# questions

title: the-most-suitable-reagent-for-the-conversion-of-r-ch-2-oh-r-cho-is-1
slug: the-most-suitable-reagent-for-the-conversion-of-r-ch-2-oh-r-cho-is-1-35195
tags: ['Chemistry', 'Aldehydes and Ketones', 'AIIMS', 'AIIMS 2004']
source_db: MarksBatch2_P3.db
question:
<div class="question">The most suitable reagent for the conversion of $R \mathrm{CH}_2 \mathrm{OH} \rightarrow R \mathrm{CHO}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{KMnO}_4$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CrO}_3$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">PCC (pyridine chloro chromate).</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">PCC (pyridine chloro chromate).</span> </div>

answer:
<div class="solution">Pyridine chloro chromate (PCC) $\left[\mathrm{C}_5 \mathrm{H}_5 \mathrm{NH}^{+} \mathrm{ClCrO}_3^{-}\right]$selectively oxidizes primary alcohols to aldehydes. Secondary alcohols can be oxidized to ketones with PCC.</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-motion-of-a-particle-is-described-as-s-2-3-t-4-t-3-what-is-the-acceleration-of-the-particle-at-the-point-where-its-velocity-is-zero

slug:
the-motion-of-a-particle-is-described-as-s-2-3-t-4-t-3-what-is-the-acceleration-of-the-particle-at-the-point-where-its-velocity-is-zero-54813

question:
<div class="question">The motion of a particle is described as $\mathrm{s}=2-3 \mathrm{t}+4 \mathrm{t}^{3}$. What is the acceleration of the particle at the point where its velocity is zero?</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">4 unit</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8 unit</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">12 unit</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">12 unit</span> </div>

answer:
<div class="solution">Given rule is:<br/>Distance, $\mathrm{s}=2-3 \mathrm{t}+4 \mathrm{t}^{3}$<br/>$\Rightarrow$ Velocity $=\frac{\mathrm{ds}}{\mathrm{dt}}=-3+12 \mathrm{t}^{2}$<br/>$\Rightarrow$ Acceleration $=\frac{\mathrm{d}^{2} \mathrm{~s}}{\mathrm{dt}^{2}}=24 \mathrm{t}$<br/>Since, velocity is zero<br/>$\therefore \quad \frac{\mathrm{ds}}{\mathrm{dt}}=0$<br/>$\Rightarrow 0=-3+12 \mathrm{t}^{2} \Rightarrow \mathrm{t}=\sqrt{\frac{3}{12}}=\frac{1}{2}$<br/>Acceleration (when velocity is zero)<br/>$\Rightarrow \quad \frac{\mathrm{d}^{2} \mathrm{~s}}{\mathrm{dt}^{2}}=24 \mathrm{t}=24 \times \frac{1}{2}=12 \mathrm{unit}$</div>


tags: ['Physics', 'Oscillations', 'JEE Main', 'JEE Main 2022 (29 Jun Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-motion-of-a-simple-pendulum-executing-shm-is-represented-by-the-following-equation-y-a-sin-t-where-time-is-measured-in-second-the-length-of-pendul

slug:
the-motion-of-a-simple-pendulum-executing-shm-is-represented-by-the-following-equation-y-a-sin-t-where-time-is-measured-in-second-the-length-of-pendul-71464

question:
<div class="question">The motion of a simple pendulum executing S.H.M. is represented by the following equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi><mi>sin</mi><mfenced><mrow><mi>π</mi><mi>t</mi><mo>+</mo><mi>ϕ</mi></mrow></mfenced></math>, where time is measured in second. The length of pendulum 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>97</mn><mo>.</mo><mn>23</mn><mo> </mo><mi>cm</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>25</mn><mo>.</mo><mn>3</mn><mo> </mo><mi>cm</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>99</mn><mo>.</mo><mn>4</mn><mo> </mo><mi>cm</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>406</mn><mo>.</mo><mn>1</mn><mo> </mo><mi>cm</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>99</mn><mo>.</mo><mn>4</mn><mo> </mo><mi>cm</mi></math></span> </div>

answer:
<div class="solution"><p>Comparing the given equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi><mi>sin</mi><mfenced><mrow><mi>π</mi><mi>t</mi><mo>+</mo><mi>ϕ</mi></mrow></mfenced></math> with a standard equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi><mi>sin</mi><mfenced><mrow><mi>ω</mi><mi>t</mi><mo>+</mo><mi>ϕ</mi></mrow></mfenced></math>. We have</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mi>π</mi><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Since time period is  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>ω</mi></mfrac><mo>=</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">s</mi></math>, it is a second's pendulum.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>2</mn><mi>π</mi><msqrt><mfrac><mi>L</mi><mi>g</mi></mfrac></msqrt><mo>⇒</mo><mi>L</mi><mo>=</mo><mfrac><mi>g</mi><msup><mi>π</mi><mn>2</mn></msup></mfrac><mo>=</mo><mn>99</mn><mo>.</mo><mn>4</mn><mo> </mo><mi>cm</mi></math></p></div>


title: the-multiplication-of-the-number-10101-2-by-1101-2-yields-which-one-of-the-following
slug: the-multiplication-of-the-number-10101-2-by-1101-2-yields-which-one-of-the-following-13349
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The multiplication of the number $(10101)_{2}$ by $(1101)_{2}$ yields which one of the following ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(100011001)_{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(100010001)_{2}$</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">$(110010011)_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(100111001)_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(100010001)_{2}$</span> </div>

answer:
<div class="solution">$\begin{aligned} \because(10101)_{2} &amp;=2^{4} \times 1+0 \times 2^{3}+1 \times 2^{2}+0 \times 2+1 \times 2^{0} \\ &amp;=16+4+1=21 \end{aligned}$<br/>and $\begin{aligned}(1101)_{2} &amp;=1 \times 2^{3}+1 \times 2^{2}+0 \times 2^{1}+1 \times 2^{0} \\ &amp;=8+4+1=13 \end{aligned}$<br/>$\therefore(10101)_{2} \times(1101)_{2}=21 \times 13$<br/>$=273=256+16+1=2^{8}+2^{4}+2^{0}$<br/>So, there will be 1 at $9^{\text {th }}, 5^{\text {th }}$ and first place from right and zero at other places So, $(273)_{10}=(100010001)_{2}$</div>


title: the-municipal-waste-material-which-is-carried-away-in-drains-and-sewers-is-called
slug: the-municipal-waste-material-which-is-carried-away-in-drains-and-sewers-is-called-54753
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Sewage</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The municipal waste material which is carried away in drains and sewers is called ___.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Bacteria</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Secondary sewage treatment</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Sewage</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">Primary sewage treatment</span> </li> </ul>

answer:
<div class="solution">The municipal waste material which is carried away in drains and sewers is called sewage.</div>


tags: ['Physics', 'Electromagnetic Induction', 'JEE Main']
answer: <div class="solution">$e=M \frac{d i}{d t}=1.25 \times 80=100 \mathrm{~V}$</div>
source_db: MarksBatch2_P3.db
title:
the-mutual-inductance-between-two-coils-is-125-henry-if-the-current-in-the-primary-changes-at-the-rate-of-80-amperesecond-then-the-induced-emf-in-the-

slug:
the-mutual-inductance-between-two-coils-is-125-henry-if-the-current-in-the-primary-changes-at-the-rate-of-80-amperesecond-then-the-induced-emf-in-the-61745

question:
<div class="question">The mutual inductance between two coils is 1.25 henry. If the current in the primary changes at the rate of 80 ampere/second, then the induced e.m.f. in the secondary is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$12.5 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$64.0 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.016 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$100.0 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$100.0 \mathrm{~V}$</span> </div>


title: the-n-th-term-of-an-ap-is-4-3-n-then-the-sum-of-first-105-terms-is
slug: the-n-th-term-of-an-ap-is-4-3-n-then-the-sum-of-first-105-terms-is-97127
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1470</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The $n$ th term of an AP. is $\frac{3+\mathrm{n}}{4}$, then the sum of first 105 terms is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">270</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">735</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1409</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1470</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">$\mathrm{T}_{\mathrm{n}}=\frac{3+\mathrm{n}}{4}$<br/>$\mathrm{~S}_{\mathrm{n}}=\sum_{\mathrm{n}=0}^{\infty} \mathrm{T}_{\mathrm{n}}=\sum\left(\frac{3}{4}+\frac{\mathrm{n}}{4}\right)$<br/>$=\frac{3}{4} \mathrm{n}+\frac{1}{4} \times \frac{\mathrm{n}(\mathrm{n}+1)}{2}=\frac{7}{8} \mathrm{n}+\frac{\mathrm{n}^{2}}{8}$<br/>$\mathrm{~S}_{105}=\frac{7}{8} \times 105+\frac{(105)^{2}}{8}=1470$</div>


title: the-natural-relative-abundance-of-isotopes-of-hydrogen-is
slug: the-natural-relative-abundance-of-isotopes-of-hydrogen-is-60523
question: <div class="question">The natural relative abundance of isotopes of hydrogen is</div>
tags: ['Chemistry', 'Hydrogen', 'TS EAMCET', 'TS EAMCET 2018 (04 May Shift 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">${ }_1^1 \mathrm{H}=99.985 \% ;{ }_1^2 \mathrm{D}=0.015 \%$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">${ }_1^1 \mathrm{H}=99.985 \% ;{ }_1^2 \mathrm{D}=0.015 \% ;{ }_1^3 \mathrm{~T}=10^{-16} \%$</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">C</span> <span class="option-data">${ }_1^1 \mathrm{H}=99.100 \% ;{ }_1^2 \mathrm{D}=0.900 \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">${ }_1^1 \mathrm{H}=99.900 \% ;{ }_1^2 \mathrm{D}=0.10 \% ;{ }_1^3 \mathrm{~T}=10^{-15} \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">${ }_1^1 \mathrm{H}=99.985 \% ;{ }_1^2 \mathrm{D}=0.015 \% ;{ }_1^3 \mathrm{~T}=10^{-16} \%$</span> </div>

answer:
<div class="solution">Isotope of hydrogen is hydrogen -2 (also called) deuterium abbreviated as D.<br/>Which contains one proton and one neutron and has a natural abundance of only $0.015 \%$.<br/>$$<br/>{ }_1^1 \mathrm{H}=99.985 \% ;{ }_1^2 \mathrm{D}=0.015 \% ;{ }_1^3 \mathrm{~T}=10^{-16} \%<br/>$$</div>


title: the-nitrogenfixing-bacteria-rhizobium-is-in-nature
slug: the-nitrogenfixing-bacteria-rhizobium-is-in-nature-33795
tags: ['Biology', 'Biological Classification', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The nitrogen-fixing bacteria <em>Rhizobium </em>is ________________ in nature.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">chemoautotrophic</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">photoautotrophic</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">chemosynthetic</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">heterotrophic</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">heterotrophic</span> </div>

answer:
<div class="solution">Heterotrophic bacteria are the most abundant in nature. The majority are important decomposers. Many of them have a significant impact on human affairs. They are helpful in making curd from milk, production of antibiotics, fixing nitrogen in legume roots like <em>Rhizobium</em>, etc.</div>


tags: ['Mathematics', 'Parabola', 'JEE Main', 'JEE Main 2003']
answer: <div class="solution">Fundamental theorem (fact) $t_2=-t_1-\frac{2}{t_1}$</div>
source_db: MarksBatch2_P3.db
title:
the-normal-at-the-point-bt-1-2-2-bt-1-on-a-parabola-meets-the-parabola-again-in-the-point-bt-2-2-2-bt-2-then

slug:
the-normal-at-the-point-bt-1-2-2-bt-1-on-a-parabola-meets-the-parabola-again-in-the-point-bt-2-2-2-bt-2-then-93874

question:
<div class="question">The normal at the point $\left(\mathrm{bt}_1{ }^2, 2 \mathrm{bt}_1\right)$ on a parabola meets the parabola again in the point $\left(\mathrm{bt}_2{ }^2, 2 \mathrm{bt}_2\right)$, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{t}_2=\mathrm{t}_1+\frac{2}{\mathrm{t}_1}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$t_2=-t_1-\frac{2}{t_1}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{t}_2=-\mathrm{t}_1+\frac{2}{\mathrm{t}_1}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{t}_2=\mathrm{t}_1-\frac{2}{\mathrm{t}_1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$t_2=-t_1-\frac{2}{t_1}$<br/></span> </div>


title: the-number-2-2-2-is
slug: the-number-2-2-2-is-96549
question: <div class="question">The number $(2+\sqrt{2})^{2}$ is</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a natural number</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">an irrational number</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 rational number</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">a whole number</span> </li> </ul>

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

answer:
<div class="solution">$(2+\sqrt{2})^{2}=4+2+4 \sqrt{2}=6+4 \sqrt{2}$<br/>So, it is an irrational number</div>


title: the-number-00011-in-binary-system-represents
slug: the-number-00011-in-binary-system-represents-56808
question: <div class="question">The number $0.0011$ in binary system represents</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">rational number $3 / 8$ in decimal system</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">rational number $1 / 8$ in decimal system</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">rational number $3 / 16$ in decimal system</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">rational number $5 / 16$ in decimal system</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">rational number $3 / 16$ in decimal system</span> </div>

answer:
<div class="solution">$(0.0011)=0 \times \frac{1}{2}+0 \times \frac{1}{2^{2}}+1 \times \frac{1}{2^{3}}+1 \times \frac{1}{2^{4}}$<br/>$=0+0+\frac{1}{8}+\frac{1}{16}=\frac{3}{16}$<br/>Hence, option (c) is correct.</div>


title: the-number-25-l-in-decimal-system-is-expressed-in-binary-system-by
slug: the-number-25-l-in-decimal-system-is-expressed-in-binary-system-by-82055
question: <div class="question">The number 25 l in decimal system is expressed in binary system by</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">11110111</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1111101</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">11111101</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">11111110</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">1111101</span> </div>

answer:
<div class="solution">\begin{array}{c|c|c}<br/>2 &amp; 251 &amp; 1 \\<br/>\hline 2 &amp; 125 &amp; 1 \\<br/>\hline 2 &amp; 62 &amp; 0 \\<br/>\hline 2 &amp; 31 &amp; 1 \\<br/>\hline 2 &amp; 15 &amp; 1 \\<br/>\hline 2 &amp; 7 &amp; 1 \\<br/>\hline 2 &amp; 3 &amp; 1 \\<br/>\hline &amp; 1 &amp;<br/>\end{array}<br/>Therefore, $(251)_{10}=(11111011)_{2}$<br/>Sol. (197-199)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/U6_MbpsFMg0LlqxwIEC7-DcLM1Sc_5I16xxy3YxSyTQ.original.fullsize.png"/></div>


title: the-number-83-is-written-in-the-binary-system-as
slug: the-number-83-is-written-in-the-binary-system-as-83807
question: <div class="question">The number 83 is written in the binary system as</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">100110</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">101101</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1010011</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">110110</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">1010011</span> </div>

answer:
<div class="solution">\begin{array}{c|c|c}<br/>2 &amp; 83 &amp; 1 \\<br/>\hline 2 &amp; 41 &amp; 1 \\<br/>\hline 2 &amp; 20 &amp; 0 \\<br/>\hline 2 &amp; 10 &amp; 0 \\<br/>\hline 2 &amp; 5 &amp; 1 \\<br/>\hline 2 &amp; 2 &amp; 0 \\<br/>\hline &amp; 1 &amp;<br/>\end{array}<br/>Therefore, $(83)_{10}=(1010011)_{2}$</div>


title: the-number-292-in-decimal-system-is-expressed-in-binary-system-by
slug: the-number-292-in-decimal-system-is-expressed-in-binary-system-by-84820
question: <div class="question">The number 292 in decimal system is expressed in binary system by</div>
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">100001010</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">10001000 .</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">100100100</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">101010000</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">100100100</span> </div>

answer:
<div class="solution">Remainder<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/n8YCkLlB3yHwKIPomFbjnG0cpz6Tw7fX2XszPQf_m_o.original.fullsize.png"/><br/><br/>Required answer $=100100$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2011 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">175</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-10101111-in-binary-system-is-represented-in-decimal-system-by-which-one-of-the-following-numbers

slug:
the-number-10101111-in-binary-system-is-represented-in-decimal-system-by-which-one-of-the-following-numbers-86043

question:
<div class="question">The number 10101111 in binary system is represented in decimal system by which one of the following numbers?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">157</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">175</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">57</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">75</span> </li> </ul>

answer:
<div class="solution">The number 10101111 can be rewritten as $10101111=2^{7} \times 1+2^{6} \times 0+2^{5} \times 1+2^{4} \times 0+2^{3} \times 1$<br/>$+2^{2} \times 1+2^{1} \times 1+2^{0} \times 1$<br/>$=128+32+8+4+2+1=175$</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">52</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-3-digit-even-numbers-that-can-be-formed-from-the-digits-0-1-2-3-4-and-5-repetition-of-digits-being-not-allowed-is

slug:
the-number-of-3-digit-even-numbers-that-can-be-formed-from-the-digits-0-1-2-3-4-and-5-repetition-of-digits-being-not-allowed-is-55439

question:
<div class="question">The number of 3 -digit even numbers that can be formed from the digits $0,1,2,3,4$ and 5 , repetition of digits being not allowed, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">60</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">56</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">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">D</span> <span class="option-data">48</span> </li> </ul>

answer:
<div class="solution">No. of digits to be filled at one's place $=3$ No. of digits to be filled at 10 's place $=5$ No. of digits to be filled at 100 's place $=4$ $\therefore$ Total no. of digits formed $=3 \times 5 \times 4=60$ If zero is at 100 's place; Then; no. of digits to be filled at one's place $=2$ \&amp; no. of digits to be filled at 10 's place $=4$ $\therefore$ No. of digits formed with zero at 100 's place $=1 \times 2 \times 4=8$<br/>$\therefore$ Required no. of digits formed $=60-8=52$.</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'KVPY', 'KVPY 2011 (SA)']
source_db: MarksBatch2_P3.db
title:
the-number-of-air-molecules-in-a-5-m-5-m-4-m-room-at-standard-temperature-and-pressure-is-of-the-order-of

slug:
the-number-of-air-molecules-in-a-5-m-5-m-4-m-room-at-standard-temperature-and-pressure-is-of-the-order-of-64095

question:
<div class="question">The number of air molecules in a $(5 \mathrm{~m} \times 5 \mathrm{~m} \times 4 \mathrm{~m})$ room at standard temperature and pressure is of the order of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6 \times 10^{23}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 \times 10^{24}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3 \times 10^{27}$</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">$6 \times 10^{30}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 \times 10^{27}$</span> </div>

answer:
<div class="solution">$\mathrm{PV}=\mathrm{N} \times \mathrm{K} \times \mathrm{T}$<br/>where $\mathrm{K}$ is Boltzmann constant<br/>$\begin{array}{l}<br/>10^{5} \times 100=\mathrm{N} \times 1.38 \times 10^{-23} \times 273 \\<br/>\mathrm{~N} \approx 3 \times 10^{27}<br/>\end{array}$</div>


title: the-number-of-chromosomes-in-a-primary-spermatocyte-is
slug: the-number-of-chromosomes-in-a-primary-spermatocyte-is-48967
question: <div class="question">The number of chromosomes in a primary spermatocyte is</div>
tags: ['Biology', 'Human Reproduction', 'JIPMER', 'JIPMER 2015']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">same as in spermatid</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">same as in spermatogonium</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">help of that in spermatogonium</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">same as in secondary spermatocyte</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">same as in spermatogonium</span> </div>

answer:
<div class="solution">Both spermatogonium and primary spermatocyte in human testes are diploid cells (2n).</div>


title: the-number-of-common-characters-among-organisms
slug: the-number-of-common-characters-among-organisms-46430
question: <div class="question">The number of common characters among organisms</div>
tags: ['Biology', 'The Living World', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Decreases (Angiospermae to Triticum)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Increases (Monocotyledone to Plantae)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Increases (Sapindales to Angiospermae)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Decreases (Poaceae to Plantae)</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">Decreases (Poaceae to Plantae)</span> </div>

answer:
<div class="solution">Maximum similarity occurs in species and this decreases with the increasing rank in the hierarchy. Plantae is the kingdom and is the highest category in the taxonomy that includes all the organisms which share a set of distinguishing characters. Poaceae is the category family and is of higher rank than that of the genus. It consists of one to many related genera, which are more similar to one another than to genera of other families.</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Main', 'JEE Main 2023 (11 Apr Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-correct-statements-from-the-following-is-a-for-1-s-orbital-the-probability-density-is-maximum-at-the-nucleus-b-for-2-s-orbital-the-proba

slug:
the-number-of-correct-statements-from-the-following-is-a-for-1-s-orbital-the-probability-density-is-maximum-at-the-nucleus-b-for-2-s-orbital-the-proba-85525

question:
<div class="question">The number of correct statements from the following is ...........<br/>A. For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mi mathvariant="normal">s</mi></math> orbital, the probability density is maximum at the nucleus<br/>B. For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">s</mi></math> orbital, the probability density first increases to maximum and then decreases sharply to zero.<br/>C. Boundary surface diagrams of the orbitals encloses a region of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>%</mo></math> probability of finding the electron.<br/>D. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi></math>-orbitals have <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> angular nodes respectively<br/>E. probability density of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi></math>-orbital is zero at the nucleus<br/> </div>

answer:
<div class="solution"><p>Probability density curves for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mi mathvariant="normal">s</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">s</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">p</mi></math> orbitals are given below.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/7ac3532e-79fb-417a-a9be-a19a904003ac.png" style="width: 400px; height: 243px;"/></p><p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mi mathvariant="normal">s</mi></math> orbital, the probability density is maximum at the nucleus. For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">s</mi></math> orbital, the probability density first decreases and then increases. At any distance from nucleus the probability density of finding electron is never zero, and it always have some finite value. The number of angular nodes are equal to azimuthal quantum number. For <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>-</mo></math>orbital it is equal to 1 and for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>-</mo></math>orbital it is equal to 2. Probability density of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi></math>-orbital is zero at the nucleus</p></div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4320</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-different-words-eightletter-words-ending-and-beginning-with-a-consonant-which-can-be-made-out-of-the-letters-of-the-word-equation-is

slug:
the-number-of-different-words-eightletter-words-ending-and-beginning-with-a-consonant-which-can-be-made-out-of-the-letters-of-the-word-equation-is-69019

question:
<div class="question">The number of different words (eight-letter words) ending and beginning with a consonant which can be made out of the letters of the word 'EQUATION' is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5200</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4320</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">3000</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2160</span> </li> </ul>

answer:
<div class="solution">EQUATION-8 letters. Consonants $-\mathrm{Q}, \mathrm{T}, \mathrm{N}-3$ letters.<br/>first letter of 8 -letter word can be any of 3 consonants Last letter of $8-$ letter word can be remaining 2 consonants. The middle 6 - letters can be arranged in $6 !$ ways. So, number of different words $=3 \times 2 \times 6 !$ $=6 \times 720=4320 .$</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main', 'JEE Main 2023 (11 Apr Shift 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-hyperconjugation-structures-involved-to-stabilize-carbocation-formed-in-the-above-reaction-is

slug:
the-number-of-hyperconjugation-structures-involved-to-stabilize-carbocation-formed-in-the-above-reaction-is-96580

question:
<div class="question"><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/ccf07c7f-ee41-4c01-91e7-c4f90f1c6b55-image.png" style="width: 400px; height: 142px;"/></p><p>The number of hyperconjugation structures involved to stabilize carbocation formed in the above reaction is __________.</p></div>

answer:
<div class="solution"><p>In the first step of the reaction, protonation of alcohol takes place and carbocation is formed after removal of water. The carbocation formed undergo rearrangement to get stability. In the given, methyl shift takes place to convert secondary carbocation to tertiary carbocation. The alpha hydrogen to the positive charged carbon are involved in hyperconjugation.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/9113451c-d035-419d-be50-7e921d6fee43-image.png" style="width: 400px; height: 452px;"/></p><p>So, number of hyperconjugation structures in most stable carbocation</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mn>6</mn><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mn>7</mn></math></p></div>


tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-number-of-male-gametes-and-the-number-of-meiotic-divisions-required-for-the-formation-of-100-seeds-in-a-typical-angiosperm-is

slug:
the-number-of-male-gametes-and-the-number-of-meiotic-divisions-required-for-the-formation-of-100-seeds-in-a-typical-angiosperm-is-72786

question:
<div class="question">The number of male gametes and the number of meiotic divisions required for the formation of 100 seeds in a typical angiosperm is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">100 male gametes and 125 meiotic divisions</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">200 male gametes and 125 meiotic divisions</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">100 male gametes and 25 meiotic divisions</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">200 male gametes and 25 meiotic divisions</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">200 male gametes and 125 meiotic divisions</span> </div>

answer:
<div class="solution">Angiosperms undergo double fertilization in which one male gamete fuses with the egg, whereas the second male gamete fuses with the secondary nucleus. Thus, for the formation of one seed, two male gametes are required. One egg is produced by one meiotic division. Four pollen grains are produced by one meiotic division. Thus, for 100 seeds, 100+25 = 125 meiosis are required with 200 male gametes [x+(x/4), 100+(100/4)=100+25=125].</div>


title: the-number-of-molecules-and-moles-in-2-8375-litres-of-o-2-at-stp-are-respectively
slug: the-number-of-molecules-and-moles-in-2-8375-litres-of-o-2-at-stp-are-respectively-83088
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'JEE Main', 'JEE Main 2023 (10 Apr Shift 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of molecules and moles in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>8375</mn></math> litres of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>STP</mi></math> are respectively</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><mo>.</mo><mn>527</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>125</mn><mo> </mo><mi>mol</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>7</mn><mo>.</mo><mn>527</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>250</mn><mo> </mo><mi>mol</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>1</mn><mo>.</mo><mn>505</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>250</mn><mo> </mo><mi>mol</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>7</mn><mo>.</mo><mn>527</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>125</mn><mo> </mo><mi>mol</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>7</mn><mo>.</mo><mn>527</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>125</mn><mo> </mo><mi>mol</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>One mole of any ideal gas occupies <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>.</mo><mn>7</mn><mi mathvariant="normal">L</mi></math> at standard temperature and pressure.</p><p>The number of moles <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mi>Given</mi><mo> </mo><mi>volume</mi></mrow><mrow><mi>Volume</mi><mo> </mo><mi>at</mi><mo> </mo><mi>STP</mi></mrow></mfrac></math></p><p>Moles <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>8375</mn></mrow><mrow><mn>22</mn><mo>.</mo><mn>7</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>125</mn></math></p><p>The number of molecules <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>moles</mi><mo>×</mo><msub><mi mathvariant="normal">N</mi><mi mathvariant="normal">A</mi></msub></math></p><p>Molecules <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>125</mn><mo>×</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>7</mn><mo>.</mo><mn>527</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></math></p></blockquote></div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-number-of-moles-of-oxygen-in-one-litre-of-air-containing-21-oxygen-by-volume-in-standard-condition-is

slug:
the-number-of-moles-of-oxygen-in-one-litre-of-air-containing-21-oxygen-by-volume-in-standard-condition-is-91310

question:
<div class="question">The number of moles of oxygen in one litre of air containing 21% oxygen by volume in standard condition is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.186 mole</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2.10 mole</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.210 mole</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">0.0093 mole</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">0.0093 mole</span> </div>

answer:
<div class="solution">Air containing 21% oxygen in one litre <math><mo>=</mo><mfrac><mrow><mn>21</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mn>0.21</mn></math> litre<br/>1 mole occupies a volume = 22.4 litre<br/>x mole occupies a volume = 0.21 litre<br/>So <math><mi mathvariant="normal">x</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">V</mi></mrow><mrow><mn>22.4</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>0.21</mn></mrow><mrow><mn>22.4</mn></mrow></mfrac><mo>=</mo><mn>0.0093</mn></math> mole of <math><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math> .</div>


tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Main', 'JEE Main 2024 (05 Apr Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-neutrons-present-in-the-more-abundant-isotope-of-boron-is-x-amorphous-boron-upon-heating-with-air-forms-a-product-in-which-the-oxidation

slug:
the-number-of-neutrons-present-in-the-more-abundant-isotope-of-boron-is-x-amorphous-boron-upon-heating-with-air-forms-a-product-in-which-the-oxidation-36711

question:
<div class="question">The number of neutrons present in the more abundant isotope of boron is ' \(x\) '. Amorphous boron upon heating with air forms a product, in which the oxidation state of boron is ' \(y\) '. The value of \(x+y\) is _______</div>

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

answer:
<div class="solution">More abundant isotope $=\mathrm{B}^{11}$<br/>[Number of neutrons $=6$ ]<br/>$\begin{aligned}<br/>&amp; \mathrm{x}=6 \\<br/>&amp; \mathrm{~B}+\mathrm{O}_2 \rightarrow \mathrm{B}_2 \mathrm{O}_3<br/>\end{aligned}$<br/>Oxidation state of $\mathrm{B}$ in $\mathrm{B}_2 \mathrm{O}_3=+3$<br/>So, $y=3$<br/>Hence $x+y=9$</div>


title: the-number-of-nonzero-integral-solutions-of-the-equation-1-2-i-x-5-x-is
slug: the-number-of-nonzero-integral-solutions-of-the-equation-1-2-i-x-5-x-is-54384
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of non-zero integral solutions of the equation $|1-2 i|^{x}=5^{x}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Zero (No solution)</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">One</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Two</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Three</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Zero (No solution)</span> </div>

answer:
<div class="solution">$|1-2 i|^{x}=5^{x}$<br/>$\Rightarrow\left(\left((1)^{2}+(-2)^{2}\right)^{\frac{1}{2}}\right)^{\mathrm{x}}=5^{\mathrm{x}} \quad \because|\mathrm{x}+\mathrm{iy}|=\sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}}$<br/>$\Rightarrow(5)^{\frac{x}{2}}=5^{x}$<br/>$\Rightarrow \frac{x}{2}=x \Rightarrow x=2 x$<br/>$\Rightarrow x=0$<br/>There is no non zero integral solution.</div>


title: the-number-of-p-d-pi-bonds-present-in-xeo-3-and-xeo-4-molecules-respectively-are
slug: the-number-of-p-d-pi-bonds-present-in-xeo-3-and-xeo-4-molecules-respectively-are-69337
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'VITEEE', 'VITEEE 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3,4</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of $\mathrm{p} \pi-\mathrm{d} \pi$ 'pi' bonds present in $\mathrm{XeO}_{3}$ and $\mathrm{XeO}_{4}$ molecules, respectively are</div>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/viteee/quPB4xyhU6sm1t_j9taq_ROFGcMEt-yss-oKW2tlndA.original.fullsize.png"/></div>


title: the-number-of-permutations-that-can-be-formed-from-all-the-letters-of-the-word-baseball-is
slug: the-number-of-permutations-that-can-be-formed-from-all-the-letters-of-the-word-baseball-is-27860
tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2012 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5040</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of permutations that can be formed from all the letters of the word 'BASEBALL' is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">540</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1260</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3780</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">5040</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">There are total 8 letters in the word BASEBALL, in which we have 2 B's, 2 A's and 2 L's.<br/>$\therefore \quad$ Required No. of permutations $=\frac{8 !}{2 ! \times 2 ! \times 2 !}$<br/>$=\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8}=5040$</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main', 'JEE Main 2023 (11 Apr Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-possible-isomeric-products-formed-when-3-chloro-1-butene-reacts-with-hcl-through-carbocation-formation-is

slug:
the-number-of-possible-isomeric-products-formed-when-3-chloro-1-butene-reacts-with-hcl-through-carbocation-formation-is-52924

question:
<div class="question">The number of possible isomeric products formed when <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>-chloro-<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>-butene reacts with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HCl</mi></math> through carbocation formation is.........</div>

answer:
<div class="solution"><p>3-chloro-1-butene undergo protonation and gives secondary carbocation according Markonikov's addition in the first step. In the second step the lone pair on the chlorine attacks the positively charged carbon to form cyclic intermediate. Now the nucleophile in the reaction i.e., chloride ion attacks cyclic intermediate and forms two structural products as shown below.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/48fec7d5-df60-4c2a-9e7f-0c7c62501753.png" style="width: 321px; height: 190px;"/></p><p>2,2-dichlorobutane exit in single isomer only, but 2,3-dichlorobutane exhibits three isomers. </p></div>


tags: ['Physics', 'Waves and Sound', 'NEET', 'NEET 2014']
source_db: MarksBatch2_P3.db
title:
the-number-of-possible-natural-oscillations-of-air-column-in-a-pipe-closed-at-one-end-of-length-85-c-m-whose-frequencies-lies-below-1250-h-z-are-veloc

slug:
the-number-of-possible-natural-oscillations-of-air-column-in-a-pipe-closed-at-one-end-of-length-85-c-m-whose-frequencies-lies-below-1250-h-z-are-veloc-45936

question:
<div class="question">The number of possible natural oscillations of air column in a pipe closed at one end of length <math><mn>85</mn><mi> </mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> whose frequencies lies below <math><mn>1250</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math> are: (velocity of sound <math><mo>=</mo><mn>340</mn><mi> </mi><msup><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">s</mi></mrow><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>4</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>5</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>7</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><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> </ul>

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

answer:
<div class="solution"><blockquote><p>Fundamental frequency of a closed organ pipe is <math><msub><mrow><mi>f</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><mo>=</mo><mfrac><mrow><mn>340</mn></mrow><mrow><mn>4</mn><mo>×</mo><mn>0.85</mn></mrow></mfrac><mo>=</mo><mn>100</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math><br/>The natural frequencies of the organ pipe will be <math><mi>f</mi><mo>=</mo><mn>100</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi><mo>,</mo><mi mathvariant="normal"> </mi><mn>300</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi><mo>,</mo><mi> </mi><mn>500</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi><mo>,</mo><mi mathvariant="normal"> </mi><mn>700</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi><mo>,</mo><mi mathvariant="normal"> </mi><mn>900</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi><mo>,</mo><mi mathvariant="normal"> </mi><mn>1100</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math> which are below <math><mn>1250</mn><mi> </mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></math></p></blockquote></div>


title: the-number-of-primary-secondary-and-tertiary-carbons-in-the-following-structure-are-respectively
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
slug:
the-number-of-primary-secondary-and-tertiary-carbons-in-the-following-structure-are-respectively-79252

question:
<div class="question">The number of primary, secondary and tertiary carbons in the following, structure are respectively<br/> <br/> <br/> <br/> <img src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/ffqccbsltxnkdhymgrrwexmyhviteozcskilbhpnbnsxlnjkrm.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">6, 3, 3</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">3, 6, 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, 6, 2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3, 2, 1</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/abs/wdbuqpnxwzehxohcicmvcivxqmupxdzvzbpwgbjmekdhudcspx.png"/> <br/><br/> <math><msup><mrow><mn>1</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></math>  carbon  <math><mo>=</mo><mn>3</mn><mo>,</mo><mi mathvariant="normal">Â </mi><msup><mrow><mn>2</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></math>  carbons  <math><mo>=</mo><mn>6</mn><mo>,</mo><mi mathvariant="normal">Â </mi><msup><mrow><mn>3</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></math>  carbons  <math><mo>=</mo><mn>3</mn></math> ,</div>


title: the-number-of-real-ro-the-equation-x-2-3-x-2-0-is
slug: the-number-of-real-ro-the-equation-x-2-3-x-2-0-is-47250
question: <div class="question">The number of real ro the equation $x^{2}-3|x|+2=0$ is</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</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">B</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1</span> </li> </ul>

answer:
<div class="solution">$x^{2}-3|x|+2=0$<br/>Case (i) when $x \geq 0$<br/>$x^{2}-3 x+2=0$<br/>$(x-1)(x-2)=0$<br/>$\mathrm{x}=1,2($ both roots satisfy the condition $\mathrm{x} \geq 0$ )<br/>Case (ii) when $\mathrm{x}   &lt; 0$ $x^{2}+3 x+2=0$<br/>$(x+1)(x+2)=0$<br/>$\mathrm{x}=-1,-2$ (both roots satisfy the condition $\mathrm{x} &lt; 0$ ) So no. of real roots is 4</div>


title: the-number-of-real-roots-for-the-equation-x-2-9-x-20-0-is
slug: the-number-of-real-roots-for-the-equation-x-2-9-x-20-0-is-38782
question: <div class="question">The number of real roots for the equation $x^{2}+9|x|+20=0$ is</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2019 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Zero</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">One</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Two</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Three</span> </li> </ul>

answer:
<div class="solution">$x^{2}+9|x|+20=0$<br/>The sum of three positive quantities can never be zero. So, the equation has no solution.</div>


title: the-number-of-roots-of-the-equation-z-2-2-z-is
slug: the-number-of-roots-of-the-equation-z-2-2-z-is-72848
question: <div class="question">The number of roots of the equation $z^{2}=2 \bar{z}$ is</div>
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
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">zero</span> </li> </ul>

answer:
<div class="solution">$\mathrm{z}^{2}=2 \overline{\mathrm{z}}$<br/>Let $\mathrm{z}=\mathrm{x}+\mathrm{iy} \Rightarrow \mathrm{z}^{2}=(\mathrm{x}+\mathrm{iy})^{2}=\mathrm{x}^{2}-\mathrm{y}^{2}+2 \mathrm{xyi}$<br/>$\therefore \quad \mathrm{z}^{2}=2 \overline{\mathrm{z}} \Rightarrow \mathrm{x}^{2}-\mathrm{y}^{2}+2 \mathrm{xyi}=2(\mathrm{x}-\mathrm{iy})$<br/>$\Rightarrow \mathrm{x}^{2}-\mathrm{y}^{2}=2 \mathrm{x} ; 2 \mathrm{xy}=-2 \mathrm{y} \Rightarrow 2(\mathrm{x}+1) \mathrm{y}=0 .$<br/>$\mathrm{x}=-1$ and $\mathrm{y}=0$<br/>$\Rightarrow(-1)^{2}-\mathrm{y}^{2}=2(-1)$<br/>$\Rightarrow 1-\mathrm{y}^{2}=-2$<br/>$\Rightarrow \mathrm{y}^{2}=3 \Rightarrow \mathrm{y}=\pm \sqrt{3}$<br/>$\therefore$ Roots are $-1+\sqrt{3} \mathrm{i}$ and $-1-\sqrt{3} \mathrm{i} .$<br/>and for $\mathrm{y}=0, \mathrm{x}^{2}-0=2 \mathrm{x}$<br/>$\mathrm{x}(\mathrm{x}-2)=0$<br/>$\mathrm{x}=0$ and $2 .$<br/>Hence, roots are 0,2</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2007 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">30</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-rows-in-a-lecture-hall-equals-the-number-of-seats-in-a-row-if-the-number-of-rows-is-doubled-and-the-number-of-seats-in-every-row-is-redu

slug:
the-number-of-rows-in-a-lecture-hall-equals-the-number-of-seats-in-a-row-if-the-number-of-rows-is-doubled-and-the-number-of-seats-in-every-row-is-redu-96492

question:
<div class="question">The number of rows in a lecture hall equals the number of seats in a row. If the number of rows is doubled and the<br/>number of seats in every row is reduced by 10 , the number ofseats is increased by 300 . If $x$ denotes the number of rows in the lecture hall, then what is the value of $x$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">10</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">15</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">20</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">30</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">As given $\Rightarrow$ Number of seats in each row $=x$ Total number of seats in the hall $=x$ Revised number of rows $=2 x$ Revised number in each row $=x-10$ Thus Revised number of seats $=2 x(x-10)=2 x^{2}-20 x$ According to question,<br/>$\Rightarrow x^{2}-20 x-300=0$<br/>$\Rightarrow x^{2}-30 x+10 x-300=0$<br/>$(x-30)(x+10)=0$<br/>$\Rightarrow x=30$<br/>$(\because \quad x \neq-10)$</div>


title: the-number-of-stereo-isomers-possible-for-the-molecule
slug: the-number-of-stereo-isomers-possible-for-the-molecule-47525
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">16</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of stereo isomers possible for the molecule, <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/34_dadjjd.JPG" style="width: 150px; height: 92px;"/></div>

answer:
<div class="solution">It has three chiral carbons<br/><br/>So number of enantiomers <math><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mn>8</mn></math> .<br/><br/>Since each pair gives cis and trans isomers (around double bond).<br/><br/>So total number of stereoisomers <math><mo>=</mo><mn>8</mn><mo>Ã</mo><mn>2</mn><mo>=</mo><mn>16</mn></math><br/><br/><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/soludndanna.JPG" style="width: 200px; height: 83px;"/></div>


title: the-number-of-structural-isomers-possible-from-the-molecular-formula-c-3-h-9-n-is
slug: the-number-of-structural-isomers-possible-from-the-molecular-formula-c-3-h-9-n-is-78829
tags: ['Chemistry', 'General Organic Chemistry', 'NEET', 'NEET 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of structural isomers possible from the 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> is:</div>

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

answer:
<div class="solution"><p>The given formula is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>3</mn></msub><msub><mi mathvariant="normal">H</mi><mn>9</mn></msub><mi mathvariant="normal">N</mi></math> which have degree of usaturation is zero i.e. compounds will be saturated.</p><p>Total possible primary amine is 2 , secondary amine 1 ans tertiary amine also 1.</p><p><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><mo>-</mo><msub><mi>CH</mi><mn>2</mn></msub><mo>-</mo><msub><mi>CH</mi><mn>2</mn></msub><mo>-</mo><msub><mi>NH</mi><mn>2</mn></msub></math> ;  <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CH</mi><mn>3</mn></msub><mo>-</mo><mi>NH</mi><mo>-</mo><msub><mi>CH</mi><mn>2</mn></msub><mo>-</mo><msub><mi>CH</mi><mn>3</mn></msub></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/neet/901cda34-017e-42ad-bc7b-c3c1943920b5-image.png" style="width: 338px; height: 63px;"/></p></div>


title: the-number-of-terms-in-the-expansion-of-x-a-100-x-a-100-after-simplification-is
slug: the-number-of-terms-in-the-expansion-of-x-a-100-x-a-100-after-simplification-is-25954
tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2017 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">51</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of terms in the expansion of $(x+a)^{100}+$ $(x-a)^{100}$ after simplification is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">202</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">101</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">51</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">50</span> </li> </ul>

answer:
<div class="solution">$(x+a)^{100}+(x-a)^{100}$<br/>Simple logic is we get ${ }^{\mathrm{n}} \mathrm{c}_{0},{ }^{\mathrm{n}} \mathrm{c}_{2},{ }^{\mathrm{n}} \mathrm{c}_{4} \ldots{ }^{\mathrm{n}} \mathrm{C}_{100}$ in this<br/>expansion.<br/>The number of terms from ${ }^{\mathrm{n}} \mathrm{c}_{0}$ to ${ }^{\mathrm{n}} \mathrm{c}_{100}$ are 51</div>


tags: ['Physics', 'Alternating Current', 'AP EAMCET', 'AP EAMCET 2008']
source_db: MarksBatch2_P3.db
title:
the-number-of-turns-in-primary-and-secondary-coils-of-a-transformer-is-50-and-200-respectively-if-the-current-in-the-primary-coil-is-4-a-then-the-curr-1

slug:
the-number-of-turns-in-primary-and-secondary-coils-of-a-transformer-is-50-and-200-respectively-if-the-current-in-the-primary-coil-is-4-a-then-the-curr-1-54017

question:
<div class="question">The number of turns in primary and secondary coils of a transformer is 50 and 200 respectively. If the current in the primary coil is $4 \mathrm{~A}$, then the current in the secondary coil is</div>

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

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

answer:
<div class="solution">In a transformer<br/>$$<br/>\begin{array}{rlrl} <br/>&amp; &amp; \frac{N_P}{N_S} &amp; =\frac{I_S}{I_P} \\<br/>&amp; \frac{50}{200} &amp; =\frac{I_S}{4} \\<br/>&amp; I_S &amp; =1 \mathrm{~A}<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'TS EAMCET', 'TS EAMCET 2008']
source_db: MarksBatch2_P3.db
title:
the-number-of-turns-in-primary-and-secondary-coils-of-a-transformer-is-50-and-200-respectively-if-the-current-in-the-primary-coil-is-4-a-then-the-curr

slug:
the-number-of-turns-in-primary-and-secondary-coils-of-a-transformer-is-50-and-200-respectively-if-the-current-in-the-primary-coil-is-4-a-then-the-curr-56619

question:
<div class="question">The number of turns in primary and secondary coils of a transformer is 50 and 200 respectively. If the current in the primary coil is $4 \mathrm{~A}$, then the current in the secondary coil is</div>

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

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

answer:
<div class="solution">In a transformer<br/>$$<br/>\begin{array}{rlrl} <br/>&amp; &amp; \frac{N_P}{N_S} &amp; =\frac{I_S}{I_P} \\<br/>&amp; \frac{50}{200} &amp; =\frac{I_S}{4} \\<br/>&amp; I_S &amp; =1 \mathrm{~A}<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Electromagnetic Induction', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-number-of-turns-of-primary-and-secondary-coils-of-a-transformer-is-5-and-10-respectively-and-mutual-inductance-of-the-transformer-is-25-h-now-the-

slug:
the-number-of-turns-of-primary-and-secondary-coils-of-a-transformer-is-5-and-10-respectively-and-mutual-inductance-of-the-transformer-is-25-h-now-the-36683

question:
<div class="question">The number of turns of primary and secondary coils of a transformer is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> respectively and mutual inductance of the transformer is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo> </mo><mi mathvariant="normal">H</mi></math>. Now, the number of turns in primary and secondary are made <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> respectively. Mutual inductance of the transformer 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>25</mn><mo> </mo><mi mathvariant="normal">H</mi></math><div id="gtx-trans" style="position: absolute; left: 61px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">H</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>50</mn><mo> </mo><mi mathvariant="normal">H</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>6</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">H</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>25</mn><mo> </mo><mi mathvariant="normal">H</mi></math><div id="gtx-trans" style="position: absolute; left: 61px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution">As <math><mi>M</mi><mi> </mi><mo>â</mo><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi> </mi></math>therefore, <math><mi>M</mi></math> remains the same.</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8000</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-ways-in-which-3-holiday-tickets-can-be-given-to-20-employees-of-an-organization-if-each-employee-is-eligible-for-any-one-or-more-of-the-

slug:
the-number-of-ways-in-which-3-holiday-tickets-can-be-given-to-20-employees-of-an-organization-if-each-employee-is-eligible-for-any-one-or-more-of-the-34028

question:
<div class="question">The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1140</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">3420</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6840</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">8000</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">$\because$ Each employee is eligible for 1 or more of the tickets. $\therefore$ No. of ways $=20 \times 20 \times 20=8000$.</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1001</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-ways-in-which-a-cricket-team-of-11-players-be-chosen-out-of-a-batch-of-15-players-so-that-the-captain-of-the-team-is-always-included-is

slug:
the-number-of-ways-in-which-a-cricket-team-of-11-players-be-chosen-out-of-a-batch-of-15-players-so-that-the-captain-of-the-team-is-always-included-is-21056

question:
<div class="question">The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">165</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">364</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1001</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">1365</span> </li> </ul>

answer:
<div class="solution">If captain is always included then we can choose 10 more players out of the remaining 14 players. So<br/>${ }^{14} \mathrm{C}_{10}=\frac{14 !}{10 ! 4 !}=1001$</div>


title: the-numbers-15-and-25-can-be-three-terms-not-necessarily-consecutive-of
slug: the-numbers-15-and-25-can-be-three-terms-not-necessarily-consecutive-of-80569
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The numbers 1,5 and 25 can be three terms (not necessarily consecutive) of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">only one AP</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">more than one but unite numbers of APs</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">inunite number of APs</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">unite number of GPs</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">inunite number of APs</span> </div>

answer:
<div class="solution">Given, numbers $1,5,25$ Let $p^{\text {th }}$ term $=1 \Rightarrow a+(p-1) d=1$ ...(1)<br/>Let $q^{\text {th }}$ term $=5 \Rightarrow a+(q-1) d=5$ ...(2)<br/>Let $\mathrm{r}^{\text {th }}$ term $=25 \Rightarrow \mathrm{a}+(\mathrm{r}-1) \mathrm{d}=25$...(3)<br/>(3),$(2) \Rightarrow \mathrm{r}-\mathrm{q}=25-5=20$<br/>(2), $(1) \Rightarrow \mathrm{q}-\mathrm{p}=5-1=4$<br/>$\frac{r-q}{q-p}=\frac{20}{4}=5$ which is an integer.<br/>So, the given series forms an $\mathrm{AP}$. <br/>Infinite AP's are possible</div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2023 (13 May Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-numbers-of-turns-in-the-primary-and-the-secondary-of-a-transformer-are-1000-and-3000-respectively-if-80-v-ac-is-applied-to-the-primary-coil-of-the

slug:
the-numbers-of-turns-in-the-primary-and-the-secondary-of-a-transformer-are-1000-and-3000-respectively-if-80-v-ac-is-applied-to-the-primary-coil-of-the-10184

question:
<div class="question">The numbers of turns in the primary and the secondary of a transformer are 1000 and 3000 respectively. If $80 \mathrm{~V}$ a.c. is applied to the primary coil of the transformer, then the potential difference per turn of the secondary coil would be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$240 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2400 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.24 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0.08 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.08 \mathrm{~V}$</span> </div>

answer:
<div class="solution">$\frac{E_p}{E_s}=\frac{N_p}{N_s}$<br/>$\frac{80}{E_{\mathrm{s}}}=\frac{1000}{3000}$<br/>$E_s=240 \mathrm{~V}$<br/>$\therefore \quad E_{\mathrm{s}}$ per turn $=\frac{240}{3000}=0.08 \mathrm{~V}$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2008 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2 unit</span> </div>
source_db: MarksBatch2_P3.db
title:
the-numerical-value-of-the-perimeter-of-a-square-exceeds-that-of-its-area-by-4-what-is-the-side-of-the-square

slug:
the-numerical-value-of-the-perimeter-of-a-square-exceeds-that-of-its-area-by-4-what-is-the-side-of-the-square-47463

question:
<div class="question">The numerical value of the perimeter of a square exceeds that of its area by 4 . What is the side of the square?</div>

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

answer:
<div class="solution">Let the side of the square $=x$ units Area of square $=x^{2}$ unit and perimeter of square $=4 \mathrm{x}$ unit According to question, $x^{2}+4=4 x$<br/>$\Rightarrow \quad x^{2}-4 x+4=0$<br/>$\Rightarrow \quad(\mathrm{x}-2)^{2}=0$<br/>$\Rightarrow \quad \mathrm{x}=2$<br/>$\therefore \quad$ Side of square $=2$ unit</div>


title: the-one-that-does-not-stabilize-2-and-3-structures-of-proteins-is
slug: the-one-that-does-not-stabilize-2-and-3-structures-of-proteins-is-33543
tags: ['Chemistry', 'Biomolecules', 'JEE Main', 'JEE Main 2023 (10 Apr Shift 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The one that does not stabilize <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mo>∘</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>3</mn><mo>∘</mo></msup></math> structures of proteins 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"><mo>–</mo><mi mathvariant="normal">S</mi><mo>–</mo><mi mathvariant="normal">S</mi><mo>–</mo></math>linkage</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi><mo>-</mo></math>bonding</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>–</mo><mi mathvariant="normal">O</mi><mo>–</mo><mi mathvariant="normal">O</mi><mo>–</mo></math>linkage</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">van der Waals forces</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"><mo>–</mo><mi mathvariant="normal">O</mi><mo>–</mo><mi mathvariant="normal">O</mi><mo>–</mo></math>linkage</span> </div>

answer:
<div class="solution"><blockquote><p>Secondary structure of protein refers to local folded structures that form within a polypeptide due to interactions between atoms of the backbone. They are found to exist in two different types of structures <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">α</mi><mo> </mo><mo>–</mo><mo> </mo></math>helix and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">β</mi><mo> </mo><mo>–</mo></math> pleated sheet structures. This structure arises due to the regular folding of the backbone of the polypeptide chain due to hydrogen bonding between <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>CO</mi></math> group and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>NH</mi></math> groups of the peptide bond. Tertiary Structure of Protein arises from further folding of the secondary structure of the protein. H-bonds, electrostatic forces, disulphide linkages, and Vander Waals forces stabilise this structure. The tertiary structure of proteins represents overall folding of the polypeptide chains, further folding of the secondary structure.</p></blockquote></div>


tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-oogonial-cells-start-dividing-and-enter-into-a-of-meiotic-division-and-get-temporarily-arrested-at-that-stage-called-b-during-oogenesis-at-puberty

slug:
the-oogonial-cells-start-dividing-and-enter-into-a-of-meiotic-division-and-get-temporarily-arrested-at-that-stage-called-b-during-oogenesis-at-puberty-81949

question:
<div class="question">The oogonial cells start dividing and enter into __A__ of meiotic division and get temporarily arrested at that stage, called __B__. During oogenesis at puberty, this oocyte gets surrounded by granulosa cells and then called __C__.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">AâMetaphase II; BâPrimary oocyte; CâPrimary follicle</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">AâProphase I; BâPrimary oocyte; CâPrimary follicle</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">AâProphase I; BâSecondary oocyte; CâSecondary follicle</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">AâProphase II; BâSecondary oocyte; CâSecondary follicle</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">AâProphase I; BâPrimary oocyte; CâPrimary follicle</span> </div>

answer:
<div class="solution">During embryonic development in females, the oogonia enter meiosis I and get halted in the pachytene stage of the prophase I (the most prolonged phase of the cell cycle) and are called a primary oocyte. During puberty, the halted meiosis I continue and forms the secondary oocyte and starts meiosis II that stops at metaphase II. In the course of development, the primary oocyte is surrounded by granulosa cells, which release estrogen and is called a primary follicle. During puberty, primary follicle matures and forms the Graafian follicle from which ovulation occurs.</div>


title: the-order-and-degree-of-the-differential-equation-1-dx-dy-2-3-2-dx-2-d-2-y-2-are-respectively
slug: the-order-and-degree-of-the-differential-equation-1-dx-dy-2-3-2-dx-2-d-2-y-2-are-respectively-11747
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The order and degree of the differential equation<br/>$\left[1+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\right]^{3}=\rho^{2}\left[\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]^{2} \quad$ are respectively</div>

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

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

answer:
<div class="solution">Degree of a differential equation is power of the highest order derivative. In the given differential equation,<br/>$\quad\left[1+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\right]^{3}=\rho^{2}\left[\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right]^{2}$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,1</span> </div>
source_db: MarksBatch2_P3.db
title:
the-order-and-degree-of-the-differential-equation-of-parabolas-having-vertex-at-the-origin-and-focus-at-a-0-where-a-0-are-respectively

slug:
the-order-and-degree-of-the-differential-equation-of-parabolas-having-vertex-at-the-origin-and-focus-at-a-0-where-a-0-are-respectively-65795

question:
<div class="question">The order and degree of the differential equation of parabolas having vertex at the origin and focus at $(a, 0)$ where a $&gt;0$, are respectively</div>

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

answer:
<div class="solution">The eq. of parabolas having vertex at $(0,0) \&amp;$ focus at $(a, 0)$, where $(a&gt;0)$ is:<br/>$$<br/>\begin{array}{l}<br/>y^{2}=4 a x \\<br/>2 y \cdot \frac{d y}{d x}=4 a<br/>\end{array}<br/>$$<br/>[on differentiating]<br/>On putting the value of $(4 a)$ in eq. (1) we get,<br/>$$<br/>2 \mathrm{x} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}-\mathrm{y}=0<br/>$$<br/>in order $=1 \&amp;$ degree $=1$.</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,2</span> </div>
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P3.db
title:
the-order-and-degree-of-the-differential-equation-y-2-4-a-x-a-where-a-is-an-arbitrary-constant-are-respectively

slug:
the-order-and-degree-of-the-differential-equation-y-2-4-a-x-a-where-a-is-an-arbitrary-constant-are-respectively-74665

question:
<div class="question">The order and degree of the differential equation $\mathrm{y}^{2}=4 \mathrm{a}(\mathrm{x}-\mathrm{a})$, where $\mathrm{a}$ ' is an arbitrary constant, are respectively</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">2,2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1,1</span> </li> </ul>


title: the-order-of-a-set-a-is-3-and-that-of-a-set-b-is-2-what-is-the-number-of-relations-from-a-to-b
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
slug:
the-order-of-a-set-a-is-3-and-that-of-a-set-b-is-2-what-is-the-number-of-relations-from-a-to-b-98104

question:
<div class="question">The order of a set $A$ is 3 and that of a set $B$ is $2 .$ What is the<br/>number of relations from $A$ to B ?</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">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">32</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">64</span> </li> </ul>

answer:
<div class="solution">Since, order of a set $\mathrm{A}$ is 3 and order of set $\mathrm{B}$ is 2 therefore<br/>$n(A)=3$ and $n(B)=2$<br/>Number of relations from $A$ to $B$<br/>$=n(A) \times n(B)=3 \times 2=6$</div>


title: the-order-of-differential-equation-of-all-circles-of-given-radius-a-is
slug: the-order-of-differential-equation-of-all-circles-of-given-radius-a-is-53970
tags: ['Mathematics', 'Binomial Theorem', 'KCET', 'KCET 2015']
source_db: MarksBatch2_P3.db
question:
<div class="question">The order of differential equation of all circles of given radius ' \( a \) ' is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\( 04 \)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\( 12 \)</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">\( 11 \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( 13 \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 12 \)</span> </div>

answer:
<div class="solution">The standard equation of a circle is<br/>\[<br/>(x-b)^{2}+(y-k)=a^{2}<br/>\]<br/>There are two arbitrary constants.<br/>So, the order of the differential equation is equal to number of arbitrary constants.<br/>Therefore, order \( =2 \)</div>


tags: ['Mathematics', 'Matrices', 'JEE Main']
answer: <div class="solution">Order will be $(1 \times 3)(3 \times 3)(3 \times 1)=(1 \times 1)$</div>
source_db: MarksBatch2_P3.db
title:
the-order-of-leftbeginarraylllx-y-z-rightendarrayleftbeginarrayllla-h-g-h-b-f-g-f-cendarrayrightleftbeginarraylx-y-zendarrayright-is

slug:
the-order-of-leftbeginarraylllx-y-z-rightendarrayleftbeginarrayllla-h-g-h-b-f-g-f-cendarrayrightleftbeginarraylx-y-zendarrayright-is-86409

question:
<div class="question">The order of $\left[\begin{array}{lll}x y z \right]\end{array}\left[\begin{array}{lll}a &amp; h &amp; g \\ h &amp; b &amp; f \\ g &amp; f &amp; c\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$ is</div>

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

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


title: the-order-of-organism-in-an-aquatic-food-chain-is
slug: the-order-of-organism-in-an-aquatic-food-chain-is-46862
question: <div class="question">The order of organism in an aquatic food chain is</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Bacteria, Seal, Diatom, Fish, Crustacea</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Crustacea, Seal, Fish, Polar Bear, Diatom</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Polar Bear, Diatom, Seal, Crustacea</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Diatom, Crustacea, Fish, Seal, Bacteria</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">Diatom, Crustacea, Fish, Seal, Bacteria</span> </div>

answer:
<div class="solution">Diatoms are producer, crustacea is primary consumer, fish is secondary consumer, seal is top consumer and bacteria are decomposers.</div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'TS EAMCET', 'TS EAMCET 2022 (18 Jul Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-order-of-reactivity-of-the-following-compounds-towards-dilute-aqueous-koh-in-s-n-1-reaction-is-ch-3-ch-2-ch-2-ch-2-br-i-h-3-cch-2-chbrch-3-ii-ch-3

slug:
the-order-of-reactivity-of-the-following-compounds-towards-dilute-aqueous-koh-in-s-n-1-reaction-is-ch-3-ch-2-ch-2-ch-2-br-i-h-3-cch-2-chbrch-3-ii-ch-3-89947

question:
<div class="question"><p>The order of reactivity of the following compounds towards dilute aqueous <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>KOH</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">N</mi></msub><mn>1</mn></math> reaction is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><mi>Br</mi></mrow><mi mathvariant="normal">I</mi></munder><mo>  </mo><munder><mrow><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub><msub><mi>CCH</mi><mn>2</mn></msub><msub><mi>CHBrCH</mi><mn>3</mn></msub></mrow><mi>II</mi></munder><mo>  </mo><munder><mrow><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>2</mn></msub><msub><mi>CHCH</mi><mn>2</mn></msub><mi>Br</mi></mrow><mi>III</mi></munder><mo>  </mo><munder><mrow><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>3</mn></msub><mi>CBr</mi></mrow><mi>IV</mi></munder></math></p></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 mathvariant="normal">I</mi><mo>&lt;</mo><mi>IV</mi><mo>&lt;</mo><mi>III</mi><mo>&lt;</mo><mi>II</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"><mi>IV</mi><mo>&lt;</mo><mi>II</mi><mo>&lt;</mo><mi>III</mi><mo>&lt;</mo><mi mathvariant="normal">I</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"><mi>III</mi><mo>&lt;</mo><mi>II</mi><mo>&lt;</mo><mi mathvariant="normal">I</mi><mo>&lt;</mo><mi>IV</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"><mi mathvariant="normal">I</mi><mo>&lt;</mo><mi>III</mi><mo>&lt;</mo><mi>II</mi><mo>&lt;</mo><mi>IV</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"><mi mathvariant="normal">I</mi><mo>&lt;</mo><mi>III</mi><mo>&lt;</mo><mi>II</mi><mo>&lt;</mo><mi>IV</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>The <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">N</mi></msub><mn>1</mn></math> reaction rate depends on the stability of cabocation formed in the rate determining step.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><msub><mi>CH</mi><mn>3</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msub><mi>CH</mi><mn>2</mn></msub><msup><msub><mi>CH</mi><mn>2</mn></msub><mo>+</mo></msup></mrow><mi mathvariant="normal">I</mi></munder><mo>  </mo><munder><mrow><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub><msub><mi>CCH</mi><mn>2</mn></msub><msup><mi>CH</mi><mo>+</mo></msup><msub><mi>CH</mi><mn>3</mn></msub></mrow><mi>II</mi></munder><mo>  </mo><munder><mrow><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>2</mn></msub><msup><msub><mi>CHCH</mi><mn>2</mn></msub><mo>+</mo></msup></mrow><mi>III</mi></munder><mo>  </mo><munder><mrow><msub><mfenced><msub><mi>CH</mi><mn>3</mn></msub></mfenced><mn>3</mn></msub><msup><mi mathvariant="normal">C</mi><mo>+</mo></msup></mrow><mi>IV</mi></munder></math></p><p>Tertiary carbocations are more stable than secondary and primary. Among the carbocations <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi><mo> </mo><mi>and</mi><mo> </mo><mi>III</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi></math> is readily formed than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math>. Hence, the correct reactivity order is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi><mo>&lt;</mo><mi>III</mi><mo>&lt;</mo><mi>II</mi><mo>&lt;</mo><mi>IV</mi></math>.</p></blockquote></div>


title: the-order-of-reactivity-of-the-following-compounds-towards-the-esterification-with-acetic-acid-is
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'TS EAMCET', 'TS EAMCET 2022 (18 Jul Shift 1)']
source_db: MarksBatch2_P3.db
slug:
the-order-of-reactivity-of-the-following-compounds-towards-the-esterification-with-acetic-acid-is-37723

question:
<div class="question"><p>The order of reactivity of the following compounds towards the esterification with acetic acid is</p><p><img height="0" src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/fd0acda8-0f23-4312-bc04-9ed98617191a-image.png" width="0"/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/e24761d1-3d63-4b61-a696-486df4231010-image.png" style="width: 709px; height: 150px;"/></p></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 mathvariant="normal">I</mi><mo>&gt;</mo><mi>II</mi><mo>&gt;</mo><mi>III</mi><mo>&gt;</mo><mi>IV</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"><mi>IV</mi><mo>&gt;</mo><mi>III</mi><mo>&gt;</mo><mi>II</mi><mo>&gt;</mo><mi mathvariant="normal">I</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"><mi mathvariant="normal">I</mi><mo>&gt;</mo><mi>IV</mi><mo>&gt;</mo><mi>II</mi><mo>&gt;</mo><mi>III</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"><mi mathvariant="normal">I</mi><mo>&gt;</mo><mi>IV</mi><mo>&gt;</mo><mi>III</mi><mo>&gt;</mo><mi>II</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"><mi mathvariant="normal">I</mi><mo>&gt;</mo><mi>IV</mi><mo>&gt;</mo><mi>II</mi><mo>&gt;</mo><mi>III</mi></math></span> </div>

answer:
<div class="solution"><blockquote><p>The chemical reaction in which alcohols and acids react with each other to form products as esters is called esterification.</p><p>Here, the organic acid group reacts with alcohol to form stable ester and water.</p><p>The mechanism of this reaction is nucleophilic acyl substitution.During this reaction the cleavage O-H bond of alcohols takes place.The reactivity for this cleavage goes down from primary to tertiary alcohol as the bulkiness of the substitutes on alcohol increases.<br/>The alcohol acts as nucleophile here and also the steric effects support the reactivity order. Thus, tertiary alcohol is the least reactive than primary and secondary.</p><p>So, with acetic acid ethanol reacts the fastest followed by propanol and then 2-methyl propan-ol while the least reactive would be 2-3-dimethyl butan-1-ol.</p><p>Hence, the correct order of reactivity would be <img alt="" src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/c3e9cf60-9235-43fd-951d-4ee42e382a1f-20-09-2022newww.png" style="width: 600px; height: 117px;"/></p><p> </p><p> </p></blockquote></div>


tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-organs-involved-in-the-reproductive-system-can-be-grouped-as-primary-and-secondary-which-of-the-following-is-not-a-secondary-sex-organ-1-prostate-

slug:
the-organs-involved-in-the-reproductive-system-can-be-grouped-as-primary-and-secondary-which-of-the-following-is-not-a-secondary-sex-organ-1-prostate-89656

question:
<div class="question">The organs involved in the reproductive system can be grouped as primary and secondary. Which of the following is not a secondary sex organ?<br/> <br/> <math><mfenced separators="|"><mrow><mn>1</mn></mrow></mfenced></math> Prostate gland<br/> <math><mfenced separators="|"><mrow><mn>2</mn></mrow></mfenced></math> Mammary gland<br/> <math><mfenced separators="|"><mrow><mn>3</mn></mrow></mfenced></math> Seminal vesicle<br/> <math><mfenced separators="|"><mrow><mn>4</mn></mrow></mfenced></math> Ovary</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Only  <math><mfenced separators="|"><mrow><mn>2</mn></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Both  <math><mfenced separators="|"><mrow><mn>2</mn></mrow></mfenced></math>  &amp;  <math><mfenced separators="|"><mrow><mn>4</mn></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Only  <math><mfenced separators="|"><mrow><mn>4</mn></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><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mfenced separators="|"><mrow><mn>1</mn></mrow></mfenced><mo>,</mo><mi>Â </mi><mfenced separators="|"><mrow><mn>2</mn></mrow></mfenced><mi>Â </mi></math> &amp;  <math><mfenced separators="|"><mrow><mn>3</mn></mrow></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Only  <math><mfenced separators="|"><mrow><mn>4</mn></mrow></mfenced></math></span> </div>

answer:
<div class="solution">Ovary is part of the reproductive system and is the primary organ as it is the one that produces the female gametic cell participating in the fertilization process. Other organs, prostate gland, mammary gland, seminal vesicle, come under the secondary group of reproductive organs.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2008 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: MarksBatch2_P3.db
title:
the-outcomes-of-5-tosses-of-a-coin-are-recorded-in-a-single-sequence-as-h-head-and-t-tail-for-each-toss-what-is-the-number-of-elementary-events-in-the

slug:
the-outcomes-of-5-tosses-of-a-coin-are-recorded-in-a-single-sequence-as-h-head-and-t-tail-for-each-toss-what-is-the-number-of-elementary-events-in-the-27992

question:
<div class="question">The outcomes of 5 tosses of a coin are recorded in a single sequence as $\mathrm{H}$ (head) and T (tail) for each toss. What is the number of elementary events in the sample space?</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">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">C</span> <span class="option-data">25</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">32</span> </li> </ul>

answer:
<div class="solution">A coin has two faces and is tossed 5 times. So, number of elements in the sample space $=10$.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-outcomes-of-an-experiment-classified-as-success-a-or-failure-a-will-followa-binomial-distribution-if

slug:
the-outcomes-of-an-experiment-classified-as-success-a-or-failure-a-will-followa-binomial-distribution-if-38352

question:
<div class="question">The outcomes of an experiment classified as success $A$ or failure $A$ will followa binomial distribution, if</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$P(A)=1 / 2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$P(A)=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$P(A)=1$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$P(A)$ remains constant in all trials</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">$P(A)$ remains constant in all trials</span> </div>

answer:
<div class="solution">Given, the outcomes of an experiment classified as success A will follow a binomial distribution if $\mathrm{P}(\mathrm{A})$ remains constant in all trials.</div>


title: the-outermost-limiting-layer-of-mycoplasma-is-made-up-of
slug: the-outermost-limiting-layer-of-mycoplasma-is-made-up-of-94040
question: <div class="question">The outermost limiting layer of mycoplasma is made up of</div>
tags: ['Biology', 'Biological Classification', 'AIIMS', 'AIIMS 2009']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">cell wall</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">cell membrane</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">mucilaginous sheath</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">slime layer.</span> </li> </ul>

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

answer:
<div class="solution">Mycoplasma are the smallest and simplest free living Gram negative prokaryotes or monerans. A cell wall is absent. Plasma membrane forms the outer boundary of the cell. A substantial amount of polysaccharides having acetyl glucosamine are associated with cell membrane.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'KCET', 'KCET 2017']
source_db: MarksBatch2_P3.db
title:
the-output-of-a-step-down-transformer-is-measured-to-be-48-mathrmv-when-connected-to-a-12-mathrmw-bulb-the-value-of-peak-current-is

slug:
the-output-of-a-step-down-transformer-is-measured-to-be-48-mathrmv-when-connected-to-a-12-mathrmw-bulb-the-value-of-peak-current-is-87637

question:
<div class="question">The output of a step down transformer is measured to be \( 48 \mathrm{~V} \) when connected to a \( 12 \mathrm{~W} \)<br/>bulb. The value of peak current is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">( \( \frac{1}{\sqrt{2}} \mathrm{~A} \)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\( \sqrt{2} A \)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\( \frac{1}{2 \sqrt{2}} A \)</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">\( \frac{1}{4} A \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( \frac{1}{2 \sqrt{2}} A \)</span> </div>

answer:
<div class="solution">Given, output of step down transformer is $48 \mathrm{~V}$<br/>$\Rightarrow$ peak secondary voltage $V_{s}=48 \mathrm{v}$<br/>Also, power at secondary $P_{s}=12 W$<br/>Now, current at secondary, $I_{s}=\frac{P_{s}}{V_{s}}=\frac{12}{48}=0.25 \mathrm{~A}$<br/>Thus, value of peak current is $I_{S} \sqrt{2}=0.25 \times \sqrt{2}=\frac{1}{2 \sqrt{2}} A$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-output-of-a-step-down-transformers-is-measured-to-be-48-v-when-connected-to-a-12-w-bulb-the-value-of-peak-current-is-1

slug:
the-output-of-a-step-down-transformers-is-measured-to-be-48-v-when-connected-to-a-12-w-bulb-the-value-of-peak-current-is-1-74244

question:
<div class="question">The output of a step down transformers is measured to be 48 V when connected to a 12 W bulb. The value of peak current is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo> A</mo></math></span> </div>

answer:
<div class="solution">Given,<br/><br/>Output of step down transformer <math><mfenced separators="|"><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>48</mn><mi> </mi><mo>V</mo></math><br/><br/>Power associated with secondary coil <math><mfenced separators="|"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>12</mn><mi> </mi><mo>W</mo></math><br/><br/><math><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>48</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mn>0.25</mn><mi> </mi><mo>A</mo></math><br/><br/>Amplitude of current <math><mfenced separators="|"><mrow><msub><mrow><mi>I</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mfenced><mo>=</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><msqrt><mn>2</mn></msqrt></math><br/><br/><math><mo>=</mo><mn>0.25</mn><mi> </mi><mfenced separators="|"><mrow><msqrt><mn>2</mn></msqrt></mrow></mfenced></math><br/><br/><math><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac></math><br/><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>A</mo></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-output-of-a-step-down-transformers-is-measured-to-be-48-v-when-connected-to-a-12-w-bulb-the-value-of-peak-current-is

slug:
the-output-of-a-step-down-transformers-is-measured-to-be-48-v-when-connected-to-a-12-w-bulb-the-value-of-peak-current-is-94283

question:
<div class="question">The output of a step down transformers is measured to be 48 V when connected to a 12 W bulb. The value of peak current is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo> A</mo></math></span> </div>

answer:
<div class="solution">Given,<br/><br/>Output of step down transformer <math><mfenced separators="|"><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>48</mn><mi> </mi><mo>V</mo></math><br/><br/>Power associated with secondary coil <math><mfenced separators="|"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>12</mn><mi> </mi><mo>W</mo></math><br/><br/><math><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>48</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mn>0.25</mn><mi> </mi><mo>A</mo></math><br/><br/>Amplitude of current <math><mfenced separators="|"><mrow><msub><mrow><mi>I</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mfenced><mo>=</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><msqrt><mn>2</mn></msqrt></math><br/><br/><math><mo>=</mo><mn>0.25</mn><mi> </mi><mfenced separators="|"><mrow><msqrt><mn>2</mn></msqrt></mrow></mfenced></math><br/><br/><math><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac></math><br/><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>A</mo></math></div>


tags: ['Physics', 'Alternating Current']
source_db: MarksBatch2_P3.db
title:
the-output-of-a-stepdown-transformer-is-measured-to-be-24-v-when-connected-to-a-12-w-light-bulb-the-value-of-the-peak-current-is

slug:
the-output-of-a-stepdown-transformer-is-measured-to-be-24-v-when-connected-to-a-12-w-light-bulb-the-value-of-the-peak-current-is-88906

question:
<div class="question">The output of a step-down transformer is measured to be $24 \mathrm{~V}$ when connected to a $12 \mathrm{~W}$ light bulb. The value of the peak current is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$1 / \sqrt{2} \mathrm{~A}$<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/>$\sqrt{2} \mathrm{~A}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$2 \mathrm{~A}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$2 \sqrt{2} \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1 / \sqrt{2} \mathrm{~A}$<br/></span> </div>

answer:
<div class="solution">As given that, Secondary voltage $\left(\mathrm{V}_{\mathrm{S}}\right)$ is :<br/>$$<br/>\mathrm{V}_{\mathrm{S}}=24 \text { Volt }<br/>$$<br/>Power associated with secondary is :<br/>$$<br/>\mathrm{P}_{\mathrm{S}}=12 \mathrm{Watt}<br/>$$<br/>As we know that $P_S=V_S I_S$<br/>$$<br/>\mathrm{I}_{\mathrm{S}}=\frac{\mathrm{P}_{\mathrm{S}}}{\mathrm{V}_{\mathrm{S}}}=\frac{12}{24}=\frac{1}{2} \mathrm{~A}=0.5 \mathrm{Amp}<br/>$$<br/>Peak value of the current in the secondary<br/>$$<br/>\begin{aligned}<br/>I_0 &amp;=I_S \sqrt{2}=0.5 \sqrt{2} \\<br/>&amp;=\frac{5}{10} \sqrt{2}\left[I_0=\frac{1}{\sqrt{2}} \text { Amp }\right]<br/>\end{aligned}<br/>$$</div>


title: the-ovule-of-an-angiosperm-is-technically-equivalent-to
slug: the-ovule-of-an-angiosperm-is-technically-equivalent-to-89943
question: <div class="question">The ovule of an angiosperm is technically equivalent to</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET', 'NEET 2016 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Megasporangium</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">Megasporophyll</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Megaspore mother cell</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Megaspore</span> </li> </ul>

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

answer:
<div class="solution">The angiosperms are heterosporous. The stamens of the flower are the male sexual parts and they are highly modified leaves called microsporophylls. The microsporophylls produce anthers or microsporangia.  Within the anther, there are special diploid cells called pollen mother cell or microspore mother cells. The microspore mother cells undergo meiosis to produce haploid microspores or pollen grains. The microspore produces a few celled male gametophytes, each male gametophyte has two cells tube cell and a generative cell. Gynoecium or pistil is the female sexual parts. The gynoecium is made up of highly modified leaves called megasporophylls or carpels. The megasporophylls fused to form ovaries. The function of carpels is to produce ovules or megasporangia. Within the ovules, there are specialized cells called the megaspore mother cells (2n). The megaspores mother cells are diploid (2n) which undergo meiosis or reduction division to form haploid megaspores (n). The megaspores produce a multicellular female gametophyte or embryo sac. The mature embryo sac has a group of three antipodal cells, two synergid cells, one female gamete or egg cell. There are two haploid polar nuclei which fuse together to produce a diploid secondary nucleus.</div>


tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-part-of-the-embryosac-which-helps-in-guiding-the-pollen-tube-towards-it-is-p-and-it-is-through-q

slug:
the-part-of-the-embryosac-which-helps-in-guiding-the-pollen-tube-towards-it-is-p-and-it-is-through-q-95800

question:
<div class="question">The part of the embryosac which helps in guiding the pollen tube towards it is __(P)___ and it is through ___(Q)____.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">P is antipodal cells and Q is thigmotaxis</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">P is egg and Q is chemotaxis</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">P is a secondary nucleus and Q is thigmotaxis</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">P is synergids and Q is chemotaxis</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">P is synergids and Q is chemotaxis</span> </div>

answer:
<div class="solution">Synergids secrete a chemical to attract pollen tube towards the embryo sac. Thus, the movement of the pollen tube is under the influence of a chemical and is called chemotaxis. The pollen tube enters into the embryo sac with the help of the filiform apparatus of synergids.</div>


tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'AP EAMCET', 'AP EAMCET 2022 (07 Jul Shift 1)']
source_db: MarksBatch2_P3.db
title:
the-percentage-of-abundance-of-three-elements-x-y-and-z-in-the-earths-crust-are-about-277-83-and-460-by-mass-respectively-x-y-and-z-are

slug:
the-percentage-of-abundance-of-three-elements-x-y-and-z-in-the-earths-crust-are-about-277-83-and-460-by-mass-respectively-x-y-and-z-are-45667

question:
<div class="question">The percentage of abundance of three elements $X, Y$ and $Z$ in the earth's crust are about $27.7,8.3$ and 46.0 by mass respectively. $X, Y$ and $\dot{Z}$ are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">O, Si, Al</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Al, Si; O</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{Si}, \mathrm{Al}, \mathrm{O}$</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">$\mathrm{Al}, \mathrm{O}, \mathrm{Si}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Si}, \mathrm{Al}, \mathrm{O}$</span> </div>

answer:
<div class="solution">Percentage abundance of elements in earth's crust are<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/fsETCcEDzoCEaDbMkH8fNoMyV3T1_Kng-_c4b31k_NM.original.fullsize.png"/></div>


title: the-periderm-is-produced-by
slug: the-periderm-is-produced-by-57409
question: <div class="question">The periderm is produced by:</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">vascular cambium</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">fascicular cambium</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">phellogen</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">intrafascicular cambium</span> </li> </ul>

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

answer:
<div class="solution">A periderm is a group of cylindrical tissues that forms a protective layer and cover the stems and roots of many plants during the secondary growth. These tissues are usually found in perennial plants and consist of three different layers, the phelloderm (inner surface of the cork cambium), the phellogen (meristematic tissue called the cork cambium) which gives rise to the periderm and the phellem which is the suberized cells.</div>


title: the-perisperm-is-the
slug: the-perisperm-is-the-29537
question: <div class="question">The perisperm is the</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">degenerate part of synergids</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">peripheral part of endosperm</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">degenerate part of secondary nucleus</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">remnant of nucellus</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">remnant of nucellus</span> </div>

answer:
<div class="solution">In some seeds such as black pepper and beet, remnants of nucellus are also persistent. This residual, persistent nucellus is the perisperm.</div>


title: the-perpendicular-distance-between-the-straight-lines-6-x-8-y-15-0-and-3-x-4-y-9-0-is
slug: the-perpendicular-distance-between-the-straight-lines-6-x-8-y-15-0-and-3-x-4-y-9-0-is-24233
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The Perpendicular distance between the straight lines $6 x+8 y+15=0$ and $3 x+4 y+9=0$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3}{2}$ units</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{3}{10}$ unit</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">$\frac{3}{4}$ unit</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2}{7}$ unit</span> </li> </ul>

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

answer:
<div class="solution">$6 \mathrm{x}+8 \mathrm{y}+15=0$...(i)<br/>and $3 x+4 y+9=0$ ...(ii)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/HQdVRaZA0gD_JAWJZNHC9EP-g5CbGnr0ZdNTCbPEuuw.original.fullsize.png"/><br/><br/>Multiply equation (ii) by 2 , we get $6 x+8 y+18=0$<br/>Distance between the straight lines<br/>$\frac{\left|c_{2}-c_{1}\right|}{\sqrt{a^{2}+b^{2}}}=\frac{18-15}{\sqrt{(6)^{2}+(8)^{2}}}=\frac{3}{10}$ unit<br/>Option (b) is correct.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-perpendiculars-that-fall-from-any-point-of-the-straight-line-2-x-11-y-5-upon-the-two-straight-lines-24-x-7-y-20-and-4-x-3-y-2-are

slug:
the-perpendiculars-that-fall-from-any-point-of-the-straight-line-2-x-11-y-5-upon-the-two-straight-lines-24-x-7-y-20-and-4-x-3-y-2-are-97525

question:
<div class="question">The perpendiculars that fall from any point of the straight line $2 \mathrm{x}+11 \mathrm{y}=5$ upon the two straight lines $24 \mathrm{x}+7 \mathrm{y}=20$ and $4 x-3 y=2$ are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">12 and 4 respectively</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">11 and 5 respectively</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Equal to each other</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">Not equal to each other</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Equal to each other</span> </div>

answer:
<div class="solution">We know, the perpendicular distance (d) from point<br/>$\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$ to line $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$ is $\frac{\mid \mathrm{ax}_{1}+\mathrm{by}_{1}+\mathrm{c}}{\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}}$<br/>Let us find a point on line $2 x+11 y-5=0$. for $\mathrm{x}=0,2(0)+11 \mathrm{y}-5=0$<br/>$\Rightarrow 11 \mathrm{y}-5=0$<br/>$\Rightarrow \mathrm{y}=\frac{5}{11}$<br/>So, $(\mathrm{x}, \mathrm{y})=\left(0, \frac{5}{11}\right)$<br/>Let us find perpendicular distances of this point to the given lines.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/bPN4QF6ysyubmdm6QXdIKzQ2W-Fo-HSqIc8LTGVQVgU.original.fullsize.png"/><br/><br/>$\therefore \quad d_{1}=d$</div>


title: the-ph-at-the-equivalence-point-of-a-titration-may-differ-from-70-because-of
slug: the-ph-at-the-equivalence-point-of-a-titration-may-differ-from-70-because-of-26900
tags: ['Chemistry', 'Ionic Equilibrium', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The pH at the equivalence point of a titration may differ from 7.0 because of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">the initial concentration of the standard solution</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">the indicator used</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">the self-ionization of <math><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">hydrolysis of the salt formed</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">hydrolysis of the salt formed</span> </div>

answer:
<div class="solution">The pH at the equivalence point of a titration may differ from 7.0 because of hydrolysis of the salt formed as due to salt-hydrolysis, the solution may become either acidic or alkaline at equivalence point.</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2022 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-phenomenon-by-which-the-undividing-parenchyma-cells-start-to-divide-mitotically-during-plant-tissue-culture-is-called-as

slug:
the-phenomenon-by-which-the-undividing-parenchyma-cells-start-to-divide-mitotically-during-plant-tissue-culture-is-called-as-99481

question:
<div class="question">The phenomenon by which the undividing parenchyma cells start to divide mitotically during plant tissue culture is called as :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Differentiation</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Dedifferentiation</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">Redifferentiation</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Secondary growth</span> </li> </ul>

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

answer:
<div class="solution">The process of conversion of a Non-dividing (permanent cell) to a dividing cell is called de-differentiation. This is an important process for secondary growth which taken place in plants.</div>


title: the-phenomenon-of-dedifferentiation-is
slug: the-phenomenon-of-dedifferentiation-is-97359
question: <div class="question">The phenomenon of dedifferentiation is</div>
tags: ['Biology', 'Plant - Growth and Development', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">regaining the capacity to divide mitotically by differentiated cells </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">the event of losing the ability to divide by dedifferentiated cells</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">regaining the capacity to divide meiotically by differentiated cells </span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">regaining the capacity to divide meiotically by redifferentiated cells </span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">regaining the capacity to divide mitotically by differentiated cells </span> </div>

answer:
<div class="solution">The living differentiated cells that have lost the capability to divide can regain the capacity of the division under certain conditions; this phenomenon is called dedifferentiation. It occurs during secondary growth when permanent cell-like parenchyma regains the power of division to form vascular cambium and cork cambium. The redifferentiation is the event of losing the ability to divide by dedifferentiated cells.</div>


title: the-planes-p-x-2-y-2-z-3-0-and-2-x-y-z-2-0-intersect-at-an-angle-4-what-is-the-value-of-p-2
slug: the-planes-p-x-2-y-2-z-3-0-and-2-x-y-z-2-0-intersect-at-an-angle-4-what-is-the-value-of-p-2-77182
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">24</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The planes $p x+2 y+2 z-3=0$ and $2 x-y+z+2=0$ intersect<br/>at an angle $\frac{\pi}{4}$. What is the value of $p^{2}$ ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">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">B</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3</span> </li> </ul>

answer:
<div class="solution">We know that the angle between the planes $a_{1} x+b_{1} y$ $+c_{1} z+d_{1}=0$ and $a_{2} x+b_{2} y+c_{2} z+d_{2}=0$ is given by<br/>$\cos \theta=\left|\frac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2} \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}}\right|$<br/>Given equation of planes are $p x+2 y+2 z-3=0$ and $2 x-y+z+2=0$<br/>On comparing with standard equations, we get<br/>$a_{1}=p, a_{2}=2, b_{1}=2, b_{2}=-1, \quad c_{1}=2, c_{2}=1$<br/>Also, $\theta=\frac{\pi}{4} \quad$ (given)<br/>$\cos \frac{\pi}{4}=\left|\frac{p \times 2+2 \times(-1)+2 \times 1}{\sqrt{p^{2}+4+4} \sqrt{4+1+1}}\right|$<br/>$\Rightarrow \frac{1}{\sqrt{2}}=\frac{2 p}{\sqrt{p^{2}+8} \sqrt{6}} \Rightarrow \frac{1}{2}=\frac{4 p^{2}}{\left(p^{2}+8\right) 6}$<br/>$\Rightarrow \frac{3}{4}=\frac{p^{2}}{p^{2}+8}$<br/>$\Rightarrow 3 p^{2}+24=4 p^{2} \Rightarrow p^{2}=24$</div>


title: the-plant-part-that-possesses-polyarch-condition-of-vascular-bundles-with-a-welldeveloped-pith-is
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
slug:
the-plant-part-that-possesses-polyarch-condition-of-vascular-bundles-with-a-welldeveloped-pith-is-28418

question:
<div class="question">The plant part that possesses polyarch condition of vascular bundles with a well-developed pith is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">dicot root.</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">monocot root.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">dicot stem.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">monocot stem.</span> </li> </ul>

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

answer:
<div class="solution">Dicot root possesses diarch to hexarch (2-6) vascular bundles. Vascular bundle refers to the xylem and phloem tissue which help in water and organic matter transport in different parts of plant. Dicot root has smaller pith and well-developed cambium tissue for secondary growth.</div>


tags: ['Biology', 'Cell - The Unit of Life', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-plasma-membrane-is-the-boundary-between-a-cells-internal-and-external-environments-both-environments-are-aqueous-to-allow-the-separation-of-these-

slug:
the-plasma-membrane-is-the-boundary-between-a-cells-internal-and-external-environments-both-environments-are-aqueous-to-allow-the-separation-of-these-20617

question:
<div class="question">The plasma membrane is the boundary between a cell's internal and external environments. Both environments are aqueous.<br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/ci/image12-02ba1ce7-9bc1-45fe-89f3-7ba7132a381b.jpg"/><br/> <br/>
To allow the separation of these aqueous environments, the regions of the plasma membrane indicated in the diagram have which of the following properties?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">(X) hydrophilic layers on the outside and (Y) hydrophobic layers on the inside of the membrane</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">X and Y are both hydrophobic layers</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">(X) hydrophobic layers on the outside and (Y) hydrophilic layers on the inside of the membrane</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">X and Y are both hydrophilic layers.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(X) hydrophilic layers on the outside and (Y) hydrophobic layers on the inside of the membrane</span> </div>

answer:
<div class="solution">Fatty acid heads are hydrophilic in nature, and their hydrocarbon tails are hydrophobic in nature. Lipids found in plasma membrane form bilayer in such a way that their hydrophilic head faces outside and hydrophobic hydrocarbon tail is sandwich between hydrophilic heads.</div>


title: the-ploidy-level-is-not-the-same-in
slug: the-ploidy-level-is-not-the-same-in-62523
question: <div class="question">The ploidy level is not the same in</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Integument and nucellus</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Root tip and shoot tip</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Secondary nucleus and endosperm</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">Antipodals and synergids</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Secondary nucleus and endosperm</span> </div>

answer:
<div class="solution">Double fertilization is a unique characteristic observed in the Angiosperm group of plants. In this, two fertilizations are observed - <math><msup><mrow><mn>1</mn></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi></mrow></msup></math> between the female and male gametic cells forming zygote and <math><msup><mrow><mn>2</mn></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi></mrow></msup></math> is between the second male gamete and polar nuclei forming the primary endosperm nucleus. The ploidy of PEN is 3n (male gamete[1n] + polar nuclei[2n]). The polar nuclei are also called as secondary nucleus which is 2n. Endosperm (3n) and secondary nucleus do not have the same ploidy level.</div>


title: the-point-in-the-interval-0-2-where-f-x-e-x-sin-x-has-maximumslope-is
slug: the-point-in-the-interval-0-2-where-f-x-e-x-sin-x-has-maximumslope-is-54262
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The point in the interval $(0,2 \pi)$ where $\mathrm{f}(\mathrm{x})=\mathrm{e}^{\mathrm{x}} \sin \mathrm{x}$ has<br/>maximumslope is</div>

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

answer:
<div class="solution">Given $f(x)=e^{x} \sin x$<br/>$\Rightarrow f^{\prime}(x)=e^{x} \cos x+e^{x} \sin x$<br/>$\Rightarrow$ slope $=e^{x}(\cos x+\sin x)$<br/>Now, $\frac{d}{d x}(\cos x+\sin x)=0$<br/>$\Rightarrow-\sin x+\cos x=0$<br/>$\Rightarrow \sin x=\cos x \Rightarrow \tan x=1 \Rightarrow x=\frac{\pi}{4}$</div>


title: the-point-of-intersection-of-the-line-joining-the-points-3-4-8-and-5-6-4-with-the-xyplane-is
slug: the-point-of-intersection-of-the-line-joining-the-points-3-4-8-and-5-6-4-with-the-xyplane-is-63869
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The point of intersection of the line joining the points $(-3,4,-8)$ and $(5,-6,4)$ with the XY-plane is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left(\frac{7}{3},-\frac{8}{3}, 0\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(-\frac{7}{3},-\frac{8}{3}, 0\right)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(-\frac{7}{3}, \frac{8}{3}, 0\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(\frac{7}{3}, \frac{8}{3}, 0\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{7}{3},-\frac{8}{3}, 0\right)$</span> </div>

answer:
<div class="solution">The equation of the line joining the points $(-3,4,-8)$ and $(5,-6,4)$ is<br/>$\frac{x+3}{8}=\frac{y-4}{-10}=\frac{z+8}{12}=k($ say $)$<br/>$8 \quad-10 \quad 12$<br/>$\Rightarrow x+3=8 k ; y-4=-10 k ; z+8=12 k$<br/>$\Rightarrow x=8 k-3 ; y=-10 k+4 ; z=12 k-8$<br/>Given that this line intersects with $x y$ plane. $S o, z=0$<br/>$12 \mathrm{k}-8=0 \Rightarrow 12 \mathrm{k}=8 \Rightarrow \mathrm{k}=\frac{8}{12}=\frac{2}{3}$<br/>$\mathrm{x}=8\left(\frac{2}{3}\right)-3 ; \mathrm{y}=-10\left(\frac{2}{3}\right)+4 ; \mathrm{z}=12\left(\frac{2}{3}\right)-8$<br/>$\Rightarrow \mathrm{x}=\frac{16}{3}-3 ; \mathrm{y}=\frac{-20}{3}+4 ; \mathrm{z}=\frac{24}{3}-8$<br/>$\Rightarrow x=\frac{7}{3} ; y=\frac{-8}{3} ; z=0$<br/>$(x, y, z)=\left(\frac{7}{3}, \frac{-8}{3}, 0\right)$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-point-of-intersection-of-the-two-lines-2-x-3-y-4-0-and-4-x-3-y-2-0-is-at-a-distance-d-from-origin-what-is-the-value-of-d

slug:
the-point-of-intersection-of-the-two-lines-2-x-3-y-4-0-and-4-x-3-y-2-0-is-at-a-distance-d-from-origin-what-is-the-value-of-d-49963

question:
<div class="question">The point of intersection of the two lines $2 x+3 y+4=0$ and $4 x+3 y+2=0$ is at a distance $d$ from origin. What is the value of $d ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sqrt{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\sqrt{5}$</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">D</span> <span class="option-data">$\sqrt{7}$</span> </li> </ul>

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

answer:
<div class="solution">Given equations are<br/>$$<br/>2 x+3 y+4=0 ...(i)<br/>$$ <br/>and $4 x+3 y+2=0$...(ii)<br/>On solving (i) and (ii), the coordinates of the intersecting point are $(1,-2)$<br/>Now, $\sqrt{(0-1)^{2}+\{0-(-2)\}^{2}}=d$<br/>$\Rightarrow d=\sqrt{1+4}=\sqrt{5}$</div>


title: the-point-on-the-parabola-y-2-4-a-x-nearest-to-the-focus-has-its-abscissa
slug: the-point-on-the-parabola-y-2-4-a-x-nearest-to-the-focus-has-its-abscissa-52570
tags: ['Mathematics', 'Parabola', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$x=0$</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The point on the parabola $y^{2}=4 a x$ nearest to the focus has its abscissa</div>

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

answer:
<div class="solution">Here, 'S' represents focus $\mathrm{O}(0,0)$ is apoint which is on parabola $y^{2}=4 a x$ and nearest to focus $(a, 0)$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/jT5WFbBQKNiEzIvVx1Ti6IVI2vBhqZSHO0xjSwPv2N0.original.fullsize.png"/><br/><br/>$\therefore$ abscissa of $\mathrm{O}(0,0)$ is $\mathrm{x}=0$<br/>4. Option (a) is correct.</div>


title: the-point-whose-abscissa-is-equal-to-its-ordinate-and-which-is-equidistant-from-a-1-0-and-b-0-5-is
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P3.db
slug:
the-point-whose-abscissa-is-equal-to-its-ordinate-and-which-is-equidistant-from-a-1-0-and-b-0-5-is-53182

question:
<div class="question">The point whose abscissa is equal to its ordinate and which is equidistant from $\mathrm{A}(-1,0)$ and $\mathrm{B}(0,5)$ is $\quad$</div>

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

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

answer:
<div class="solution">Let the required point be $\mathrm{P}(\mathrm{x}, \mathrm{x})$ Since $\mathrm{PA}=\mathrm{PB}$<br/>$\Rightarrow \quad(\mathrm{PA})^{2}=(\mathrm{PB})^{2}$<br/>$\Rightarrow \quad(\mathrm{x}+1)^{2}+\mathrm{x}^{2}=\mathrm{x}^{2}+(\mathrm{x}-5)^{2}$<br/>$\Rightarrow \quad x^{2}+1+2 x=x^{2}+25-10 x$<br/>$\Rightarrow \quad 12 \mathrm{x}=24 \Rightarrow \mathrm{x}=2$<br/>Hence, Required point is $(2,2)$.</div>


title: the-points-1-3-4-1-6-10-7-4-7-and-5-1-1-are-the-vertices-of-a
slug: the-points-1-3-4-1-6-10-7-4-7-and-5-1-1-are-the-vertices-of-a-45420
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The points $(1,3,4),(-1,6,10),(-7,4,7)$ and $(-5,1,1)$ are the vertices of a</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">rhombus</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">rectangle</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">parallelogram</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">square</span> </li> </ul>

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

answer:
<div class="solution">Let $(1,3,4),(-1,6,10),(-7,4,7)$ and $(-5,1,1)$ be the<br/>coordinates of points $A, B, C$ and $D$ respectively.<br/>$\begin{aligned} A B &amp;=\sqrt{(-1-1)^{2}+(6-3)^{2}+(10-4)^{2}} \\ &amp;=\sqrt{4+9+36}=7 \\ B C &amp;=\sqrt{(-7+1)^{2}+(4-6)^{2}+(7-10)^{2}} \\ &amp;=\sqrt{36+4+9}=7 \\ C D &amp;=\sqrt{(-5+7)^{2}+(1-4)^{2}+(1-7)^{2}} \\ &amp;=\sqrt{4+9+36}=7 \\ D A &amp;=\sqrt{(1+5)^{2}+(3-1)^{2}+(4-1)^{2}} \\ &amp;=\sqrt{36+4+9}=7 \\ A C &amp;=\sqrt{(-7-1)^{2}+(4-3)^{2}+(7-4)^{2}} \\ &amp;=\sqrt{64+1+9}=\sqrt{74} \end{aligned}$<br/>and $B D=\sqrt{(-5+1)^{2}+(1-6)^{2}+(1-10)^{2}}$<br/>$=\sqrt{16+25+81}=\sqrt{122}$<br/>$\therefore A B=B C=C D=D A$<br/>But $B D \neq A C$<br/>\therefore Points $A$, $B, C$ and $D$ are the vertices of a rhombus</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2019 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-4$</span> </div>
source_db: MarksBatch2_P3.db
title:
the-points-1-3-and-5-1-are-two-opposite-vertices-of-a-rectangle-the-other-two-vertices-lie-on-the-line-y-2-x-c-what-is-the-value-of-c

slug:
the-points-1-3-and-5-1-are-two-opposite-vertices-of-a-rectangle-the-other-two-vertices-lie-on-the-line-y-2-x-c-what-is-the-value-of-c-25665

question:
<div class="question">The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $\mathrm{y}=2 \mathrm{x}+\mathrm{c}$. What is the value of c?</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">$-2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">Given, opposite vertices of rectangle are $\mathrm{A}(1,3)$ and $\mathrm{C}$ $(5,1)$<br/>We know, diagonals of rectangle bisect each other. So, midpoint of AC lies on line $\mathrm{y}=2 \mathrm{x}+\mathrm{c}$.<br/>Mid point of $\mathrm{AC}=\left(\frac{1+5}{2}, \frac{3+1}{2}\right)=\left(\frac{6}{2}, \frac{4}{2}\right)=(3,2)$<br/>$\mathrm{y}=2 \mathrm{x}+\mathrm{c} \Rightarrow 2=2(3)+\mathrm{c}$<br/>$\Rightarrow c=2-6=-4$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-points-2-2-8-4-4-6-and-1-1-in-order-are-the-vertices-of-which-one-of-the-following-quadrilaterals

slug:
the-points-2-2-8-4-4-6-and-1-1-in-order-are-the-vertices-of-which-one-of-the-following-quadrilaterals-28644

question:
<div class="question">The points $(2,-2),(8,4),(4,6)$ and $(-1,1)$ in order are the vertices of which one of the following quadrilaterals?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Square</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Rhombus</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Rectangle(but not square)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Trapezium</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">Trapezium</span> </div>

answer:
<div class="solution">Let points be $\mathrm{A}(2,-2), \mathrm{B}(8,4), \mathrm{C}(4,6)$ and $\mathrm{D}(-1,1)$ in<br/>order and are vertices of a quadrilateral. $\mathrm{AB}^{2}=(8-2)^{2}+(4+2)^{2}=36+36=72$<br/>$\mathrm{BC}^{2}=(4-8)^{2}+(6-4)^{2}=16+4=20$<br/>$\mathrm{CD}^{2}=(4+1)^{2}+(6-1)^{2}=25+25=50$<br/>$\mathrm{AD}^{2}=(2+1)^{2}+(-2-1)^{2}=9+9=18$<br/>Thus $\mathrm{AB} \neq \mathrm{BC} \neq \mathrm{CD} \neq \mathrm{AD}$<br/>Hence, quadrilateral is a trapezium.</div>


title: the-points-5-1-1-1-and-11-4-are
slug: the-points-5-1-1-1-and-11-4-are-52693
question: <div class="question">The points $(5,1),(1,-1)$ and $(11,4)$ are:</div>
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">collinear</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">vertices of right angled triangle</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">vertices of equilateral triangle</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">vertices of an isosceles triangle</span> </li> </ul>

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

answer:
<div class="solution">Let $\mathrm{A}(5,1) ; \mathrm{B}(1,-1)$ and $\mathrm{C}(11,4)$ are the given points.<br/>Slope of $A B=\frac{-1-1}{-4}=\frac{-2}{-4}=\frac{1}{2}$<br/>Slope of $\mathrm{BC}=\frac{4-(-1)}{11-1}=\frac{5}{10}=\frac{1}{2}$<br/>Slope of $\mathrm{AB}=$ Slope of $\mathrm{BC}$ $\Rightarrow \quad \mathrm{AB} \| \mathrm{BC}$ and $\mathrm{B}$ is a common point<br/>$\Rightarrow$ Points, $A, B, C$ lie on a same straight line. $\Rightarrow \mathrm{A}(5,1) ; \mathrm{B}(1,-1)$ and $\mathrm{C}(11,4)$ are collinear.</div>


title: the-points-a-b-0-0-a-b-and-ab-b-2-are
slug: the-points-a-b-0-0-a-b-and-ab-b-2-are-92192
question: <div class="question">The points $(a, b),(0,0),(-a,-b)$ and $\left(a b, b^{2}\right)$ are</div>
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">the vertices of a parallelogram</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">the vertices of a rectangle</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">the vertices of a square</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">collinear</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the vertices of a rectangle</span> </div>

answer:
<div class="solution">Given points, $\mathrm{A}(\mathrm{a}, \mathrm{b}), \mathrm{B}(0,0), \mathrm{C}(-\mathrm{a},-\mathrm{b}), \mathrm{D}\left(\mathrm{ab}, \mathrm{b}^{2}\right)$.<br/>Slope of $A B=\frac{b-0}{a-0}=\frac{b}{a}$<br/>Slope of $\mathrm{BC}=\frac{\mathrm{b}}{\mathrm{a}}$<br/>Slope of $A C=\frac{b}{a}$<br/>Slope of $\mathrm{BD}=\frac{\mathrm{b}}{\mathrm{a}}$.<br/>So. the points are collinear.</div>


tags: ['Mathematics', 'Ellipse', 'AP EAMCET', 'AP EAMCET 2018 (25 Apr Shift 1)']
source_db: MarksBatch2_P3.db
title:
the-points-of-intersection-of-the-perpendicular-tangents-drawn-to-the-ellipse-4-x-2-9-y-2-36-lie-on-the-curve-1

slug:
the-points-of-intersection-of-the-perpendicular-tangents-drawn-to-the-ellipse-4-x-2-9-y-2-36-lie-on-the-curve-1-21784

question:
<div class="question">The points of intersection of the perpendicular tangents drawn to the ellipse <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>36</mn></math> lie on the curve </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"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>13</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"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>5</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"><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>5</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"><mfrac><msup><mi>x</mi><mn>2</mn></msup><mn>9</mn></mfrac><mo>+</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mn>4</mn></mfrac><mo>=</mo><mn>1</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"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>13</mn></math></span> </div>

answer:
<div class="solution"><p>Given:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>36</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mn>9</mn></mfrac><mo>+</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mn>4</mn></mfrac><mo>=</mo><mn>1</mn></math></p><p>Comparing with the standard form <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>x</mi><mn>2</mn></msup><msup><mi>a</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><msup><mi>b</mi><mn>2</mn></msup></mfrac><mo>=</mo><mn>1</mn></math>, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mn>2</mn></msup><mo>=</mo><mn>9</mn><mo> </mo><mo>&amp;</mo><mo> </mo><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn></math></p><p>Now, we know that the locus of two perpendicular tangents drawn to the ellipse is the director circle of the ellipse.</p><p>Now, equation of the director circle to the ellipse <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>x</mi><mn>2</mn></msup><msup><mi>a</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><msup><mi>b</mi><mn>2</mn></msup></mfrac><mo>=</mo><mn>1</mn></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></math>.</p><p>Therefore, required curve is </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>9</mn><mo>+</mo><mn>4</mn></math></p><p>or<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>13</mn></math>.</p></div>


title: the-points-p-3-2-4-q-4-5-2-r-5-8-0-and-s-2-1-6-are
slug: the-points-p-3-2-4-q-4-5-2-r-5-8-0-and-s-2-1-6-are-29745
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The points $\mathrm{P}(3,2,4), \mathrm{Q}(4,5,2), \mathrm{R}(5,8,0)$ and $\mathrm{S}(2,-1,6)$ are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">vertices of a rhombus which is not a square/2017-I]</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">non-coplanar</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">collinear</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">coplanar but not collinear</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{P}(3,2,4), \mathrm{Q}(4,5,2), \mathrm{R}(5,8,0), \mathrm{S}(2,-1,6)$<br/>$\mathrm{PQ}=\sqrt{(4-3)^{2}+(5-2)^{2}+(2-4)^{2}}$<br/>$=\sqrt{1+9+4}=\sqrt{14}$<br/>$\mathrm{QR}=\sqrt{(5-4)^{2}+(8-5)^{2}+(0-2)^{2}}$<br/>$=\sqrt{1+9+4}=\sqrt{14}$<br/>$\mathrm{RS}=\sqrt{(2-5)^{2}+(-1-8)^{2}+(6-0)^{2}}$<br/>$=\sqrt{9+81+36}=\sqrt{126}=3 \sqrt{14}$<br/>$\mathrm{PS}=\sqrt{(2-3)^{2}+(-1-2)^{2}+(6-4)^{2}}$<br/>$=\sqrt{1+9+4}=\sqrt{14}$<br/>\begin{array}{llll}<br/>\multicolumn{2}{c} {\sqrt{14}} &amp; &amp; \sqrt{14} &amp; \multicolumn{2}{c} {\sqrt{14}} \\<br/>\hline &amp; Q &amp; R &amp; S<br/>\end{array}<br/>Since, $\mathrm{PQ}+\mathrm{QR}+\mathrm{PS}=\mathrm{RS}$, points are collinear.</div>


title: the-points-with-position-vectors-10-i-3-j-12-i-5-j-i-11-j-are-collinear-if-the-value-of-a-is
slug: the-points-with-position-vectors-10-i-3-j-12-i-5-j-i-11-j-are-collinear-if-the-value-of-a-is-52768
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2011 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The points with position vectors<br/>$10 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}, 12 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}, \hat{\mathbf{i}}+11 \hat{\mathbf{j}}$ are collinear, if the value of $a$ is</div>

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

answer:
<div class="solution">Since, the points with position vectors $10 \hat{i}+3 \hat{j}$,<br/>$12 \hat{i}-5 \hat{j}, a \hat{i}+11 \hat{j}$ are collinear.<br/>$\therefore \quad\left|\begin{array}{ccc}10 &amp; 3 &amp; 1 \\ 12 &amp; -5 &amp; 1 \\ a &amp; 11 &amp; 1\end{array}\right|=0$<br/>$\Rightarrow 10(-5-11)-3(12-a)+1(132+5 a)=0$<br/>$\Rightarrow-160-36+3 a+132+5 a=0$<br/>$\Rightarrow-196+132+8 a=0$<br/>$\Rightarrow 8 a=64$<br/>$\Rightarrow a=8$</div>


tags: ['Chemistry', 'Environmental Chemistry']
source_db: MarksBatch2_P3.db
title:
the-pollutants-which-come-directly-in-the-air-from-sources-are-called-primary-pollutants-primary-pollutants-are-sometimes-converted-into-secondary-pol

slug:
the-pollutants-which-come-directly-in-the-air-from-sources-are-called-primary-pollutants-primary-pollutants-are-sometimes-converted-into-secondary-pol-12445

question:
<div class="question">The pollutants which come directly in the air from sources are called primary pollutants. Primary pollutants are sometimes converted into secondary pollutants. Which of the following belongs to secondary air pollutants?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{CO}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Hydrocarbon<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Peroxyacetyl nitrate<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/>NO</span> </li> </ul>

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

answer:
<div class="solution">Hydrocarbons present in atmosphere combine with oxygen atom produced by the photolysis of $\mathrm{NO}_2$ to form highly reactive intermediate called free radical. Free radical initiates a series of reaction.<br/>Peroxyacetyl nitrates are formed, which can be said as secondary pollutants.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/Q9nxokK2ViNdbxGnY521y6xNyxqKvBDch9HrTBwa1Qg.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Polymers', 'TS EAMCET', 'TS EAMCET 2016']
source_db: MarksBatch2_P3.db
title:
the-poly-dispersity-index-pdi-of-a-polymer-is-m-w-weight-average-molecular-mass-and-m-n-number-average-molecular-mass

slug:
the-poly-dispersity-index-pdi-of-a-polymer-is-m-w-weight-average-molecular-mass-and-m-n-number-average-molecular-mass-67477

question:
<div class="question">The poly dispersity index (PDI) of a polymer is ( $\bar{M}_W=$ weight average molecular mass and $\bar{M}_n=$ number average molecular mass)</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the ratio between $\bar{M}_w$ and $\bar{M}_n$</span> </div>

answer:
<div class="solution">The polydispersity index (PDl) of a polymer is the ratio of $\bar{M}_w$ and $\bar{M}_n$.<br/>$$<br/>\mathrm{PDI}=\frac{\bar{M}_w}{\bar{M}_n}<br/>$$<br/>It is directly related to the standard deviation of polymer molecular weight distribution. Polydispersity index can be used as a measure of the width of the molecular mass distribution.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2008 (Phase 1)']
answer: <div class="solution">Bar chart is most appropriate</div>
source_db: MarksBatch2_P3.db
title:
the-populations-of-four-towns-a-b-c-and-d-as-on-2001-are-as-follows-beginarrayll-hline-town-population-hline-a-6863-b-519-c-12185-d-1755-hline-endarra

slug:
the-populations-of-four-towns-a-b-c-and-d-as-on-2001-are-as-follows-beginarrayll-hline-town-population-hline-a-6863-b-519-c-12185-d-1755-hline-endarra-62550

question:
<div class="question">The populations of four towns $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ as on $2001 \mathrm{are}$ as follows<br/>\begin{array}{ll}<br/>\hline Town &amp; Population \\<br/>\hline A &amp; 6863 \\<br/>B &amp; 519 \\<br/>C &amp; 12185 \\<br/>D &amp; 1755 \\<br/>\hline<br/>\end{array} What is the most appropriate diagram to present the above data?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Pie diagram</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Bar chart</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">Cubic chart</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Histogram</span> </li> </ul>

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


title: the-position-of-br-in-the-compound-ch-3-ch-chc-br-ch-3-2-can-be-classified-as
slug: the-position-of-br-in-the-compound-ch-3-ch-chc-br-ch-3-2-can-be-classified-as-19933
tags: ['Chemistry', 'Haloalkanes and Haloarenes']
source_db: MarksBatch2_P3.db
question:
<div class="question">The position of $\mathrm{Br}$ in the compound $\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHC}(\mathrm{Br})$ $\left(\mathrm{CH}_3\right)_2$ can be classified as</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>allyl<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/>aryl<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>vinyl<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>secondary</span> </li> </ul>

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

answer:
<div class="solution">Compounds in which the halogen atom is bonded to $s p^3$ hybridised carbon atom next to carbon carbon-double bond are known as allyl halides.<br/>$$<br/>\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHC}(\mathrm{Br})\left(\mathrm{CH}_3\right)_2<br/>$$</div>


title: the-position-of-the-point-1-2-relative-to-the-ellipse-2-x-2-7-y-2-20-is
slug: the-position-of-the-point-1-2-relative-to-the-ellipse-2-x-2-7-y-2-20-is-97969
tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The position of the point $(1,2)$ relative to the ellipse $2 x^{2}+7 y^{2}=20$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">outside the ellipse</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">inside the ellipse but not at the focus</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">on the ellipse</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">at the focus</span> </li> </ul>

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

answer:
<div class="solution">Given ellipse, $2 \mathrm{x}^{2}+7 \mathrm{y}^{2}=20$. Given point, $(1,2)$ $2(1)^{2}+7(2)^{2}-20=2+28-20=38-20=18&gt;0 .$<br/>$\therefore$ Point is outside the ellipse.</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2013 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P3.db
title:
the-position-vectors-of-the-points-a-and-b-are-respectively-3-i-5-j-2-k-and-i-j-k-what-is-the-length-of-a-b

slug:
the-position-vectors-of-the-points-a-and-b-are-respectively-3-i-5-j-2-k-and-i-j-k-what-is-the-length-of-a-b-71546

question:
<div class="question">The position vectors of the points $A$ and $B$ are respectively $3 \hat{i}-5 \hat{j}+2 \hat{k}$ and $\hat{i}+\hat{j}-\hat{k} .$ What is the length of $A B$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">11</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">9</span> </li><li class="correct"> <span class="option-label">C</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">D</span> <span class="option-data">6</span> </li> </ul>

answer:
<div class="solution">$\quad \overrightarrow{\mathrm{AB}}=-2 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$<br/>$$<br/>|\overrightarrow{\mathrm{AB}}|=\sqrt{(-2)^{2}+6^{2}+(-3)^{2}}=\sqrt{49}=7<br/>$$</div>


title: the-possible-value-of-x-if-sd-of-the-numbers-2-3-2x-and-11-is-35-is-equal-to-1
slug: the-possible-value-of-x-if-sd-of-the-numbers-2-3-2x-and-11-is-35-is-equal-to-1-25484
tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch2_P3.db
question:
<div class="question">The possible value of x if SD of the numbers 2, 3, 2x and 11 is 3.5 is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4, \frac{5}{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5, \frac{7}{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3, \frac{7}{3}$</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">D</span> <span class="option-data">$2, \frac{5}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3, \frac{7}{3}$</span> </div>

answer:
<div class="solution">Given Standard deviation of 2, 3, 2x and 11 is 3.5.<br/>$\begin{aligned} &amp; \because \text { Mean }(\bar{x})=\frac{2+3+2 x+11}{4}=\frac{8+x}{2} \\ &amp; \text { Now, } \sum_{i=1}^4\left(x_i-\bar{x}\right)^2\left\{2-\left(\frac{8+x}{2}\right)\right\}^2+\left\{3-\left(\frac{8+x}{2}\right)\right\}^2 \\ &amp;+\left\{2 x-\left(\frac{8+x}{2}\right)\right\}^2+\left\{11-\left(\frac{8+x}{2}\right)\right\}^2 \\ &amp;=\left(\frac{4+x}{2}\right)^2+\left(\frac{2+x}{2}\right)^2+\left(\frac{3 x-8}{2}\right)^2+\left(\frac{14-x}{2}\right)^2\end{aligned}$<br/>$\begin{aligned} &amp; \because \mathrm{SD}=\sqrt{\left[\begin{array}{l}{\left[\frac{4+x}{4}\right)^2+\left(\frac{2+x}{2}\right)^2+\left(\frac{3 x-8}{2}\right)^2} \\ +\left(\frac{14-x}{2}\right)^2\end{array}\right]} \\ &amp; (3 \cdot 5)^2 \times 4=\frac{1}{4}\end{aligned}$<br/>$\begin{aligned} &amp; {\left[16+x^2+8 x+4+x^2+4 x+9 x^2+64-48 x\right.} \\ &amp; \left.\quad+196+x^2-28 x\right] \\ &amp; \\ &amp; \Rightarrow 12 x^2-64 x+84=0 \\ &amp; \Rightarrow \quad x=3,7 / 3\end{aligned}$</div>


title: the-potential-of-hydrogen-electrode-of-ph-10-with-respect-to-standard-hydrogen-electrode-is
slug: the-potential-of-hydrogen-electrode-of-ph-10-with-respect-to-standard-hydrogen-electrode-is-91459
tags: ['Chemistry', 'Electrochemistry', 'TS EAMCET', 'TS EAMCET 2018 (05 May Shift 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The potential of hydrogen electrode of $\mathrm{pH}=10$ with respect to standard hydrogen electrode is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-0.0591 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-0.591 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.2 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-0.591 \mathrm{~V}$</span> </div>

answer:
<div class="solution">For, hydrogen electrode<br/>$$<br/>\mathrm{pH}=10 \quad\left[\mathrm{H}^{+}\right]=10^{-10} \mathrm{M} \quad \mathrm{H}^{+}+e^{-}=\frac{1}{2} \mathrm{H}_2<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; E_{\text {cell }}=E^{\circ}-\frac{0.0591}{1} \log \frac{\left[\mathrm{H}_2\right]}{\left[\mathrm{H}^{+}\right]} \\<br/>&amp; E^{\circ}=0 ; \log \mathrm{H}_2=0 \text { because } \\<br/>&amp; E_{\text {cell }}=-\frac{0.0591}{1} \log \left(\frac{1}{10^{-10}}\right)-0.0591 \times 10 \\<br/>&amp; E_{\text {cell }}=-0.591 \mathrm{~V}<br/>\end{aligned}<br/>$$</div>


title: the-powerhouse-of-cell-is-first-discovered-by
slug: the-powerhouse-of-cell-is-first-discovered-by-62673
question: <div class="question">The powerhouse of cell is first discovered by</div>
tags: ['Biology', 'Cell - The Unit of Life', 'JIPMER', 'JIPMER 2016']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">C Benda in 1897</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Kolliker in 1850</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">Claude in 1880</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Kingsburg in 1882</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Kolliker in 1850</span> </div>

answer:
<div class="solution">Mitochondria which is also known as the power house of the cell was first discovered by Kolliker in 1850. It is the site of cellular respiration.</div>


tags: ['Physics', 'Alternating Current', 'JIPMER', 'JIPMER 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">120 V</span> </div>
source_db: MarksBatch2_P3.db
title:
the-primary-and-secondary-coils-of-a-transformer-have-50-and-1500-turns-respectively-if-the-magnetic-flux-linked-with-the-primary-coil-is-given-by-0-4

slug:
the-primary-and-secondary-coils-of-a-transformer-have-50-and-1500-turns-respectively-if-the-magnetic-flux-linked-with-the-primary-coil-is-given-by-0-4-28950

question:
<div class="question">The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi=\phi_0+4 t$, where $\phi$ is in weber, $t$ is time in second and $\phi_0$ is a constant, the output voltage across the secondary coil is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">90 V</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">120 V</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">220 V</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">30 V</span> </li> </ul>

answer:
<div class="solution">The magnetic flux linked with the primary $c$ is given by<br/>$\phi=\phi_0+4 t$<br/>So, voltage across primary<br/>$\begin{aligned}<br/>V_p &amp; =\frac{d \phi}{d t}=\frac{d}{d t}\left(\phi_0+4 t\right) \\<br/>&amp; =4 \mathrm{volt} \quad\left(\text { as } \phi_0=\right.\text { consta }<br/>\end{aligned}$<br/>Also, we have<br/>$N_p=50 \text { and } N_s=1500$<br/>From relation,<br/>or<br/>$\begin{aligned}<br/>\frac{V_s}{V_p} &amp; =\frac{N_s}{N_p} \\<br/>V_s &amp; =V_p \frac{N_s}{N_p} \\<br/>&amp; =4\left(\frac{1500}{50}\right) \\<br/>&amp; =120 \mathrm{~V}<br/>\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-primary-and-secondary-coils-of-a-transformer-have-50-and-1500-turns-respectively-if-the-magnetic-flux-linked-with-the-primary-coil-is-given-by-v-4-1

slug:
the-primary-and-secondary-coils-of-a-transformer-have-50-and-1500-turns-respectively-if-the-magnetic-flux-linked-with-the-primary-coil-is-given-by-v-4-1-11903

question:
<div class="question">The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi=\phi_v+4 t$, where $\phi$ is in webers, $t$ is time in seconds and $\phi_v$ is a constant, the output voltage across the output voltage across the secondary coil is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">120 volts</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">220 volts</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">30 volts</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">90 volts.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">120 volts</span> </div>

answer:
<div class="solution">The magnetic flux linked with the primary coil is given by
<br/>\(\phi=\phi_0+4 t\)
<br/>So, voltage across primary
<br/>\(\begin{aligned}
<br/>&amp; V_p=\frac{d \phi}{d t}=\frac{d}{d t}\left(\phi_0+4 t\right) \\
<br/>&amp; \left.=4 \text { volt (as } \phi_0=\text { constant }\right)
<br/>\end{aligned}\)
<br/>Also, we have
<br/>\(N_p=50 \text { and } N_s=1500\)
<br/>From relation,
<br/>\(\begin{aligned}
<br/>&amp; \frac{V_s}{V_p}=\frac{N_s}{N_p} \\
<br/>&amp; \text {or } V_s=V_p \frac{N_s}{N_p} \\
<br/>&amp; =4\left(\frac{1500}{50}\right) \\
<br/>&amp; =120 \mathrm{~V}
<br/>\end{aligned}\)</div>


tags: ['Physics', 'Alternating Current', 'NEET', 'NEET 2007']
source_db: MarksBatch2_P3.db
title:
the-primary-and-secondary-coils-of-a-transformer-have-50-and-1500-turns-respectively-if-the-magnetic-flux-linked-with-the-primary-coil-is-given-by-v-4

slug:
the-primary-and-secondary-coils-of-a-transformer-have-50-and-1500-turns-respectively-if-the-magnetic-flux-linked-with-the-primary-coil-is-given-by-v-4-50762

question:
<div class="question">The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi=\phi_v+4 t$, where $\phi$ is in webers, $t$ is time in seconds and $\phi_v$ is a constant, the output voltage across the output voltage across the secondary coil is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">120 volts</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">220 volts</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">30 volts</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">90 volts.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">120 volts</span> </div>

answer:
<div class="solution">The magnetic flux linked with the primary coil is given by
<br/>\(\phi=\phi_0+4 t\)
<br/>So, voltage across primary
<br/>\(\begin{aligned}
<br/>&amp; V_p=\frac{d \phi}{d t}=\frac{d}{d t}\left(\phi_0+4 t\right) \\
<br/>&amp; \left.=4 \text { volt (as } \phi_0=\text { constant }\right)
<br/>\end{aligned}\)
<br/>Also, we have
<br/>\(N_p=50 \text { and } N_s=1500\)
<br/>From relation,
<br/>\(\begin{aligned}
<br/>&amp; \frac{V_s}{V_p}=\frac{N_s}{N_p} \\
<br/>&amp; \text {or } V_s=V_p \frac{N_s}{N_p} \\
<br/>&amp; =4\left(\frac{1500}{50}\right) \\
<br/>&amp; =120 \mathrm{~V}
<br/>\end{aligned}\)</div>


title: the-primary-and-secondary-valencies-of-cobalt-respectively-in-co-nh-3-5-cl-cl-2-are
slug: the-primary-and-secondary-valencies-of-cobalt-respectively-in-co-nh-3-5-cl-cl-2-are-18922
tags: ['Chemistry', 'Coordination Compounds', 'JEE Main', 'JEE Main 2023 (24 Jan Shift 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The primary and secondary valencies of cobalt respectively in <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mi>Co</mi><mo>(</mo><msub><mi>NH</mi><mn>3</mn></msub><msub><mo>)</mo><mn>5</mn></msub><mi>Cl</mi></mrow></mfenced><msub><mi>Cl</mi><mn>2</mn></msub></math> are:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3 and 5</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2 and 6</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2 and 8</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">3 and 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> </ul>

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

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mi>Co</mi><mo>(</mo><msub><mi>NH</mi><mn>3</mn></msub><msub><mo>)</mo><mn>5</mn></msub><mi>Cl</mi></mrow></mfenced><msub><mi>Cl</mi><mn>2</mn></msub></math></p><p>The primary valency is the ionisable valency.  Oxidation number of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Co</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>3</mn></math>. So, primary valency is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math>. Secondary valency refers the coordination number. It is an octahedral complex so, secondary valency is 6.</p></div>


tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2022 (10 Aug Shift 1)']
source_db: MarksBatch2_P3.db
title:
the-primary-and-secondary-voltage-of-an-ideal-stepdown-transformer-is-200-v-and-25-v-respectively-the-secondary-is-connected-to-a-device-which-draws-a

slug:
the-primary-and-secondary-voltage-of-an-ideal-stepdown-transformer-is-200-v-and-25-v-respectively-the-secondary-is-connected-to-a-device-which-draws-a-24983

question:
<div class="question">The primary and secondary voltage of an ideal step-down transformer is $200 \mathrm{~V}$ and $25 \mathrm{~V}$ respectively. The secondary is connected to a device, which draws a current of $2 \mathrm{~A}$. The current in the primary is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$25 \mathrm{~mA}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$42 \mathrm{~mA}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$160 \mathrm{~mA}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$250 \mathrm{~mA}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$250 \mathrm{~mA}$</span> </div>

answer:
<div class="solution">For a lossless transformer, with primary coil $\left(I_P, V_P\right)$ and secondary coil $\left(I_S, V_S\right)$, there has to be conservation of energy per unit time:<br/>$\begin{aligned} &amp; I_P V_P=I_S V_S \\ &amp; \Rightarrow \frac{I_P}{I_S}=\frac{V_S}{V_P} \\ &amp; \therefore \frac{I_P}{2}=\frac{25}{500} \\ &amp; \therefore I_P=\frac{1}{4} \mathrm{~A}=250 \mathrm{~mA}\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'KVPY', 'KVPY 2016 (SA)']
source_db: MarksBatch2_P3.db
title:
the-primary-and-the-secondary-coils-of-a-transformer-contain-10-and-100-turns-respectively-the-primary-coil-is-connected-to-a-battery-that-supplies-a-

slug:
the-primary-and-the-secondary-coils-of-a-transformer-contain-10-and-100-turns-respectively-the-primary-coil-is-connected-to-a-battery-that-supplies-a-74738

question:
<div class="question">The primary and the secondary coils of a transformer contain 10 and 100 turns, respectively. The primary coil is connected to a battery that supplies a constant voltage of $1.5$ volts. the voltage across the secondary coil is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.5 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.15 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.0 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$15 \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.0 \mathrm{~V}$</span> </div>

answer:
<div class="solution">Since the voltage production is based upon A.C. supply and this voltage is D.C which is constant. Therefore, no flux will change in secondary and no voltage will be induced.<br/>Answer is (C) $0 \mathrm{~V}$.</div>


tags: ['Physics', 'Alternating Current', 'AP EAMCET', 'AP EAMCET 2020 (21 Sep Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2000</span> </div>
source_db: MarksBatch2_P3.db
title:
the-primary-of-a-transformer-has-100-turns-and-operates-at-100-mathrmv200-mathrmw-the-number-of-turns-in-the-secondary-if-the-output-voltage-is-2000-m

slug:
the-primary-of-a-transformer-has-100-turns-and-operates-at-100-mathrmv200-mathrmw-the-number-of-turns-in-the-secondary-if-the-output-voltage-is-2000-m-92784

question:
<div class="question">The primary of a transformer has 100 turns and operates at \(100 \mathrm{~V}-200 \mathrm{~W}\). The number of turns in the secondary, if the output voltage is \(2000 \mathrm{~V}\), then</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2000</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">200</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">100</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">500</span> </li> </ul>

answer:
<div class="solution">For a transformer, it is given that, \(N_P=100\),<br/>\(V_P=100 \mathrm{~V}, V_S=2000 \mathrm{~V}\)<br/>We know that,<br/>\(\begin{aligned}<br/>&amp; \frac{N_S}{N_P}=\frac{V_S}{V_P} \\<br/>\Rightarrow \quad &amp; N_S=\frac{V_S N_P}{V_P}=\frac{2000 \times 100}{100}=2000<br/>\end{aligned}\)</div>


tags: ['Physics', 'Alternating Current', 'COMEDK', 'COMEDK 2013']
source_db: MarksBatch2_P3.db
title:
the-primary-of-a-transformer-when-connected-to-a-dc-battery-of-10-v-draws-a-current-of-1-ma-the-number-of-turns-of-the-primary-and-secondary-windings-

slug:
the-primary-of-a-transformer-when-connected-to-a-dc-battery-of-10-v-draws-a-current-of-1-ma-the-number-of-turns-of-the-primary-and-secondary-windings-51743

question:
<div class="question">The primary of a transformer when connected to a DC battery of $10 \mathrm{~V}$ draws a current of $1 \mathrm{~mA}$. The number of turns of the primary and secondary windings are 50 and 100 , respectively. The voltage in the secondary and the current drawn by the circuit in the secondary are respectively</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20 \mathrm{~V}$ and $2.0 \mathrm{~mA}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{~V}$ and $0.5 \mathrm{~mA}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0$ and $0$</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">D</span> <span class="option-data">$20 \mathrm{~V}$ and $0.5 \mathrm{~mA}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0$ and $0$</span> </div>

answer:
<div class="solution">A transformer does not work on DC supply because mutual induction does not take place due to constant value of current. So, $V_{\mathrm{S}}=0$ and $I_{\mathrm{S}}=0$.</div>


title: the-primary-treatment-basically-involves-the-physical-removal-of-particles-from-the-sewage-through
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch2_P3.db
slug:
the-primary-treatment-basically-involves-the-physical-removal-of-particles-from-the-sewage-through-32281

question:
<div class="question">The primary treatment basically involves the physical removal of particles from the sewage through</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">filtration.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">sedimentation.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">microbial treatment.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Both <math><mfenced separators="|"><mrow><mi mathvariant="normal">A</mi></mrow></mfenced></math> and <math><mfenced separators="|"><mrow><mi mathvariant="normal">B</mi></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">Both <math><mfenced separators="|"><mrow><mi mathvariant="normal">A</mi></mrow></mfenced></math> and <math><mfenced separators="|"><mrow><mi mathvariant="normal">B</mi></mrow></mfenced></math></span> </div>

answer:
<div class="solution">Primary water treatment removes large pieces of floating debris, oily substances from the sewage. Secondary treatment is called bio-chemical or microbial treatment where many useful aerobic bacteria and fungus grow together to form flocs. These microbes consume major part of the organic matter in the effluent as they grow and reduces the BOD of water. BOD of pure water is 1-2 ppm and BOD of polluted water is 15-18 ppm.</div>


title: the-primary-treatment-of-waste-water-involves-the-removal-of
slug: the-primary-treatment-of-waste-water-involves-the-removal-of-27835
question: <div class="question">The primary treatment of waste water involves the removal of</div>
tags: ['Biology', 'Microbes in Human Welfare']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>dissolved impurities <br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>stable particles<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/> toxic substances<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>harmful bacteria</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">The primary treatment of waste water involves physical removal of both larger and small particles (stable particles) through filtration and sedimentation from the sewage. These are removed in stages; initially, floating debris is removed by sequential filtration.<br/>Then by sedimentation the grit (Soil and small pebbles) are removed. All solids that settle from the secondary treatment.<br/>The primary treatment does not remove the dissolved impurities (a), toxic substances (c) and harmful bacteria (d).</div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-primary-winding-of-a-transformer-has-100-t-u-r-n-s-and-its-secondary-winding-has-200-turns-the-primary-winding-is-connected-to-an-ac-supply-of-120

slug:
the-primary-winding-of-a-transformer-has-100-t-u-r-n-s-and-its-secondary-winding-has-200-turns-the-primary-winding-is-connected-to-an-ac-supply-of-120-80916

question:
<div class="question">The primary winding of a transformer has <math><mn>100</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi></math> and its secondary winding has <math><mi>200 turns</mi></math>. The primary winding is connected to an AC supply of <math><mn>120</mn><mi> </mi><mn>V</mn></math> and the current flowing in it is <math><mn>10</mn><mi> </mi><mi mathvariant="normal">A</mi></math>. The voltage and the current in the secondary winding is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mn>240</mn><mi> </mi><mn>V</mn><mo>,</mo><mi> </mi><mn>5</mn><mi> </mi><mn>A</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>240</mn><mi>Â </mi><mn>V</mn><mo>,</mo><mi>Â </mi><mn>10</mn><mi>Â </mi><mn>A</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>60</mn><mi>Â </mi><mn>V</mn><mo>,</mo><mi>Â </mi><mn>20</mn><mi>Â </mi><mn>A</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>120</mn><mi>Â </mi><mn>V</mn><mo>,</mo><mi>Â </mi><mn>20</mn><mi>Â </mi><mn>A</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>240</mn><mi> </mi><mn>V</mn><mo>,</mo><mi> </mi><mn>5</mn><mi> </mi><mn>A</mn></math></span> </div>

answer:
<div class="solution"><math><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mo>â</mo><mfrac><mrow><mn>200</mn></mrow><mrow><mn>100</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><mn>120</mn></mrow></mfrac><mo>â</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>240</mn><mi> </mi><mn>V</mn></math><br/><br/>also <math><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>i</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac><mo>â</mo><mfrac><mrow><mn>240</mn></mrow><mrow><mn>120</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>10</mn></mrow><mrow><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac><mo>â</mo><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>5</mn><mi mathvariant="normal"> </mi><mn>A</mn></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-primary-winding-of-a-transformer-has-100-turns-and-its-secondary-winding-has-200-turns-the-primary-is-connected-to-an-ac-supply-of-120-v-and-the-c-1

slug:
the-primary-winding-of-a-transformer-has-100-turns-and-its-secondary-winding-has-200-turns-the-primary-is-connected-to-an-ac-supply-of-120-v-and-the-c-1-46930

question:
<div class="question">The primary winding of a transformer has 100 turns and its secondary winding has 200 turns. The primary is connected to an AC supply of 120 V and the current flowing in it is 10 A. The voltage and the current in the secondary are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">240 V, 5 A</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">240 V, 10 A</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">60 V, 20 A</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">120 V, 20 A</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">240 V, 5 A</span> </div>

answer:
<div class="solution"><math><mfrac><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mi> </mi><mi> </mi><mi>o</mi><mi>r</mi><mi> </mi><mi> </mi><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>Ã</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac></mrow></mfenced></math><br/><br/><math><mo>â´</mo></math> <math><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>120</mn><mi> </mi><mo>Ã</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>200</mn></mrow><mrow><mn>100</mn></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>240 V</mn></math><br/><br/><math><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mi> </mi><mi> </mi><mi>o</mi><mi>r</mi><mi> </mi><mi> </mi><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac></mrow></mfenced></math><br/><br/><math><mo>â´</mo></math> <math><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>10</mn><mfenced separators="|"><mrow><mfrac><mrow><mn>100</mn></mrow><mrow><mn>200</mn></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>5</mn><mi> A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-primary-winding-of-a-transformer-has-100-turns-and-its-secondary-winding-has-200-turns-the-primary-is-connected-to-an-ac-supply-of-120-v-and-the-c

slug:
the-primary-winding-of-a-transformer-has-100-turns-and-its-secondary-winding-has-200-turns-the-primary-is-connected-to-an-ac-supply-of-120-v-and-the-c-69176

question:
<div class="question">The primary winding of a transformer has 100 turns and its secondary winding has 200 turns. The primary is connected to an AC supply of 120 V and the current flowing in it is 10 A. The voltage and the current in the secondary are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">240 V, 5 A</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">240 V, 10 A</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">60 V, 20 A</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">120 V, 20 A</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">240 V, 5 A</span> </div>

answer:
<div class="solution"><math><mfrac><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mi> </mi><mi> </mi><mi>o</mi><mi>r</mi><mi> </mi><mi> </mi><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>Ã</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac></mrow></mfenced></math><br/><br/><math><mo>â´</mo></math> <math><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>120</mn><mi> </mi><mo>Ã</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>200</mn></mrow><mrow><mn>100</mn></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>240 V</mn></math><br/><br/><math><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac><mi> </mi><mi> </mi><mi>o</mi><mi>r</mi><mi> </mi><mi> </mi><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac></mrow></mfenced></math><br/><br/><math><mo>â´</mo></math> <math><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>10</mn><mfenced separators="|"><mrow><mfrac><mrow><mn>100</mn></mrow><mrow><mn>200</mn></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>5</mn><mi> A</mi></math></div>


tags: ['Physics', 'Alternating Current', 'NEET', 'NEET 2013 (Karnataka)']
answer: <div class="solution">Transformer can not work on dc.</div>
source_db: MarksBatch2_P3.db
title:
the-primary-winding-of-transformer-when-connected-to-a-d-c-battery-of-10-volt-draws-a-current-of-1-ma-the-number-of-turns-of-the-primary-and-secondary

slug:
the-primary-winding-of-transformer-when-connected-to-a-d-c-battery-of-10-volt-draws-a-current-of-1-ma-the-number-of-turns-of-the-primary-and-secondary-26496

question:
<div class="question">The primary winding of transformer when connected to a $d c$ battery of 10 Volt draws a current of $1 \mathrm{~mA}$. The number of turns of the primary and secondary windings are 50 and 100 respectively. The voltage in the secondary and the current drawn by the circuit in the secondary are respectively:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20 \mathrm{~V}$ and $2.0 \mathrm{~mA}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{~V}$ and $0.5 \mathrm{~mA}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Zero volt and therefore no current</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20 \mathrm{~V}$ and $0.5 \mathrm{~mA}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Zero volt and therefore no current</span> </div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-primary-winding-of-transformers-has-500-turns-whereas-its-secondary-has-5000-turns-the-primary-is-connected-to-an-a-c-supply-of-20-mathrmv-50-math

slug:
the-primary-winding-of-transformers-has-500-turns-whereas-its-secondary-has-5000-turns-the-primary-is-connected-to-an-a-c-supply-of-20-mathrmv-50-math-52518

question:
<div class="question">The primary winding of transformers has \( 500 \) turns whereas its secondary has \( 5000 \) turns. The primary is connected to an \( A . C \). supply of \( 20 \mathrm{~V}, 50 \mathrm{~Hz} \). The secondary will have an output of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\( 2 \mathrm{~V}, 5 \mathrm{~Hz} \)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\( 200 \mathrm{~V}, 500 \mathrm{~Hz} \)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( 2 \mathrm{~V}, 50 \mathrm{~Hz} \)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\( 200 \mathrm{~V}, 50 \mathrm{~Hz} \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 200 \mathrm{~V}, 50 \mathrm{~Hz} \)</span> </div>

answer:
<div class="solution"><blockquote><p>Given,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>p</mi></msub><mo>=</mo><mn>20</mn><mo> </mo><mi mathvariant="normal">V</mi></math>,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>p</mi></msub><mo>=</mo><mn>500</mn></math>,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>s</mi></msub><mo>=</mo><mn>5000</mn></math>,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>50</mn><mo> </mo><mi>Hz</mi></math>,</p><p>We know that for a transformer,</p><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></blockquote><blockquote><p>Putting in the given values,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>10</mn></mfrac><mo>=</mo><mfrac><mn>20</mn><msub><mi>V</mi><mi>s</mi></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>V</mi><mi>s</mi></msub><mo>=</mo><mn>200</mn><mo> </mo><mi mathvariant="normal">V</mi></math></p><p>Also, we know that transformer doesn't affect the frequency of the source.</p></blockquote></div>


title: the-principal-value-of-sin-1-x-lies-in-the-interval
slug: the-principal-value-of-sin-1-x-lies-in-the-interval-63061
question: <div class="question">The principal value of $\sin ^{-1}$ x lies in the interval</div>
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$</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">C</span> <span class="option-data">$\left[0, \frac{\pi}{2}\right]$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$[0, \pi]$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$</span> </div>

answer:
<div class="solution">The principal value of $\sin ^{-1} x$ lies in it's range. The range of $\sin ^{-1} x$ is $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2009 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.5</span> </div>
source_db: MarksBatch2_P3.db
title:
the-probabilities-of-two-events-a-and-b-are-given-as-p-a-08-and-p-b-07-what-is-the-minimum-value-of-p-a-b

slug:
the-probabilities-of-two-events-a-and-b-are-given-as-p-a-08-and-p-b-07-what-is-the-minimum-value-of-p-a-b-36574

question:
<div class="question">The probabilities of two events $A$ and $B$ are given as $P(A)=0.8$ and $P(B)=0.7$. What is the minimum value of $P(A \cap B) ?$</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">0.1</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">0.5</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">D</span> <span class="option-data">1</span> </li> </ul>

answer:
<div class="solution">As we know $P(A \cup B) \leq 1$ $\therefore P(A)+P(B)-P(A \cap B) \leq 1$<br/>$\Rightarrow 0.8+0.7-P(A \cap B) \leq 1$<br/>$\Rightarrow P(A \cap B) \geq 1.5-1$<br/>$\Rightarrow P(A \cap B) \geq 0.5$<br/>Hence, the minimum value of $P(A \cap B)$ is $0.5$.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$0.7$</span> </div>
source_db: MarksBatch2_P3.db
title:
the-probabilities-that-a-student-will-solve-question-a-and-question-b-are-04-and-05-respectively-what-is-the-probability-that-he-solves-at-least-one-o

slug:
the-probabilities-that-a-student-will-solve-question-a-and-question-b-are-04-and-05-respectively-what-is-the-probability-that-he-solves-at-least-one-o-79685

question:
<div class="question">The probabilities that a student will solve Question $\mathrm{A}$ and Question $\mathrm{B}$ are $0.4$ and $0.5$ respectively. What is the probability that he solves at least one of the two questions?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.6$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.7$</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">C</span> <span class="option-data">$0.8$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.9$</span> </li> </ul>

answer:
<div class="solution">Probability of solving Question A, $\mathrm{P}(\mathrm{A})=0.4$ Probability of solving Question B, $\mathrm{P}(\mathrm{B})=0.5$ $\therefore \mathrm{P}\left(\mathrm{A}^{\prime}\right)=1-\mathrm{P}(\mathrm{A})=1-0.4=0.6$<br/>$\mathrm{P}\left(\mathrm{B}^{\prime}\right)=1-\mathrm{P}(\mathrm{B})=1-0.5=0.5$<br/>Probability to solve atleast one question $=\mathrm{P}(\mathrm{A} \cup \mathrm{B})$ $\mathrm{P}(\mathrm{A} \cup \mathrm{B})=1-\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$<br/>$=1-(0.6 \times 0.5)$<br/>$=1-0.3$<br/>$=0.7$</div>


tags: ['Mathematics', 'Probability', 'MHT CET', 'MHT CET 2020 (14 Oct Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-probability-distribution-of-a-discrete-r-v-x-is-beginarraycccccc-hline-mathrmxx-0-1-2-3-4-hline-mathrmpmathrmxx-k-2-k-4-mathrmk-2-k-k-hline-endarr

slug:
the-probability-distribution-of-a-discrete-r-v-x-is-beginarraycccccc-hline-mathrmxx-0-1-2-3-4-hline-mathrmpmathrmxx-k-2-k-4-mathrmk-2-k-k-hline-endarr-12232

question:
<div class="question">The probability distribution of a discrete r. v. $X$ is \begin{array}{|c|c|c|c|c|c|}<br/>\hline \mathrm{X}=x &amp; 0 &amp; 1 &amp; 2 &amp; 3 &amp; 4 \\<br/>\hline \mathrm{P}(\mathrm{X}=x) &amp; k &amp; 2 k &amp; 4 \mathrm{k} &amp; 2 k &amp; k \\<br/>\hline<br/>\end{array}<br/>then value of $\mathrm{P}(\mathrm{X} \leq 2)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{10}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{7}{10}$</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">C</span> <span class="option-data">$\frac{3}{10}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{9}{10}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{7}{10}$</span> </div>

answer:
<div class="solution">Here $\mathrm{k}+2 \mathrm{k}+4 \mathrm{k}+2 \mathrm{k}+\mathrm{k}=10 \mathrm{k}=1 \Rightarrow \mathrm{k}=\frac{1}{10}$<br/>Now $\mathrm{P}(\mathrm{X} \leq 2)=\mathrm{P}(0)+\mathrm{P}(1)+\mathrm{P}(2)=\frac{1}{10}+\frac{2}{10}+\frac{4}{10}=\frac{7}{10}$</div>


tags: ['Mathematics', 'Probability', 'AP EAMCET', 'AP EAMCET 2007']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1.76$</span> </div>
source_db: MarksBatch2_P3.db
title:
the-probability-distribution-of-a-random-variable-x-is-given-by-beginarraylrrrrc-hlinexx-0-1-2-3-4-hlinepxx-04-03-01-01-01-hline-endarray-the-variance-1

slug:
the-probability-distribution-of-a-random-variable-x-is-given-by-beginarraylrrrrc-hlinexx-0-1-2-3-4-hlinepxx-04-03-01-01-01-hline-endarray-the-variance-1-47165

question:
<div class="question">The probability distribution of a random variable $X$ is given by<br/>\begin{array}{l|r|r|r|r|c}<br/>\hlineX=X &amp; 0 &amp; 1 &amp; 2 &amp; 3 &amp; 4 \\<br/>\hlineP(X=x) &amp; 0.4 &amp; 0.3 &amp; 0.1 &amp; 0.1 &amp; 0.1 \\<br/>\hline<br/>\end{array}<br/>The variance of $X$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1.76$</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">$2.45$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4.8$</span> </li> </ul>

answer:
<div class="solution">Given,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/4ECistwOYcR74P0estg8-FUM8RG2_vxuArgIjLW8Iv0.original.fullsize.png"/><br/><br/>$\begin{aligned} \text { Mean } \bar{x} &amp; =\sum_{i=0}^4 p_i x_i=1.2 \\ \text { Variance } &amp; =\sum_{i=0}^4 p_i x_i^2-\bar{x}^2 \\ &amp; =3.20-1.44=1.76\end{aligned}$</div>


tags: ['Mathematics', 'Probability', 'TS EAMCET', 'TS EAMCET 2007']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1.76$</span> </div>
source_db: MarksBatch2_P3.db
title:
the-probability-distribution-of-a-random-variable-x-is-given-by-beginarraylrrrrc-hlinexx-0-1-2-3-4-hlinepxx-04-03-01-01-01-hline-endarray-the-variance

slug:
the-probability-distribution-of-a-random-variable-x-is-given-by-beginarraylrrrrc-hlinexx-0-1-2-3-4-hlinepxx-04-03-01-01-01-hline-endarray-the-variance-99647

question:
<div class="question">The probability distribution of a random variable $X$ is given by<br/>\begin{array}{l|r|r|r|r|c}<br/>\hlineX=X &amp; 0 &amp; 1 &amp; 2 &amp; 3 &amp; 4 \\<br/>\hlineP(X=x) &amp; 0.4 &amp; 0.3 &amp; 0.1 &amp; 0.1 &amp; 0.1 \\<br/>\hline<br/>\end{array}<br/>The variance of $X$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1.76$</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">$2.45$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4.8$</span> </li> </ul>

answer:
<div class="solution">Given,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/4ECistwOYcR74P0estg8-FUM8RG2_vxuArgIjLW8Iv0.original.fullsize.png"/><br/><br/>$\begin{aligned} \text { Mean } \bar{x} &amp; =\sum_{i=0}^4 p_i x_i=1.2 \\ \text { Variance } &amp; =\sum_{i=0}^4 p_i x_i^2-\bar{x}^2 \\ &amp; =3.20-1.44=1.76\end{aligned}$</div>


title: the-probability-distribution-of-a-random-variable-x-is-then-the-standard-deviation-of-x-is
slug: the-probability-distribution-of-a-random-variable-x-is-then-the-standard-deviation-of-x-is-26123
tags: ['Mathematics', 'Probability', 'AP EAMCET', 'AP EAMCET 2017 (26 Apr Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The probability distribution of a random variable $\mathrm{X}$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/wIYt47MnYLPgdURtVu9cGEC4-WMb04pY2M5cjsxfQ9M.original.fullsize.png"/><br/><br/>Then the standard deviation of $\mathrm{X}$ 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">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">7</span> </li> </ul>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-probability-distribution-of-random-variable-x-with-two-missing-probabilities-p-1-and-p-2-is-given-below-x-1-2-3-4-5-p-x-k-p-1-4-k-p-2-2-k-it-is-fu

slug:
the-probability-distribution-of-random-variable-x-with-two-missing-probabilities-p-1-and-p-2-is-given-below-x-1-2-3-4-5-p-x-k-p-1-4-k-p-2-2-k-it-is-fu-81715

question:
<div class="question">The probability distribution of random variable $X$ with two missing probabilities $p_{1}$ and $p_{2}$ is given below<br/>$\begin{array}{cc}\boldsymbol{X} &amp; \boldsymbol{P}(\boldsymbol{X}) \\ 1 &amp; k \\ 2 &amp; p_{1} \\ 3 &amp; 4 k \\ 4 &amp; p_{2} \\ 5 &amp; 2 k\end{array}$<br/>It is further given that $P(X \leq 2)=0.25$ and $P(X \geq 4)=0.35$. Consider the following statements <br/>$1.$ $p_{1}=p_{2}$<br/>$2.$ $p_{1}+p_{2}=P(X=3)$<br/>Which of the statements given above is/are correct?</div>

answer:
<div class="solution">Let $P(X \leq 2)=0.25$<br/>$\Rightarrow \quad P(X=1)+P(X=2)=0.25$<br/>$\Rightarrow k+p_{1}=0.25($ from the table $)$<br/>$\Rightarrow p_{1}=0.25-k$<br/>and $P(X \geq 4)=0.35$<br/>$\Rightarrow \quad P(X=4)+P(X=5)=0.35$<br/>$\Rightarrow p_{2}+2 k=0.35$ (from the table)<br/>$\Rightarrow p_{2}=0.35-2 k$<br/>From (1) and (2)<br/>$p_{1} \neq p_{2}$<br/>and $p_{1}+p_{2}=0.25-k+0.35-2 k=0.6-3 k$<br/>$\neq P(X=3)$<br/>Hence, neither 1 nor 2 is correct</div>


title: the-probability-of-a-nonleap-year-having-53-mondays-is
slug: the-probability-of-a-nonleap-year-having-53-mondays-is-35655
question: <div class="question">The probability of a non-leap year having 53 Mondays is .........</div>
tags: ['Mathematics', 'Probability', 'AP EAMCET', 'AP EAMCET 2020 (22 Sep Shift 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{7}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{7}$</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">C</span> <span class="option-data">$\frac{5}{7}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{6}{7}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{7}$</span> </div>

answer:
<div class="solution">Number of days in non Leap year $=365$<br/>$$<br/>\begin{aligned}<br/>&amp; =52 \times 7+1 \\<br/>&amp; =52 \text { weeks }+1 \text { day }<br/>\end{aligned}<br/>$$<br/>The one additional day may be any one of the day<br/>$$<br/>\begin{aligned}<br/>\therefore \quad n(A) &amp; =1 \\<br/>n(s) &amp; =7 \\<br/>\mathrm{P}(\text { Getting } 53 \text { sundays }) &amp; =\frac{n(A)}{n(S)}=\frac{1}{7}<br/>\end{aligned}<br/>$$<br/>Hence, option (2) is correct.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
the-probability-of-guessing-a-correct-answer-is-12-x-if-the-probability-of-not-guessing-the-correct-answer-is-3-2-then-what-is-x-equal-to

slug:
the-probability-of-guessing-a-correct-answer-is-12-x-if-the-probability-of-not-guessing-the-correct-answer-is-3-2-then-what-is-x-equal-to-48236

question:
<div class="question">The probability of guessing a correct answer is $\frac{x}{12}$. If the probability of not guessing the correct answer is $\frac{2}{3}$, then what is $x$ equal to?</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">6</span> </li> </ul>

answer:
<div class="solution">Given Probability of guessing a correct answer $=\frac{x}{12}$<br/>and probability of not guessing the correct answer $=\frac{2}{3}$<br/>As we know<br/>$P$ (occurence of an event) $+P$ (non-occurence of an event $)=1$<br/>$\therefore \quad \frac{x}{12}+\frac{2}{3}=1 \Rightarrow \frac{x+8}{12}=1 \Rightarrow x=12-8=4$</div>


title: the-probability-that-a-nonleap-year-contains-53-sunday-is
slug: the-probability-that-a-nonleap-year-contains-53-sunday-is-76676
question: <div class="question">The probability that a non-leap year contains 53 Sunday is</div>
tags: ['Mathematics', 'Probability', 'AP EAMCET', 'AP EAMCET 2023 (19 May Shift 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{7}$</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">$\frac{1}{9}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2}{7}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{5}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{7}$</span> </div>

answer:
<div class="solution">A non-leap year contains 365 days and there are total 52 weeks and 1 day in a non-leap year. Hence there should be 52 Sunday also.<br/>But the 1 extra day apart from those 52 weeks may be either Monday, Tuesday, Wednesday, Thursday, Friday, Saturday or a Sunday.<br/>Clearly, total possible events are $=7$<br/>and Number of favourable events $=1$<br/>Hence probability $=\frac{1}{7}$</div>


title: the-probability-that-a-nonleap-year-selected-at-random-will-have-53-sunday-is
slug: the-probability-that-a-nonleap-year-selected-at-random-will-have-53-sunday-is-59397
tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2017']
source_db: MarksBatch2_P3.db
question:
<div class="question">The probability that a non-leap year selected at random will have 53 Sunday is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 / 7$</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">C</span> <span class="option-data">$2 / 7$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 / 7$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 / 7$</span> </div>

answer:
<div class="solution">In a non-leap year,total number of days is 365 . Out of them, there are 52 weeks and 1 day extra. Thus, a non-leap year always has 52 Sunday. The remaining 1 day can be Sunday, Monday, Tuenday, Wednesday, Thursday, Friday and Sarurday. Out of these 7 cases, we have Sunday in one
<br/>case
<br/>$\therefore$ Total number of outcomes = 7 
<br/>Number of favourable outcomes = 1
<br/>Hence, required probability $=\frac{1}{7}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-probability-that-a-ship-safely-reaches-a-port-is-3-1-the-probability-that-out-of-5-ships-at-least-4-ships-would-arrive-safely-is

slug:
the-probability-that-a-ship-safely-reaches-a-port-is-3-1-the-probability-that-out-of-5-ships-at-least-4-ships-would-arrive-safely-is-75923

question:
<div class="question">The probability that a ship safely reaches a port is $\frac{1}{3}$. The probability that out of 5 ships, at least 4 ships would arrive safely is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{243}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{10}{243}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{11}{243}$</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">$\frac{13}{243}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{11}{243}$</span> </div>

answer:
<div class="solution">Probability that a ship reaches port $=\frac{1}{3}$<br/>Probability that a ship not reaching port $=1-\frac{1}{3}=\frac{2}{3}$ Number of ships $(\mathrm{n})=5$. $\mathrm{r}=4,5$<br/>$\mathrm{p}(4)+\mathrm{p}(5)={ }^{5} \mathrm{c}_{4}\left(\frac{1}{3}\right)^{4}\left(\frac{2}{3}\right)^{5-4}+{ }^{5} \mathrm{c}_{5}\left(\frac{1}{3}\right)^{5}\left(\frac{2}{3}\right)^{5-5}$<br/>$=5\left(\frac{2}{3^{5}}\right)+\frac{1}{3^{5}}$<br/>$=\frac{10}{243}+\frac{1}{243}=\frac{11}{243}$</div>


