# questions

title: if-y-e-t-a-n-1-x-then
slug: if-y-e-t-a-n-1-x-then-50357
question: <div class="question">If $y=e^{\tan ^{-1} x}$ then</div>
tags: ['Mathematics', 'Differentiation', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left(1+x^2\right) y_2+(2 x-1) y_1=0$</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">$\left(1+x^2\right) y_2+2 x y=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(1+x^2\right) y_2-y_1=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(1+x^2\right) y_2+3 x y_1+4 y=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(1+x^2\right) y_2+(2 x-1) y_1=0$</span> </div>

answer:
<div class="solution">$\frac{d y}{d x}=e^{\tan ^{-1} x} \times \frac{1}{1+x^2}$<br/>$\Rightarrow\left(1+x^2\right) y^{\prime}=y$<br/>or $2 x y^{\prime}+\left(1+x^2\right) y^{\prime \prime}=y^{\prime}$<br/>or $\left(1+x^2\right) y^{\prime \prime}+y^{\prime}(2 x-1)=0$</div>


title: if-y-e-x-cos-2-x-then-which-of-the-following-differential-equation-is-satisfied
slug: if-y-e-x-cos-2-x-then-which-of-the-following-differential-equation-is-satisfied-66871
tags: ['Mathematics', 'Differential Equations', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If $y=e^{-x} \cos 2 x$, then which of the following differential equation is satisfied?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+5 y=0$</span> </div>

answer:
<div class="solution">Given, $y=e^{-x} \cos 2 x$
<br/>$\therefore \quad \frac{d y}{d x}=e^{-x}(-\sin 2 x) 2+\cos 2 x \cdot e^{-x}(-1)$
<br/>$\Rightarrow \quad \frac{d y}{d x}=-2 \sin 2 x \cdot e^{-x}-y$
<br/>$\Rightarrow \quad \frac{d y}{d x}+y=-2 \sin 2 x \cdot e^{-x}$
<br/>$\Rightarrow \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=-2\left[\sin 2 x \cdot e^{-x}(-1)\right. \left.e^{-x} 2 \cos 2 x\right]$
<br/>$=2 \sin 2 x \cdot e^{-x}-4 y \quad$ |from Eq. $\left.(0)\right]$
<br/>$\Rightarrow \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=-\frac{d y}{d x}-y-4 y$
<br/>$\Rightarrow \quad \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}+5 y=0$</div>


title: if-y-tan-1-1-s-i-n-x-1-s-i-n-x-then-the-value-of-d-x-d-y-at-x-6-is
slug: if-y-tan-1-1-s-i-n-x-1-s-i-n-x-then-the-value-of-d-x-d-y-at-x-6-is-28997
tags: ['Mathematics', 'Differentiation', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If $y=\tan ^{-1} \sqrt{\frac{1-\sin x}{1+\sin x}}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{6}$ is</div>

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

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

answer:
<div class="solution">$$<br/>\text { Hints : } \begin{aligned}<br/>&amp; y=\tan ^{-1} \sqrt{\frac{1-\cos \left(\frac{\pi}{2}-x\right)}{1+\cos \left(\frac{\pi}{2}-x\right)}} \\<br/>&amp; =\tan ^{-1} \sqrt{\frac{2 \sin ^2\left(\frac{\pi}{4}-\frac{x}{2}\right)}{2 \cos ^2\left(\frac{\pi}{4}-\frac{x}{2}\right)}}=\tan ^{-1}\left|\tan \left(\frac{\pi}{4}-\frac{x}{2}\right)\right|=\left(\frac{\pi}{4}-\frac{x}{2}\right) \\<br/>&amp; \frac{d y}{d x}=-\frac{1}{2}<br/>\end{aligned}<br/>$$</div>


title: if-y2-x32-x23-x5-then-for-x2-and-delta-x01-value-of-delta-y-is
slug: if-y2-x32-x23-x5-then-for-x2-and-delta-x01-value-of-delta-y-is-94693
tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1.9</span> </div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If \(y=2 x^3-2 x^2+3 x-5\), then for \(x=2\) and \(\Delta x=0.1\) value of \(\Delta y\) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2.002</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1.9</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">0</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">09</span> </li> </ul>

answer:
<div class="solution">\(\text { Hints: } \frac{\mathrm{dy}}{\mathrm{dx}}=6 \mathrm{x}^2-4 \mathrm{x}+3 \quad \Delta \mathrm{y}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{x}-2} \Delta \mathrm{x}=1.9\)</div>


title: if-yfracaxb-x2-then-x2-fracd2-yd-x2
slug: if-yfracaxb-x2-then-x2-fracd2-yd-x2-84980
question: <div class="question">If \(y=\frac{A}{x}+B x^2\), then \(x^2 \frac{d^2 y}{d x^2}=\)</div>
tags: ['Mathematics', 'Differentiation', 'WBJEE', 'WBJEE 2011']
answer: <div class="solution">Hints: \(\frac{x^2 d^2 y}{d x^2}=2\left(A / x+B x^2\right)=2 y\)</div>
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(2 y\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">\(y^2\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\mathrm{y}^3\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\mathrm{y}^4\)</span> </li> </ul>

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


tags: ['Mathematics', 'Differential Equations', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P1.db
title:
if-yfracxlog-ec-x-is-the-solution-of-the-differential-equation-fracd-yd-xfracyxphileftfracxyright-then-phileftfracxyright-is-given-by

slug:
if-yfracxlog-ec-x-is-the-solution-of-the-differential-equation-fracd-yd-xfracyxphileftfracxyright-then-phileftfracxyright-is-given-by-56705

question:
<div class="question">If \(y=\frac{x}{\log _e|c x|}\) is the solution of the differential equation \(\frac{d y}{d x}=\frac{y}{x}+\phi\left(\frac{x}{y}\right)\), then \(\phi\left(\frac{x}{y}\right)\) is given by</div>

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

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

answer:
<div class="solution">Hint : \(y=\frac{x}{\ell n|c x|}\)<br/>\(\begin{aligned}<br/>&amp; \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\ell \mathrm{n}|c x|-1}{(\ell \mathrm{n}|\mathrm{cx}|)^2}=\frac{1}{\ell \mathrm{n}|\mathrm{cx}|}-\frac{1}{(\ell \mathrm{n}|\mathrm{cx}|)^2} \\<br/>&amp; \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}}{\mathrm{x}}-\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^2 \quad \therefore \phi\left(\frac{\mathrm{x}}{\mathrm{y}}\right)=-\frac{\mathrm{y}^2}{\mathrm{x}^2}<br/>\end{aligned}\)</div>


tags: ['Mathematics', 'Basic of Mathematics', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P1.db
title:
if-ylog-n-x-where-log-n-means-log-e-log-e-log-e-ldots-repeated-n-times-then-x-log-x-log-2-x-log-3-x-ldots-log-n1-x-log-n-x-fracd-yd-x-is-equal-to

slug:
if-ylog-n-x-where-log-n-means-log-e-log-e-log-e-ldots-repeated-n-times-then-x-log-x-log-2-x-log-3-x-ldots-log-n1-x-log-n-x-fracd-yd-x-is-equal-to-36125

question:
<div class="question">If \(y=\log ^n x\), where \(\log ^n\) means \(\log _e \log _e \log _e \ldots\) (repeated \(n\) times), then \(x \log x \log ^2 x \log ^3 x \ldots . . \log ^{n-1} x \log ^n x \frac{d y}{d x}\) is equal to</div>

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

answer:
<div class="solution">Hint : \(\because \frac{d y}{d x}=\frac{1}{x \log ^{n-1} x \quad \log ^{n-2} x \ldots . \log x}\)</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P1.db
title:
if-youngs-double-slit-experiment-is-done-with-white-light-which-of-the-following-statements-will-be-true

slug:
if-youngs-double-slit-experiment-is-done-with-white-light-which-of-the-following-statements-will-be-true-80627

question:
<div class="question">If Young's double slit experiment is done with white light, which of the following statements will be true?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The central fringe will be white.</span> </div>

answer:
<div class="solution">Young's double slit experiment with white light which consist wavelength from range $4000 Ã$ to $7000 Ã$
<br/>$\because$ At the centre of the screen, the path difference is zero for all wavelengths. The bright fringes of these wavelengths overlap at the centre. Thus, the white fringe at the centre is formed.</div>


title: if-ytan-1-fracsqrt1x21x-then-yprime1
slug: if-ytan-1-fracsqrt1x21x-then-yprime1-53171
question: <div class="question">If \(y=\tan ^{-1} \frac{\sqrt{1+x^2}-1}{x}\), then \(y^{\prime}(1)=\)</div>
tags: ['Mathematics', 'Differentiation', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(1 / 4\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(1 / 2\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(-1 / 4\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(-1 / 2\)</span> </li> </ul>

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

answer:
<div class="solution">Hints: \(y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right) \quad\) Put \(x=\tan \theta\)<br/>\(\begin{aligned} &amp; =\tan ^{-1}\left(\frac{\sec \theta-1}{\tan \theta}\right)=\tan ^{-1}\left(\frac{1-\cos \theta}{\sin \theta}\right) \\ &amp; =\tan ^{-1}\left(\frac{2 \sin ^2 \frac{\theta}{2}}{2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}}\right)=\tan ^{-1} \tan \frac{\theta}{2} \\ &amp; =\frac{\theta}{2}=\frac{1}{2} \cdot \tan ^{-1} x, y^{\prime}=\frac{1}{2\left(1+x^2\right)} \\ &amp; y^{\prime}(1)=\frac{1}{2.2}=\frac{1}{4}\end{aligned}\)</div>


tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
title:
if-z-1-2-3-i-and-z-2-3-4-i-be-two-points-on-the-complex-plane-then-the-set-of-complex-number-z-satisfying-z-z-1-2-z-z-2-2-z-1-z-2-2-represents

slug:
if-z-1-2-3-i-and-z-2-3-4-i-be-two-points-on-the-complex-plane-then-the-set-of-complex-number-z-satisfying-z-z-1-2-z-z-2-2-z-1-z-2-2-represents-99638

question:
<div class="question">If $z_{1}=2+3 i$ and $z_{2}=3+4 i$ be two points on the complex plane. Then, the set of complex number $z$ satisfying $\left|z-z_{1}\right|^{2}+\left|z-z_{2}\right|^{2}$
<br/>$=\left|z_{1}-z_{2}\right|^{2}$ represents</div>

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

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

answer:
<div class="solution">Given, $z_{1}=2+3 i$ and $z_{2}=3+4 i$
<br/>Now, we have $\left|z-z_{1}\right|^{2}+\left|z-z_{2}\right|^{2}=\left|z_{1}-z_{2}\right|^{2}$
<br/>(let $z=x+i y)$
<br/>$\Rightarrow|(x+i y)-(2+3 i)|^{2}+|(x+i y)-(3+4 i)|^{2}$
<br/>$\quad=|(2+3 i)-(3+4 i)|^{2}$
<br/>$\Rightarrow|(x-2)+i(y-3)|^{2}+|(x-3)+i(y-4)|^{2}$
<br/>$\quad=|-1-i|^{2}$
<br/>$\Rightarrow(x-2)^{2}+(y-3)^{2}+(x-3)^{2}+(y-4)^{2}=1+1$
<br/>$\Rightarrow \quad x^{2}+4-4 x+y^{2}+9-6 y$
<br/>$\quad+x^{2}+9-6 x+y^{2}+16-8 y=2$
<br/>$\Rightarrow \quad 2 x^{2}+2 y^{2}-10 x-14 y+36=0$
<br/>$\Rightarrow \quad x^{2}+y^{2}-5 x-7 y+18=0$
<br/>which represent a circle with centre $\left(\frac{5}{2}, \frac{7}{2}\right)$ and radius $\sqrt{\frac{25}{4}+\frac{49}{4}-18}=\frac{1}{\sqrt{2}}$</div>


title: if-z-1-and-z-1-then-all-the-points-representing-1-z-2-z-lie-on-1
slug: if-z-1-and-z-1-then-all-the-points-representing-1-z-2-z-lie-on-1-17918
tags: ['Mathematics', 'Complex Number', 'JEE Main']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If $|z|=1$ and $z \neq \pm 1$, then all the points representing $\frac{z}{1-z^{2}}$ lie on;</div>

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

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

answer:
<div class="solution">Let $z=e^{i \theta}, \theta \neq \pm n \pi ~ n \in I$
<br/>Let $w=\frac{e^{i \theta}}{1-e^{i 2 \theta}}=\frac{1}{e^{-i \theta}-e^{i \theta}}=\frac{1}{-2 \cdot i \sin \theta}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/lmK8SwOwnDk6k0gCM8Bj7b9yXiP7dMn3TpAj0QF3e_4.original.fullsize.png"/><br/> <br/>$\therefore$ Locus is y-axis</div>


tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P1.db
title:
if-z-1-and-z-2-be-two-nonzero-complex-numbers-such-that-z-2-z-1-z-1-z-2-1-then-the-origin-and-the-points-represented-by-z-1-and-z-2

slug:
if-z-1-and-z-2-be-two-nonzero-complex-numbers-such-that-z-2-z-1-z-1-z-2-1-then-the-origin-and-the-points-represented-by-z-1-and-z-2-68236

question:
<div class="question">If $z_{1}$ and $z_{2}$ be two non-zero complex numbers such that $\frac{z_{1}}{z_{2}}+\frac{z_{2}}{z_{1}}=1,$ then the origin and the points represented by $z_{1}$ and $z_{2}$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">form an equilateral triangle</span> </div>

answer:
<div class="solution">We know that, if $z_{1}, z_{2}$ and $z_{3}$ are the vertices of an equilateral triangle. Then,
<br/>$$
<br/>z_{1}^{2}+z_{2}^{2}+z_{3}^{2}-z_{1} z_{2}-z_{2} z_{3}-z_{3} z_{1}=0
<br/>$$
<br/>Now, but we have
<br/>$$
<br/>\begin{aligned}
<br/>\frac{z_{1}}{z_{2}}+\frac{z_{2}}{z_{1}} &amp;=1 \\
<br/>\Rightarrow \quad z_{1}^{2}+z_{2}^{2} &amp;=z_{1} z_{2} \\
<br/>\Rightarrow \quad z_{1}^{2}+z_{2}^{2}-z_{1} z_{2} &amp;=0 \\
<br/>z_{3} &amp;=0
<br/>\end{aligned}
<br/>$$
<br/>Hence, given points form an equilateral triangle.</div>


title: if-z-1-i-4-then-z-is-where-z-is-complex-conjugate-of-z
slug: if-z-1-i-4-then-z-is-where-z-is-complex-conjugate-of-z-69116
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If $z=\frac{4}{1-i}$, then $\bar{z}$ is (where $\bar{z}$ is complex conjugate of $z$ )</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4}{1+\mathrm{i}}$</span> </div>

answer:
<div class="solution">Hints: $z=\frac{4}{1-i}$<br/>$$<br/>\overline{\mathrm{z}}=\frac{4}{1+\mathrm{i}}<br/>$$</div>


title: if-z-1-z-1-is-purely-imaginary-then
slug: if-z-1-z-1-is-purely-imaginary-then-41119
question: <div class="question">If $\frac{z-1}{z+1}$ is purely imaginary, then</div>
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$|z|=\frac{1}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$|z|=1$</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">$|z|=2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$|z|=3$</span> </li> </ul>

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

answer:
<div class="solution">Let $\omega=\frac{z-1}{z+1}$
<br/>Then, using componendo and dividendo, we get
<br/>$$
<br/>\begin{array}{l}
<br/>\quad z=\frac{1+\omega}{1-\omega} \\
<br/>\Rightarrow \quad|z|=\left|\frac{\omega+1}{\omega-1}\right| \\
<br/>\Rightarrow \quad|z|=1 \\
<br/>\Rightarrow \quad|\omega+1|=|\omega-1|
<br/>\end{array}
<br/>$$
<br/>Let $6=u+i v$
<br/>Then, $|\omega+1|=|u+i v+1|$
<br/>$$
<br/>=|(u+1)+i v|=\sqrt{(u+1)^{2}+v^{2}}
<br/>$$
<br/>and $|\omega-1|=\sqrt{(t u-1)^{2}+v^{2}}$
<br/>$\therefore$ From Eq. (i)
<br/>$$
<br/>\begin{array}{rlr} 
<br/>&amp; \sqrt{(u+1)^{2}+v^{2}}=\sqrt{(u-1)^{2}+v^{2}} \\
<br/>\Rightarrow &amp; (u+1)^{2}+v^{2} &amp; =(v-1)^{2}+v^{2} \\
<br/>\Rightarrow &amp; u=0
<br/>\end{array}
<br/>$$
<br/>$\therefore \omega=\frac{z-1}{z+1}$ is a pure imaginary number.</div>


title: if-z-1-z-2-z-3-are-imaginary-numbers-such-that-z-1-z-2-z-3-z-1-1-z-2-1-z-3-1-1-then-z-1-z-2-z-3-is
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P1.db
slug:
if-z-1-z-2-z-3-are-imaginary-numbers-such-that-z-1-z-2-z-3-z-1-1-z-2-1-z-3-1-1-then-z-1-z-2-z-3-is-76616

question:
<div class="question">If $z_{1}, z_{2}, z_{3}$ are imaginary numbers such that $\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=\left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}\right|=1,$ then
<br/>$\left|z_{1}+z_{2}+z_{3}\right|$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">equal to 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">less than 1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">greater than 1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">equal to 3</span> </li> </ul>

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

answer:
<div class="solution">We have, $\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=1$
<br/>$\Rightarrow \quad\left|z_{1}\right|^{2}=\left|z_{2}\right|^{2}=\left|z_{3}\right|^{2}=1$
<br/>$\Rightarrow \quad \quad z_{1} \bar{z}_{1}=z_{2} \bar{z}_{2}=z_{3} \bar{z}_{3}=1$
<br/>$\Rightarrow \quad \frac{1}{z_{1}}=\bar{z}_{1} \frac{1}{z_{2}}=\bar{z}_{2} \frac{1}{z_{3}}=\bar{z}_{3}$
<br/>Now. $\quad\left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}\right|=1$
<br/>$\begin{array}{ll}\Rightarrow &amp; \left|\bar{z}_{1}+\bar{z}_{2}+\bar{z}_{3}\right|=1 \\ \Rightarrow &amp; \left|\overline{z_{1}+z_{2}+z_{3}}\right|=1 \\ \therefore &amp; \left|z_{1}+z_{2}+z_{j}\right|=1\end{array}$</div>


title: if-z-25-i-15-then-maximum-ar-g-z-minimum-ar-g-z-is-equal-to
slug: if-z-25-i-15-then-maximum-ar-g-z-minimum-ar-g-z-is-equal-to-11922
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If $|z-25 i| \leq 15$, then Maximum $\arg (z)-$ Minimum $\arg (z)$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \cos ^{-1}\left(\frac{3}{5}\right)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$2 \cos ^{-1}\left(\frac{4}{5}\right)$</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">$\frac{\pi}{2}+\cos ^{-1}\left(\frac{3}{5}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sin ^{-1}\left(\frac{3}{5}\right)-\cos ^{-1}\left(\frac{3}{5}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \cos ^{-1}\left(\frac{4}{5}\right)$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/EKK5RMJuiePKuqWkXVpnlShupSdjYsl-X-0i7uXrlMA.original.fullsize.png"/><br/><br/>$$<br/>\because \cos \theta=\frac{15}{25}=\frac{3}{5}<br/>$$<br/>$\therefore \operatorname{Min} \arg (z)=\cos ^{-1}\left(\frac{3}{5}\right)$<br/>$\operatorname{Max} \arg (z)=\pi-\cos ^{-1}\left(\frac{3}{5}\right)=\frac{\pi}{2}+\sin ^{-1}\left(\frac{3}{5}\right)$<br/>$\therefore$ difference $=\frac{\pi}{2}+\sin ^{-1}\left(\frac{3}{5}\right)-\cos ^{-1}\left(\frac{3}{5}\right)=2 \sin ^{-1}\left(\frac{3}{5}\right)=2 \cos ^{-1}\left(\frac{4}{5}\right)$</div>


title: if-z-i-z-1-z-2-0-for-a-complex-number-z-then-z
slug: if-z-i-z-1-z-2-0-for-a-complex-number-z-then-z-37097
question: <div class="question">If $|z+i|-|z-1|=|z|-2=0$ for a complex number $z$, then $z=$</div>
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{2}(1+i)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{2}(1-i)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\sqrt{2}(-1+i)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{2}(-1-\mathrm{i})$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\sqrt{2}(1-i)$, $\sqrt{2}(-1+i)$</span> </div>

answer:
<div class="solution">$|z| =2$ represents circle
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/in6Eo9iKPZGsZshWOXXo0_95nNrcIVx5yqN3-sU3vSg.original.fullsize.png"/><br/> <br/>$|z+i|=|z-1|$ represents<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/r5ORFn6uNK460rTzmVoJEvNxfTFi0Is6IMzpeS613AM.original.fullsize.png"/><br/> <br/>Solving $x^{2}+y^{2}=4$ and $y=-x$<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/g3YXuzaqeMIKwOWDwBHLnXx_uoHJCi7eJEuHG2rUgAc.original.fullsize.png"/><br/> <br/>$z=\sqrt{2}(1-i), \quad \sqrt{2}(-1+i)$</div>


title: if-z-r-sin-11-2-i-cos-11-2-then-r-0-10-z-r-is-equal-to
slug: if-z-r-sin-11-2-i-cos-11-2-then-r-0-10-z-r-is-equal-to-81824
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2018']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If $Z_{r}=\sin \frac{2 \pi}{11}-i \cos \frac{2 \pi}{11},$ then $\sum_{r=0}^{10} Z_{r}$ is equal to</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">0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">i</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-i$</span> </li> </ul>

answer:
<div class="solution">We have, $Z,=\sin \frac{2 \pi r}{11}-i \cos \frac{2 \pi}{11}$
<br/>$$
<br/>=-i\left(\cos \frac{2 \pi r}{11}+i \sin \frac{2 \pi r}{11}\right)
<br/>$$
<br/>$\therefore$
<br/>$$
<br/>\begin{aligned}
<br/>&amp;=-i e^{\frac{i 2 \pi}{11}} \\
<br/>\sum_{r=0}^{10} Z_{r} &amp;=-i \sum_{r=0}^{10} e^{\frac{i 2 \pi}{11}}
<br/>\end{aligned}
<br/>$$
<br/>$$
<br/>=-i \times 0=0
<br/>$$</div>


title: if-z-sin-i-cos-then-for-any-integer-n
slug: if-z-sin-i-cos-then-for-any-integer-n-45135
question: <div class="question">If $z=\sin \theta-i \cos \theta,$ then for any integer $n$</div>
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$z^{n}+\frac{1}{z^{n}}=2 \cos \left(\frac{n \pi}{2}-n \theta\right)$</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">$z^{n}+\frac{1}{z^{n}}=2 \sin \left(\frac{n \pi}{2}-n \theta\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$z^{n}-\frac{1}{z^{n}}=2 i \sin \left(n \theta-\frac{n \pi}{2}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$z^{n}-\frac{1}{z^{n}}=2 i \cos \left(\frac{n \pi}{2}-n \theta\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$z^{n}+\frac{1}{z^{n}}=2 \cos \left(\frac{n \pi}{2}-n \theta\right)$, $z^{n}-\frac{1}{z^{n}}=2 i \sin \left(n \theta-\frac{n \pi}{2}\right)$</span> </div>

answer:
<div class="solution">Given, $z=\sin \theta-i \cos \theta$
<br/>$=\cos \left(\theta-\frac{\pi}{2}\right)+i \sin \left(\theta-\frac{\pi}{2}\right)=e^{i(\theta-\frac{\pi}{2}).}$
<br/>Now. $z^{n}=e^{i(n\theta-\frac{n\pi}{2}).}=\cos \left(n \theta-\frac{n \pi}{2}\right)+i \sin \left(n \theta-\frac{n \pi}{2}\right)$
<br/>$\Rightarrow \frac{1}{z^{n}}=e^{i\left(\frac{n \pi}{2}-n\theta\right)}=\cos \left(n \theta-\frac{n \pi}{2}\right)-i \sin \left(n \theta-\frac{n \pi}{2}\right)$
<br/>$\therefore \quad z^{n}+\frac{1}{z^{n}}=2 \cos \left(n \theta-\frac{n \pi}{2}\right)=2 \cos \left(\frac{n \pi}{2}-n \theta\right)$
<br/>and $z^{n}-\frac{1}{z^{n}}=2 i \sin \left(n \theta-\frac{n \pi}{2}\right)$</div>


tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
title:
if-z-x-i-y-where-x-and-y-are-real-numbers-and-i-1-then-the-points-x-y-for-which-z-i-z-1-is-real-lie-on

slug:
if-z-x-i-y-where-x-and-y-are-real-numbers-and-i-1-then-the-points-x-y-for-which-z-i-z-1-is-real-lie-on-37138

question:
<div class="question">If $z=x+i y,$ where $x$ and $y$ are real numbers and $i=\sqrt{-1}$, then the points $(x, y)$ for which $\frac{z-1}{z-i}$ is real, lie on</div>

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

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

answer:
<div class="solution">Given, $z=x+i y$
<br/>Now, $\frac{z-1}{z-i}=\frac{(x+y)-1}{(x+i y)-i}$
<br/>$=\frac{(x-1)+i y}{x+i(y-1)} \times \frac{x-i(y-1)}{x-i(y-1)}$
<br/>$=\frac{x(x-1)+i x y-i(x-1)(y-1)+y(y-1)}{x^{2}+(y-1)^{2}}$
<br/>$=\frac{\left(x^{2}+y^{2}-x-y\right)+i(x y-x y+y+x-1)}{\left(x^{2}+y^{2}+1^{-2 y}\right)}$
<br/>$=\left(\frac{x^{2}+y^{2}-x-y}{x^{2}+y^{2}-2 y+1}\right)+i\left(\frac{x+y-1}{x^{2}+y^{2}-2 y+1}\right) \ldots(0)$
<br/>Given, $\frac{z-1}{z-i}$ is real.
<br/>So, its imaginary part should be zero. i.e.. $\quad \frac{x+y-1}{x^{2}+y^{2}-2 y+1}=0$
<br/>$\Rightarrow \quad x+y=1$
<br/>$\left(\because x^{2}+y^{2}-2 y+1 \neq 0\right)$
<br/>Which represent a straight line.</div>


title: if-z-x-iy-and-z-13-p-iq-x-y-p-q-r-then-p-2-q-2-p-x-q-y-is-equal-to
slug: if-z-x-iy-and-z-13-p-iq-x-y-p-q-r-then-p-2-q-2-p-x-q-y-is-equal-to-84797
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2022']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-2$</span> </div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If $z=x$ - iy and $z^{1 / 3}=p+$ iq $(x, y, p, q \in \mathbb{R})$, then $\frac{\left(\frac{x}{p}+\frac{y}{q}\right)}{\left(p^2+q^2\right)}$ is 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">-1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">$z=p^3-3 p q^2+i\left(3 p^2 q-q^3\right)=x-i y$<br/>$\begin{aligned}<br/>&amp;x=p\left(p^2-3 q^2\right) \\<br/>&amp;y=-q\left(3 p^2-q^2\right) \\<br/>&amp;\therefore \frac{x}{p}+\frac{y}{q}=p^2-3 q^2-3 p^2+q^2=-2\left(p^2+q^2\right)<br/>\end{aligned}$</div>


tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P1.db
title:
if-z1-and-z2-are-two-complex-numbers-satisfying-the-equation-leftfracz1z2z1z2right1-then-fracz1z2-may-be

slug:
if-z1-and-z2-are-two-complex-numbers-satisfying-the-equation-leftfracz1z2z1z2right1-then-fracz1z2-may-be-98375

question:
<div class="question">If \(z_1\) and \(z_2\) are two complex numbers satisfying the equation \(\left|\frac{z_1+z_2}{z_1-z_2}\right|=1\), then \(\frac{z_1}{z_2}\) may be</div>

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

answer:
<div class="solution">Hint : \(\left|\frac{z_1+z_2}{z_1-z_2}\right|=1\)<br/>\(\left|z_1 / z_2+1\right|=\left|z_1 / z_2-1\right|\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/7kA_PKtwY5dS9DzWJKbmF4Fhc-V99wO7SgcNwqIwOn8.original.fullsize.png"/><br/><br/>Distance of \(\frac{z_1}{z_2}\) from -1 and 1 are equal<br/>So, locus of \(\frac{z_1}{z_2}\) is perpendicular bisector of line joining \((-1,0) ~\&amp;~(1,0)\)<br/>\(\therefore \frac{\boldsymbol{z}_1}{\mathbf{z}_2} \Rightarrow\) purely imaginary or 0</div>


title: if-zleftbeginarrayccc1-12-i-5-i-12-i-3-53-i-5-i-53-i-7endarrayright-then-isqrt1
slug: if-zleftbeginarrayccc1-12-i-5-i-12-i-3-53-i-5-i-53-i-7endarrayright-then-isqrt1-77355
tags: ['Mathematics', 'Determinants', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">If \(z=\left(\begin{array}{ccc}1 &amp; 1+2 i &amp; -5 i \\ 1-2 i &amp; -3 &amp; 5+3 i \\ 5 i &amp; 5-3 i &amp; 7\end{array}\right)\) then \((i=\sqrt{-1})\)</div>

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

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

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \text { Hints : } z=\left|\begin{array}{ccc}<br/>1 &amp; 1+2 i &amp; -5 i \\<br/>1-2 i &amp; -3 &amp; 5+3 i \\<br/>5 i &amp; 5-3 i &amp; 7<br/>\end{array}\right|=1(-21-64)-((1-2 i)(7(1+2 i)+5 i(5-3 i)))+5 i((1+2 i)(5+3 i)-15 i) \\<br/>&amp; \text { = Real } \\<br/>&amp;<br/>\end{aligned}\)</div>


title: in-2-butene-which-one-of-the-following-statements-is-true
slug: in-2-butene-which-one-of-the-following-statements-is-true-31438
question: <div class="question">In 2 -butene, which one of the following statements is true?</div>
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{C}_{1}-\mathrm{C}_{2}$ bond is a $\mathrm{sp}^{3}-\mathrm{sp}^{3}-\mathrm{\sigma}$ -bond</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}_{2}-\mathrm{C}_{3}$ bond is $s \mathrm{p}^{3}-\mathrm{sp}^{2}-\mathrm{\sigma}$ -bond</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{C}_{1}-\mathrm{C}_{2}$ bond is a $s \mathrm{p}^{3}-\mathrm{sp}^{2}-\mathrm{\sigma}$ -bond</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\mathrm{C}_{1}-\mathrm{C}_{2}$ bond is a $s \mathrm{p}^{2}-\mathrm{sp}^{2}-\mathrm{\sigma}$ -bond</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}_{1}-\mathrm{C}_{2}$ bond is a $s \mathrm{p}^{3}-\mathrm{sp}^{2}-\mathrm{\sigma}$ -bond</span> </div>

answer:
<div class="solution">The structure of 2 -butene is as
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_che_a5.png"/></div>


tags: ['Mathematics', 'Permutation Combination', 'WBJEE', 'WBJEE 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">720</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-a-12-storied-building-3-persons-enter-a-lift-cabin-it-is-known-that-they-will-leave-the-lift-at-different-floors-in-how-many-ways-can-they-do-so-if

slug:
in-a-12-storied-building-3-persons-enter-a-lift-cabin-it-is-known-that-they-will-leave-the-lift-at-different-floors-in-how-many-ways-can-they-do-so-if-96355

question:
<div class="question">In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">36</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">120</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">240</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">720</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Hint: 
<br/>Total no. of ways $=10_{p_{3}}=720$ (except the floor they enter and second floor)</div>


tags: ['Mathematics', 'Properties of Triangles', 'WBJEE', 'WBJEE 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-a-a-bc-a-b-c-are-the-sides-of-the-triangle-opposite-to-the-angles-a-b-c-respectively-then-the-value-of-a-3-sin-b-c-b-3-sin-c-a-c-3-sin-a-b-is-equal

slug:
in-a-a-bc-a-b-c-are-the-sides-of-the-triangle-opposite-to-the-angles-a-b-c-respectively-then-the-value-of-a-3-sin-b-c-b-3-sin-c-a-c-3-sin-a-b-is-equal-30866

question:
<div class="question">In a $\triangle A B C, a, b, c$ are the sides of the triangle opposite to the angles $A, B, C,$ respectively. Then, the value of $a^{3} \sin (B-C)$ $+b^{3} \sin (C-A)+c^{3} \sin (A-B)$ is equal to</div>

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

answer:
<div class="solution">$\sum a^{3} \sin (B-C)$
<br/>$=\sum k^{3} \sin ^{3} A \sin (B-C)$
<br/>$$
<br/>\begin{aligned}\left[\because \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=k\right] \\=\sum k^{3}\left[\sin ^{2} A \sin (B+C) \sin (B-C)\right] \\=k^{3}\left[\left\{\sin ^{2} A \times \frac{1}{2}(\cos 2 C-\cos 2 B)\right\}\right.\\+\sin ^{2} B \times \frac{1}{2}(\cos 2 A-\cos 2 C) \\\left.+\sin ^{2} C \times \frac{1}{2}(\cos 2 B-\cos 2 A)\right] \end{aligned}
<br/>$$
<br/>$=\frac{k^{3}}{2}\left[\sin ^{2} A\left(1-2 \sin ^{2} C-1+2 \sin ^{2} B\right)\right.$
<br/>$+\sin ^{2} B\left(1-2 \sin ^{2} A-1+2 \sin ^{2} C\right)$
<br/>$\left.+\sin ^{2} C\left(1-2 \sin ^{2} B-1+2 \sin ^{2} A\right)\right]$
<br/>$=\frac{k^{3}}{2}\left[-2 \sin ^{2} A \sin ^{2} C+2 \sin ^{2} A \sin ^{2} B\right.$
<br/>$-2 \sin ^{2} B \sin ^{2} A+2 \sin ^{2} B \sin ^{2} C$
<br/>$\left.-2 \sin ^{2} C \sin ^{2} B+2 \sin ^{2} C \sin ^{2} A\right]$
<br/>$=\frac{k^{3}}{2}[0]=0$</div>


title: in-a-a-bc-tan-a-and-tan-b-are-the-roota-pq-x-2-1-r-2-x-then-a-bc-is
slug: in-a-a-bc-tan-a-and-tan-b-are-the-roota-pq-x-2-1-r-2-x-then-a-bc-is-11612
tags: ['Mathematics', 'Quadratic Equation', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In a $\triangle A B C$, tan $A$ and $\tan B$ are the roota $p q\left(x^{2}+1\right)=r^{2} x$ Then, $\Delta A B C$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a right angled triangle</span> </div>

answer:
<div class="solution">Given equation can be rewritten as $x^{2}-\frac{r^{2}}{p q} x+1=0$
<br/>$\therefore \quad \tan A+\tan B=\frac{r^{2}}{p q}$
<br/>and $\tan A \tan B=1$
<br/>We know, $A+B+C=180^{\circ}$
<br/>$\Rightarrow \quad(A+B)=180^{\circ}-C$
<br/>$\Rightarrow \quad \tan (A+B)=\tan \left(180^{\circ}-C\right)$
<br/>$\Rightarrow \quad \frac{\tan A+\tan B}{1-\tan A \tan B}=-\tan C$
<br/>$\Rightarrow \quad \frac{r^{2} / p q}{1-1}=-\tan C$
<br/>$\Rightarrow \quad \infty=-\tan C \Rightarrow C=90^{\circ}$
<br/>Hence, $\triangle A B C$ is a right angled triangle.</div>


title: in-a-abc-2-acsin-2-a-b-c-is-equal-to
slug: in-a-abc-2-acsin-2-a-b-c-is-equal-to-82914
tags: ['Mathematics', 'Properties of Triangles', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In $\mathrm{a} \triangle \mathrm{ABC}, 2 \operatorname{acsin} \frac{\mathrm{A}-\mathrm{B}+\mathrm{C}}{2}$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{a}^2+\mathrm{b}^2-\mathrm{c}^2$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$c^2+a^2-b^2$</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">$\mathrm{b}^2-\mathrm{a}^2-\mathrm{c}^2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{c}^2-\mathrm{a}^2-\mathrm{b}^2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$c^2+a^2-b^2$</span> </div>

answer:
<div class="solution">Hints : $2 \mathrm{ac} \sin \left(\frac{\mathrm{A}+\mathrm{C}-\mathrm{B}}{2}\right) \quad\left[\frac{\mathrm{A}+\mathrm{C}}{2}=\frac{\pi}{2}-\frac{\mathrm{B}}{2}\right],=2 \mathrm{ac} \sin \left(\frac{\pi}{2}-\mathrm{B}\right)=2 \mathrm{ac} \cos \mathrm{B} \quad=\mathrm{a}^2+\mathrm{c}^2-\mathrm{b}^2$</div>


title: in-a-bc-if-a-2-cos-2-a-b-2-c-2-0-then
slug: in-a-bc-if-a-2-cos-2-a-b-2-c-2-0-then-12545
question: <div class="question">In $\Delta A B C$, if $a^{2} \cos ^{2} A-b^{2}-c^{2}=0,$ then</div>
tags: ['Mathematics', 'Properties of Triangles', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{4}    &lt; A &lt; \frac{\pi}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{2}    &lt; A &lt; \pi$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$A=\frac{\pi}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$A    &lt; \frac{\pi}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{2}    &lt; A &lt; \pi$</span> </div>

answer:
<div class="solution">We have, $a^{2} \cos ^{2} A-b^{2}-c^{2}=0$
<br/>$\Rightarrow \quad a^{2} \cos ^{2} A=b^{2}+c^{2}$
<br/>Also in $\triangle A B C$, we have $\begin{aligned} \cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c} &amp;=\frac{a^{2} \cos ^{2} A-a^{2}}{2 b c} \\=&amp; \frac{-a^{2}\left(1-\cos ^{2} A\right)}{2 b c}=\frac{-a^{2} \sin ^{2} A}{2 b c}    &lt; 0 \\ &amp; \quad \because 0 &lt; A &lt; \pi, a, b, c&gt;0 \end{aligned}$
<br/>$\Rightarrow \cos A &lt; 0 \Rightarrow A$ lies in IInd quadrant.
<br/>$\Rightarrow \quad \frac{\pi}{2} &lt; A &lt; \pi$</div>


tags: ['Mathematics', 'Permutation Combination', 'WBJEE', 'WBJEE 2020']
correct_option: <div class="correct-answer"> The correct answers are: <span class="option-value">11</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-a-certain-test-there-are-n-questions-in-this-test-2-n-i-students-gave-wrong-answers-to-at-least-i-questions-where-i-1-2-n-if-the-total-number-of-wr

slug:
in-a-certain-test-there-are-n-questions-in-this-test-2-n-i-students-gave-wrong-answers-to-at-least-i-questions-where-i-1-2-n-if-the-total-number-of-wr-93495

question:
<div class="question">In a certain test, there are n questions. In this test $2^{n-i}$ students gave wrong answers to at least i questions, where i $=1,2, \ldots \ldots \mathrm{n}$. If the total number of wrong answers given is 2047 , then $\mathrm{n}$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">10</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">11</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">13</span> </li> </ul>

answer:
<div class="solution">Hint: 
<br/>Total students was gave wrong answer to exactly i - questions $=2^{n-i}-2^{n-(i+1)}$
<br/>Total wrong answer given \(\sum_{i=0}^{n-1} i \times \left(2^{n-i}-2^{n-(i+1)}\right)+n \times 1\)
<br/>$\Rightarrow 2^{n-1}+\ldots \ldots 1=2047$
<br/>$\Rightarrow 2^{n}=2048$
<br/>$\Rightarrow \mathrm{n}=11$</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.5</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-a-certain-town-60-of-the-families-own-a-car-30-own-a-house-and-20-own-both-car-and-house-if-a-family-is-randomly-chosen-then-what-is-the-probabilit

slug:
in-a-certain-town-60-of-the-families-own-a-car-30-own-a-house-and-20-own-both-car-and-house-if-a-family-is-randomly-chosen-then-what-is-the-probabilit-72934

question:
<div class="question">In a certain town, $60 \%$ of the families own a car, $30 \%$ own a house and $20 \%$ own both car and house. If a family is randomly chosen. then what is the probability that this family owns a car or a house but not both?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</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">B</span> <span class="option-data">0.7</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.9</span> </li> </ul>

answer:
<div class="solution">Let $A$ be the set of families who own a car and $B$ be the set of families who own a house.
<br/>Then, $\quad P(A)=60 \%, P(B)=30 \%$
<br/>and $P(A \cap B)=20 \%$
<br/>Now, $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
<br/>$=60+30-20=70 \%$
<br/>Now, families who owns a car or a house but not both $=A \Delta B$
<br/>$$
<br/>\begin{aligned}
<br/>\Rightarrow \quad P(A \Delta B) &amp;=P(A \cup B)-P(A \cap B) \\
<br/>&amp;=70-20=50 \%=0.5
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P1.db
title:
in-a-closed-circuit-there-is-only-a-coil-of-inductance-l-and-resistance-100-the-coil-is-situated-in-a-uniform-magnetic-field-all-on-a-sudden-the-magne

slug:
in-a-closed-circuit-there-is-only-a-coil-of-inductance-l-and-resistance-100-the-coil-is-situated-in-a-uniform-magnetic-field-all-on-a-sudden-the-magne-46194

question:
<div class="question">In a closed circuit there is only a coil of inductance $L$ and resistance $100 \Omega$. The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by $5 \mathrm{Weber}$. What amount of charge will flow in the circuit as a result?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$500 \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.05 \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Value of $L$ is to be known to find the charge flown</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.05 \mathrm{C}$</span> </div>

answer:
<div class="solution">Emf $=-\frac{\mathrm{d} \phi}{\mathrm{dt}}($ Faraday's Law $)$<br/>$\mathrm{i}_{\text {induced }}=\frac{\mathrm{Emf}}{\mathrm{R}}=-\frac{\mathrm{d} \phi}{\mathrm{dt}} \times \frac{1}{\mathrm{R}}$<br/>$\Rightarrow \frac{\mathrm{dq}}{\mathrm{dt}}=-\frac{1}{\mathrm{R}} \frac{\mathrm{d} \phi}{\mathrm{dt}} \Rightarrow \mathrm{dq}=-\frac{\mathrm{d} \phi}{\mathrm{R}} \Rightarrow \int \mathrm{dq}=-\int \frac{\mathrm{d} \phi}{\mathrm{R}}$<br/>$\Rightarrow \mathrm{q}_{\text {flown }}=\frac{\phi_{\mathrm{i}}-\phi_{\mathrm{f}}}{\mathrm{R}}=\frac{5 \text { weber }}{100}=0.05 \mathrm{C} .$</div>


tags: ['Chemistry', 'Solid State', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P1.db
title:
in-a-closepacked-bodycentred-cubic-lattice-of-potassium-the-correct-relation-between-the-atomic-radius-r-of-potassium-and-the-edgelength-of-the-cube-i

slug:
in-a-closepacked-bodycentred-cubic-lattice-of-potassium-the-correct-relation-between-the-atomic-radius-r-of-potassium-and-the-edgelength-of-the-cube-i-56496

question:
<div class="question">In a close-packed body-centred cubic lattice of potassium, the correct relation between the atomic radius $(r)$ of potassium and the edge-length  of the cube is</div>

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

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

answer:
<div class="solution">$\because$ For be packing, $\sqrt{3} a=4 r \therefore r=\frac{\sqrt{3}}{4} \cdot a$
<br/>where $a=$ edge length $r=$ radius of lattice sphere</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
title:
in-a-common-emitter-configuration-a-transistor-has-50-and-input-resistance-1-k-if-the-peak-value-of-ac-input-is-001-v-then-the-peak-value-of-collector

slug:
in-a-common-emitter-configuration-a-transistor-has-50-and-input-resistance-1-k-if-the-peak-value-of-ac-input-is-001-v-then-the-peak-value-of-collector-21537

question:
<div class="question">In a common emitter configuration, a transistor has $\beta=50$ and input resistance $1 \mathrm{k} \Omega$. If the peak value of a.c. input is $0.01 \mathrm{~V}$ then the peak value of collector current is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.01 \mu \mathrm{A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.25 \mu \mathrm{A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$100 \mu \mathrm{A}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$500 \mu \mathrm{A}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$500 \mu \mathrm{A}$</span> </div>

answer:
<div class="solution">$$<br/>\text { Hints: } \beta=50 \Rightarrow \beta=\frac{\Delta \mathrm{I}_{\mathrm{C}}}{\Delta \mathrm{I}_{\mathrm{B}}} \Rightarrow \Delta \mathrm{I}_{\mathrm{C}}=\beta \times \Delta \mathrm{I}_{\mathrm{B}}<br/>$$<br/>$$<br/>\begin{aligned}<br/>&amp; \Delta \mathrm{I}_{\mathrm{B}}=\frac{0.01}{10^3}=10^{-2} \times 10^{-3}=10^{-5} \\<br/>&amp; \Delta \mathrm{I}_{\mathrm{C}}=50 \times 10^{-5}=500 \times 10^{-6}=500 \mu \mathrm{A}<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P1.db
title:
in-a-flask-the-weight-ratio-of-ch-4-g-and-so-2-g-at-298-k-and-1-bar-is-1-2-the-ratio-of-the-number-of-molecules-of-so-2-g-and-ch-4-g-is

slug:
in-a-flask-the-weight-ratio-of-ch-4-g-and-so-2-g-at-298-k-and-1-bar-is-1-2-the-ratio-of-the-number-of-molecules-of-so-2-g-and-ch-4-g-is-11784

question:
<div class="question">In a flask, the weight ratio of $\mathrm{CH}_{4}(g)$ and $\mathrm{SO}_{2}(g)$ at $298 \mathrm{K}$ and 1 bar is $1: 2 .$ The ratio of the number of molecules of $\mathrm{SO}_{2}(\mathrm{g})$ and $\mathrm{CH}_{4}(g)$ is</div>

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

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

answer:
<div class="solution">Given, weight ratio : $W_{\mathrm{C H_{4}},}: W_{\mathrm{SO}_{2}}=1: 2$ $\because \quad n=\frac{w}{m} \quad\left[\begin{array}{l}n=\text { no. of mole } \\ w=\text { mass } \\ M=\text { molar mas: }\end{array}\right.$
<br/>$\therefore \quad \frac{n_{1}}{n_{2}}=\frac{W_{1}}{M_{1}} \times \frac{M_{2}}{W_{2}}\left\{\begin{array}{l}n_{1}=n_{\mathrm{so}_{1}} \\ n_{2}=n_{\mathrm{Oi}_{2}}\end{array}\right.$
<br/>$=\frac{2}{64} \times \frac{16}{1}$
<br/>$\frac{n_{1}}{n_{2}}=\frac{1}{2},$ i.e. 1: 2
<br/>Also $n \propto N$
<br/>$\therefore$ Ratio of number of molecules is 1: 2.</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P1.db
title:
in-a-frounhofer-diffraction-experiment-a-single-slit-of-width-05-mm-is-illuminated-by-a-monochromatic-light-of-wavelength-600-nm-the-diffraction-patte

slug:
in-a-frounhofer-diffraction-experiment-a-single-slit-of-width-05-mm-is-illuminated-by-a-monochromatic-light-of-wavelength-600-nm-the-diffraction-patte-36834

question:
<div class="question">In a Frounhofer diffraction experiment, a single slit of width $0.5 \mathrm{~mm}$ is illuminated by a monochromatic light of wavelength $600 \mathrm{~nm}$. The diffraction pattern is observed on a screen at a distance of $50 \mathrm{~cm}$ from the slit. What will be the linear separation of the first order minima?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.0 \mathrm{~mm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.1 \mathrm{~mm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.6 \mathrm{~mm}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1.2 \mathrm{~mm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.2 \mathrm{~mm}$</span> </div>

answer:
<div class="solution">Hint:
<br/>$\mathrm{d}=0.5 \mathrm{~mm} .$
<br/>$\lambda=600 \mathrm{~nm} .$ Width of central maxima $=\frac{2 \lambda \mathrm{D}}{\mathrm{d}}$
<br/>$\mathrm{D}=50 \mathrm{~cm}$
<br/>$\frac{2 \lambda \mathrm{D}}{\mathrm{d}}=\frac{2 \times 600 \times 50 \times 10^{-2} \times 10^{-9}}{0.5 \times 10^{-3}}=1.2 \mathrm{~mm}$</div>


tags: ['Mathematics', 'Sequences and Series', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P1.db
title:
in-a-gp-series-consisting-of-positive-terms-each-term-is-equal-to-the-sum-of-next-two-terms-then-the-common-ratio-of-this-gp-series-is

slug:
in-a-gp-series-consisting-of-positive-terms-each-term-is-equal-to-the-sum-of-next-two-terms-then-the-common-ratio-of-this-gp-series-is-95033

question:
<div class="question">In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\sqrt{5}-1}{2}$</span> </div>

answer:
<div class="solution">Let $a_{n}$ be the general term of a GP whose first term is $a$ and common ratio is $r$. Now according to the question,
<br/>$$
<br/>\begin{aligned}
<br/>a_{n} &amp;=a_{n+1}+a_{n+2} \\
<br/>a r^{n-1} &amp;=a r^{n}+a r^{n+1}
<br/>\end{aligned}
<br/>$$
<br/>$\Rightarrow \quad r^{n-1}=r^{n}+r^{n+1}$
<br/>$\Rightarrow \quad 1=\frac{r^{n}}{r^{n-1}}+\frac{r^{n+1}}{r^{n-1}}$
<br/>$\Rightarrow \quad 1=r+r^{2}$
<br/>$\Rightarrow r^{2}+r-1=0$
<br/>$\Rightarrow \begin{aligned}r=&amp; \frac{-1 \pm \sqrt{(1)^{2}-4(1)(-1)}}{2(1)} \\ &amp;=\frac{-1 \pm \sqrt{1+4}}{2}=\frac{-1 \pm \sqrt{5}}{2} \end{aligned}$
<br/>since, GP consists only positive terms
<br/>$\therefore$
<br/>$r=\frac{\sqrt{5}-1}{2}$</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P1.db
title:
in-a-group-of-14-males-and-6-females-8-and-3-of-the-males-and-females-respectively-are-aged-above-40-yr-the-probability-that-a-selected-at-random-from

slug:
in-a-group-of-14-males-and-6-females-8-and-3-of-the-males-and-females-respectively-are-aged-above-40-yr-the-probability-that-a-selected-at-random-from-23779

question:
<div class="question">In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a selected at random from the group is person aged above $40 \mathrm{yr}$ given that the selected person is a female, is</div>

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

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

answer:
<div class="solution">Number of males = 14
<br/>and females $=6$
<br/>Total =14+6=20
<br/>Males above $40 \mathrm{yr}=8$ 
<br/>and females above $40 \mathrm{y}=3$
<br/>Now, P (selected person is female and above 40 yn) $=\frac{3}{6}=\frac{1}{2}$</div>


tags: ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P1.db
title:
in-a-mercury-thermometer-the-ice-point-lower-fixed-point-is-marked-as-1-0-and-the-steam-point-upper-fixed-point-is-marked-as-13-0-at-4-0-c-temperature

slug:
in-a-mercury-thermometer-the-ice-point-lower-fixed-point-is-marked-as-1-0-and-the-steam-point-upper-fixed-point-is-marked-as-13-0-at-4-0-c-temperature-87362

question:
<div class="question">In a mercury thermometer, the ice point (lower fixed point) is marked as $10^{\circ}$ and the steam point (upper fixed point) is marked as $130^{\circ}$. At $40^{\circ} \mathrm{C}$ temperature, what will this thermometer read?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$78^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$66^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$62^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$58^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$58^{\circ}$</span> </div>

answer:
<div class="solution">$\frac{x-10}{130-10}=\frac{40}{100}$
<br/>$$
<br/>\begin{array}{r}
<br/>100 x-1000=4800 \\
<br/>100 x=5800 \\
<br/>x=58^{\circ}
<br/>\end{array}
<br/>$$</div>


tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P1.db
title:
in-a-mixture-two-enantioners-are-found-to-be-present-in-85-and-15-respectively-the-enantiomeric-excess-ee-is

slug:
in-a-mixture-two-enantioners-are-found-to-be-present-in-85-and-15-respectively-the-enantiomeric-excess-ee-is-23290

question:
<div class="question">In a mixture, two enantioners are found to be present in 85\% and $15 \%$ respectively. The enantiomeric. excess (ee) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$85 \%$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$15 \%$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$70 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$60 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$70 \%$</span> </div>

answer:
<div class="solution">$15 \%$ will form racemic mixture with another $15 \%$. Hence. the enantiomeric excess is $=(85-15)=70 \%$</div>


title: in-a-periodic-table-the-basic-character-of-oxides
slug: in-a-periodic-table-the-basic-character-of-oxides-59873
question: <div class="question">In a periodic table the basic character of oxides</div>
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">increases from left to right and decreases from top to bottom</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">decreases from right to left and increases from top to bottom</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">decreases from left to right and increases from top to bottom</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">decreases from left to right and increases from bottom to top</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">decreases from left to right and increases from top to bottom</span> </div>


tags: ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P1.db
title:
in-a-region-the-intensity-of-an-electric-field-is-given-by-e-2-i-3-j-k-in-nc-1-the-electric-flux-through-a-surface-s-10-i-m-2-in-the-region-is

slug:
in-a-region-the-intensity-of-an-electric-field-is-given-by-e-2-i-3-j-k-in-nc-1-the-electric-flux-through-a-surface-s-10-i-m-2-in-the-region-is-71184

question:
<div class="question">In a region, the intensity of an electric field is given by $\mathbf{E}=2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}$ in $\mathrm{NC}^{-1}$. The electric flux through a surface $\mathbf{S}=10 \mathbf{i} \mathrm{m}^{2}$ in the region is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \mathrm{Nm}^{2} \mathrm{C}^{-1}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{Nm}^{2} \mathrm{C}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$15 \mathrm{Nm}^{2} \mathrm{C}^{-1}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$20 \mathrm{Nm}^{2} \mathrm{C}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$20 \mathrm{Nm}^{2} \mathrm{C}^{-1}$</span> </div>

answer:
<div class="solution">Given $\mathbf{E}=(2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}) \mathrm{NC}^{-1}$
<br/>and $\quad \mathrm{S}=10 \mathrm{i} \mathrm{m}^{2}$
<br/>We know that
<br/>$$
<br/>\begin{array}{l}
<br/>\phi=\mathbf{E} \cdot \mathbf{S} \\
<br/>\phi=(2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}) \cdot(10 \mathbf{i}) \\
<br/>\phi=20 \mathrm{Nm}^{2} \mathrm{C}^{-1}
<br/>\end{array}
<br/>$$</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'WBJEE', 'WBJEE 2012']
answer: <div class="solution">Equilibrium constant is independent of the concentration of reactants.</div>
source_db: db\MarksBatch2_P1.db
title:
in-a-reversible-chemical-reaction-at-equilibrium-if-the-concentration-of-any-one-of-the-reactants-is-doubled-then-the-equilibrium-constant-will

slug:
in-a-reversible-chemical-reaction-at-equilibrium-if-the-concentration-of-any-one-of-the-reactants-is-doubled-then-the-equilibrium-constant-will-69451

question:
<div class="question">In a reversible chemical reaction at equilibrium, if the concentration of any one of the reactants is doubled, then the equilibrium constant will</div>

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

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


tags: ['Mathematics', 'Basic of Mathematics', 'WBJEE', 'WBJEE 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-a-rightangled-triangle-the-sides-are-a-b-and-c-with-c-as-hypotenuse-and-c-b-1-c-b-1-then-the-value-of-lo-g-c-b-a-lo-g-c-b-a-2-lo-g-c-b-a-lo-g-c-b-a

slug:
in-a-rightangled-triangle-the-sides-are-a-b-and-c-with-c-as-hypotenuse-and-c-b-1-c-b-1-then-the-value-of-lo-g-c-b-a-lo-g-c-b-a-2-lo-g-c-b-a-lo-g-c-b-a-69681

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

answer:
<div class="solution">Hints : $c^2=a^2+b^2$<br/>$\Rightarrow \mathrm{c}^2-\mathrm{b}^2=\mathrm{a}^2$<br/>$\frac{\frac{\log a}{\log (c+b)}+\frac{\log a}{\log (c-b)}}{\frac{2 \log a \times \log a}{\log (c+b) \log (c-b)}}=\frac{\log a\left(\log \left(c^2-b^2\right)\right)}{2 \log a \log a}=\frac{\log a^2}{\log a^2}=1$</div>


tags: ['Physics', 'Oscillations', 'JEE Main']
source_db: db\MarksBatch2_P1.db
title:
in-a-simple-harmonic-motion-let-mathrmf-be-the-acceleration-and-mathrmt-be-the-time-period-if-x-denotes-the-displacement-then-ft-vs-x-graph-will-look--1

slug:
in-a-simple-harmonic-motion-let-mathrmf-be-the-acceleration-and-mathrmt-be-the-time-period-if-x-denotes-the-displacement-then-ft-vs-x-graph-will-look-1-49865

question:
<div class="question">In a simple harmonic motion, let \(\mathrm{f}\) be the acceleration and \(\mathrm{T}\) be the time period. If \(x\) denotes the displacement, then |fT| vs. X graph will look like,</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/UEwRR0Tw7usv7o2yLhEHtckfhZf2tkDJZ2AcZOeweTU.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mf65-e0fETkVv7rBR8giz3MysUyXWL3jVG4pDMXl4Mo.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/--og3_dtzbLOsn6aCOcnshF_50kqOzACmTBFk3pChfY.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/r2kWjuPCcGD2nKeXh-sPdB-386RFRpwbNlr9TzEqApw.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mf65-e0fETkVv7rBR8giz3MysUyXWL3jVG4pDMXl4Mo.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">\(\begin{gathered}\text {Hint: } F \cdot T=\omega^2 x \cdot \frac{2 \pi}{\omega}=2 \pi \omega x \\ \because \text { F.T }=2 \pi \omega x\end{gathered}\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/WGMv6lNi2guaQUDqKO63Hf2g3JkjZbxG8grNmul8lvY.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P1.db
title:
in-a-simple-harmonic-motion-let-mathrmf-be-the-acceleration-and-mathrmt-be-the-time-period-if-x-denotes-the-displacement-then-ft-vs-x-graph-will-look-

slug:
in-a-simple-harmonic-motion-let-mathrmf-be-the-acceleration-and-mathrmt-be-the-time-period-if-x-denotes-the-displacement-then-ft-vs-x-graph-will-look-66686

question:
<div class="question">In a simple harmonic motion, let \(\mathrm{f}\) be the acceleration and \(\mathrm{T}\) be the time period. If \(x\) denotes the displacement, then |fT| vs. X graph will look like,</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/UEwRR0Tw7usv7o2yLhEHtckfhZf2tkDJZ2AcZOeweTU.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mf65-e0fETkVv7rBR8giz3MysUyXWL3jVG4pDMXl4Mo.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/--og3_dtzbLOsn6aCOcnshF_50kqOzACmTBFk3pChfY.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/r2kWjuPCcGD2nKeXh-sPdB-386RFRpwbNlr9TzEqApw.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mf65-e0fETkVv7rBR8giz3MysUyXWL3jVG4pDMXl4Mo.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">\(\begin{gathered}\text {Hint: } F \cdot T=\omega^2 x \cdot \frac{2 \pi}{\omega}=2 \pi \omega x \\ \because \text { F.T }=2 \pi \omega x\end{gathered}\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/WGMv6lNi2guaQUDqKO63Hf2g3JkjZbxG8grNmul8lvY.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Experimental Physics', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P1.db
title:
in-a-slide-caliper-m-1-number-of-vernier-divisions-is-equal-to-m-number-of-smallest-main-scale-divisions-if-d-unit-is-the-magnitude-of-the-smallest-ma

slug:
in-a-slide-caliper-m-1-number-of-vernier-divisions-is-equal-to-m-number-of-smallest-main-scale-divisions-if-d-unit-is-the-magnitude-of-the-smallest-ma-72031

question:
<div class="question">In a slide caliper, $(m+1)$ number of vernier divisions is equal to $m$ number of smallest main scale divisions. If $d$ unit is the magnitude of the smallest main scale division, then the magnitude of the vernicr constant is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$d /(m+1)$ 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">B</span> <span class="option-data">$d / m$ unit</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">md/ $(m+1)$ unit</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(m+1) d / m$ unit</span> </li> </ul>

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

answer:
<div class="solution">$(m+1)$ vernier division $=m$ main scale division One division on vernier scale $=\left(\frac{m}{m+1}\right)$ division on main scale Vernier constant $=\left(1-\frac{m}{m+1}\right) d=\frac{d}{m+1}$</div>


tags: ['Mathematics', 'Matrices', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P1.db
title:
in-a-third-order-matrix-a-a-0-denotes-the-element-in-the-ith-row-and-j-th-column-if-a-ij-0-for-i-j-1-for-i-j-1-for-i-j-then-the-matrix-is

slug:
in-a-third-order-matrix-a-a-0-denotes-the-element-in-the-ith-row-and-j-th-column-if-a-ij-0-for-i-j-1-for-i-j-1-for-i-j-then-the-matrix-is-75654

question:
<div class="question">In a third order matrix $A$, $a_{0}$ denotes the element in the ith row and $j$ th column. If $a_{i j}=0$ for $i=j,1$ for $i&gt;j,-1$ for $i    &lt; j$ Then the matrix is</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">skew symmetric, not invertible</span> </div>

answer:
<div class="solution">$$
<br/>A=\left[\begin{array}{ccc}
<br/>0 &amp; -1 &amp; -1 \\
<br/>1 &amp; 0 &amp; -1 \\
<br/>1 &amp; 1 &amp; 0
<br/>\end{array}\right]
<br/>$$
<br/>$\Rightarrow$
<br/>$A^{\prime}=\left[\begin{array}{ccc}0 &amp; 1 &amp; 1 \\ -1 &amp; 0 &amp; 1 \\ -1 &amp; -1 &amp; 0\end{array}\right]=-A$
<br/>$\Rightarrow A$ is a skew-symmetric matrix. $\begin{aligned}|A| &amp;=0+1(0+1)-1(-0) \\ &amp;=0+1-1=0=\text { singular } \end{aligned}$
<br/>$\Rightarrow A$ is not invertible.</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
title:
in-a-transistor-output-characteristicy-commonly-used-in-common-emitter-configuration-the-base-current-i-b-the-collector-current-i-c-and-the-collectore

slug:
in-a-transistor-output-characteristicy-commonly-used-in-common-emitter-configuration-the-base-current-i-b-the-collector-current-i-c-and-the-collectore-88395

question:
<div class="question">In a transistor output characteristicy commonly used in common emitter configuration, the base current $I_{B}$, the collector current $I_{C}$ and the collector-emitter voltage $V_{C E}$ have values of the following orders of magnitude in the active region</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$I_{B}$ is in $\mathrm{\mu A}$ and $\mathrm{I_C}$ is in $\mathrm{mA}$ and $\mathrm{V}_{\mathrm{CE}}$ in volt</span> </div>

answer:
<div class="solution">$I_{g}$ is in $\mu$ amp. $I_{c}$ is in $\mathrm{m}$ amp and $V_{CE}$ in volt.</div>


tags: ['Physics', 'Mathematics in Physics', 'JEE Main']
source_db: db\MarksBatch2_P1.db
title:
in-a-triangle-a-bc-the-sides-a-b-and-a-c-are-represented-by-the-vectors-3-i-j-k-and-i-2-j-k-respectively-calculate-the-angle-a-bc-1

slug:
in-a-triangle-a-bc-the-sides-a-b-and-a-c-are-represented-by-the-vectors-3-i-j-k-and-i-2-j-k-respectively-calculate-the-angle-a-bc-1-18829

question:
<div class="question">In a triangle $A B C$, the sides $A B$ and $A C$ are represented by the vectors $3 \mathrm{i}+\mathrm{j}+\mathrm{k}$ and $\mathrm{i}+2 \mathrm{j}+\mathrm{k}$, respectively. Calculate the angle $\angle A B C$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\cos ^{-1} \sqrt{\frac{5}{11}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\cos ^{-1} \sqrt{\frac{6}{11}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(90^{\circ}-\cos ^{-1} \sqrt{\frac{5}{11}}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(180^{\circ}-\cos ^{-1} \sqrt{\frac{5}{11}}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\cos ^{-1} \sqrt{\frac{5}{11}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a14.png"/> <br/> <br/>$A B=3 i+j+\hat{k}$ and $A C=i+2 j+i$
<br/>$8 A=-(3 i+j+k)$
<br/>$\angle A B C$ is angle between $B A$ and $B C$
<br/>$B C=A C+B A$
<br/>$=A C-A B$
<br/>$=\hat{i}+2 \hat{j}+\hat{k}-(3 \hat{i}+\hat{j}+\hat{k})=-2 \hat{i}+\hat{j}$
<br/>$B A \cdot B C=|B A \| B C| \cos \theta$
<br/>$-(3 \hat{i}+\hat{j}+\hat{k}) \cdot(-2 \hat{i}+\hat{j})$
<br/>$=\left(\sqrt{3^{2}+1^{2}+1^{2}}\right) \cdot\left(\sqrt{2^{2}+1^{2}}\right) \cos \theta$
<br/>$\Rightarrow \quad 6-1=\sqrt{11 \times 5} \cdot \cos \theta$
<br/>$\cos \theta=\frac{5}{\sqrt{55}}=\sqrt{\frac{5}{11}}=\theta=\cos ^{-1}=\sqrt{\frac{5}{11}}$</div>


tags: ['Physics', 'Mathematics in Physics', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P1.db
title:
in-a-triangle-a-bc-the-sides-a-b-and-a-c-are-represented-by-the-vectors-3-i-j-k-and-i-2-j-k-respectively-calculate-the-angle-a-bc

slug:
in-a-triangle-a-bc-the-sides-a-b-and-a-c-are-represented-by-the-vectors-3-i-j-k-and-i-2-j-k-respectively-calculate-the-angle-a-bc-33487

question:
<div class="question">In a triangle $A B C$, the sides $A B$ and $A C$ are represented by the vectors $3 \mathrm{i}+\mathrm{j}+\mathrm{k}$ and $\mathrm{i}+2 \mathrm{j}+\mathrm{k}$, respectively. Calculate the angle $\angle A B C$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\cos ^{-1} \sqrt{\frac{5}{11}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\cos ^{-1} \sqrt{\frac{6}{11}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(90^{\circ}-\cos ^{-1} \sqrt{\frac{5}{11}}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(180^{\circ}-\cos ^{-1} \sqrt{\frac{5}{11}}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\cos ^{-1} \sqrt{\frac{5}{11}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a14.png"/> <br/> <br/>$A B=3 i+j+\hat{k}$ and $A C=i+2 j+i$
<br/>$8 A=-(3 i+j+k)$
<br/>$\angle A B C$ is angle between $B A$ and $B C$
<br/>$B C=A C+B A$
<br/>$=A C-A B$
<br/>$=\hat{i}+2 \hat{j}+\hat{k}-(3 \hat{i}+\hat{j}+\hat{k})=-2 \hat{i}+\hat{j}$
<br/>$B A \cdot B C=|B A \| B C| \cos \theta$
<br/>$-(3 \hat{i}+\hat{j}+\hat{k}) \cdot(-2 \hat{i}+\hat{j})$
<br/>$=\left(\sqrt{3^{2}+1^{2}+1^{2}}\right) \cdot\left(\sqrt{2^{2}+1^{2}}\right) \cos \theta$
<br/>$\Rightarrow \quad 6-1=\sqrt{11 \times 5} \cdot \cos \theta$
<br/>$\cos \theta=\frac{5}{\sqrt{55}}=\sqrt{\frac{5}{11}}=\theta=\cos ^{-1}=\sqrt{\frac{5}{11}}$</div>


title: in-a-triangle-abc-if-sin-a-sin-b-c-2-ab-then-the-triangle-is
slug: in-a-triangle-abc-if-sin-a-sin-b-c-2-ab-then-the-triangle-is-55753
tags: ['Mathematics', 'Properties of Triangles', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In a triangle $\mathrm{ABC}$ if $\sin \mathrm{A} \sin \mathrm{B}=\frac{\mathrm{ab}}{\mathrm{c}^2}$, then the triangle is</div>

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

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

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { Hints }: \sin A \sin B=\frac{a b}{c^2} \\<br/>&amp; \Rightarrow c^2=\frac{a b}{\sin A \sin B}=\left(\frac{a}{\sin A}\right)\left(\frac{b}{\sin B}\right) \\<br/>&amp; \Rightarrow c^2=\left(\frac{c}{\sin C}\right)^2 \Rightarrow \sin ^2 C=1 \Rightarrow \sin C=1 \Rightarrow C=90^{\circ}<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Quadratic Equation', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
title:
in-a-triangle-pqr-r-2-if-tan-2-p-and-tan-2-q-are-roots-of-ax-2-bx-c-0-where-a-0-then-which-one-is-true

slug:
in-a-triangle-pqr-r-2-if-tan-2-p-and-tan-2-q-are-roots-of-ax-2-bx-c-0-where-a-0-then-which-one-is-true-61650

question:
<div class="question">In a triangle $\mathrm{PQR}, \angle \mathrm{R}=\pi / 2$. If $\tan \left(\frac{\mathrm{p}}{2}\right)$ and $\tan \left(\frac{\mathrm{Q}}{2}\right)$ are roots of $\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0$, where $\mathrm{a} \neq 0$, then which one is true ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$c=a+b$</span> </div>

answer:
<div class="solution">Hints: $\frac{\mathrm{P}}{2}+\frac{\mathrm{Q}}{2}=\frac{\pi}{2}-\frac{\mathrm{P}}{2}=\frac{\pi}{2}-\frac{\pi}{4}=\frac{\pi}{4}$<br/>$$<br/>\begin{aligned}<br/>&amp; \tan \left(\frac{\rho}{2}+\frac{Q}{2}\right)=1, \frac{-b / a}{1-c / a}=1 \Rightarrow \frac{-b}{a-c}=1 \\<br/>&amp; -b=a-c \Rightarrow a+b=c<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2022']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.5I</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-a-youngs-double-slit-experiment-the-intensity-of-light-at-a-point-on-the-screen-where-the-path-difference-between-the-interfering-waves-is-being-th

slug:
in-a-youngs-double-slit-experiment-the-intensity-of-light-at-a-point-on-the-screen-where-the-path-difference-between-the-interfering-waves-is-being-th-97620

question:
<div class="question">In a Young's double slit experiment, the intensity of light at a point on the screen where the path difference between the interfering waves is $\lambda$, ( $\lambda$ being the wavelength of light used) is $\mathrm{I}$. The intensity at a point where the path difference is $\frac{\lambda}{4}$ will be (assume two waves have same amplitude)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">I</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">0.5I</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.25I</span> </li> </ul>

answer:
<div class="solution">$\mathrm{I}^{\prime}=\mathrm{I} \cos ^2 \phi / 2$<br/>$\phi=\frac{2 \pi}{\lambda} \Delta \mathrm{x}, \quad \phi=\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{4}=\frac{\pi}{2}$<br/>$\frac{\phi}{2}=\frac{\lambda}{4}, \quad \mathrm{I}^{\prime}=\mathrm{I}^2 \cos ^2 \frac{\pi}{4}=\frac{\mathrm{I}}{2}$</div>


tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'WBJEE', 'WBJEE 2009']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P1.db
title:
in-aluminium-extraction-by-the-bayer-process-alumina-is-extracted-from-bauxite-by-sodium-hydroxide-at-high-temperature-and-pressures-al-2-o-3-s-2-oh-a

slug:
in-aluminium-extraction-by-the-bayer-process-alumina-is-extracted-from-bauxite-by-sodium-hydroxide-at-high-temperature-and-pressures-al-2-o-3-s-2-oh-a-38099

question:
<div class="question">In aluminium extraction by the Bayer process, alumina is extracted from bauxite by sodium hydroxide at high temperature and pressures :<br/>$\mathrm{Al}_2 \mathrm{O}_3(\mathrm{~s})+2 \mathrm{OH}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{Al}_2 \mathrm{O}_2(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(1)$<br/><br/>Solid impurities such as $\mathrm{Fe}_2 \mathrm{O}_3$ and $\mathrm{SiO}_2$ are removed and then $\mathrm{Al}(\mathrm{OH})_4^{-}$is reprecipitated : $2 \mathrm{Al}(\mathrm{OH})_4^{-} \rightarrow \mathrm{Al}_2 \mathrm{O}_3 \cdot 3 \mathrm{H}_2 \mathrm{O}(\mathrm{s})+2 \mathrm{OH}^{-}$(aq) . In the industrial world :</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Temperature and pressure are dropped and the supersaturated solution seeded</span> </div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P1.db
title:
in-an-experiment-on-a-circuit-as-shown-in-the-figure-the-voltmeter-shows-8-mathrmv-reading-the-resistance-of-the-voltmeter-is

slug:
in-an-experiment-on-a-circuit-as-shown-in-the-figure-the-voltmeter-shows-8-mathrmv-reading-the-resistance-of-the-voltmeter-is-92350

question:
<div class="question">In an experiment on a circuit as shown in the figure, the voltmeter shows \(8 \mathrm{~V}\) reading. The resistance of the voltmeter is,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/9yiW5b3EPP3ydpLVc32AhSEIgQwLm_8iTuEB6DAQvxU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(20 \Omega\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(320 \Omega\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(160 \Omega\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">\(1.44 \mathrm{k} \Omega\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(160 \Omega\)</span> </div>

answer:
<div class="solution">Hint: Voltage across \(20 \Omega=2 \mathrm{~V}\)<br/>Main current \(=\frac{2}{20}=0.1 \mathrm{~A}\)<br/>Current through \(160 \Omega=\frac{8}{160}=\frac{1}{20}=0.05 \mathrm{~A}\)<br/>Also, \(8 \mathrm{~V}=0.05 \times \mathrm{R}\)<br/>\(R=\frac{8}{0.05}=160 \Omega\)</div>


tags: ['Physics', 'Mathematics in Physics', 'WBJEE', 'WBJEE 2023']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
answer: <div class="solution">Hint :</div>
source_db: db\MarksBatch2_P1.db
title:
in-an-experiment-the-length-of-an-object-is-measured-to-be-650-mathrmcm-this-measured-value-can-be-written-as-00650-mathrmm-the-number-of-significant-

slug:
in-an-experiment-the-length-of-an-object-is-measured-to-be-650-mathrmcm-this-measured-value-can-be-written-as-00650-mathrmm-the-number-of-significant-27490

question:
<div class="question">In an experiment, the length of an object is measured to be \(6.50 \mathrm{~cm}\). This measured value can be written as \(0.0650 \mathrm{~m}\). The number of significant figures on \(0.0650 \mathrm{~m}\) is</div>

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


tags: ['Physics', 'Atomic Physics', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P1.db
title:
in-an-inelastic-collision-an-electron-excites-as-hydrogen-atom-from-its-ground-state-to-a-mshell-state-a-second-electron-collides-instantaneously-with

slug:
in-an-inelastic-collision-an-electron-excites-as-hydrogen-atom-from-its-ground-state-to-a-mshell-state-a-second-electron-collides-instantaneously-with-52486

question:
<div class="question">In an inelastic collision an electron excites as hydrogen atom from its ground state to a M-shell state. A second electron collides instantaneously with the excited hydrogen atom in the M-State and ionizes it. At least how much energy the second electron transfers to the atom in the M-state?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(+3.4 \mathrm{eV}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(+1.51 \mathrm{eV}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">\(-3.4 \mathrm{eV}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(-1.51 \mathrm{eV}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(+1.51 \mathrm{eV}\)</span> </div>

answer:
<div class="solution">Hints: \(E_m=-\frac{13.6}{(3)^2}=-1.51\)<br/>Minimum energy required by electron should be \(+1.51 \mathrm{eV}\)</div>


title: in-an-n-p-n-transistor
slug: in-an-n-p-n-transistor-45176
question: <div class="question">In an $n-p-n$ transistor</div>
tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">the emitter has higher degree of doping compared to that of the collector</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 collector has higher degree of doping compared to that of the emitter</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both the emitter and collector have same degree of doping</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">the base region is most heavily doped</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the emitter has higher degree of doping compared to that of the collector</span> </div>

answer:
<div class="solution">In an $n-p-n$ or $p-n-p$ transistor, the left hand side thick layer of the transistor is heavily doped known as emitter and right hand side thick layer of the transistor is moderately doped known as collector.</div>


title: in-aqueous-alkaline-solution-two-electrons-reduction-of-ho-2-gives
slug: in-aqueous-alkaline-solution-two-electrons-reduction-of-ho-2-gives-28863
tags: ['Chemistry', 'Redox Reactions', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In aqueous alkaline solution, two electrons reduction of $\mathrm{HO}_{2}^{-}$ gives</div>

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

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

answer:
<div class="solution">In aqueous alkaline solution, two electron reduction of $\mathrm{HO}_{2}^{-}$ gives OH The reaction is as follows:<br/>$\begin{array}{l}<br/>\mathrm{H}_{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{H}^{+}+\mathrm{HO}_{2}^{-} \\<br/>\mathrm{HO}_{2}^{-}+\mathrm{H}_{2} \mathrm{O}+2 e^{-} \rightleftharpoons 3 \mathrm{OH}<br/>\end{array}$</div>


title: in-aqueous-solution-glucose-remains-as
slug: in-aqueous-solution-glucose-remains-as-53353
question: <div class="question">In aqueous solution glucose remains as</div>
tags: ['Chemistry', 'Biomolecules', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Only in open chain form</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Only in pyranoze form</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Only in furanose forms</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">In all three forms in equilibrium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">In all three forms in equilibrium</span> </div>

answer:
<div class="solution">Hints: \(\begin{aligned} &amp; \beta-\mathrm{D}-\text { glucose } \rightleftharpoons \mathrm{D}-\text { glucose } \rightleftharpoons \alpha-\mathrm{D}-\text { glucose } \\ &amp; (\approx 64 \%) \quad\qquad(\text {open chain } \approx 0.02 \%) \qquad~~(\approx 34 \%)\end{aligned}\)</div>


tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
title:
in-basic-medium-the-amount-of-ni-2-in-a-solution-can-be-estimated-with-the-dimethylglyoxime-reagent-the-correct-statements-about-the-reaction-and-the-

slug:
in-basic-medium-the-amount-of-ni-2-in-a-solution-can-be-estimated-with-the-dimethylglyoxime-reagent-the-correct-statements-about-the-reaction-and-the-27249

question:
<div class="question">In basic medium the amount of $\mathrm{Ni}^{2+}$ in a solution can be estimated with the dimethylglyoxime reagent. The correct statement(s) about the reaction and the product is (are)</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">in a ammoniacal solution $\mathrm{Ni}^{2+}$ salts give cherry-red precipitate of nickel(il) dimethylglyoximate, two dimethylglyoximate units are bound to one $\mathrm{Ni}^{2 *}$, in the complex two dimethylglyoximate units are hydrogen bonded to each other, each dimethylglyoximate unit forms a six membered chelate ring with $\mathrm{Ni}^{2+}$</span> </div>

answer:
<div class="solution">Estimation of $\mathrm{Ni}^{2+}$ is carried out as. 
<br/>Filtrate of group III $+\mathrm{NH}_{4} \mathrm{OH}+\mathrm{NH}_{4} \mathrm{Cl} \longrightarrow$
<br/>passing $\mathrm{H}_{2} \mathrm{S}$ gas $\rightarrow$ black pPt of NiS. 
<br/>This black ppt of NiS is soluble in conc. HCl in presence of oxidising agent like $\mathrm{KClO}_{3}$ $\mathrm{NiS}+\underset{\mathrm{COnc}}{2 \mathrm{HCl}}+\mathrm{O} \longrightarrow \mathrm{NiCl}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{S}$
<br/>Now this $\mathrm{NiCl}_{2}$, in basic medium, treated with dimethyl glyoxime, cherry red ppt of nickel (II) dimethyl glyoximate is obtained, in which two dimethyl glyoximate units are hydrogen bonded to each other and each unit forms a six-membered chelate ring with $\mathrm{Ni}^{2+}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a56.png"/></div>


tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P1.db
title:
in-bohr-model-of-atom-radius-of-hydrogen-atom-in-ground-state-is-r-1-and-radius-of-he-ion-in-ground-state-is-r-2-which-of-the-following-is-correct

slug:
in-bohr-model-of-atom-radius-of-hydrogen-atom-in-ground-state-is-r-1-and-radius-of-he-ion-in-ground-state-is-r-2-which-of-the-following-is-correct-22722

question:
<div class="question">In Bohr model of atom, radius of hydrogen atom in ground state is $\mathrm{r}_1$ and radius of $\mathrm{He}^{+}$ion in ground state is $\mathrm{r}_2$. Which of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{r_1}{r_2}=4$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{r_1}{r_2}=\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{r_2}{r_1}=\frac{1}{4}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{r_2}{r_1}=\frac{1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{r_2}{r_1}=\frac{1}{2}$</span> </div>

answer:
<div class="solution">$r_n=a_0 \times \frac{n^2}{z}$<br/>$\underline{\text {For H-atom}}$<br/>$r_1=a_0$<br/>$\underline{\text {Also, For}}$ $\underline {\mathrm{He}^{+}}$ - $\underline{\text { ion }}$<br/>$r_2=a_0 \times \frac{1^2}{2}=\frac{r_1}{2}$<br/>$\therefore \frac{r_2}{r_1}=\frac{1}{2}$</div>


title: in-borax-the-number-of-b-o-b-links-and-b-oh-bonds-present-are-respectively
slug: in-borax-the-number-of-b-o-b-links-and-b-oh-bonds-present-are-respectively-52898
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In borax the number of B $-\mathrm{O}-\mathrm{B}$ links and B - OH bonds present are, respectively</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a46.png"/> <br/>$5 B-O-B bonds
<br/>4 B-O H bonds</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P1.db
title:
in-case-of-a-bipolar-transistor-45-the-potential-drop-across-the-collector-resistance-of-1-k-is-5-v-the-base-current-is-approximately

slug:
in-case-of-a-bipolar-transistor-45-the-potential-drop-across-the-collector-resistance-of-1-k-is-5-v-the-base-current-is-approximately-63050

question:
<div class="question">In case of a bipolar transistor $\beta=45$. The potential drop across the collector resistance $\begin{array}{llllll}\text { of } 1 \mathrm{k} \Omega &amp; \text { is } 5 \mathrm{V} . &amp; \text { The base } &amp; \text { current } &amp; \text { is }\end{array}$ approximately</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$222 \mu \mathrm{A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$55 \mu \mathrm{A}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$111 \mu \mathrm{A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$45 \mu \mathrm{A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$111 \mu \mathrm{A}$</span> </div>

answer:
<div class="solution">Current gain $\beta=45$ 
<br/>We know that, $\quad \beta=\frac{\Delta I_{c}}{\Delta I_{b}}$
<br/>$\therefore$
<br/>$$
<br/>\frac{\Delta I_{c}}{\Delta I_{b}}=45
<br/>$$
<br/>Potential drop across $1 \mathrm{k} \Omega$ or $1 \times 10^{3} \Omega$
<br/>Collector resistor is $5 \mathrm{V}$.
<br/>$$
<br/>\begin{aligned}
<br/>V &amp;=I_{C} R \\
<br/>I_{C} &amp;=\frac{V}{R}=\frac{5}{1 \times 10^{3}} \\
<br/>&amp;=5 \times 10^{-3} \mathrm{A}
<br/>\end{aligned}
<br/>$$
<br/>From Eqs. (i) and (ii).
<br/>$$
<br/>\begin{aligned}
<br/>\Delta I_{B} &amp;-\frac{\Delta I_{C}}{45} \\
<br/>&amp;=\frac{5 \times 10^{-3}}{45}=\frac{1}{9} \times 10^{-3} \\
<br/>&amp;=0.111 \times 10^{-3} \mathrm{A} \\
<br/>&amp;=111 \times 10^{-6} \mathrm{A}=111 \mu \mathrm{A}
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P1.db
title:
in-case-of-a-simple-harmonic-motion-if-the-velocity-is-plotted-along-the-x-axis-and-the-displacement-from-the-equilibrium-position-is-plotted-along-th

slug:
in-case-of-a-simple-harmonic-motion-if-the-velocity-is-plotted-along-the-x-axis-and-the-displacement-from-the-equilibrium-position-is-plotted-along-th-56001

question:
<div class="question">In case of a simple harmonic motion, if the velocity is plotted along the $X$ -axis and the displacement (from the equilibrium position) is plotted along the $Y$ -axis, the resultant curve happens to be an ellipse with the ratio:
<br/>major axis (along X) $=20 \pi$ minor axis (along $Y)$
<br/>What is the frequency of the simple harmonic motion?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$100 \mathrm{Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$20 \mathrm{Hz}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{10} \mathrm{Hz}$</span> </li> </ul>

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

answer:
<div class="solution">In representation of simple harmonic motion in ellipse as velocity along $X$ -axis and displacement along $Y$ -axis. $\frac{\text { Major axis (along } X \text { -axis) }}{\text { Minor axis (along } X \text { -axis) }}=20 \pi$
<br/>$\Rightarrow \quad \frac{\omega A}{A}=20 \pi \Rightarrow \omega=20 \pi$
<br/>The frequency of the simple harmonic motion</div>


tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
title:
in-case-of-heteronuclear-diatomics-of-the-type-a-b-where-a-is-more-electronegative-than-b-bonding-molecular-orbital-resembles-the-character-of-a-more-

slug:
in-case-of-heteronuclear-diatomics-of-the-type-a-b-where-a-is-more-electronegative-than-b-bonding-molecular-orbital-resembles-the-character-of-a-more-17643

question:
<div class="question">In case of heteronuclear diatomics of the type $A B,$ where $A$ is more electronegative than $B$, bonding molecular orbital resembles the character of $A$ more than that of $B$. The statement</div>

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

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

answer:
<div class="solution">The given statement is true as electrons are shifted more towards the more electronegative atom.</div>


tags: ['Physics', 'Motion In Two Dimensions', 'WBJEE', 'WBJEE 2021']
answer: <div class="solution">Horizontal component of velocity remains constant.</div>
source_db: db\MarksBatch2_P1.db
title:
in-case-of-projectile-motion-which-one-of-the-following-figures-represent-variation-of-horizontal-component-of-velocity-u-x-with-time-t-assume-that-ai

slug:
in-case-of-projectile-motion-which-one-of-the-following-figures-represent-variation-of-horizontal-component-of-velocity-u-x-with-time-t-assume-that-ai-25839

question:
<div class="question">In case of projectile motion, which one of the following figures represent variation of horizontal component of velocity $\left(\mathrm{u}_{\mathrm{x}}\right)$ with time $\mathrm{t} ?$ (assume that air resistance is negligible)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/BLt8n-_o-x6HQjRUQ242japxyVX5KPjw_7rndaObE3Y.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/nVFSHZFHSuimxd_9QH8l9bACoXvJDwhC640QLuBJN3M.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/uRQt51lbc3qKtQ5wxEOIcRT8rwJ9vKwhgU_R2Hzb0ZM.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/SxTnpvv0fWN-QluAWMaxWmq0MvOc2TxwL5XC3zeziMY.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/nVFSHZFHSuimxd_9QH8l9bACoXvJDwhC640QLuBJN3M.original.fullsize.png"/></span> </div>


title: in-cuammonia-complex-the-state-of-hybridization-of-cu-2-is
slug: in-cuammonia-complex-the-state-of-hybridization-of-cu-2-is-46921
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In Cu-ammonia complex, the state of hybridization of $\mathrm{Cu}^{+2}$ is</div>

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

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

answer:
<div class="solution">In $\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{+}$<br/>$\mathrm{Cu}^{+2}$ is in a state of $d s p^2$ hybridization and shape of the complex is square planar. (One $e^{-}$is excited from $3 d$ to $4 p$ during complex formation)</div>


title: in-diborane-the-number-of-electrons-that-accounts-for-bonding-in-the-bridges-is
slug: in-diborane-the-number-of-electrons-that-accounts-for-bonding-in-the-bridges-is-10927
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'WBJEE', 'WBJEE 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">four</span> </div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In diborane, the number of electrons that accounts for bonding in the bridges is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">six</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">two</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">eight</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">four</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a20.png"/> <br/> <br/>In diborone, odd-electron bonds are found in the bridges. From figure, it is clear that 4 electrons are present for bonding in the bridges.</div>


title: in-dna-the-consecutive-deoxynucleotides-are-connected-via
slug: in-dna-the-consecutive-deoxynucleotides-are-connected-via-27994
question: <div class="question">In DNA, the consecutive deoxynucleotides are connected via</div>
tags: ['Chemistry', 'Biomolecules', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">phosphodiester 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">B</span> <span class="option-data">phosphomonoester linkage</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">phosphotriester linkage</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">amide linkage</span> </li> </ul>

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

answer:
<div class="solution">In DNA, the consecutive deoxynucleotides are linked through phosphodiester linkage.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a43.png"/></div>


title: in-hemoglobin-the-metal-ion-present-is
slug: in-hemoglobin-the-metal-ion-present-is-55610
question: <div class="question">In hemoglobin the metal ion present is</div>
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Fe}^{2+}$</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">$\mathrm{Zn}^{2+}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Co}^{2+}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Cu}^{2+}$</span> </li> </ul>

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


tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
title:
in-o-2-and-h-2-o-2-the-o-o-bond-lengths-are-121-and-148-respectively-in-ozone-the-average-o-o-bond-length-is

slug:
in-o-2-and-h-2-o-2-the-o-o-bond-lengths-are-121-and-148-respectively-in-ozone-the-average-o-o-bond-length-is-33125

question:
<div class="question">In $\mathrm{O}_{2}$ and $\mathrm{H}_{2} \mathrm{O}_{2}$, the $\mathrm{O}-\mathrm{O}$ bond lengths are 1.21 Ãâ¦ and 1.48 Ãâ¦ respectively. In ozone, the average $O-O$ bond length is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1.28 Ãâ¦$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.18 Ãâ¦$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.44 Ãâ¦$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.52 Ãâ¦$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.28 Ãâ¦$</span> </div>

answer:
<div class="solution">Ozone shows following resonance structure
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a11.png"/> <br/> <br/>It contains bond angle $116.8^{\circ}$ and $O-O$ bond length $1.28 Ãâ¦$</div>


title: in-open-interval-0-2
slug: in-open-interval-0-2-76658
question: <div class="question">In open interval $\left(0, \frac{\pi}{2}\right)$,</div>
tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\cos x+x \sin x    &lt; 1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\cos x+x \sin x&gt;1$</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">no specific order relation can be ascertained between $\cos x+x \sin x$ and 1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\cos x+x \sin x    &lt; \frac{1}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\cos x+x \sin x&gt;1$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$f(x)=\cos x+x \sin x-1$
<br/>$\Rightarrow f^{\prime}(x)=-\sin x+\sin x+x \cos x&gt;0 ; x \in\left(0, \frac{\pi}{2}\right)$
<br/>$\Rightarrow f(x)$ is increasing function
<br/>$\begin{array}{l}
<br/>\Rightarrow f(x)&gt;f(0) \\
<br/>\cos x+x \sin x-1&gt;0 \\
<br/>\cos x+x \sin x&gt;1
<br/>\end{array}$</div>


tags: ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2018']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-order-to-get-a-head-at-least-once-with-probability-09-the-minimum-number-of-times-a-unbiased-coin-needs-to-be-tossed-is

slug:
in-order-to-get-a-head-at-least-once-with-probability-09-the-minimum-number-of-times-a-unbiased-coin-needs-to-be-tossed-is-95183

question:
<div class="question">In order to get a head at least once with probability $\geq 0.9$, the minimum number of times a unbiased coin needs to be tossed 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">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">C</span> <span class="option-data">5</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6</span> </li> </ul>

answer:
<div class="solution">We have, $P(H)=\frac{1}{2}, P(T)=\frac{1}{2}$ 
<br/>Now, $P(X \geq 1)=1-P(X=0$
<br/>$=1-{ }^{n} C_{o}(p)^{0}(q)^{n}=1-\left(\frac{1}{2}\right)^{n}$
<br/>$1-\frac{1}{2^{n}} \geq 0.9$
<br/>$\Rightarrow$
<br/>$0.1 \geq \frac{1}{2 n}$
<br/>$\Rightarrow$
<br/>$\frac{1}{10} \geq \frac{1}{2^{n}}$
<br/>$\Rightarrow$
<br/>$z^{n} \geq 10$
<br/>$\Rightarrow$
<br/>$n \geq 4$
<br/>Minimum number of tossed = 4</div>


title: in-socl-2-the-cl-s-cl-and-cl-s-o-bond-angles-are
slug: in-socl-2-the-cl-s-cl-and-cl-s-o-bond-angles-are-20704
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In $\mathrm{SOCl}_{2}$, the $\mathrm{Cl} - \mathrm{S}-\mathrm{Cl}$ and $\mathrm{Cl}-\mathrm{S}-\mathrm{O}$
<br/>bond angles are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">130 and $115^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">106 and $96^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">107 and $108^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$96^{\circ}$ and $106^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$96^{\circ}$ and $106^{\circ}$</span> </div>

answer:
<div class="solution">In $\mathrm{SOCl}_{2}$, the $\mathrm{Cl}-\mathrm{S}-\mathrm{Cl}$ and $\mathrm{Cl}-\mathrm{S}-\mathrm{O}$ bond
<br/>angles are respectively $96^{\circ}$ and $106^{\circ}$</div>


title: in-sommerfelds-modification-of-bohrs-theory-the-trajectory-of-an-electron-in-a-hydrogen-atom-is
tags: ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P1.db
slug:
in-sommerfelds-modification-of-bohrs-theory-the-trajectory-of-an-electron-in-a-hydrogen-atom-is-10488

question:
<div class="question">In Sommerfeld's modification of Bohr's theory, the trajectory of an electron in a hydrogen atom is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a closed loop on spherical surface</span> </div>


tags: ['Physics', 'Capacitance', 'WBJEE', 'WBJEE 2012']
source_db: db\MarksBatch2_P1.db
title:
in-the-adjoining-figure-the-potential-difference-between-x-and-y-is-60-v-the-potential-difference-between-the-points-m-and-n-will-be

slug:
in-the-adjoining-figure-the-potential-difference-between-x-and-y-is-60-v-the-potential-difference-between-the-points-m-and-n-will-be-64512

question:
<div class="question">In the adjoining figure, the potential difference between $X$ and $Y$ is 60 V. The potential difference between the points $M$ and $N$ will be  <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_phy_q32.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$15 \mathrm{V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$30 \mathrm{V}$</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">$30 \mathrm{V}$</span> </div>

answer:
<div class="solution">Capacitors in series
<br/>\(2 C_{1} \times V_{1}=C \times V_{2}\)
<br/>\(2 V_{1}=V_{2} \ldots\) (i)
<br/>and \(V_{1}+V_{2}+V_{1}=60 \ldots\) (ii)
<br/>Solving Eqs. (i) and (ii), we get
<br/>\(V_{2}=30 \mathrm{~V}\)</div>


title: in-the-argand-plane-the-distinct-roots-of-1-z-z-3-z-4-0-z-is-a-complex-number-represent-vertices-of
tags: ['Mathematics', 'Complex Number', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
slug:
in-the-argand-plane-the-distinct-roots-of-1-z-z-3-z-4-0-z-is-a-complex-number-represent-vertices-of-96553

question:
<div class="question">In the argand plane, the distinct roots of $1+z+z^{3}+z^{4}=0(z$ is a complex number) represent vertices of</div>

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

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

answer:
<div class="solution">Given equation is
<br/>$1+z+z^{3}+z^{4}=0$
<br/>$\Rightarrow \quad(1+z)+z^{3}(1+z)=0$
<br/>$\Rightarrow \quad(1+z)\left(1+z^{3}\right)=1$
<br/>$\Rightarrow \quad z=-1, z^{3}=-1$
<br/>$\Rightarrow \quad z=-1, z=-1,-\omega-\omega^{2}$
<br/>Hence, these roots are the vertices of an equilateral triangle.</div>


title: in-the-bandgap-between-valence-band-and-conduction-band-in-a-material-is-50-ev-then-the-material-is
tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
slug:
in-the-bandgap-between-valence-band-and-conduction-band-in-a-material-is-50-ev-then-the-material-is-64466

question:
<div class="question">In the bandgap between valence band and conduction band in a material is $5.0 \mathrm{eV},$ then the material is</div>

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

answer:
<div class="solution">The band gap of $5 \mathrm{eV}$ corresponds to that of an
<br/>insulator.</div>


title: in-the-bayers-process-the-leaching-of-alumina-is-done-by-using
slug: in-the-bayers-process-the-leaching-of-alumina-is-done-by-using-35233
question: <div class="question">In the Bayer's process, the leaching of alumina is done by using</div>
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'WBJEE', 'WBJEE 2019']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">NaOH</span> </div>
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{CO}_{3}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">NaOH</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{SiO}_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CaO}$</span> </li> </ul>

answer:
<div class="solution">In the Bayer's process, the leaching of alumina is done by using $\mathrm{NaOH}$.
<br/>$\mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{NaOH}(a q) \stackrel{150^{\circ} \mathrm{C}, 35 \mathrm{atm}}{\longrightarrow} 2 \mathrm{Na}\left[\mathrm{Al}(\mathrm{OH})_{4}\right]+3 \mathrm{H}_{2} \mathrm{O}$
<br/>$2 \mathrm{Na}\left[\mathrm{Al}(\mathrm{OH})_{4}\right]+\mathrm{CO}_{2} \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3} \cdot x \mathrm{H}_{2} \mathrm{O}+2 \mathrm{NaHCO}_{3}$
<br/>$\mathrm{Al}_{2} \mathrm{O}_{3} \cdot x \mathrm{H}_{2} \mathrm{O}(s) \underset{\longrightarrow}{\text{1470K}} \mathrm{Al}_{2} \mathrm{O}_{3}(s)+x \mathrm{H}_{2} \mathrm{O}(g)$
<br/>So, the option (b) is correct answer.</div>


title: in-the-brown-ring-complex-fe-h-2-o-5-no-so-4-nitric-oxide-behaves-as
slug: in-the-brown-ring-complex-fe-h-2-o-5-no-so-4-nitric-oxide-behaves-as-52815
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2012']
answer: <div class="solution">In Fe-complexes, NO behaves as $\mathrm{NO}^{+}$.</div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the brown ring complex $\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{NO})\right] \mathrm{SO}_{4}$
<br/>nitric oxide behaves as</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{NO}^{+}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">neutral NO molecule</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{NO}^{-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{NO}^{2-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{NO}^{+}$</span> </div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">20</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-the-circuit-shown-assume-the-diode-to-be-ideal-when-v-i-increases-from-2-v-to-6-v-the-change-in-the-current-is-in-ma

slug:
in-the-circuit-shown-assume-the-diode-to-be-ideal-when-v-i-increases-from-2-v-to-6-v-the-change-in-the-current-is-in-ma-66713

question:
<div class="question">In the circuit shown assume the diode to be ideal. When $V_{i}$ increases from $2 \mathrm{V}$ to $6 \mathrm{V},$ the change in the current is (in mA) <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_q34.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">20</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$80 / 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">40</span> </li> </ul>

answer:
<div class="solution">$I_{\text {intitial }}=0$,
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_a34.png"/> <br/> <br/>$I_{\text {final }}=\frac{3}{150}=0.02 \mathrm{A}$
<br/>So, change in $I=0.02 \mathrm{A}=20 \mathrm{mA}$</div>


tags: ['Physics', 'Alternating Current', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P1.db
title:
in-the-circuit-shown-below-the-switch-is-kept-in-position-a-for-a-long-time-and-is-then-thrown-to-position-b-the-amplitude-of-the-resulting-oscillatin

slug:
in-the-circuit-shown-below-the-switch-is-kept-in-position-a-for-a-long-time-and-is-then-thrown-to-position-b-the-amplitude-of-the-resulting-oscillatin-20802

question:
<div class="question">In the circuit shown below, the switch is kept in position $a$ for a long time and is then thrown to position $b .$ The amplitude of the resulting oscillating current is given by
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q33.png"/></div>

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

answer:
<div class="solution">When switch is in position $a$, then capacitor will be charged, such that Charge on capacitor, $q=C E$ Energy stored in capacitor, $U=q^{2} / 2 C$ When switch is in position $b$, then circuit becomes an $L C$ oscillator. Let amplitude of current in $L C$ circuit be $I_{o}$. From conservation of energy, maximum electrical energy = maximum magnetic energy $\frac{q^{2}}{2 C}=\frac{1}{2} L I_{0}^{2}$
<br/>$[\because q=C E]$
<br/>$\Rightarrow \quad \frac{C^{2} E^{2}}{C}=L I_{0}^{2}$
<br/>$\therefore \quad I_{0}=E \sqrt{\frac{C}{L}}$</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2018']
source_db: db\MarksBatch2_P1.db
title:
in-the-circuit-shown-inputs-a-and-b-are-in-states-1-and-0-respectively-what-is-the-only-possible-stable-state-of-the-outputs-x-and-y

slug:
in-the-circuit-shown-inputs-a-and-b-are-in-states-1-and-0-respectively-what-is-the-only-possible-stable-state-of-the-outputs-x-and-y-80771

question:
<div class="question">In the circuit shown, inputs $A$ and $B$ are in states 1 and 0 respectively. What is the only possible stable state of the outputs $X$ and $Y ?$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q10.png"/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$X=0, Y=1$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a10.png"/> <br/> <br/>$X=\overline{A Y}=\bar{Y}=0$
<br/>$\therefore$
<br/>$$
<br/>Y=\overline{B X}=1
<br/>$$</div>


tags: ['Physics', 'Semiconductors', 'JEE Main']
source_db: db\MarksBatch2_P1.db
title:
in-the-circuit-shown-the-value-of-of-the-transistor-is-48-if-the-base-current-supplied-is-200-a-what-is-the-voltage-at-the-terminal-y-1

slug:
in-the-circuit-shown-the-value-of-of-the-transistor-is-48-if-the-base-current-supplied-is-200-a-what-is-the-voltage-at-the-terminal-y-1-45197

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/SqPFigW1VHySAuVLRlXe3qc1bzMrZY5iA3w-pJx819g.original.fullsize.png"/><br/> <br/>In the circuit shown, the value of $\beta$ of the transistor is 48 . If the base current supplied is $200 \mu \mathrm{A}$, what is the voltage at the terminal $\mathrm{Y}$?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.2 \mathrm{~V}$</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">B</span> <span class="option-data">$0.5 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4.8 \mathrm{~V}$</span> </li> </ul>

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

answer:
<div class="solution">Hint:
<br/>$\beta=48$
<br/>$l_{B}=200 \mu \mathrm{A}$
<br/>$I_{C}=\beta I_{B}=48 \times 200 \times 10^{-6}$
<br/>$V_{\mathrm{CC}}=I_{C} R_{C}+V_{C E} \therefore V_{C E}=5-\left(96 \times 10^{-4}\right) \times 500=5-4.8=0.2$ volt</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P1.db
title:
in-the-circuit-shown-the-value-of-of-the-transistor-is-48-if-the-base-current-supplied-is-200-a-what-is-the-voltage-at-the-terminal-y

slug:
in-the-circuit-shown-the-value-of-of-the-transistor-is-48-if-the-base-current-supplied-is-200-a-what-is-the-voltage-at-the-terminal-y-31283

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/SqPFigW1VHySAuVLRlXe3qc1bzMrZY5iA3w-pJx819g.original.fullsize.png"/><br/> <br/>In the circuit shown, the value of $\beta$ of the transistor is 48 . If the base current supplied is $200 \mu \mathrm{A}$, what is the voltage at the terminal $\mathrm{Y}$?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.2 \mathrm{~V}$</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">B</span> <span class="option-data">$0.5 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4.8 \mathrm{~V}$</span> </li> </ul>

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

answer:
<div class="solution">Hint:
<br/>$\beta=48$
<br/>$l_{B}=200 \mu \mathrm{A}$
<br/>$I_{C}=\beta I_{B}=48 \times 200 \times 10^{-6}$
<br/>$V_{\mathrm{CC}}=I_{C} R_{C}+V_{C E} \therefore V_{C E}=5-\left(96 \times 10^{-4}\right) \times 500=5-4.8=0.2$ volt</div>


title: in-the-circuit-shown-what-will-be-the-current-through-the-6-v-zener
slug: in-the-circuit-shown-what-will-be-the-current-through-the-6-v-zener-83266
tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2019']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Zero</span> </div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the circuit shown, what will be the current through the $6 \mathrm{V}$ zener? <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_q5.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6 \mathrm{mA}$, from $\mathrm{A}$ to $\mathrm{B}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{mA},$ from $\mathrm{A}$ to $\mathrm{B}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \mathrm{mA},$ from $B$ to $\mathrm{A}$</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">According to the question
<br/>Input voltage $V_{s}=10 \mathrm{V}$ 
<br/>Source resistance $R_{S}=1 \mathrm{k} \Omega$ 
<br/>Zener diode voltage $V_{Z}=6 \mathrm{V}$
<br/>$\because$ Breakdown voltage of zener diode is $=6 \mathrm{V},$ and the potential difference across the zener diode $5 \mathrm{V}$.
<br/>$\therefore$ Current flow in zener diode $I_{z}=0$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a5.png"/></div>


tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P1.db
title:
in-the-circult-shown-in-the-figure-all-the-resistance-are-identical-and-each-has-the-value-r-the-equivalent-resistance-of-the-combination-between-the-

slug:
in-the-circult-shown-in-the-figure-all-the-resistance-are-identical-and-each-has-the-value-r-the-equivalent-resistance-of-the-combination-between-the-42336

question:
<div class="question">In the circult shown in the figure all the resistance are identical and each has the value $r \Omega$. The equivalent resistance of the combination between the points $A$ and $B$ will remain unchanged even when the followring pairs of points marked in the figure are connected through a resistance $\mathbb{R}$.   <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_q39.png"/></div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">2 and 6, 4 and 7</span> </div>

answer:
<div class="solution">The circuit diagram is as shown below, 
<br/>According to question, when given pair of point in options are connected through a resistance $R$, then equivalent resistance between point $A$ and $B\left(R_{A}\right)$ remains unchanged. It is only possible when current. does not flows through resistance $R$ and circuit become Wheatstone bridge as shown in the figure below.
<br/>At the balanced condition, $\frac{P}{Q}=\frac{R}{S}$
<br/>The current flow in $C D$ branch will be zero.
<br/>Now by checking each option, from option (a), circuit is,
<br/>Now, $\because \frac{P}{Q}=\frac{R}{S} \Rightarrow \frac{2 r}{4 r}=\frac{r}{2 r} \Rightarrow \frac{1}{2}=\frac{1}{2}$
<br/>Hence, option is correct. From option (b), circuit is
<br/>Now, $\frac{P}{Q}=\frac{R}{S} \Rightarrow \frac{3 r}{3 r} \neq \frac{r}{2 r}$
<br/>So, option (b) is also incorrect. From option (c) circuit is,
<br/>Now, $\frac{P}{Q}=\frac{R}{S} \Rightarrow \frac{4 r}{2 r}=\frac{2 r}{r} \Rightarrow \frac{2}{1}=\frac{2}{1}$
<br/>So, option (c) is also correct. From option (d), circuit is
<br/>Now, $\frac{P}{Q}=\frac{R}{S} \Rightarrow \frac{4 r}{2 r} \neq \frac{r}{2 r}$
<br/>So, option (d) is also incorrect. Hence, option (a) and (c) are correct.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a39.png"/></div>


title: in-the-compound-hc-c-ch-ch-2-the-hybridization-of-c-2-and-c-3-carbons-are-respectively-1
slug: in-the-compound-hc-c-ch-ch-2-the-hybridization-of-c-2-and-c-3-carbons-are-respectively-1-96745
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'JEE Main']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the compound $\mathrm{HC} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}_2$ the hybridization of $\mathrm{C}-2$ and $\mathrm{C}-3$ carbons are respectively:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{sp}^2 \&amp; \mathrm{sp}$</span> </div>

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/lSqjFsvyZP5KaTrDybgp2ilBC-X1x-pCXKJ94YwlqSc.original.fullsize.png"/><br/><br/>(Double bond is preferred)</div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'WBJEE', 'WBJEE 2019']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-the-crystalline-solid-m-so-4-n-h-2-o-of-molar-mass-250-g-m-o-l-1-the-percentage-of-anhydrous-salt-is-64-by-weight-the-value-of-n-is

slug:
in-the-crystalline-solid-m-so-4-n-h-2-o-of-molar-mass-250-g-m-o-l-1-the-percentage-of-anhydrous-salt-is-64-by-weight-the-value-of-n-is-38169

question:
<div class="question">In the crystalline solid $M \mathrm{SO}_{4} \cdot n \mathrm{H}_{2} \mathrm{O}$ of molar mass 250 g $mol^{-1}$ , the percentage of anhydrous salt is 64 by weight. The value of $n$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">3</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">7</span> </li> </ul>

answer:
<div class="solution">$$
<br/>\begin{aligned}
<br/>&amp;\text {Mass of } \mathrm{H}_{2} \mathrm{O}=\frac{36}{100} \times 250=90 \mathrm{g}\\
<br/>&amp;\text { Moles of } \mathrm{H}_{2} \mathrm{O}=\frac{90}{18}=5 \mathrm{mol}
<br/>\end{aligned}
<br/>$$
<br/>In the crystalline solid $M \mathrm{SO}_{4} \cdot n \mathrm{H}_{2} \mathrm{O},$ the value of $n$ is 5
<br/>Hence, option (c) is correct answer.</div>


title: in-the-electrical-circuit-shown-in-the-figure-the-current-through-the-4-resistor-is
slug: in-the-electrical-circuit-shown-in-the-figure-the-current-through-the-4-resistor-is-84774
tags: ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the electrical circuit shown in the figure, the current through the $4 \Omega$ resistor is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_q8.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{A}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.25 \mathrm{A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.1 \mathrm{A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.5 \mathrm{A}$</span> </div>

answer:
<div class="solution">The current through the various branches of the circuit will be shown as <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_a8.png"/> <br/> <br/>According to Kirchhoff's second law in closed circuit $B C D E B$
<br/>$$
<br/>\begin{array}{r}
<br/>2 I_{1}+4 l_{1}+2 l_{1}-8\left(1-l_{1}\right)=0 \\
<br/>\Rightarrow \quad 16 l_{1}-81=0
<br/>\end{array}
<br/>$$
<br/>$\Rightarrow \quad l_{1}=\frac{8 l}{16} \Rightarrow l_{1}=\frac{1}{2} l$
<br/>In closed circuit ABEFA
<br/>$$
<br/>-9+3 l+8\left(1-l_{1}\right)+2 l=0
<br/>$$
<br/>$\Rightarrow \quad 13l-8 I_{1}=9 \Rightarrow 13 /-8\left(\frac{1}{2} I\right)=9$
<br/>$\Rightarrow \quad I=\frac{9}{9}=1 \mathrm{A}$
<br/>So current through $4 \Omega$ resistor $l_{1}=\frac{1}{2} \times 1=0.5 \mathrm{A}$</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P1.db
title:
in-the-equilibrium-h-2-i-2-2-hi-if-at-a-given-temperature-the-concentrations-of-the-reactants-are-increased-the-value-of-the-cquilibrium-constant-k-c-

slug:
in-the-equilibrium-h-2-i-2-2-hi-if-at-a-given-temperature-the-concentrations-of-the-reactants-are-increased-the-value-of-the-cquilibrium-constant-k-c-83545

question:
<div class="question">In the equilibrium, $\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI},$ if at a given temperature the concentrations of the reactants are increased, the value of the cquilibrium constant, $K_{C}$, will</div>

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

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

answer:
<div class="solution">In the equilibrium $\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}$, if at a
<br/>given temperature, the concentrations of the reactants are increased, the value of the equilibrium constant $K_{C}$ will remain the same because equilibrium constant does not depend on the molar concentration of reactants.
<br/>The option (c) is correct answer.</div>


title: in-the-expansion-of-x-1-x-2-x-18-the-coefficient-of-x-17-is
slug: in-the-expansion-of-x-1-x-2-x-18-the-coefficient-of-x-17-is-40910
tags: ['Mathematics', 'Binomial Theorem', 'WBJEE', 'WBJEE 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">-171</span> </div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the expansion of $(x-1)(x-2) \ldots(x-18)$ the coefficient of $x^{17}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">684</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">-171</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">171</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">-342</span> </li> </ul>

answer:
<div class="solution">Coefficient of $x^{17}$ in $(x-1)(x-2) \ldots(x-18)$
<br/>$$
<br/>\begin{array}{l}
<br/>=-(1+2+3+\ldots+16) \\
<br/>=-(171)=-171
<br/>\end{array}
<br/>$$</div>


tags: ['Chemistry', 's Block Elements', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P1.db
title:
in-the-extraction-of-ca-by-electro-reduction-of-molten-cacl-2-some-caf-2-is-added-to-the-electrolyte-for-the-following-reason

slug:
in-the-extraction-of-ca-by-electro-reduction-of-molten-cacl-2-some-caf-2-is-added-to-the-electrolyte-for-the-following-reason-81715

question:
<div class="question">In the extraction of Ca by electro reduction of molten $\mathrm{CaCl}_{2}$ some $\mathrm{CaF}_{2}$ is added to the electrolyte for the following reason:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">To keep the electrolyte in liquid state at temperature lower than the m. p. of $\mathrm{CaCl}_{2}$</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">To effect precipitation of Ca</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">To effect the electrolysis at lower voltage</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">To increase the current efficiency</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To keep the electrolyte in liquid state at temperature lower than the m. p. of $\mathrm{CaCl}_{2}$</span> </div>

answer:
<div class="solution">Hint: 
<br/>$\mathrm{CaF}_{2}$ decreases the melting point of $\mathrm{CaCl}_{2}$</div>


tags: ['Chemistry', 'Solid State', 'WBJEE', 'WBJEE 2020']
source_db: db\MarksBatch2_P1.db
title:
in-the-facecentred-cubic-lattice-structure-of-gold-the-closest-distance-between-gold-atoms-is-a-being-the-edge-length-of-the-cubic-unit-cell

slug:
in-the-facecentred-cubic-lattice-structure-of-gold-the-closest-distance-between-gold-atoms-is-a-being-the-edge-length-of-the-cubic-unit-cell-21939

question:
<div class="question">In the face-centred cubic lattice structure of gold the closest distance between gold atoms is ('a' being the edge length of the cubic unit cell)</div>

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

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

answer:
<div class="solution">Hint: 
<br/>Closest distance between two gold atoms in fcc lattice of gold is $\frac{a}{\sqrt{2}} .$ This is the distance between the corner atom and the closest face centre atom.</div>


tags: ['Physics', 'Capacitance', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
title:
in-the-figure-below-the-capacitance-of-each-capacitor-is-3-f-the-effective-capacitance-between-a-and-b-is

slug:
in-the-figure-below-the-capacitance-of-each-capacitor-is-3-f-the-effective-capacitance-between-a-and-b-is-15738

question:
<div class="question">$$<br/>\text { In the figure below, the capacitance of each capacitor is } 3 \mu \mathrm{F} \text {. The effective capacitance between } \mathrm{A} \text { and } \mathrm{B} \text { is : }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/V2HDeoSj5dkPhhDEE5nlZV4dPSMBxUeR5dXnKyS86IA.original.fullsize.png"/><br/></div>

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

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

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/-CUT1NryVsBVy_RJXwRwNLljAthmImiUpf8sPUqOJpA.original.fullsize.png"/><br/><br/><br/>$$<br/>\frac{2 \mathrm{C}}{3}+\mathrm{C}=2+3=5 \mu \mathrm{F}<br/>$$</div>


title: in-the-following-compound-the-number-of-spbybridised-carbons-are
slug: in-the-following-compound-the-number-of-spbybridised-carbons-are-21018
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the following compound, the number of sp-bybridised carbons are <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_q49.png"/></div>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_a49.png"/> <br/> <br/>$$
<br/>\text { Thus, number of } s p \text { -hybridised } C=4
<br/>$$</div>


tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P1.db
title:
in-the-following-electron-dot-structure-calculate-the-formal-charge-from-left-to-right-nitrogen-atom-ddotmathrmnmathrmnddotmathrmn

slug:
in-the-following-electron-dot-structure-calculate-the-formal-charge-from-left-to-right-nitrogen-atom-ddotmathrmnmathrmnddotmathrmn-56792

question:
<div class="question">In the following electron - dot structure, calculate the formal charge from left to right nitrogen atom; \(\ddot{\mathrm{N}}=\mathrm{N}=\ddot{\mathrm{N}}\)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(-1,-1,+1\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(-1,+1,-1\)</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">C</span> <span class="option-data">\(+1,-1,-1\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(+1,-1,+1\)</span> </li> </ul>

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

answer:
<div class="solution">Hints: Formal chargl= Number of electrons in<br/>Valence shell \(-\left(\frac{1}{2} \times\right.\) numbers of electrons as bond pair + numbers of electrons as lone pair)<br/>\(\begin{gathered}<br/>1 \quad~~ 2 ~~\quad 3\\<br/>: \ddot{\mathrm{N}}=\mathrm{N}=\ddot{\mathrm{N}}:<br/>\end{gathered}\)<br/>For \(\mathrm{N}_1 ~\&amp;~ \mathrm{~N}_3\)<br/>Formal charge \(=5-\left(\frac{4}{2}+4\right)=5-(6)=-1\)<br/>For \(\mathrm{N}_2=5-\frac{1}{2} \times 8-0=5-4=+1\)</div>


title: in-the-following-reaction-the-product-e-is
slug: in-the-following-reaction-the-product-e-is-59263
tags: ['Chemistry', 'Aldehydes and Ketones', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the following reaction, the product $E$ is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q22.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q22_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q22_optb.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q22_optc.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q22_optd.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_q22_optc.png"/></span> </div>

answer:
<div class="solution">Aldehydes lacking $\alpha-\mathrm{H}$ atom, undergo Cannizzaro reaction if treated with concentrated alkali (NaOH), i.e., one mole of the aldehyde is reduced to alcohol and other mole is oxidised to salt of acid. Thus, the given aldehyde (glyoxal) undergoes intramolecular Cannizzaro reaction, ie. its half part is oxidised and half is reduced.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_che_a22.png"/></div>


tags: ['Chemistry', 'Aldehydes and Ketones', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
title:
in-the-following-species-the-one-which-is-likely-to-be-the-intermediate-during-benzoin-condensation-of-benzaldehyde-is

slug:
in-the-following-species-the-one-which-is-likely-to-be-the-intermediate-during-benzoin-condensation-of-benzaldehyde-is-88198

question:
<div class="question">In the following species, the one which is likely to be the intermediate during benzoin condensation of benzaldehyde is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q10_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q10_optb.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q10_optc.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q10_optd.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q10_optc.png"/></span> </div>

answer:
<div class="solution">When benzaldehyde is heated with aqueous ethanolic NaCN or $\mathrm{KCN},$ it dimerises to form an $\alpha$ -hydroxy ketone called benzoin, and this reaction is formed as benzoin condensation. It involves self condensation of an aromatic aldehyde in the presence of $\mathrm{CN}^{-}$ as catalyst.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a10.png"/></div>


title: in-the-given-circuit-find-the-voltage-drop-vl-in-the-load-resistance-rl
slug: in-the-given-circuit-find-the-voltage-drop-vl-in-the-load-resistance-rl-93827
tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P1.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/pxS4l5sWL5NEddq3RFP00q0Zf4Qh0d_hQ_7tuN-D14o.original.fullsize.png"/><br/><br/>In the given circuit, find the voltage drop \(V_L\) in the load resistance \(R_L\).</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(5 \mathrm{~V}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(3 \mathrm{~V}\)</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">\(9 \mathrm{~V}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(6 \mathrm{~V}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(3 \mathrm{~V}\)</span> </div>

answer:
<div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Z3Qq99anX32BJe2yYkbH19ZzqUBtpsjytkSX1j32pQ0.original.fullsize.png"/><br/><br/>\(\mathrm{i}=\frac{9}{300} \mathrm{~A}\)<br/>So, \(V_a-V_a=\frac{9}{300} \times 100=3 V\)<br/>So, diode is not activated,<br/>So, voltage across load is \(3 \mathrm{~V}\).</div>


tags: ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2017']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0,0</span> </div>
source_db: db\MarksBatch2_P1.db
title:
in-the-given-circuit-the-binary-inputs-at-a-and-b-are-both-1-in-one-case-and-both-0-in-the-next-case-the-respective-outputs-at-y-in-these-two-cases-wi

slug:
in-the-given-circuit-the-binary-inputs-at-a-and-b-are-both-1-in-one-case-and-both-0-in-the-next-case-the-respective-outputs-at-y-in-these-two-cases-wi-52655

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_q25.png"/> <br/> <br/>In the given circuit, the binary inputs at $A$ and $B$ are both 1 in one case and both 0 in the next case. The respective outputs at $Y$ in these two cases will be</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">0,0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0,1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1,0</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a25.png"/> <br/> <br/>The output of logic gate circuit
<br/>for
<br/>$$
<br/>\begin{array}{l}
<br/>Y=\frac{}{A \cdot B+\bar{A} \bar{B}} \\
<br/>A=1
<br/>\end{array}
<br/>$$
<br/>$$
<br/>B=1 \Rightarrow Y=0
<br/>$$
<br/>and for $\quad A=0, B=0$
<br/>$\Rightarrow \quad Y=0$</div>


tags: ['Physics', 'Thermodynamics', 'JEE Main']
source_db: db\MarksBatch2_P1.db
title:
in-the-given-figure-1-represents-isobaric-2-represents-isothermal-and-3-represents-adiabatic-processes-of-an-ideal-gas-if-u-1-u-2-u-3-be-the-changes-i-1

slug:
in-the-given-figure-1-represents-isobaric-2-represents-isothermal-and-3-represents-adiabatic-processes-of-an-ideal-gas-if-u-1-u-2-u-3-be-the-changes-i-1-75177

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/8gKeb24rKz0uX01kXhnRgX-nB2cNXk30SwAV9zJ98gc.original.fullsize.png"/><br/> <br/>In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas. If $\Delta \mathrm{U}_{1}, \Delta \mathrm{U}_{2}, \Delta \mathrm{U}_{3}$ be the changes in internal energy in these processes respectively, then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\Delta \mathrm{U}_{1}&gt;\Delta \mathrm{U}_{2}&gt;\Delta \mathrm{U}_{3}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/FTsRPunAvtnJAqYa1H018lAEH9lVr0BMPzrqGGT-K04.original.fullsize.png"/><br/> <br/>$\Delta \mathrm{T}_{1}=\mathrm{T}_{0}$
<br/>$\Delta \mathrm{T}_{2}=0$
<br/>$\Delta \mathrm{T}_{3}=-\mathrm{ve}$
<br/>$\Rightarrow \Delta \mathrm{U}_{1}&gt;\Delta \mathrm{U}_{2}&gt;\Delta \mathrm{U}_{3}$</div>


tags: ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P1.db
title:
in-the-given-figure-1-represents-isobaric-2-represents-isothermal-and-3-represents-adiabatic-processes-of-an-ideal-gas-if-u-1-u-2-u-3-be-the-changes-i

slug:
in-the-given-figure-1-represents-isobaric-2-represents-isothermal-and-3-represents-adiabatic-processes-of-an-ideal-gas-if-u-1-u-2-u-3-be-the-changes-i-49616

question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/8gKeb24rKz0uX01kXhnRgX-nB2cNXk30SwAV9zJ98gc.original.fullsize.png"/><br/> <br/>In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas. If $\Delta \mathrm{U}_{1}, \Delta \mathrm{U}_{2}, \Delta \mathrm{U}_{3}$ be the changes in internal energy in these processes respectively, then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\Delta \mathrm{U}_{1}&gt;\Delta \mathrm{U}_{2}&gt;\Delta \mathrm{U}_{3}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/FTsRPunAvtnJAqYa1H018lAEH9lVr0BMPzrqGGT-K04.original.fullsize.png"/><br/> <br/>$\Delta \mathrm{T}_{1}=\mathrm{T}_{0}$
<br/>$\Delta \mathrm{T}_{2}=0$
<br/>$\Delta \mathrm{T}_{3}=-\mathrm{ve}$
<br/>$\Rightarrow \Delta \mathrm{U}_{1}&gt;\Delta \mathrm{U}_{2}&gt;\Delta \mathrm{U}_{3}$</div>


title: in-the-hydrolysis-of-an-organic-chloride-in-presence-of-large-excess-of-water-rci-h-2-o-roh-hcl
tags: ['Chemistry', 'Chemical Kinetics', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">Hints : As water used is in large excess.</div>
source_db: db\MarksBatch2_P1.db
slug:
in-the-hydrolysis-of-an-organic-chloride-in-presence-of-large-excess-of-water-rci-h-2-o-roh-hcl-48100

question:
<div class="question">In the hydrolysis of an organic chloride in presence of large excess of water; $\mathrm{RCI}+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{ROH}+\mathrm{HCl}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Molecularity and order of reaction both are 2</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Molecularity is 2 but order of reaction is 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">Molecularity is 1 but order of reaction is 2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Molecularity is 1 and order of reaction is also 1</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Molecularity is 2 but order of reaction is 1</span> </div>


title: in-the-interval-2-pi-0-the-function-fxsin-leftfrac1x3right
slug: in-the-interval-2-pi-0-the-function-fxsin-leftfrac1x3right-36253
tags: ['Mathematics', 'Functions', 'WBJEE', 'WBJEE 2023']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the interval \((-2 \pi, 0)\), the function \(f(x)=\sin \left(\frac{1}{x^3}\right)\)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">never changes sign</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">changes sign only once</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">changes sign more than once but finitely many times</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">changes sign infinitely many times</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">changes sign infinitely many times</span> </div>

answer:
<div class="solution">Hint : \(x \in(-2 \pi, 0), f(x)=\sin \left(\frac{1}{x^3}\right)\)<br/>\(\begin{aligned}<br/>&amp; \because-2 \pi  &lt; x &lt; 0 \\<br/>&amp; \Rightarrow-8 \pi^3 &lt; x^3 &lt; 0 \\<br/>&amp; \Rightarrow-\infty &lt; \frac{1}{x^3} &lt; -\frac{1}{8 \pi^3}<br/>\end{aligned}\)<br/>Hence, \(\sin \left(\frac{1}{x^3}\right)\) will take all values from -1 to 1 , and will change its sign infinitely many times since it is a periodic function</div>


title: in-the-iupac-system-p-h-c-h-2-c-h-2-co-2-h-is-named-as
slug: in-the-iupac-system-p-h-c-h-2-c-h-2-co-2-h-is-named-as-78150
tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2017']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the IUPAC system, $PhCH_{2}CH_{2}\mathrm{CO}_{2} \mathrm{H}$ is named as</div>

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

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

answer:
<div class="solution">IUPAC name of $\mathrm{Ph} \cdot \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}$ is,
<br/>3-phenylpropanoic acid
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_che_a58.png"/></div>


tags: ['Chemistry', 'General Organic Chemistry', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P1.db
title:
in-the-lassaignes-test-for-the-detection-of-nitrogen-in-an-onganic-compound-the-appearance-of-blue-coloured-compound-is-due-to

slug:
in-the-lassaignes-test-for-the-detection-of-nitrogen-in-an-onganic-compound-the-appearance-of-blue-coloured-compound-is-due-to-18746

question:
<div class="question">In the Lassaigne's test for the detection of nitrogen in an onganic compound. the appearance of blue coloured compound is due to</div>

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

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

answer:
<div class="solution">To a part of sodium extract, FeSO $_{4}$ solution is added and the contents are warmed. A few drops of $\mathrm{FeCl}_{3}$ solution are then added and resulting $\begin{array}{lllll}\text { solution } &amp; \text { is } &amp; \text { acidified } &amp; \text { with } &amp; \text { conc. } &amp; \text { HCl. } &amp; \text { The }\end{array}$ appearance of bluish green or Prussian blue colouration confirms the presence of nitrogen. The reactions that occur during this test are as
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_a69.png"/></div>


title: in-the-nuclear-reaction-714-mathrmnmathrmx-rightarrow-614-mathrmc-11-mathrmh-the-mathrmx-will-be
tags: ['Physics', 'Nuclear Physics', 'WBJEE', 'WBJEE 2011']
answer: <div class="solution">\(\text {Hints: } \mathrm{X} \rightarrow{ }_0^1 \mathrm{n}\)</div>
source_db: db\MarksBatch2_P1.db
slug:
in-the-nuclear-reaction-714-mathrmnmathrmx-rightarrow-614-mathrmc-11-mathrmh-the-mathrmx-will-be-26075

question:
<div class="question">In the nuclear reaction \({ }_7^{14} \mathrm{~N}+\mathrm{X} \rightarrow{ }_6^{14} \mathrm{C}+{ }_1^1 \mathrm{H}\) the \(\mathrm{X}\) will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\({ }_{-1}^0 \mathrm{e}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\({ }_1^1 \mathrm{H}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\({ }_1^2 \mathrm{H}\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\({ }_0^1 \mathrm{n}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\({ }_0^1 \mathrm{n}\)</span> </div>


tags: ['Chemistry', 'Redox Reactions', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
title:
in-the-reaction-of-sodium-thiosulphate-with-i-2-in-aqueous-medium-the-equivalent-weight-of-sodium-thiosulphate-is-equal-to

slug:
in-the-reaction-of-sodium-thiosulphate-with-i-2-in-aqueous-medium-the-equivalent-weight-of-sodium-thiosulphate-is-equal-to-31576

question:
<div class="question">In the reaction of sodium thiosulphate with $\mathrm{I}_2$ in aqueous medium the equivalent weight of sodium thiosulphate is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">molar mass of sodium thiosulphate</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 average of molr masses of $\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ and $\mathrm{I}_2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">half the molar mass of sodium thiosulphate</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">molar mass of sodium thiosulphate $\times 2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">molar mass of sodium thiosulphate</span> </div>

answer:
<div class="solution">$\begin{gathered}<br/>\text {Hints : } 2 \mathrm{Na}_2 \stackrel{+2}{\mathrm{~S}_2} \mathrm{O}_3+\mathrm{I}_2 \longrightarrow \mathrm{Na}_2 \stackrel{+25}{\mathrm{~S}_4} \mathrm{O}_6+2 \mathrm{NaI} \\<br/>\text {n-factor }=1 \\<br/>\mathrm{E}=\frac{\mathrm{M}}{1}=\mathrm{M}<br/>\end{gathered}$</div>


title: in-the-reaction-r-mgbr-hc-oet-3-ether-h-3-o-p-the-proxtuct-p-is
slug: in-the-reaction-r-mgbr-hc-oet-3-ether-h-3-o-p-the-proxtuct-p-is-17047
tags: ['Chemistry', 'Aldehydes and Ketones', 'WBJEE', 'WBJEE 2015']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In the reaction $R \mathrm{MgBr}+\mathrm{HC}(\mathrm{OEt})_{3} \stackrel{\text { Ether } \mathrm{H}_{3} \mathrm{O}^{+}}{\longrightarrow} P$ the proxtuct $P$ is</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_che_a70.png"/></div>


tags: ['Mathematics', 'Sets and Relations', 'WBJEE', 'WBJEE 2013']
source_db: db\MarksBatch2_P1.db
title:
in-the-set-of-all-3-3-real-matrices-a-relation-is-defined-as-follows-a-matrix-a-is-related-to-a-matrix-b-if-and-only-if-there-is-a-nonsingular-3-3-mat

slug:
in-the-set-of-all-3-3-real-matrices-a-relation-is-defined-as-follows-a-matrix-a-is-related-to-a-matrix-b-if-and-only-if-there-is-a-nonsingular-3-3-mat-85601

question:
<div class="question">In the set of all $3 \times 3$ real matrices a relation is defined as follows. A matrix $A$ is related to a matrix $B,$ if and only if there is a non-singular $3 \times 3$ matrix $P,$ such that $B=P^{-1} A P .$ This relation is</div>

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

answer:
<div class="solution">Let the relation defined as $R=\left\{(A, B) \mid B=P^{-1} A P\right\}$
<br/>For reflexive, $A=I^{-1} A l$
<br/>$\Rightarrow (A, A) \in R$
<br/>$\Rightarrow R$ is reflexive
<br/>For symmetric $\operatorname{Let}(A B) \in R$
<br/>$\because$
<br/>$B=P^{-1} A P$
<br/>$\Rightarrow P B=A P \Rightarrow P B P^{-1}=A$
<br/>$\Rightarrow$
<br/>$A=\left(P^{-1}\right)^{-1} B\left(P^{-1}\right)$
<br/>$\Rightarrow (B, A) \in R \Rightarrow R$ is symmetric.
<br/>For transitive
<br/>Let $(A, B) \in R,(B, C) \in R$
<br/>$\because A=P^{-1} B P$ and $B=Q^{-} C Q$
<br/>$\Rightarrow A=P^{-} Q^{-1} C Q P=(Q P)^{-1} C(Q P)$
<br/>$\Rightarrow (A, C) \in R$
<br/>$\Rightarrow R$ is transitive. since, $A$ is reflexive, symmetric and transitive. So, $R$ is an equivalence relation.</div>


title: in-the-solid-state-pcl-5-exists-as
slug: in-the-solid-state-pcl-5-exists-as-33595
question: <div class="question">In the solid state, $\mathrm{PCl}_{5}$ exists as</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left[\mathrm{PCl}_{4}\right]^{-}$ and $\left[\mathrm{PCl}_{6}\right]^{+}$ ions</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">covalent $\mathrm{PCl}_{5}$ molecules only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left[\mathrm{PCl}_{4}\right]^{+}$ and $\left[\mathrm{PCl}_{6}\right]^{-}$ ions</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">covalent $\mathrm{P}_{2} \mathrm{Cl}_{10}$ molecules only</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left[\mathrm{PCl}_{4}\right]^{+}$ and $\left[\mathrm{PCl}_{6}\right]^{-}$ ions</span> </div>

answer:
<div class="solution">$\mathrm{PCl}_{5}$ exists as $\left[\mathrm{PCl}_{4}\right]^{+}$ and $\left[\mathrm{PCl}_{6}\right]^{-}$ in solid state.
<br/>$$
<br/>2 \mathrm{PCl}_{5} \longrightarrow\left[\mathrm{PCl}_{4}\right]^{+}\left[\mathrm{PCl}_{6}]^{-}\right.
<br/>$$</div>


title: in-triangle-abc-a-2-b-3-and-sin-a-3-2-then-b-is-equal-to
slug: in-triangle-abc-a-2-b-3-and-sin-a-3-2-then-b-is-equal-to-45030
tags: ['Mathematics', 'Properties of Triangles', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In triangle $\mathrm{ABC}, \mathrm{a}=2, \mathrm{~b}=3$ and $\sin \mathrm{A}=\frac{2}{3}$, then $\mathrm{B}$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$30^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$60^{\circ}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$90^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$120^{\circ}$</span> </li> </ul>

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

answer:
<div class="solution">Hints: $\frac{a}{\sin A}=\frac{b}{\sin B}$<br/>$\sin B=\frac{b}{a} \cdot \sin A=\frac{3}{2} \cdot \frac{2}{3}=1$<br/>$$<br/>\mathrm{B}=\frac{\pi}{2}<br/>$$</div>


title: in-which-of-the-following-functions-rolles-theorem-is-applicable
slug: in-which-of-the-following-functions-rolles-theorem-is-applicable-40657
question: <div class="question">In which of the following functions, Rolle's theorem is applicable?</div>
tags: ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$f(x)=|x|$ in $-2 \leq x \leq 2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{f}(\mathrm{x})=\tan \mathrm{x}$ in $0 \leq \mathrm{x} \leq \pi$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{f}(\mathrm{x})=1+(\mathrm{x}-2)^{\frac{2}{3}}$ in $1 \leq \mathrm{x} \leq 3$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{f}(\mathrm{x})=\mathrm{x}(\mathrm{x}-2)^2$ in $0 \leq \mathrm{x} \leq 2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{f}(\mathrm{x})=\mathrm{x}(\mathrm{x}-2)^2$ in $0 \leq \mathrm{x} \leq 2$</span> </div>

answer:
<div class="solution">Hints: $(\mathrm{A}) \mathrm{f}(\mathrm{x})=|\mathrm{x}|$ not differentiable at $\mathrm{x}=0$</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'WBJEE', 'WBJEE 2016']
source_db: db\MarksBatch2_P1.db
title:
in-which-of-the-following-mixed-aqueous-solutions-ph-p-k-a-at-equilibrium-1-100-ml-of-01-m-ch-3-cooh-100-ml-of-01-mch-3-coona-2-100-ml-of-01-mch-3-coo

slug:
in-which-of-the-following-mixed-aqueous-solutions-ph-p-k-a-at-equilibrium-1-100-ml-of-01-m-ch-3-cooh-100-ml-of-01-mch-3-coona-2-100-ml-of-01-mch-3-coo-89420

question:
<div class="question">In which of the following mixed aqueous solutions, $\mathrm{pH}=\mathrm{p} K_{a}$ at equilibrium?
<br/>(1) $100 \mathrm{mL}$ of $0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+100 \mathrm{mL}$ of $0.1 \mathrm{MCH}_{3} \mathrm{COONa}$
<br/>(2) $100 \mathrm{mL}$ of $0.1 \mathrm{MCH}_{3} \mathrm{COOH}+50 \mathrm{mL}$ of 0.1 $\mathrm{M} \mathrm{NaOH}$
<br/>(3) $100 \mathrm{mL}$ of $0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+100 \mathrm{mL}$ of $0.1 \mathrm{M} \mathrm{NaOH}$
<br/>(4) $100 \mathrm{mL}$ of $0.1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+100 \mathrm{mL}$ of $0.1 \mathrm{M} \mathrm{NH}_{3}$</div>

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

answer:
<div class="solution">pH of buffer solutions is given by
<br/>$$
<br/>\mathrm{pH}=\mathrm{pK}_{a}+\mathrm{log} \frac{[\mathrm{salt}]}{[\mathrm{acid}]}
<br/>$$
<br/>(1) $\mathrm{CH}_{3} \mathrm{COOH}$ and $\mathrm{CH}_{3} \mathrm{COONa}$
<br/>$\quad \quad$ $100 \times 0.1$ $\quad \quad$$100 \times 0.1$
<br/>No. of milimoles $=10 \quad=10$ 
<br/>$\because[$ salt $]=\mid a c i d]=10,  p H=p K_{a}+\log \frac{10}{10}$
<br/>$\therefore \mathrm{pH}=\mathrm{pK_{a}}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a39.png"/> <br/>$\because \quad$ (salt) $=[\mathrm{acid}]=5, \mathrm{pH}=\mathrm{pK}_{\mathrm{a}}+\log \frac{5}{5}$
<br/>$\therefore \quad \mathrm{pH}=\mathrm{p} K_{\mathrm{a}}$<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_che_a39a.png"/> <br/>$[$ salt $]=10$ and $[a c i d]=0$
<br/>$p H=p K_{a}+\log \frac{10}{0}$
<br/>$\therefore \quad \mathrm{pH} \neq \mathrm{pK}_{a}$
<br/>(4) $\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{NH}_{3} \longrightarrow \mathrm{CH}_{3} \mathrm{COONH}_{4}$
<br/>initial $10 \quad \quad \quad \quad 10 \rightarrow$ No buffer action
<br/>Final Due to weak $\mathrm{CH}_{3} \mathrm{COONH}_{4}$ salt
<br/>$\therefore \quad p H \neq p K_{a}$</div>


title: in-which-of-the-following-molecules-is-hydrogen-bridge-bond-present
slug: in-which-of-the-following-molecules-is-hydrogen-bridge-bond-present-49383
question: <div class="question">In which of the following molecules is hydrogen bridge bond present?</div>
tags: ['Chemistry', 'Hydrogen', 'WBJEE', 'WBJEE 2010']
source_db: db\MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Water</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Inorganic benzene</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Diborane</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Methanol</span> </li> </ul>

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

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mSDhUtpAjgYMikK8J8p_OpBnHKzjxteSHKWQgEI7QGo.original.fullsize.png"/><br/></div>


title: in-which-of-the-following-pairs-the-two-physical-quantities-have-different-dimensions
slug: in-which-of-the-following-pairs-the-two-physical-quantities-have-different-dimensions-14417
tags: ['Physics', 'Units and Dimensions', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In which of the following pairs, the two physical quantities have different dimensions?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Moment of inertia and moment of a force</span> </div>

answer:
<div class="solution">(a) Planck's constant = Energy<br/>$=\left[\mathrm{ML}^{2} \mathrm{T}^{-1}\right]$<br/>Angular momentum = Moment of inertia Angular velocity<br/>$=\left[\mathrm{ML}^{2}\right] \times\left[\mathrm{T}^{-1}\right)=\left[\mathrm{ML}^{2} \mathrm{T}^{-1}\right]$<br/>(b) Impulse = Force x Time<br/>$=\left[\mathrm{MLT}^{-2}\right] \mathrm{IT}=\left[\mathrm{MLT}^{-1}\right]$<br/>and linear momentum = Mass $\times$ Velocity<br/>$=\left[\mathrm{M}\left[\mathrm{LT}^{-1}\right]=\left[\mathrm{MLT}^{-1}\right)\right.$<br/>(c) Moment of inertia = Mass $\times(\text { Distance })^{2}$<br/>$=\left[M L^{2}\right]$<br/>and moment of force = Force x Distance<br/>$=\left[\mathrm{MLT}^{-2}\right] \mathrm{U}=\left[\mathrm{M}^{2} \mathrm{T}^{-2}\right]$<br/>(d) Energy $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2} \mathrm{l}\right.$ and torque $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2} 1\right.$<br/>So, (c) option has different dimensions.</div>


tags: ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2014']
source_db: db\MarksBatch2_P1.db
title:
in-which-of-the-following-phenomena-the-heat-waves-travel-along-straight-lines-with-the-speed-of-light

slug:
in-which-of-the-following-phenomena-the-heat-waves-travel-along-straight-lines-with-the-speed-of-light-84424

question:
<div class="question">In which of the following phenomena, the heat waves travel along straight lines with the speed of light?</div>

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

answer:
<div class="solution">Thermal radiation is the heat waves travel along straight lines with the speed of light.</div>


title: in-which-of-the-following-reactions-new-carboncarbon-bond-is-not-formed
slug: in-which-of-the-following-reactions-new-carboncarbon-bond-is-not-formed-37266
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2009']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">In which of the following reactions new carbon-carbon bond is not formed :</div>

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

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

answer:
<div class="solution">In cannizaro's reaction no new $\mathrm{C}-\mathrm{C}$ bond is formed<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/-bAmB4AGsgB_SoFl5_zb6vEuUEMfDu_-wD_ZPSbtl_s.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P1.db
title:
in-youngs-double-slit-experiment-light-of-wavelength-passes-through-the-doubleslit-and-forms-interference-fringes-on-a-screen-12-m-away-if-the-differe

slug:
in-youngs-double-slit-experiment-light-of-wavelength-passes-through-the-doubleslit-and-forms-interference-fringes-on-a-screen-12-m-away-if-the-differe-38194

question:
<div class="question">In Young's double slit experiment, light of wavelength $\lambda$ passes through the double-slit and forms interference fringes on a screen $1.2 \mathrm{~m}$ away. If the difference between 3 rd order maximum and 3 rd order minimum is $0.18 \mathrm{~cm}$ and the slits are $0.02 \mathrm{~cm}$ apart, then $\lambda$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1200 \mathrm{~nm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$450 \mathrm{~nm}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$600 \mathrm{~nm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$300 \mathrm{~nm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$600 \mathrm{~nm}$</span> </div>

answer:
<div class="solution">Distance between 3 rd order minima and 3 rd order maxima is $\frac{\beta}{2}$
<br/>$
<br/>\begin{array}{l}
<br/>\frac{\beta}{2}=0.18 \mathrm{~cm} \\
<br/>\beta=0.36 \mathrm{~cm} \\
<br/>\beta=\frac{\mathrm{D} \lambda}{\mathrm{d}} \\
<br/>\therefore \lambda=600 \mathrm{~nm}
<br/>\end{array}
<br/>$</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2010']
answer: <div class="solution">No Solution Available</div>
source_db: db\MarksBatch2_P1.db
title:
in-youngs-double-slit-experiment-the-fringe-width-is-if-the-entire-arrangement-is-placed-in-a-liquid-of-refractive-index-n-the-fringe-width-becomes

slug:
in-youngs-double-slit-experiment-the-fringe-width-is-if-the-entire-arrangement-is-placed-in-a-liquid-of-refractive-index-n-the-fringe-width-becomes-94860

question:
<div class="question">In Young's double slit experiment, the fringe width is $\beta$. If the entire arrangement is placed in a liquid of refractive index $n$, the fringe width becomes :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$n \beta$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\beta}{n+1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\beta}{n-1}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{\beta}{n}$</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">$\frac{\beta}{n}$</span> </div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2011']
source_db: db\MarksBatch2_P1.db
title:
in-youngs-double-slit-experiment-the-two-slits-are-d-distance-apart-interference-pattern-is-observed-on-a-screen-at-a-distance-d-from-the-slits-a-dark

slug:
in-youngs-double-slit-experiment-the-two-slits-are-d-distance-apart-interference-pattern-is-observed-on-a-screen-at-a-distance-d-from-the-slits-a-dark-14979

question:
<div class="question">In Young's double slit experiment the two slits are d distance apart. Interference pattern is observed on a screen at a distance D from the slits. A dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{\mathrm{d}^2}{\mathrm{D}}\)</span> </div>

answer:
<div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/YELJhfyCXGImSRqAppODWI6pyWPkKEZyjYNUm5nuSQc.original.fullsize.png"/><br/><br/>\(\mathrm{n}^{\text {th }}\) Dark fringe<br/>\(\begin{aligned}<br/>&amp; (2 n-1) \frac{D \lambda}{2 d}=\frac{d}{2} \\<br/>&amp; \lambda=\frac{d^2}{(2 n-1) D}=\frac{d^2}{D} \quad[\text { for } n=1]<br/>\end{aligned}\)</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2022']
source_db: db\MarksBatch2_P1.db
title:
in-youngs-double-slit-experiment-with-a-monochromatic-light-maximum-intensity-is-4-times-the-minimum-intensity-in-the-interference-pattern-what-is-the

slug:
in-youngs-double-slit-experiment-with-a-monochromatic-light-maximum-intensity-is-4-times-the-minimum-intensity-in-the-interference-pattern-what-is-the-22748

question:
<div class="question">In Young's double slit experiment with a monochromatic light, maximum intensity is 4 times the minimum intensity in the interference pattern. What is the ratio of the intensities of the two interfering waves?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1 / 9$</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">B</span> <span class="option-data">$1 / 3$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 16$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 / 9$</span> </div>

answer:
<div class="solution">$\left(\sqrt{I_1}+\sqrt{I_2}\right)^2=4\left(\sqrt{I_1}-\sqrt{I_2}\right)^2$<br/>$\sqrt{l_1}+\sqrt{I_2}=2\left(\sqrt{l_1}-\sqrt{I_2}\right), 3 \sqrt{I_2}=\sqrt{I_1}, \frac{l_2}{I_1}=\frac{1}{9}$</div>


tags: ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2019']
source_db: db\MarksBatch2_P1.db
title:
in-youngs-experiment-for-the-interference-of-light-the-separation-between-the-slits-is-d-and-the-distance-of-the-screen-from-the-slits-is-d-if-d-is-in

slug:
in-youngs-experiment-for-the-interference-of-light-the-separation-between-the-slits-is-d-and-the-distance-of-the-screen-from-the-slits-is-d-if-d-is-in-23475

question:
<div class="question">In Young's experiment for the interference of light, the separation between the slits is $d$ and the distance of the screen from the slits is $D$. If $D$ is increased by $0.5 \%$ and $d$ is decreased by $0.3 \%$ then for the light of a given wavelength, which one of the following is true? "The fringe width.........</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">increases by $0.8 \%$</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">B</span> <span class="option-data">decreases by $0.8 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">increases by $0.2 \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">decreases by $0.2 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">increases by $0.8 \%$</span> </div>

answer:
<div class="solution">As we know that, fringe width, $\beta=\frac{\lambda D}{d}$
<br/>where, 
<br/>$\lambda=$ wavelength of light 
<br/>$D=$ Distance of the screen from the slits 
<br/>$d=$ separation between the slits 
<br/>Now, $\frac{\Delta \beta}{\beta} \times 100=\frac{\Delta D}{D} \times 100-\frac{\Delta d}{d} \times 100$
<br/>According to the question.
<br/>$$
<br/>\frac{\Delta \beta}{\beta} \times 100=0.5-(-0.3)=0.8 \%
<br/>$$
<br/>Hence, the fringe width increases by $0.2 \%$</div>


title: indicate-the-correct-iupac-name-of-the-coordination-compound-shown-in-the-figure-1
slug: indicate-the-correct-iupac-name-of-the-coordination-compound-shown-in-the-figure-1-89564
tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">Indicate the correct IUPAC name of the co-ordination compound shown in the figure.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/9qEBSrHutrre8VfFTZ3oqBvxqSmAQBIj-8zGPAJNTvY.original.fullsize.png"/></div>

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

answer:
<div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/a0xarWYvRc-m2aOsPrklOcyuYN7mahFl8ulsr9fLzbU.original.fullsize.png"/></div>


title: indicate-the-number-of-unpaired-electrons-in-k-3-fe-cn-6-and-k-4-fe-cn-6
slug: indicate-the-number-of-unpaired-electrons-in-k-3-fe-cn-6-and-k-4-fe-cn-6-33707
tags: ['Chemistry', 'Coordination Compounds', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">Indicate the number of unpaired electrons in $\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$ and $\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1 \quad 0$</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">$5 \quad 6$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$6 \quad 5$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0\quad 1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \quad 0$</span> </div>

answer:
<div class="solution">$\begin{array}{l}
<br/>\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \quad \mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \\
<br/>\mathrm{Fe}=[\mathrm{Ar}] 3 \mathrm{~d}^{6} 4 \mathrm{~s}^{2} \\
<br/>\mathrm{Fe}^{+3} \rightarrow(\mathrm{Ar}) 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{0} 4 \mathrm{p}^{0} \quad \mathrm{Fe}^{+2} \rightarrow(\mathrm{Ar}) 3 \mathrm{~d}^{6} 4 \mathrm{~s}^{0} 4 \mathrm{p}^{0}
<br/>\end{array}$
<br/>As $\mathrm{CN}$ is the strong field ligand; we pair up
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/vCUNRUqOKbT6uyHd6P4BIH33vzciScb9NhdwAfy7LZw.original.fullsize.png"/></div>


title: indicate-the-products-x-and-y-in-the-following-reactions-na-2-s-ns-n-1-8-na-2-so-3-s-x-y-x-y
slug: indicate-the-products-x-and-y-in-the-following-reactions-na-2-s-ns-n-1-8-na-2-so-3-s-x-y-x-y-94552
tags: ['Chemistry', 'Redox Reactions', 'WBJEE', 'WBJEE 2021']
source_db: db\MarksBatch2_P1.db
question:
<div class="question">Indicate the products $(\mathrm{X})$ and $(\mathrm{Y})$ in the following reactions:
<br/>$\begin{array}{lr}
<br/>\mathrm{Na}_{2} \mathrm{~S}+\mathrm{nS}(\mathrm{n}=1-8) &amp; \rightarrow(\mathrm{X}) \\
<br/>\mathrm{Na}_{2} \mathrm{SO}_{3}+\mathrm{S} &amp; \rightarrow(\mathrm{Y})
<br/>\end{array}$
<br/>$\begin{array}{ll}(\mathrm{X}) &amp; (\mathrm{Y})\end{array}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} \quad \mathrm{Na}_{2} \mathrm{~S}_{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{~S}_{(n+1)} \quad \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$</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">$\mathrm{Na}_{2} \mathrm{~S}_{\mathrm{n}} \quad \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{~S}_{5} \quad \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Na}_{2} \mathrm{~S}_{(n+1)} \quad \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$</span> </div>

answer:
<div class="solution">$\begin{array}{l}
<br/>\mathrm{Na}_{2} \mathrm{~S}+\mathrm{nS} \longrightarrow \mathrm{Na}_{2} \mathrm{~S}_{(\mathrm{n}+1)} \\
<br/>\mathrm{Na}_{2} \mathrm{SO}_{3}+\mathrm{S} \longrightarrow \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}
<br/>\end{array}$</div>


