $\quad \ldots .($ from $(1))$ $\therefore \mathrm{k}=2$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2019 (21 Apr Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-ends-has-a-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-60-of-the-tube-is-in-water-th

slug:
a-cylindrical-tube-open-at-both-ends-has-a-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-60-of-the-tube-is-in-water-th-30160

question:
<div class="question">A cylindrical tube open at both ends has a fundamental frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> in air. The tube is dipped vertically in water so that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mo>%</mo></math> of the tube is in water. Then the fundamental frequency of air column 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><mi>f</mi><mn>2</mn></mfrac></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"><mfrac><mrow><mn>5</mn><mi>f</mi></mrow><mn>4</mn></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">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>f</mi></mrow><mn>4</mn></mfrac></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><mi>f</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"><mfrac><mrow><mn>5</mn><mi>f</mi></mrow><mn>4</mn></mfrac></math></span> </div>

answer:
<div class="solution"><blockquote><p>Consider the length of the tube be <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></p><p>The fundamental frequency for the open organ pipe is,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>V</mi><mrow><mn>2</mn><mo> </mo><mi mathvariant="normal">L</mi></mrow></mfrac></math></p><p>The figure below represents the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mo>%</mo></math> of tube is dipped<br/>vertically in water.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/b52a9dee-2b03-41a1-ba10-f55730a990b6-image.png" style="width: 292px; height: 271px;"/></p><p>The length of the closed organ pipe is,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>l</mi><mo>'</mo></msup><mo>=</mo><mfrac><mn>40</mn><mn>100</mn></mfrac><mo> </mo><mi>L</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>l</mi><mo>'</mo></msup><mo>=</mo><mfrac><mrow><mn>2</mn><mo> </mo><mi mathvariant="normal">L</mi></mrow><mn>5</mn></mfrac></math></p><p>The fundamental frequency of air column is,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>=</mo><mfrac><mi>V</mi><mrow><mn>4</mn><msup><mi mathvariant="normal">l</mi><mo>'</mo></msup></mrow></mfrac></math></p><p>Substitute the values in the above equation.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>=</mo><mfrac><mi>V</mi><mrow><mn>4</mn><mo> </mo><mfenced><mfrac><mrow><mn>2</mn><mo> </mo><mi mathvariant="normal">L</mi></mrow><mn>5</mn></mfrac></mfenced></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>=</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mfenced><mfrac><mi>V</mi><mrow><mn>2</mn><mo> </mo><mi mathvariant="normal">L</mi></mrow></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>=</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mi>f</mi></math></p></blockquote></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2012 (Offline)']
answer: <div class="solution">$f_o=\frac{v}{2 \ell}$<br/>$f_c=\frac{v}{2 \ell}$</div>
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-ends-has-a-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-half-of-it-is-in-water-the-fu

slug:
a-cylindrical-tube-open-at-both-ends-has-a-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-half-of-it-is-in-water-the-fu-20645

question:
<div class="question">A cylindrical tube, open at both ends, has a fundamental frequency, $\mathrm{f}$, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$f$<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">B</span> <span class="option-data"><br/>$\frac{f}{2}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{3 f}{4}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$2 f$</span> </li> </ul>

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


tags: ['Physics', 'Waves and Sound', 'TS EAMCET', 'TS EAMCET 2022 (20 Jul Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">f</span> </div>
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-ends-has-a-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-half-of-it-is-in-water-the-ne

slug:
a-cylindrical-tube-open-at-both-ends-has-a-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-half-of-it-is-in-water-the-ne-95320

question:
<div class="question">A cylindrical tube open at both ends has a fundamental<br/>frequency 'f' in air. The tube is dipped vertically in water so<br/>that half of it is in water. The new fundamental frequency is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">f</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">$\frac{f}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2f</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4f</span> </li> </ul>

answer:
<div class="solution">Initially<br/>$$<br/>\mathrm{f}=\frac{\mathrm{V}}{2 \ell}<br/>$$<br/>Finally<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/Ot8N3cebrtqcSIfR_8GYmZy20ecKUhNwPxquRW6lAjI.original.fullsize.png"/><br/><br/>From diagram, we can see<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{\lambda}{4}=\frac{\ell}{2} \\<br/>&amp; \Rightarrow \lambda=21<br/>\end{aligned}<br/>$$<br/>Now, fundamental frequency<br/>$$<br/>=\frac{\mathrm{V}}{\lambda}=\frac{\mathrm{V}}{2 \ell}=\mathrm{f}<br/>$$<br/>So, there will be no change in fundamental frequency.</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (08 Aug Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">f</span> </div>
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-ends-has-a-vibrating-air-column-of-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-half-

slug:
a-cylindrical-tube-open-at-both-ends-has-a-vibrating-air-column-of-fundamental-frequency-f-in-air-the-tube-is-dipped-vertically-in-water-so-that-half-44111

question:
<div class="question">A cylindrical tube open at both ends, has a vibrating air column of fundamental frequency ' $\mathrm{f}$ ' in air. The tube is dipped vertically in water so that half of its is in water. The fundamental frequency of the vibrating air column is now</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">f</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">$\frac{\mathrm{f}}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3 \mathrm{f}}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2f</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/UxqHgqwid1NmekK3JPUyzBSLiEFwfoTePN00SElba-A.original.fullsize.png"/><br/><br/>$v=\lambda f$<br/>Fundamental frequency's $\lambda=\frac{v}{f} \Rightarrow f_0=\frac{v}{2 L}=f$<br/>If the tube is dipped half into liquid then it acts as if closed at $\frac{\mathrm{L}}{2}$.<br/>See figure<img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/jaHyZdtALYyuizLlAhNeNHSUgva7lLNdXAmz-7jZZro.original.fullsize.png"/><br/><br/>The frequency can be written as $\mathrm{f}_{\mathrm{c}}=\frac{\mathrm{v}}{\lambda_1}=\frac{\mathrm{v}}{2 \mathrm{~L}}=\mathrm{f}$<br/>$\therefore$ Fundamental frequency would remain the same ' $\mathrm{f}$ '.</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (10 Aug Shift 1)']
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-ends-has-fundamental-frequency-f-in-air-when-the-tube-is-dipped-vertically-in-water-so-that-onethird-part-of-the-tube-

slug:
a-cylindrical-tube-open-at-both-ends-has-fundamental-frequency-f-in-air-when-the-tube-is-dipped-vertically-in-water-so-that-onethird-part-of-the-tube-78478

question:
<div class="question">A cylindrical tube open at both ends has fundamental frequency $f$ in air. When the tube is dipped vertically in water so that one-third part of the tube is in water, the fundamental frequency of air column becomes (neglect end correction)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{f}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{3 f}{2}$</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">$\frac{f}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{3 f}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3 f}{2}$</span> </div>

answer:
<div class="solution">We know. Frequency is ratio of velocity of sound and wavelength:<br/>$f=\frac{v}{\lambda}$<br/>For tube of length , in fundamental mode wavelength is given by $\frac{\lambda}{2}=L$<br/>$\frac{\lambda}{2}=L$.<br/>$\therefore f=\frac{v}{2 L}$<br/>Now, if tube is dipped one third, then for fundamental mode in air column has:<br/>$\begin{aligned} &amp; \frac{\lambda^{\prime}}{2}=\left(\frac{2}{3} L\right) \\ &amp; \therefore f^{\prime}=\frac{3 v}{4 L}=\frac{3}{2} f\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2021 (24 Sep Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-ends-has-fundamental-frequency-n-in-air-the-tube-is-dipped-vertically-in-water-so-that-onefourth-of-it-is-in-water-the

slug:
a-cylindrical-tube-open-at-both-ends-has-fundamental-frequency-n-in-air-the-tube-is-dipped-vertically-in-water-so-that-onefourth-of-it-is-in-water-the-47083

question:
<div class="question">A cylindrical tube open at both ends has fundamental frequency ' $n$ ' in air. The tube is dipped vertically in water so that one-fourth of it is in water. The fundamental frequency of the air column becomes</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3 n}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{n}}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">n</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{2 n}{3}$</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">$\frac{2 n}{3}$</span> </div>

answer:
<div class="solution">The fundamental frequency of open tube is<br/>$\mathrm{n}_1=\frac{\mathrm{v}}{2 \ell_1}$<br/>When tube is dipped in water, one-fourth of it is in water and three-fourth is in air.<br/><br/>Hence, it becomes a tube closed at one end with length $\ell_2=\frac{3}{4} \ell_1$ The fundamental frequency of closed tube is<br/>$\begin{aligned}<br/>&amp; \mathrm{n}_2=\frac{\mathrm{v}}{4 \ell_2} \\<br/>&amp; \therefore \frac{\mathrm{n}_2}{\mathrm{n}_1}=\frac{1}{4 \ell_2} \times 2 \ell_1=\frac{\ell_1}{2 \ell_2}=\frac{4}{2 \times 3} \quad\left[\because \frac{\ell_1}{\ell_2}=\frac{4}{3}\right] \\<br/>&amp; \therefore \mathrm{n}_2=\frac{2}{3} \mathrm{n}_1=\frac{2}{3} \mathrm{n}<br/>\end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'KCET', 'KCET 2009']
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-the-ends-has-a-fundamental-frequency-of-390-hz-in-air-if-4-1-th-of-the-tube-is-immersed-vertically-in-water-the-fundam

slug:
a-cylindrical-tube-open-at-both-the-ends-has-a-fundamental-frequency-of-390-hz-in-air-if-4-1-th-of-the-tube-is-immersed-vertically-in-water-the-fundam-59140

question:
<div class="question">A cylindrical tube open at both the ends has a fundamental frequency of $390 \mathrm{~Hz}$ in air. If $\frac{1}{4}$ th of the tube is immersed vertically in water the fundamental frequency of air column is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$260 \mathrm{~Hz}$</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">B</span> <span class="option-data">$130 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$390 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$520 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$260 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">Fundamental frequency of cylindrical open tube<br/>$$<br/>\mathrm{n}=\frac{\mathrm{v}}{2 \mathrm{~L}}=390 \mathrm{~Hz}<br/>$$<br/>When it is immersed in water it becomes a closed tube of length $\frac{3}{4}$ th of the initial length.<br/>Therefore, its fundamental frequency is<br/>$$<br/>\begin{aligned}<br/>\mathrm{n}^{\prime} &amp;=\frac{\mathrm{V}}{4\left(\frac{3}{4} \mathrm{~L}\right)}=\frac{\mathrm{v}}{3 \mathrm{~L}}=\frac{2}{3}\left(\frac{\mathrm{V}}{2 \mathrm{~L}}\right) \\<br/>&amp;=\frac{2}{3} \times 390 \mathrm{~Hz}=260 \mathrm{~Hz}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-the-ends-has-a-fundamental-frequency-of-390-hz-in-the-air-if-1-4-of-the-tube-is-immersed-vertically-in-water-the-funda

slug:
a-cylindrical-tube-open-at-both-the-ends-has-a-fundamental-frequency-of-390-hz-in-the-air-if-1-4-of-the-tube-is-immersed-vertically-in-water-the-funda-93967

question:
<div class="question">A cylindrical tube open at both the ends has a fundamental frequency of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>390</mn><mo> </mo><mi>Hz</mi></math> in the air. If <math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math> of the tube is immersed vertically in water, the fundamental frequency of air column 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>260</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 129px; 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>130</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 129px; 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>390</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 129px; 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>520</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 129px; 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>260</mn><mo> </mo><mi>Hz</mi></math><div id="gtx-trans" style="position: absolute; left: 129px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution">The fundamental frequency of cylindrical open tube<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mi>v</mi><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mo>=</mo><mn>390</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math><br/><br/>When it is immersed in water it becomes a closed tube of length, <math><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">h</mi></mrow></msup></math> of the initial length.<br/><br/>Therefore, its fundamental frequency is<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>n</mi><mi mathvariant="normal">′</mi></msup><mo>=</mo><mfrac><mi>v</mi><mrow><mn>4</mn><mfenced separators="|"><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>L</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mi>v</mi><mrow><mn>3</mn><mi>L</mi></mrow></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mfenced separators="|"><mfrac><mi>v</mi><mrow><mn>2</mn><mi>L</mi></mrow></mfrac></mfenced></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>×</mo><mn>390</mn><mo> </mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi><mo>=</mo><mn>260</mn><mo> </mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></div>


tags: ['Physics', 'Oscillations', 'NEET']
source_db: MarksBatch1_P1.db
title:
a-cylindrical-tube-open-at-both-the-ends-has-fundamental-frequency-n-if-one-of-the-ends-is-closed-the-fundamental-frequency-will-become

slug:
a-cylindrical-tube-open-at-both-the-ends-has-fundamental-frequency-n-if-one-of-the-ends-is-closed-the-fundamental-frequency-will-become-98433

question:
<div class="question">A cylindrical tube, open at both the ends has fundamental frequency <math><mi>n</mi></math> . If one of the ends is closed, the fundamental frequency will become</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></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">B</span> <span class="option-data"><math><mn>2</mn><mi>n</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mi>n</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>3</mn><mi>n</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> </div>

answer:
<div class="solution">For a cylindrical tube <br/><br/>If both the ends is closed then<br/><br/>Fundamental frequency,  <math><mi>n</mi><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>2</mn><mi>l</mi></mrow></mfrac></math>              .....(i)<br/><br/>If one of the ends is closed then fundamental frequency,  <math><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac></math>    ....(ii)<br/><br/>from equation (i) and (ii)<br/><br/> <math><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></div>


tags: ['Mathematics', 'Statistics', 'JEE Main', 'JEE Main 2019 (09 Jan Shift 2)']
source_db: MarksBatch1_P1.db
title:
a-data-consists-of-n-observations-x-1-x-2-x-n-if-i-1-n-x-i-1-2-9-n-and-i-1-n-x-i-1-2-5-n-then-the-standard-deviation-of-this-data-is

slug:
a-data-consists-of-n-observations-x-1-x-2-x-n-if-i-1-n-x-i-1-2-9-n-and-i-1-n-x-i-1-2-5-n-then-the-standard-deviation-of-this-data-is-82048

question:
<div class="question">A data consists of <math><mi>n</mi></math> observations: <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>,</mo><mi> </mi><msub><mi>x</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><mo>…</mo><mo> </mo><mo>,</mo><mi> </mi><msub><mi>x</mi><mi>n</mi></msub><mo>.</mo></math> If <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mfenced><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>9</mn><mi>n</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo stretchy="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mfenced separators="|"><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>5</mn><mi>n</mi></math>, then the standard deviation of this data is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>5</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><msqrt><mn>7</mn></msqrt></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><msqrt><mn>5</mn></msqrt></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>2</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><msqrt><mn>5</mn></msqrt></math></span> </div>

answer:
<div class="solution"><blockquote><p>Given:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mfenced separators="|"><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>9</mn><mi>n</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfenced separators="|"><mrow><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mn>2</mn><msub><mi>x</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>9</mn><mi>n</mi><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>1</mn></mfenced></math></p><p>And, <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mfenced separators="|"><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>5</mn><mi>n</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfenced separators="|"><mrow><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup><mo>-</mo><mn>2</mn><msub><mi>x</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>5</mn><mi>n</mi><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>2</mn></mfenced></math> </p><p>Form <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mn>1</mn></mfenced><mo>+</mo><mfenced><mn>2</mn></mfenced></math>, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfenced><mrow><mn>2</mn><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup><mo>+</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>14</mn><mi>n</mi></math> </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msubsup><mi>x</mi><mi>i</mi><mn>2</mn></msubsup><mo>=</mo><mn>6</mn><mi>n</mi><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>3</mn></mfenced><mo> </mo></math></p><p>From <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mn>1</mn></mfenced><mo>-</mo><mfenced><mn>2</mn></mfenced></math>, we get </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>x</mi><mi>i</mi></msub><mo>=</mo><mi>n</mi><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>4</mn></mfenced></math></p><p><math><mo>∴</mo></math> Variance, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>σ</mi><mn>2</mn></msup><mo>=</mo><mi>E</mi><mfenced separators="|"><msup><mi>x</mi><mn>2</mn></msup></mfenced><mo>-</mo><msup><mfenced separators="|"><mrow><mi>E</mi><mfenced separators="|"><mi>x</mi></mfenced></mrow></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>σ</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mo>∑</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mi>n</mi></mfrac><mo>-</mo><mfrac><mrow><mo>∑</mo><mi>x</mi></mrow><mi>n</mi></mfrac><mo> </mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>σ</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>6</mn><mi>n</mi></mrow><mi>n</mi></mfrac><mo>-</mo><msup><mfenced separators="|"><mfrac><mi>n</mi><mi>n</mi></mfrac></mfenced><mn>2</mn></msup><mo>=</mo><mn>6</mn><mo>-</mo><mn>1</mn><mo>=</mo><mn>5</mn></math></p><p><math><mo>∴</mo></math> Standard deviation, <math><mi>σ</mi><mo>=</mo><msqrt><mn>5</mn></msqrt></math>.</p></blockquote></div>


title: a-fair-coin-is-tossed-100-times-what-is-the-probability-of-getting-tails-an-odd-number-of-times
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P1.db
slug:
a-fair-coin-is-tossed-100-times-what-is-the-probability-of-getting-tails-an-odd-number-of-times-60012

question:
<div class="question">A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2}$</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><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{8}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{8}$</span> </li> </ul>

answer:
<div class="solution">Let $\mathrm{x}$ denote number of tails. Then, $\mathrm{X}$ is a binomial variate with parameters:<br/>$\mathrm{x}=100 \&amp; \mathrm{p}=\frac{1}{2}$<br/>$\therefore \mathrm{p}(\mathrm{x}=\mathrm{r})={ }^{100} \mathrm{C}_{\mathrm{r}}\left(\frac{1}{2}\right)^{100} ;(\mathrm{r}=0,1,2, \ldots \ldots .100)$<br/>Req. probability $=\mathrm{P}(\mathrm{x}=1)+\mathrm{P}(\mathrm{x}=3)+\ldots .+\mathrm{P}(\mathrm{x}=99)$<br/>$=\left[\frac{1}{2}\right]^{100}\left[{ }^{100} \mathrm{C}_{1}+{ }^{100} \mathrm{C}_{3}+\ldots .+{ }^{100} \mathrm{C}_{99}\right]$<br/>$=\frac{1}{2^{100}} 2^{99}=\frac{1}{2}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch1_P1.db
title:
a-fair-coin-is-tossed-and-an-unbiased-dice-is-rolled-together-what-is-the-probability-of-getting-a-2-or-4-or-6-along-with-head

slug:
a-fair-coin-is-tossed-and-an-unbiased-dice-is-rolled-together-what-is-the-probability-of-getting-a-2-or-4-or-6-along-with-head-88137

question:
<div class="question">A fair coin is tossed and an unbiased dice is rolled together. What is the probability of getting a 2 or 4 or 6 along with head?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</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">$\frac{1}{6}$</span> </li> </ul>

answer:
<div class="solution">Total number of events with dice and coin $=6 \times 2=12$ Number of possibilities $=(2, \mathrm{H}),(4, \mathrm{H})$ and $(6, \mathrm{H})$ i.e., 3<br/>$\therefore$ Probability $=\frac{3}{12}=\frac{1}{4}$</div>


