# questions

title: the-reagents-used-for-softening-the-temporary-hardness-of-water-isare
slug: the-reagents-used-for-softening-the-temporary-hardness-of-water-isare-62551
tags: ['Chemistry', 'Hydrogen', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The reagent(s) used for softening the temporary hardness of water is(are)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Ca}(\mathrm{OH})_2$<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="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Na}_2 \mathrm{CO}_3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{NaOCl}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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"><br/>$\mathrm{Ca}(\mathrm{OH})_2$<br/>, <br/>$\mathrm{Na}_2 \mathrm{CO}_3$<br/>, <br/>$\mathrm{NaOCl}$</span> </div>

answer:
<div class="solution">Softening the temporary hardness of water means conversion of bicarbonate into calcium carbonate (precipitation)<br/>$$<br/>\begin{gathered}<br/>\mathrm{Ca}\left(\mathrm{HCO}_3\right)_2+\mathrm{Ca}(\mathrm{OH})_2 \longrightarrow \\<br/>2 \mathrm{CaCO}_3 \downarrow+2 \mathrm{H}_2 \mathrm{O} \\<br/>\mathrm{Ca}\left(\mathrm{HCO}_3\right)_2+\mathrm{Na}_2 \mathrm{CO}_3 \longrightarrow \\<br/>\mathrm{CaCO}_3 \downarrow+2 \mathrm{NaHCO}_3<br/>\end{gathered}<br/>$$<br/>Even $\mathrm{NaOCl}$ can be used, as in aqueous medium $\overline{\mathrm{O}} \mathrm{Cl}$ gets hydrolysed and makes solution alkaline enough to cause precipitation of $\mathrm{CaCO}_3$.<br/>$$<br/>\begin{aligned}<br/>\mathrm{NaOCl}+\mathrm{H}_2 \mathrm{O} &amp; \rightleftharpoons \mathrm{HOCl}+\mathrm{NaOH} \\<br/>\mathrm{OH}^{-}+\mathrm{HCO}_3^{-} &amp; \longrightarrow \mathrm{CO}_3^{2-}+\mathrm{H}_2 \mathrm{O}<br/>\end{aligned}<br/>$$<br/>Representative elements (Hydrogen and its compounds)<br/>Conceptual<br/>II</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
the-reversible-expansion-of-an-ideal-gas-under-adiabatic-and-isothermal-conditions-is-shown-in-the-figure-which-of-the-following-statements-is-are-cor

slug:
the-reversible-expansion-of-an-ideal-gas-under-adiabatic-and-isothermal-conditions-is-shown-in-the-figure-which-of-the-following-statements-is-are-cor-66854

question:
<div class="question">The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/eo2Y8s7OU5kL5byObpI5g2PjgFs-pKTedMEUhZEyH5E.original.fullsize.png"/><br/></div>

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

answer:
<div class="solution">$T_{1}=T_{2}$ because process is isothermal.
<br/> <br/>Work done in adiabatic process is less than in isothermal process because area covered by isothermal curve is more than the area covered by the adiabatic curve.
<br/> <br/>In adiabatic process expansion occurs byusing internal energy, hence, it decreases while in isothermal process temperature remains constant, that's why no change in internal energy.</div>


title: the-set-of-values-of-satisfying-the-inequation-2-sin-2-5-sin-2-0-where-0-2-is
slug: the-set-of-values-of-satisfying-the-inequation-2-sin-2-5-sin-2-0-where-0-2-is-50578
tags: ['Mathematics', 'Trigonometric Equations', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P3.db
question:
<div class="question">The set of values of $\theta$ satisfying the inequation $2 \sin ^2 \theta-5 \sin \theta+2&gt;0$, where $0 &lt; \theta &lt; 2 \pi$, is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(0, \frac{\pi}{6}\right) \cup\left(\frac{5 \pi}{6}, 2 \pi\right)$<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { As, } 2 \sin ^2 \theta-5 \sin \theta+2&gt;0 \\<br/>&amp; \Rightarrow(2 \sin \theta-1)(\sin \theta-2)&gt;0 \\<br/>&amp; \quad[\text { where, }(\sin \theta-2) &lt; 0 \text { for all } \theta \in R] \\<br/>&amp; \therefore \quad(2 \sin \theta-1) &lt; 0<br/>\end{aligned}<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SKUf5eaj68_7yEgcuBmEhMZj9ZevTUY2gjOCmj2PQDY.original.fullsize.png"/><br/><br/>$$<br/>\begin{array}{ll}<br/>\Rightarrow &amp; \sin \theta &lt; \frac{1}{2}, \text { shown as } \\<br/>\therefore &amp; \theta \in\left(0, \frac{\pi}{6}\right) \cup\left(\frac{5 \pi}{6}, 2 \pi\right)<br/>\end{array}<br/>$$</div>


title: the-shape-of-xeo-2-f-2-molecule-is
slug: the-shape-of-xeo-2-f-2-molecule-is-58473
question: <div class="question">The shape of $\mathrm{XeO}_{2} \mathrm{~F}_{2}$ molecule is</div>
source_db: MarksBatch2_P3.db
tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']

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

answer:
<div class="solution">$\mathrm{XeO}_{2} \mathrm{~F}_{2}$ has trigonal bipyramidal geometry, but due to presence of lone pair of electrons on equitorial position, its shape is see-saw.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/UDbnJR18VA91hjdnr_weUkNg1dpNa8443FkeOQd2380.original.fullsize.png"/></div>


title: the-smallest-ketone-and-its-next-homologoue-are-reacted-with-nh-2-oh-to-form-oxime
slug: the-smallest-ketone-and-its-next-homologoue-are-reacted-with-nh-2-oh-to-form-oxime-72441
tags: ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P3.db
question:
<div class="question">The smallest ketone and its next homologoue are reacted with $\mathrm{NH}_2 \mathrm{OH}$ to form oxime</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>three different oximes are formed<br/></span> </div>

answer:
<div class="solution">Lowest ketone is $\mathrm{CH}_3 \mathrm{COCH}_3$ (which form an oxime) and its next homologue is $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COCH}_3$ which form oxime with $\mathrm{NH}_2 \mathrm{OH}$. Such oxime shows the property of geometrical isomerism, i.e., it shows two isomers, symmetric and antisymmertic. (These are differ w.r.t. arrangement towards the space of $-\mathrm{C}=\mathrm{N}$, their different behaviour, can be confirmed with the help of Beckmann's rearrangement.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/EWRM37fa9BtKe7lTnyup6dAulowJ4gn46tYeyO_eSUE.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/piTLmcB5fVTIitK6u_WWUOlNpuukGwUWmlkLBHrK3qA.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Quadratic Equation', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
the-smallest-value-of-k-for-which-both-the-roots-of-the-equation-x-2-8-k-x-16-k-2-k-1-0-are-real-distinct-and-have-values-atleast-4-is

slug:
the-smallest-value-of-k-for-which-both-the-roots-of-the-equation-x-2-8-k-x-16-k-2-k-1-0-are-real-distinct-and-have-values-atleast-4-is-67549

question:
<div class="question">The smallest value of $k$, for which both the roots of the equation $x^2-8 k x+16\left(k^2-k+1\right)=0$ are real, distinct and have values atleast 4 , is</div>

answer:
<div class="solution">(i) Given, $x^2-8 k x+16\left(k^2-k+1\right)=0$<br/>Now, $\quad D=64\left\{k^2-\left(k^2-k+1\right)\right\}$<br/>$$<br/>\begin{aligned}<br/>&amp; =64(k-1)&gt;0 \\<br/>&amp; \therefore \quad k&gt;1 \\<br/>&amp; 16-32 k+16\left(k^2-k+1\right) \geq 0 \\<br/>&amp; \Rightarrow \quad k^2-3 k+2 \geq 0 \\<br/>&amp; \Rightarrow(k-2)(k-1) \geq 0 \Rightarrow k \leq 1 \text { or } k \geq 2 \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Hence, $k=2$</div>


title: the-species-having-bond-order-different-from-that-in-co-is
slug: the-species-having-bond-order-different-from-that-in-co-is-77772
question: <div class="question">The species having bond order different from that in $\mathrm{CO}$ is</div>
source_db: MarksBatch2_P3.db
tags:
['Chemistry', 'Chemical Bonding and Molecular Structure', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{NO}^{-}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{NO}^{+}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{CN}^{-}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{N}_2$</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{CO}$ : total $e^{-s}=6+8=14$<br/>$$<br/>\begin{gathered}<br/>\sigma 1 s^2, \sigma^* 1 s^2, \sigma 2 s^2, \sigma^* 2 s^2, \pi 2 p_x^{1+1}=\pi 2 p_y^{1+1}, \sigma 2 p_z^2 \\<br/>\mathrm{BO}=\frac{10-4}{2}=3 \\<br/>\mathrm{NO}^{-}=\text {Total } e^{-} s=7+8+1=16 \\<br/>\sigma 1 s^2, \sigma^* 1 s^2, \sigma 2 s^2, \sigma^* 2 s^2, \sigma 2 p_z^2, \pi 2 p_x^{1+1} \\<br/>=\pi 2 p_y^{1+1}, \pi^* 2 p_x^1=\pi^* 2 p_y^1 \\<br/>\mathrm{BO}=\frac{10-6}{2}=\frac{4}{2}=2<br/>\end{gathered}<br/>$$<br/>Total number of $e^{-} s: \mathrm{CN}^{-}=6+7+1=14$<br/>$$<br/>\mathrm{N}_2=7+7=14<br/>$$</div>


title: the-species-having-pyramidal-shape-is-1
slug: the-species-having-pyramidal-shape-is-1-25284
question: <div class="question">The species having pyramidal shape is</div>
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'JEE Main']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{SO}_3$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{BrF}_3$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{SiO}_3^{2-}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{OSF}_2$</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"><br/>$\mathrm{OSF}_2$</span> </div>

answer:
<div class="solution">$\mathrm{OSF}_2$ has pyramidal shape Chemical bonding Basic understanding II<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0NPwQcWl6LuOUDzu4GeX_DlbKuVQS3hYkGBv_4tMvYM.original.fullsize.png"/><br/></div>


title: the-species-having-pyramidal-shape-is
slug: the-species-having-pyramidal-shape-is-79876
question: <div class="question">The species having pyramidal shape is</div>
source_db: MarksBatch2_P3.db
tags:
['Chemistry', 'Chemical Bonding and Molecular Structure', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{SO}_3$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{BrF}_3$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{SiO}_3^{2-}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{OSF}_2$</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"><br/>$\mathrm{OSF}_2$</span> </div>

answer:
<div class="solution">$\mathrm{OSF}_2$ has pyramidal shape Chemical bonding Basic understanding II<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0NPwQcWl6LuOUDzu4GeX_DlbKuVQS3hYkGBv_4tMvYM.original.fullsize.png"/><br/></div>


title: the-species-present-in-solution-when-co-2-is-dissolved-in-water-are
slug: the-species-present-in-solution-when-co-2-is-dissolved-in-water-are-14979
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P3.db
question:
<div class="question">The species present in solution when $\mathrm{CO}_2$ is dissolved in water are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{CO}_2, \mathrm{H}_2 \mathrm{CO}_3, \mathrm{HCO}_3^{-}, \mathrm{CO}_3^{2-}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{H}_2 \mathrm{CO}_3, \mathrm{CO}_3^{2-}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{CO}_3^{2-}, \mathrm{HCO}_3^{-}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{CO}_2, \mathrm{H}_2 \mathrm{CO}_3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\mathrm{CO}_2, \mathrm{H}_2 \mathrm{CO}_3, \mathrm{HCO}_3^{-}, \mathrm{CO}_3^{2-}$<br/></span> </div>

answer:
<div class="solution">When $\mathrm{CO}_2$ is dissolved in water, therefore it forms dibasic carbonic acid, which gives $\mathrm{HCO}_3^{-}$ and $\mathrm{CO}_3^{2-}$ ions on ionisation. Hence in solution $\mathrm{CO}_2, \mathrm{H}_2 \mathrm{CO}_3, \mathrm{HCO}_3^{-}$and $\mathrm{CO}_3^{2-}$ are present.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/eZ-xAZkHk1P-k6OdkfipgaRrtdiTqe1veNGCrErZJ80.original.fullsize.png"/><br/></div>


title: the-species-which-by-definition-has-zero-standard-molar-enthalpy-of-formation-at-298-k-is
slug: the-species-which-by-definition-has-zero-standard-molar-enthalpy-of-formation-at-298-k-is-23279
tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The species which by definition has zero standard molar enthalpy of formation at $298 \mathrm{~K}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Br}_2(g)$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Cl}_2(g)$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{H}_2 \mathrm{O}(g)$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{CH}_4(g)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Cl}_2(g)$<br/></span> </div>

answer:
<div class="solution">$\Delta H_f^{\circ}\left(\mathrm{Cl}_2, g\right)=0$<br/>$\Delta H_f^{\circ}$ of elements in their standard state is taken to be zero. $\mathrm{Cl}_2$ is gas, $\mathrm{Br}_2$ is liquid and $\mathrm{I}_2$ is solid at room temperature.<br/>Energetics<br/>Conceptual, implication of rules/laws III</div>


title: the-spin-only-magnetic-moment-value-in-bohr-magneton-units-of-mathrmcrmathrmco6-is
slug: the-spin-only-magnetic-moment-value-in-bohr-magneton-units-of-mathrmcrmathrmco6-is-90966
source_db: MarksBatch2_P3.db
question:
<div class="question">The spin only magnetic moment value (in Bohr magneton units) of \mathrm{Cr}(\mathrm{CO})_6$ is</div>

tags:
['Chemistry', 'Chemical Bonding and Molecular Structure', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$2.84$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$4.90$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$5.92$</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{CO}$ is a strong ligand, all the six electron of the valence shell of $\mathrm{Cr}$ is paired and spin only magnetic moment $=0$.</div>


tags: ['Mathematics', 'Circle', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
the-straight-line-2-x-3-y-1-divides-the-circular-region-x-2-y-2-6-into-two-parts-if-s-2-4-3-2-5-4-3-4-1-4-1-8-1-4-1-then-the-number-of-points-in-s-lyi-1

slug:
the-straight-line-2-x-3-y-1-divides-the-circular-region-x-2-y-2-6-into-two-parts-if-s-2-4-3-2-5-4-3-4-1-4-1-8-1-4-1-then-the-number-of-points-in-s-lyi-1-49997

question:
<div class="question">The straight line $2 x-3 y=1$ divides the circular region $x^2+y^2 \leq 6$ into two parts. If $S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2}, \frac{3}{4}\right),\left(\frac{1}{4},-\frac{1}{4}\right),\left(\frac{1}{8}, \frac{1}{4}\right)\right\}$, then the number of point(s) in $S$ lying inside the smaller part is</div>

answer:
<div class="solution">$x^2+y^2 \leq 6$ and $2 x-3 y=1$ is shown as, For the point to lie in the shaded part, origin and the point lie on opposite side of straight line $L$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/dVwnyTkUUvsDQ18fHYOVS4iDdvsVr-wqh05DruuYZs0.original.fullsize.png"/><br/><br/>$\therefore$ For any point in shaded part $L&gt;0$ and for any point inside the circle $S &lt; 0$.<br/>Now, for $\left(2, \frac{3}{4}\right) L: 2 x-3 y-1$<br/>$$<br/>L: 4-\frac{9}{4}-1=\frac{3}{4}&gt;0<br/>$$<br/>and $S: x^2+y^2-6$,<br/>$$<br/>S: 4+\frac{9}{16}-6 &lt; 0<br/>$$<br/>$\Rightarrow\left(2 \frac{3}{4}\right)$ lies in shaded part.<br/>For $\left(\frac{5}{2}, \frac{3}{4}\right) L: 5-9-1 &lt; 0 \quad$ [neglect]<br/>For $\left.\left(\frac{1}{4},-\frac{1}{4}\right) L: \frac{1}{2}+\frac{3}{4}-1&gt;0\right\}$<br/>$\therefore\left(\frac{1}{4},-\frac{1}{4}\right)$ lies in the shaded part. For $\left(\frac{1}{8}, \frac{1}{4}\right) L: \frac{1}{4}-\frac{3}{4}-1 &lt; 0$ [neglect] $\Rightarrow$ Only 2 points lie in the shaded part.</div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
the-straight-line-2-x-3-y-1-divides-the-circular-region-x-2-y-2-6-into-two-parts-if-s-2-4-3-2-5-4-3-4-1-4-1-8-1-4-1-then-the-number-of-points-in-s-lyi

slug:
the-straight-line-2-x-3-y-1-divides-the-circular-region-x-2-y-2-6-into-two-parts-if-s-2-4-3-2-5-4-3-4-1-4-1-8-1-4-1-then-the-number-of-points-in-s-lyi-27937

question:
<div class="question">The straight line $2 x-3 y=1$ divides the circular region $x^2+y^2 \leq 6$ into two parts. If $S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2}, \frac{3}{4}\right),\left(\frac{1}{4},-\frac{1}{4}\right),\left(\frac{1}{8}, \frac{1}{4}\right)\right\}$, then the number of point(s) in $S$ lying inside the smaller part is</div>

answer:
<div class="solution">$x^2+y^2 \leq 6$ and $2 x-3 y=1$ is shown as, For the point to lie in the shaded part, origin and the point lie on opposite side of straight line $L$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/dVwnyTkUUvsDQ18fHYOVS4iDdvsVr-wqh05DruuYZs0.original.fullsize.png"/><br/><br/>$\therefore$ For any point in shaded part $L&gt;0$ and for any point inside the circle $S &lt; 0$.<br/>Now, for $\left(2, \frac{3}{4}\right) L: 2 x-3 y-1$<br/>$$<br/>L: 4-\frac{9}{4}-1=\frac{3}{4}&gt;0<br/>$$<br/>and $S: x^2+y^2-6$,<br/>$$<br/>S: 4+\frac{9}{16}-6 &lt; 0<br/>$$<br/>$\Rightarrow\left(2 \frac{3}{4}\right)$ lies in shaded part.<br/>For $\left(\frac{5}{2}, \frac{3}{4}\right) L: 5-9-1 &lt; 0 \quad$ [neglect]<br/>For $\left.\left(\frac{1}{4},-\frac{1}{4}\right) L: \frac{1}{2}+\frac{3}{4}-1&gt;0\right\}$<br/>$\therefore\left(\frac{1}{4},-\frac{1}{4}\right)$ lies in the shaded part. For $\left(\frac{1}{8}, \frac{1}{4}\right) L: \frac{1}{4}-\frac{3}{4}-1 &lt; 0$ [neglect] $\Rightarrow$ Only 2 points lie in the shaded part.</div>


tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
the-substituents-r-1-and-r-2-for-nine-peptides-are-listed-in-the-table-given-below-how-many-of-these-peptides-are-positively-charged-at-ph-70-beginarr

slug:
the-substituents-r-1-and-r-2-for-nine-peptides-are-listed-in-the-table-given-below-how-many-of-these-peptides-are-positively-charged-at-ph-70-beginarr-12056

question:
<div class="question">The substituents $R_{1}$ and $R_{2}$ for nine peptides are listed in the table given below. How many of these peptides are positively charged at $\mathrm{pH}=7.0$ ?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/rmBF2AWjJ_eIJZodviWtqeiE2VUVclDkDbIdYCGd73w.original.fullsize.png"/><br/> <br/> <br/>\begin{array}{|c|c|c|}
<br/> <br/>\hline Peptide &amp; \mathbf{R}_{\mathbf{1}} &amp; \mathbf{R}_{\mathbf{2}} \\
<br/> <br/>\hline I &amp; \mathrm{H} &amp; \mathrm{H} \\
<br/> <br/>\hline II &amp; \mathrm{H} &amp; \mathrm{CH}_{3} \\
<br/> <br/>\hline III &amp; \mathrm{CH}_{2} \mathrm{COOH} &amp; \mathrm{H} \\
<br/> <br/>\hline IV &amp; \mathrm{CH}_{2} \mathrm{CONH}_{2} &amp; \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\
<br/> <br/>\hline V &amp; \mathrm{CH}_{2} \mathrm{CONH}_{2} &amp; \mathrm{CH}_{2} \mathrm{CONH}_{2} \\
<br/> <br/>\hline VI &amp; \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} &amp; \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\
<br/> <br/>\hline VII &amp; \mathrm{CH}_{2} \mathrm{COOH} &amp; \mathrm{CH}_{2} \mathrm{CONH}_{2} \\
<br/> <br/>\hline VIII &amp; \mathrm{CH}_{2} \mathrm{OH} &amp; \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\
<br/> <br/>\hline IX &amp; \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} &amp; \mathrm{CH}_{3} \\
<br/> <br/>\hline
<br/> <br/>\end{array}</div>

answer:
<div class="solution">Peptides with isoelectric point (pI) more than 7 would exist as cation in neutral solution $(\mathrm{pH}=7)$ which means the given polypeptide is of basic nature, so it must contain two or more amino groups. Hence IV, VI, VIII and IX are correct options.</div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-synthesis-of-3octyne-is-achieved-by-adding-a-bromoalkane-into-a-mixture-of-sodium-amide-and-an-alkyne-the-bromoalkane-and-alkyne-respectively-are

slug:
the-synthesis-of-3octyne-is-achieved-by-adding-a-bromoalkane-into-a-mixture-of-sodium-amide-and-an-alkyne-the-bromoalkane-and-alkyne-respectively-are-25924

question:
<div class="question">The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_3$ and $$<br/>\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{C} \equiv \mathrm{CH}<br/>$$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{CH}_3$ and<br/>$$<br/>\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{C} \equiv \mathrm{CH}<br/>$$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_3$ and $$<br/>\mathrm{CH}_3 \mathrm{C} \equiv \equiv \mathrm{CH}<br/>$$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_3$ and<br/>$$<br/>\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{C} \equiv \mathrm{CH}<br/>$$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"><br/>$\mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_3$ and<br/>$$<br/>\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{C} \equiv \mathrm{CH}<br/>$$a)</span> </div>

answer:
<div class="solution">$\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_2$ $-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{CH}_3$ There are two (marked) possibility of halides<br/>Thus, in the given context<br/>$$<br/>\begin{array}{r}<br/>\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{C} \equiv \mathrm{CH}+\mathrm{NaNH}_2 \longrightarrow \\<br/>\mathrm{CH}_3 \mathrm{CH}_2-\mathrm{C} \equiv \overline{\mathrm{CNa}^{+}}<br/>\end{array}<br/>$$<br/>$$<br/>\begin{aligned}<br/>\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{C} \equiv \overline{\mathrm{CNa}} \\<br/>\longrightarrow \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{C} \equiv \mathrm{BrCH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_3 \\<br/>\text { 3-octyne } \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_3<br/>\end{aligned}<br/>$$<br/>Hydrocarbon<br/>Conceptual, reaction understanding II</div>


title: the-tangent-pt-and-the-normal-pn-to-the-parabola-y-2-4-a-x-at-a-point-p-on
slug: the-tangent-pt-and-the-normal-pn-to-the-parabola-y-2-4-a-x-at-a-point-p-on-77187
tags: ['Mathematics', 'Parabola', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The tangent $P T$ and the normal $P N$ to the parabola $y^2=4 a x$ at a point $P$ on</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>vertex is $\left(\frac{2 a}{3}, 0\right)$ it meet its axis at points $T$ and $N$,<br/>, <br/>focus is $(a, 0)$</span> </div>

answer:
<div class="solution">Equation of tangent and normal at point $P\left(a t^2, 2 a t\right)$ is $t y=x=a t^2$ and $y=-t x+2 a t+a t^2$ Let centroid of $\triangle P T N$ is $R(h, k)$. $\therefore \quad h=\frac{a t^2+\left(-a t^2\right)+2 a+a t^2}{3}$ and $k=\frac{2 a t}{3}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4a3vezqrNAkiZDaoRNkBLB4ffR1OoWaQNx3mDCAWlks.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{array}{rlrl} <br/>&amp; \Rightarrow &amp; 3 h &amp; =2 a+a \cdot\left(\frac{3 k}{2 a}\right)^2 \\<br/>\Rightarrow &amp; &amp; 3 h &amp; =2 a+\frac{9 k^2}{4 a} \\<br/>\Rightarrow &amp; 9 k^2 &amp; =4 a(3 h-2 a)<br/>\end{array}<br/>$$<br/>$\therefore$ Locus of centroid is<br/>$$<br/>y^2=\frac{4 a}{3}\left(x-\frac{2 a}{3}\right)<br/>$$<br/>$\therefore \operatorname{Vertex}\left(\frac{2 a}{3}, 0\right)$; directrix<br/>$$<br/>x-\frac{2 a}{3}=-\frac{a}{3} \Rightarrow x=\frac{a}{3}<br/>$$<br/>Latusrectum $=\frac{4 a}{3}$<br/>$\therefore$ Focus $\left(\frac{a}{3}+\frac{2 a}{3}, 0\right)$ i.e. $(a, 0)$</div>


tags: ['Mathematics', 'Application of Derivatives', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-tangent-to-the-curve-y-e-x-drawn-at-the-point-c-e-c-intersects-the-line-joining-the-points-c-1-e-c-1-and-c-1-e-c-1

slug:
the-tangent-to-the-curve-y-e-x-drawn-at-the-point-c-e-c-intersects-the-line-joining-the-points-c-1-e-c-1-and-c-1-e-c-1-27361

question:
<div class="question">The tangent to the curve $y=e^x$ drawn at the point $\left(c, e^c\right)$ intersects the line joining the points $\left(c-1, e^{c-1}\right)$ and $\left(c+1, e^{c+1}\right)$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>on the left of $x=c$<br/></span> </div>

answer:
<div class="solution">Slope of the line joining the points $\left(c-1, e^{c-1}\right)$ and $\left(c+1, e^{c+1}\right)$ is equal to $\frac{e^{c+1}-e^{c-1}}{2}&gt;e^c$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VGvkClDxV8F-gNTzbTW1cbZ_e9vEpZ4KBurvN0ItKJk.original.fullsize.png"/><br/><br/>$$<br/>\text { Tangent to the curve } y=e^x \text { will intersect the given line to the left of the line } x=c \text {. }<br/>$$<br/>ALITER<br/>The equation of the tangent to the curve $y=e^x$ at $\left(c, e^c\right)$ is<br/>$$<br/>y-e^c=e^c(x-c)<br/>$$<br/>Equation of the line joining the given points is<br/>$$<br/>y-e^{c-1}=\frac{e^c\left(e-e^{-1}\right)}{2}[x-(c-1)]<br/>$$<br/>Eliminating $y$ from Eqs. (i) and (ii), we get<br/>$$<br/>\begin{aligned}<br/>{[x-(c-1)]\left[2-\left(e-e^{-1}\right)\right] } &amp; =2 e^{-1} \\<br/>x-c &amp; =\frac{e+e^{-1}-2}{2-\left(e-e^{-1}\right)} &lt; 0 \Rightarrow x &lt; c .<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'States of Matter', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-term-that-corrects-for-the-attractive-forces-present-in-a-real-gas-in-the-van-der-waals-equation-is

slug:
the-term-that-corrects-for-the-attractive-forces-present-in-a-real-gas-in-the-van-der-waals-equation-is-18369

question:
<div class="question">The term that corrects for the attractive forces present in a real gas in the van der Waals' equation is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$n^2 a / V^2$<br/></span> </div>

answer:
<div class="solution">In the van der Waals' equation<br/>$$<br/>\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T<br/>$$<br/>The pressure correction factor $\left(n^2 a / V^2\right)$ accounts for intermolecular attraction in real gas.</div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-alkenes-possible-by-dehydrobromination-of-3bromo3cyclopentylhexane-using-alcoholic-koh-is-1

slug:
the-total-number-of-alkenes-possible-by-dehydrobromination-of-3bromo3cyclopentylhexane-using-alcoholic-koh-is-1-23367

question:
<div class="question">The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic $\mathrm{KOH}$ is</div>

answer:
<div class="solution">The substrate has three different types of $\mathrm{B}-\mathrm{H}$, therefore, first, three structural isomers of alkenes are expected as<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/2E-6lbXzWSzSfeC6dpZeGVGXsO8Qk5ByuknVh5D7qCA.original.fullsize.png"/><br/><br/>The last two alkenes II and III are also capable of showing geometrical isomerism hence two geometrical isomers for each of them will be counted giving a total of five isomers.</div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-alkenes-possible-by-dehydrobromination-of-3bromo3cyclopentylhexane-using-alcoholic-koh-is

slug:
the-total-number-of-alkenes-possible-by-dehydrobromination-of-3bromo3cyclopentylhexane-using-alcoholic-koh-is-52431

question:
<div class="question">The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic $\mathrm{KOH}$ is</div>

answer:
<div class="solution">The substrate has three different types of $\mathrm{B}-\mathrm{H}$, therefore, first, three structural isomers of alkenes are expected as<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/2E-6lbXzWSzSfeC6dpZeGVGXsO8Qk5ByuknVh5D7qCA.original.fullsize.png"/><br/><br/>The last two alkenes II and III are also capable of showing geometrical isomerism hence two geometrical isomers for each of them will be counted giving a total of five isomers.</div>


title: the-total-number-of-and-particles-emitted-in-the-nuclear-reaction-92-u-238-82-pb-214-is
slug: the-total-number-of-and-particles-emitted-in-the-nuclear-reaction-92-u-238-82-pb-214-is-64077
tags: ['Chemistry', 'Chemical Kinetics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The total number of $\alpha$ and $\beta$-particles emitted in the nuclear reaction ${ }_{92} \mathrm{U}^{238} \longrightarrow{ }_{82} \mathrm{~Pb}^{214}$ is</div>

answer:
<div class="solution">${ }_{92} \mathrm{U}^{238} \rightarrow_{82} \mathrm{U}^{214}+6_2 \mathrm{He}^{\mathrm{H}}(\alpha)+2_{-1} e^0(\beta)$</div>


title: the-total-number-of-basic-groups-in-the-following-form-of-lysine-is
slug: the-total-number-of-basic-groups-in-the-following-form-of-lysine-is-98974
tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The total number of basic groups in the following form of lysine is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/CDh0L1QC28BehxYBcQjQr3xBovuGv8IJ4caySMfOPKw.original.fullsize.png"/><br/></div>

answer:
<div class="solution">Lysine contains two basic groups, e.g., $\mathrm{NH}_2$<br/>Biomolecules<br/>Basic straight<br/>I</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-contributing-structures-showing-hyperconjugation-involving-c-h-bonds-for-the-following-carbocation-is

slug:
the-total-number-of-contributing-structures-showing-hyperconjugation-involving-c-h-bonds-for-the-following-carbocation-is-49475

question:
<div class="question">The total number of contributing structures showing hyperconjugation (involving $\mathrm{C}-\mathrm{H}$ bonds) for the following carbocation is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VfidOLoxYCm3igeNrgMWD0hG7NJ2-dwLHdPvrOUT2j8.original.fullsize.png"/><br/></div>

answer:
<div class="solution">$$<br/>\text { These are total } 6 \alpha-\mathrm{H} \text { to } \mathrm{sp}^2 \text { carbon and they all can participate in hyperconjugation. }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/II1kwlG6okw8yRPNujVqEME5WC9ZnIn4HQN8buk0GuQ.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-cyclic-isomers-possible-for-a-hydrocarbon-with-the-molecular-formula-c-4-h-6-is-1

slug:
the-total-number-of-cyclic-isomers-possible-for-a-hydrocarbon-with-the-molecular-formula-c-4-h-6-is-1-30886

question:
<div class="question">The total number of cyclic isomers possible for a hydrocarbon with the molecular formula $\mathrm{C}_4 \mathrm{H}_6$ is</div>

answer:
<div class="solution">$\mathrm{C}_4 \mathrm{H}_6$ can have five cyclic isomers<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/uWspoI_a3kuheqUIAVyQWI7Zgcnrd37WXbP7Ncyn_F4.original.fullsize.png"/><br/><br/>Isomerism (organic)<br/>Structural manipulation III</div>


title: the-total-number-of-cyclic-isomers-possible-for-a-hydrocarbon-with-the-molecular-formula-c-4-h-6-is
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
slug:
the-total-number-of-cyclic-isomers-possible-for-a-hydrocarbon-with-the-molecular-formula-c-4-h-6-is-26460

question:
<div class="question">The total number of cyclic isomers possible for a hydrocarbon with the molecular formula $\mathrm{C}_4 \mathrm{H}_6$ is</div>

answer:
<div class="solution">$\mathrm{C}_4 \mathrm{H}_6$ can have five cyclic isomers<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/uWspoI_a3kuheqUIAVyQWI7Zgcnrd37WXbP7Ncyn_F4.original.fullsize.png"/><br/><br/>Isomerism (organic)<br/>Structural manipulation III</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-cyclic-structural-as-well-as-stereoisomers-possible-for-a-compound-with-the-molecular-formula-c-5-h-10-is

slug:
the-total-number-of-cyclic-structural-as-well-as-stereoisomers-possible-for-a-compound-with-the-molecular-formula-c-5-h-10-is-49797

question:
<div class="question">The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula $=\mathrm{C}_5 \mathrm{H}_{10}$ is</div>

answer:
<div class="solution">$$<br/>\text { The total number of cyclic isomers are seven as shown below. }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/mBHM73yyN51KjE7GWf8NgPUVslv5I1StONWNTiVMcC4.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Ionic Equilibrium', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-diprotic-acids-among-the-following-is-h-3-po-4-h-2-co-3-h-3-po-2-h-2-so-4-h-2-s-2-o-7-h-2-cro-4-h-3-po-3-h-3-bo-3-h-2-so-3

slug:
the-total-number-of-diprotic-acids-among-the-following-is-h-3-po-4-h-2-co-3-h-3-po-2-h-2-so-4-h-2-s-2-o-7-h-2-cro-4-h-3-po-3-h-3-bo-3-h-2-so-3-93146

question:
<div class="question">The total number of diprotic acids among the following is<br/>$\begin{array}{lll}\mathrm{H}_3 \mathrm{PO}_4 &amp; \mathrm{H}_2 \mathrm{SO}_4 &amp; \mathrm{H}_3 \mathrm{PO}_3 \\ \mathrm{H}_2 \mathrm{CO}_3 &amp; \mathrm{H}_2 \mathrm{~S}_2 \mathrm{O}_7 &amp; \mathrm{H}_3 \mathrm{BO}_3 \\ \mathrm{H}_3 \mathrm{PO}_2 &amp; \mathrm{H}_2 \mathrm{CrO}_4 &amp; \mathrm{H}_2 \mathrm{SO}_3\end{array}$</div>

answer:
<div class="solution">$\mathrm{H}_2 \mathrm{SO}_4, \mathrm{H}_2 \mathrm{CO}_3, \mathrm{H}_2 \mathrm{~S}_2 \mathrm{O}_7, \mathrm{H}_2 \mathrm{CrO}_4, \mathrm{H}_3 \mathrm{PO}_3, \mathrm{H}_2 \mathrm{SO}_3$<br/>Acid-base-salt<br/>Basic structural understanding II</div>


title: the-total-number-of-local-maxima-and-local-minima-of-the-function-f-x-2-x-3-x-3-2-3-x-1-1-x-2-is
tags: ['Mathematics', 'Application of Derivatives', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P3.db
slug:
the-total-number-of-local-maxima-and-local-minima-of-the-function-f-x-2-x-3-x-3-2-3-x-1-1-x-2-is-45082

question:
<div class="question">The total number of local maxima and local minima of the function $f(x)=\left\{\begin{array}{lc}(2+x)^3 ; &amp; -3 &lt; x \leq-1 \\ x^{\frac{2}{3}} ; &amp; -1 &lt; x &lt; 2\end{array}\right.$ is</div>

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

answer:
<div class="solution">Given that, $f(x)=\left\{\begin{array}{l}(2+x)^3 ;-3 &lt; x \leq-1 \\ x^{2 / 3} ; \quad-1 &lt; x &lt; 2\end{array}\right.$<br/>$$<br/>\Rightarrow \quad f^{\prime}(x)=\left\{\begin{array}{l}<br/>3(2+x)^2 ;-3 &lt; x \leq 1 \\<br/>\frac{2}{3} x^{-\frac{1}{3}} ; \quad-1 &lt; x &lt; 2<br/>\end{array}\right.<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/O3q5lbRV0bbl0iS0OWGpiOvzf4DQr3JZZm7V5HR-HEY.original.fullsize.png"/><br/><br/>Clearly, $f^{\prime}(x)$ changes its sign at $x=-1$ from $+$ ve to -ve and so $f(x)$ has local maxima at $x=-1$.<br/>Also, $f^{\prime}(0)$ does not exist but $f^{\prime}\left(0^{-}\right) &lt; 0$ and $f^{\prime}\left(0^{+}\right) &lt; 0$.<br/>It can only be inferred that $f(x)$ has a possibility of a minima at $x=0$.<br/>Hence, the given function has one local maxima at $x=-1$ and one local minima at $x=0$.</div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">150</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-ways-in-which-5-balls-of-different-colours-can-be-distributed-among-3-persons-so-that-each-person-gets-at-least-one-ball-is

slug:
the-total-number-of-ways-in-which-5-balls-of-different-colours-can-be-distributed-among-3-persons-so-that-each-person-gets-at-least-one-ball-is-57662

question:
<div class="question">The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">75</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">150</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">210</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">243</span> </li> </ul>

answer:
<div class="solution">$\because \quad$ Each person gets at least one ball.
<br/> <br/>$\therefore \quad 3$ Persons can have 5 balls as follow.
<br/> <br/>\begin{array}{|c|c|c|}
<br/> <br/>\hline Person &amp; No. of balls &amp; No. of balls \\
<br/> <br/>\hline I &amp; 1 &amp; 1 \\
<br/> <br/>\hline II &amp; 1 &amp; 2 \\
<br/> <br/>\hline III &amp; 3 &amp; 2 \\
<br/> <br/>\hline
<br/> <br/>\end{array}
<br/> <br/>The number of ways to distribute balls 1,1,3 in first to three persons
<br/> <br/>$={ }^{5} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{1} \times{ }^{3} \mathrm{C}_{3}$
<br/> <br/>Also 3 , persons having 1,1 and 3 balls can be arranged in $\frac{3 !}{2 !}$ ways.
<br/> <br/>$\therefore \quad$ Total no. of ways to distribute $1,1,3$ balls to the three persons
<br/> <br/>$={ }^{5} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{1} \times{ }^{3} \mathrm{C}_{3} \times \frac{3 !}{2 !}=60$
<br/> <br/>Similarly, total no. of ways to distribute $1,2,2$ balls to
<br/> <br/>three persons $={ }^{5} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{2} \times{ }^{2} \mathrm{C}_{2} \times \frac{3 !}{2 !}=90$
<br/> <br/>$\therefore \quad$ The required number of ways $=60+90=150$</div>


title: the-type-of-placenta-with-a-unilocular-ovary-and-a-single-ovule
slug: the-type-of-placenta-with-a-unilocular-ovary-and-a-single-ovule-99217
question: <div class="question">The type of placenta with a unilocular ovary and a single ovule</div>
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Basal</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Marginal</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Basal</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Free central</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Axile</span> </li> </ul>

answer:
<div class="solution">In basal placentation, the ovary is bicarpellary, syncarpous and unilocular and a single ovule is borne at the base of ovary. Basal placentation is the most advance type of placentation. It is observed in most advanced family like Asteraceae and Poaceae.</div>


title: the-value-of-0-1-1-x-50-101-d-x-5050-0-1-1-x-50-100-d-x
slug: the-value-of-0-1-1-x-50-101-d-x-5050-0-1-1-x-50-100-d-x-60504
tags: ['Mathematics', 'Definite Integration', 'JEE Advanced', 'JEE Advanced 2006']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5051</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $\frac{(5050) \int_0^1\left(1-x^{50}\right)^{100} d x}{\int_0^1\left(1-x^{50}\right)^{101} d x}$</div>

answer:
<div class="solution">Let $I_2=\int_0^1\left(1-x^{50}\right)^{101} d x$, using integration by parts<br/>$$<br/>\begin{aligned}<br/>&amp; \left.=\left[(1-x)^{50}\right)^{101} \cdot x\right]_0^1+\int_0^1\left(1-x^{50}\right)^{100} 50 \cdot x^{49} \cdot x d x \\<br/>&amp; =0-\int_0^1(50)(101)\left(1-x^{50}\right)^{100}(-x)^{50} d x \\<br/>&amp; =-(50)(101) \int_0^1\left(1-x^{50}\right)^{101} d x+(50)(101) \int_0^1\left(1-x^{50}\right)^{100} d x \\<br/>&amp; =5050 I_2+5050 I_1<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>\therefore &amp; I_2+5050 I_2 &amp; =5050 I_1 \\<br/>\therefore &amp; \frac{(5050) I_1}{I_2} &amp; =5051<br/>\end{aligned}<br/>$$</div>


title: the-value-of-6-lo-g-2-3-3-2-1-4-3-2-1-4-3-2-1-4-3-2-1-is
slug: the-value-of-6-lo-g-2-3-3-2-1-4-3-2-1-4-3-2-1-4-3-2-1-is-62842
tags: ['Mathematics', 'Quadratic Equation', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of
<br/> <br/>$6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}}} \cdots}}\right) \text { is }$</div>

answer:
<div class="solution">Let $x=\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}}}}} \ldots \ldots$
<br/> <br/>$\Rightarrow \quad x=\frac{1}{3 \sqrt{2}} \sqrt{4-x}$ 
<br/> <br/>$\Rightarrow \quad 3 \sqrt{2} x=\sqrt{4-x}$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\Rightarrow \quad 18 x^{2}=4-x \\
<br/> <br/>\Rightarrow \quad 18 x^{2}+x-4=0 \\
<br/> <br/>\Rightarrow \quad(9 x-4)(2 x+1)=0 \\
<br/> <br/>\Rightarrow \quad x=\frac{4}{9} \text { or } x=-\frac{1}{2}
<br/> <br/>\end{array}$
<br/> <br/>(Not possible because log is not define for -ve value)
<br/> <br/>$\begin{aligned}
<br/> <br/>\therefore \quad &amp; 6+\log _{\frac{3}{2}}\left(\frac{4}{9}\right)=6+\log _{\frac{3}{2}}\left(\frac{3}{2}\right)^{-2} \\
<br/> <br/>&amp;=6-2=4
<br/> <br/>\end{aligned}$</div>


title: the-value-of-b-for-which-the-equations-x-2-b-x-1-0-x-2-x-b-0-have-one-root-in-common-is
slug: the-value-of-b-for-which-the-equations-x-2-b-x-1-0-x-2-x-b-0-have-one-root-in-common-is-35130
tags: ['Mathematics', 'Quadratic Equation', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $b$ for which the equations $x^2+b x-1=0, x^2+x+b=0$ have one root in common is</div>

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

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

answer:
<div class="solution">If $\quad a_1 x^2+b_1 x+c_1=0$<br/>and $a_2 x^2+b_2 x+c_2=0$<br/>have a common real root, then<br/>$$<br/>\begin{aligned}<br/>\Rightarrow \quad\left(a_1 c_2-a_2 c_1\right)^2=\left(b_1 c_2-\right. &amp; \left.b_2 c_1\right) \\<br/>&amp; \left(a_1 b_2-a_2 b_1\right)<br/>\end{aligned}<br/>$$<br/>$\left.\therefore \begin{array}{l}x^2+b x-1=0 \\ x^2+x+b=0\end{array}\right\}$ have a common root.<br/>$\Rightarrow \quad(1+b)^2=\left(b^2+1\right)(1-b)$<br/>$\Rightarrow b^2+2 b+1=b^2-b^3+1-b$<br/>$\Rightarrow \quad b^3+3 b=0 \Rightarrow b\left(b^2+3\right)=0$<br/>$\Rightarrow \quad b=0, \pm \sqrt{3} i$</div>


title: the-value-of-l-o-g-2-l-o-g-3-s-i-n-x-2-s-i-n-l-o-g-6-x-2-x-s-i-n-x-2-d-x-is
slug: the-value-of-l-o-g-2-l-o-g-3-s-i-n-x-2-s-i-n-l-o-g-6-x-2-x-s-i-n-x-2-d-x-is-63916
tags: ['Mathematics', 'Definite Integration', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $\int_{\sqrt{\log 2}}^{\sqrt{\log 3}} \frac{x \sin x^2}{\sin x^2+\sin \left(\log 6-x^2\right)} d x$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{4} \log \frac{3}{2}$<br/></span> </div>

answer:
<div class="solution">Put $x^2=t \Rightarrow x d x=\frac{d t}{2}$ $\therefore \quad I=\int_{\log 2}^{\log 3} \frac{\sin t \cdot \frac{d t}{2}}{\sin t+\sin (\log 6-t)}$<br/>Using, $\quad \int_a^b f(x) d x=\int_a^b f(a+b-x) d x$<br/>$$<br/>\begin{aligned}<br/>&amp; I=\frac{1}{2} \int_{\log 2}^{\log 3} \frac{\sin (\log 2+\log 3-t)}{\sin (\log 2+\log 3-t)+\sin } d t \\<br/>&amp; I=\frac{1}{2} \int_{\log 2}^{\log 3} \frac{\sin (\log 6-t)}{\sin (\log 6-t)+\sin (t)} d t \\<br/>&amp; \therefore I=\int_{\log 2}^{\log 3} \frac{\sin (\log 6-t)}{\sin (\log 6-t)+\sin t} d t \quad \ldots(\mathrm{li})<br/>\end{aligned}<br/>$$<br/>On adding Eqs. (i) and (ii), we get<br/>$$<br/>2 I=\frac{1}{2} \int_{\log 2}^{\log 3} \frac{\sin t+\sin (\log 6-t)}{\sin (\log 6-t)+\sin t} d t<br/>$$<br/>$$<br/>\begin{gathered}<br/>\therefore \quad 2 I=\frac{1}{2}(t)_{\log 2}^{\log 3}=\frac{1}{2}(\log 3-\log 2) \\<br/>\Rightarrow I=\frac{1}{4} \log \left(\frac{3}{2}\right)<br/>\end{gathered}<br/>$$</div>


title: the-value-of-lim-x-0-x-3-1-0-x-t-4-4-t-l-o-g-1-t-d-t-is
slug: the-value-of-lim-x-0-x-3-1-0-x-t-4-4-t-l-o-g-1-t-d-t-is-18050
tags: ['Mathematics', 'Limits', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $\lim _{x \rightarrow 0} \frac{1}{x^3} \int_0^x \frac{t \log (1+t)}{t^4+4} d t$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{12}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{24}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{64}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{12}$<br/></span> </div>

answer:
<div class="solution">$\lim _{x \rightarrow 0} \frac{1}{x^3} \int_0^{x t} \frac{\log (1+t)}{4+t^4} d t$<br/>Using L' Hospital's rule,<br/>$$<br/>\begin{aligned}<br/>&amp; =\lim _{x \rightarrow 0} \frac{\frac{x \log (1+x)}{4+x^4}}{3 x^2} \\<br/>= &amp; \lim _{x \rightarrow 0} \frac{\log (1+x)}{3 x} \cdot \frac{1}{4+x^4} \\<br/>= &amp; \frac{1}{3} \cdot \frac{1}{4}=\frac{1}{12}\left[\text { using, } \lim _{x \rightarrow 0} \frac{\log (1+x)}{x}=1\right]<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-value-of-lo-g-10-k-for-a-reaction-a-b-is-given-r-h-298-k-5407-kj-mol-1-r-s-298-k-10-jk-1-mol-1-and-r-8314-jk-1-mol-1-2303-8314-298-5705

slug:
the-value-of-lo-g-10-k-for-a-reaction-a-b-is-given-r-h-298-k-5407-kj-mol-1-r-s-298-k-10-jk-1-mol-1-and-r-8314-jk-1-mol-1-2303-8314-298-5705-58052

question:
<div class="question">The value of $\log _{10} \mathrm{~K}$ for a reaction $A \rightleftharpoons B$ is (Given: $\Delta_{\mathrm{r}} H_{298 \mathrm{~K}}^{\circ}=-54.07 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{\mathrm{r}} S_{298 \mathrm{~K}}^{\circ}=10 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ and $R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} ; 2.303 \times 8.314 \times 298=5705$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>5<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>10<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>95<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>100</span> </li> </ul>

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

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>A &amp; \rightleftharpoons B \\<br/>\Delta G^{\circ} &amp; =\Delta H^{\circ}-T \Delta S^{\circ} \\<br/>\Delta G^{\circ} &amp; =-2303 R T \log K \\<br/>\log K &amp; =\frac{\Delta H^{\circ}-T \Delta S^{\circ}}{-2303 R T} \\<br/>&amp; =\frac{-54.07 \times 10^3-298 \times 10}{-2303 \times 8.314 \times 298} \\<br/>&amp; =\frac{-57050}{-5705}=10<br/>\end{aligned}<br/>$$</div>


title: the-value-of-n-in-the-molecular-formula-be-n-al-2-si-6-o-18-is
slug: the-value-of-n-in-the-molecular-formula-be-n-al-2-si-6-o-18-is-37365
tags: ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $n$ in the molecular formula $\mathrm{Be}_n \mathrm{Al}_2 \mathrm{Si}_6 \mathrm{O}_{18}$ is</div>

answer:
<div class="solution">For $\mathrm{Be}_n \mathrm{Al}_2 \mathrm{Si}_6 \mathrm{O}_{18} \quad n=3$<br/>$$<br/>2 n+6+24-36=0 \quad n=3<br/>$$<br/>Chemical bonding<br/>Basic application<br/>II</div>


title: the-value-of-the-integral-2-2-x-2-ln-x-x-cos-x-d-x-is
slug: the-value-of-the-integral-2-2-x-2-ln-x-x-cos-x-d-x-is-17411
tags: ['Mathematics', 'Definite Integration', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of the integral $\int_{-\pi / 2}^{\pi / 2}\left(x^{2}+\ln \frac{\pi+x}{\pi-x}\right) \cos x d x$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\pi^{2}}{2}-4$</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">$\frac{\pi^{2}}{2}+4$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi^{2}}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi^{2}}{2}-4$</span> </div>

answer:
<div class="solution">$\int_{-\pi / 2}^{\pi / 2}\left[x^{2}+\ln \left(\frac{\pi+x}{\pi-x}\right)\right] \cos x d x$ $=\int_{-\pi / 2}^{\pi / 2} x^{2} \cos x d x+\int_{-\pi / 2}^{\pi / 2} \ln \left(\frac{\pi+x}{\pi-x}\right) \cos x d x$ $=2 \int_{0}^{\pi / 2} x^{2} \cos x d x+0 \quad\left[\because x^{2} \cos x\right.$ is an even function and $\ln \left(\frac{\pi+x}{\pi-x}\right) \cos x$ is an odd function] $=2\left[x^{2} \sin x+2 x \cos x-2 \sin x\right]_{0}^{\pi / 2}=\frac{\pi^{2}}{2}-4$</div>


title: the-value-of-x-3-2-x-4-2-x-2-1-x-2-1-d-x-is
slug: the-value-of-x-3-2-x-4-2-x-2-1-x-2-1-d-x-is-53728
tags: ['Mathematics', 'Indefinite Integration', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $\int \frac{\left(x^2-1\right) d x}{x^3 \sqrt{2 x^4-2 x^2+1}}$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{2} \sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}+C$<br/></span> </div>

answer:
<div class="solution">Let $\quad I=\int \frac{\left(x^2-1\right) d x}{x^3 \sqrt{2 x^4-2 x^2+1}}$,<br/>On dividing numerater and denominator by $x^5$, we get<br/>$$<br/>=\int \frac{\left(\frac{1}{x^3}-\frac{1}{x^5}\right) d x}{\sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}}<br/>$$<br/>put $2-\frac{2}{x^2}+\frac{1}{x^4}=t \Rightarrow\left(\frac{4}{x^3}-\frac{4}{x^5}\right) d x=d t$<br/>$$<br/>\therefore \quad I=\frac{1}{4} \int \frac{d t}{\sqrt{t}}=\frac{1}{4} \cdot \frac{t^{1 / 2}}{1 / 2}=\frac{1}{2} \sqrt{t}+c=\frac{1}{2} \sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}+C<br/>$$</div>


title: the-values-of-0-1-1-x-2-x-4-1-x-4-d-x-is-are
slug: the-values-of-0-1-1-x-2-x-4-1-x-4-d-x-is-are-29397
question: <div class="question">The value(s) of $\int_0^1 \frac{x^4(1-x)^4}{1+x^2} d x$ is (are)</div>
tags: ['Mathematics', 'Definite Integration', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{22}{7}-\pi$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{2}{105}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>0<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{71}{15}-\frac{3 \pi}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\frac{22}{7}-\pi$<br/></span> </div>

answer:
<div class="solution">Let $I=\int_0^1 \frac{x^4(1-x)^4}{1+x^2} d x$<br/>$$<br/>\begin{aligned}<br/>&amp; =\int_0^1 \frac{\left(x^4-1\right)(1-x)^4+(1-x)^4}{\left(1+x^2\right)} d x \\<br/>&amp; =\int_0^1\left(x^2-1\right)(1-x)^4 d x \\<br/>&amp; +\int_0^1 \frac{\left(1+x^2-2 x\right)^2}{\left(1+x^2\right)} d x \\<br/>&amp; =\int_0^1\left\{\left(x^2-1\right)(1-x)^4+\left(1+x^2\right)-4 x\right. \\<br/>&amp; \left.+\frac{4 x^2}{\left(1+x^2\right)}\right\} d x \\<br/>&amp; =\int_0^1\left(\left(x^2-1\right)(1-x)^4+\left(1+x^2\right)-4 x\right. \\<br/>&amp; \left.+4-\frac{4}{1-x^2}\right) d x \\<br/>&amp; =\int_0^1\left(x^6-4 x^5+5 x^4-4 x^2\right. \\<br/>&amp; \left.+4-\frac{4}{1+x^2}\right) d x \\<br/>&amp; =\left[\frac{x^7}{7}-\frac{4 x^6}{6}+\frac{5 x^5}{5}\right. \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; \left.\quad-\frac{4 x^3}{3}+4 x-4 \tan ^{-1} x\right]_0^1 \\<br/>= &amp; \frac{1}{7}-\frac{4}{6}+\frac{5}{5}-\frac{4}{3}+4-4\left(\frac{\pi}{4}-0\right) \\<br/>= &amp; \frac{22}{7}-\pi<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Vector Algebra', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-vectors-which-isare-coplanar-with-vectors-i-j-2-k-and-i-2-j-k-are-perpendicular-to-the-vector-i-j-k-isare

slug:
the-vectors-which-isare-coplanar-with-vectors-i-j-2-k-and-i-2-j-k-are-perpendicular-to-the-vector-i-j-k-isare-30510

question:
<div class="question">The vector(s) which is/are coplanar with vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$, are perpendicular to the vector $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ is/are</div>

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

answer:
<div class="solution">Let $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$<br/>$\therefore$ A vector coplanar to $\mathbf{a}$ and $\mathbf{b}$, and perpendicular to $\mathbf{c}$.<br/>Now, $\quad \lambda(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}$<br/>$\Rightarrow \quad \lambda\{(\mathbf{a} \cdot \mathbf{c}) \mathbf{b}-(\mathbf{b} \cdot \mathbf{c}) \mathbf{a}\}$<br/>$\Rightarrow \quad \lambda\{(1+1+4)(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})$<br/>$-(1+2+1)(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}})\}$<br/>$\Rightarrow \lambda\{6 \hat{\mathbf{i}}+12 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}-6 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-12 \hat{\mathbf{k}}\}$<br/>$\Rightarrow \lambda\{6 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}\} \Rightarrow 6 \lambda(\hat{\mathbf{j}}-\hat{\mathbf{k}})$<br/>For $\lambda=\frac{1}{6} \Rightarrow$ Option (a) is correct.<br/>For $\lambda=-\frac{1}{6} \Rightarrow$ Option (d) is correct.</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
title:
the-volume-in-ml-of-01-m-agno-3-required-for-complete-precipitation-of-chloride-ions-present-in-30-ml-of-001-m-solution-of-cr-h-2-o-5-cl-cl-2-as-silve

slug:
the-volume-in-ml-of-01-m-agno-3-required-for-complete-precipitation-of-chloride-ions-present-in-30-ml-of-001-m-solution-of-cr-h-2-o-5-cl-cl-2-as-silve-26283

question:
<div class="question">The volume (in $\mathrm{mL}$ ) of $0.1 \mathrm{M} \mathrm{AgNO}_3$ required for complete precipitation of chloride ions present in $30 \mathrm{~mL}$ of $0.01 \mathrm{M}$ solution of $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}_{)_5} \mathrm{Cl}\right] \mathrm{Cl}_2\right.$, as silver chloride is close to</div>

answer:
<div class="solution">$\mathrm{mmol}$ of complex $=30 \times 0.01=0.3$ Also, 1 mole of complex $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{Cl}\right] \mathrm{Cl}_2$ gives only two moles of chloride ion when dissolved in solution<br/>$$<br/>\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{Cl}\right] \mathrm{Cl}_2 \longrightarrow\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{Cl}^{2+}+2 \mathrm{Cl}^{-}\right.<br/>$$<br/>$\Rightarrow \mathrm{mmol}$ of $\mathrm{Cl}^{-}$ion produced from its $0.3 \mathrm{mmol}=0.6$<br/>Hence, $0.6 \mathrm{mmol}$ of $\mathrm{Ag}^{+}$would be required for precipitation.<br/>$$<br/>\begin{aligned}<br/>&amp; \Rightarrow 0.60 \mathrm{mmol} \text { of } \mathrm{Ag}^{+}=0.1 \mathrm{M} \times \mathrm{V}(\text { in } \mathrm{mL}) \\<br/>&amp; \Rightarrow \quad V=6 \mathrm{~mL} .<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-wavelength-of-the-first-spectral-line-in-the-balmer-series-of-hydrogen-atom-is-6561-a-the-wavelength-of-the-second-spectral-line-in-the-balmer-ser

slug:
the-wavelength-of-the-first-spectral-line-in-the-balmer-series-of-hydrogen-atom-is-6561-a-the-wavelength-of-the-second-spectral-line-in-the-balmer-ser-11811

question:
<div class="question">The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561 Ã$. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$1215 Ã$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1640 Ã$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$2430 Ã$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4687 Ã$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1215 Ã$<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XRJ6v1JVlrCZBqpa-LQ4pLfbcmoBQqnYVCizhODhtqU.original.fullsize.png"/><br/><br/>For hydrogen or hydrogen type atoms<br/>$$<br/>\frac{1}{\lambda}=R Z^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)<br/>$$<br/>In the transition from $n_i \longrightarrow n_f$<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore \quad \lambda \propto \frac{1}{Z^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)} \\<br/>&amp; \therefore \quad \frac{\lambda_2}{\lambda_1}=\frac{Z_1^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)_1}{Z_2^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)_2} \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\lambda_2=\frac{\lambda_1 Z_1^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)_1}{Z_2^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)_2}<br/>$$<br/>Substituting the values, we have<br/>$$<br/>=\frac{(6561 Ã)(1)^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right)}{(2)^2\left(\frac{1}{2^2}-\frac{1}{4^2}\right)}=1215 Ã<br/>$$<br/>$\therefore$ Correct option is (a).<br/>Analysis of Question<br/>(i) Question is simple.<br/>(ii) In modern physics, mostly questions are asked on the emission of photon by the transition of electron from some higher energy state to some lower energy state.<br/>(iii) For hydrogen and hydrogen like atoms which have only single electron, we can use the formula<br/>$$<br/>\frac{1}{\lambda}=R Z^2\left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)<br/>$$<br/>(iv) Further, the student should also remember different series, as shown in figure below.<br/>$\mathrm{I} \rightarrow$ Lymen series<br/>II $\rightarrow$ Balmer series<br/>III $\rightarrow$ Paschen series<br/>IV $\rightarrow$ Brackett series<br/>$\mathrm{V} \rightarrow$ Pfund series</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
the-work-function-of-some-metals-is-listed-below-the-number-of-metals-which-will-show-photoelectric-effect-when-light-of-300-nm-wavelength-falls-on-th-1

slug:
the-work-function-of-some-metals-is-listed-below-the-number-of-metals-which-will-show-photoelectric-effect-when-light-of-300-nm-wavelength-falls-on-th-1-38874

question:
<div class="question">The work function ( $\Phi$ ) of some metals is listed below. The number of metals which will show photoelectric effect when light of $300 \mathrm{~nm}$ wavelength falls on the metal is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/qjg8-cy_nIyPUEtxddRWQLX42FJA540xJOu1flYoXEk.original.fullsize.png"/><br/></div>

answer:
<div class="solution">Energy of photon $=\frac{h c}{\lambda} \mathrm{J}=\frac{h c}{e \lambda} \mathrm{eV}=\frac{6.625 \times 10^{-34} \times 3 \times 10^8}{300 \times 10^{-9} \times 1.602 \times 10^{-19}}=4.14 \mathrm{eV}$<br/>For photoelectric effect to occur, energy of incident photons must be greater than work function of metal. Hence, only $\mathrm{Li}, \mathrm{Na}, \mathrm{K}$ and $\mathrm{Mg}$ have work functions less than $4.14 \mathrm{~V}$.</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-x-t-graph-of-a-particle-undergoing-simple-harmonic-motion-is-shown-below-the-acceleration-of-the-particle-at-t-3-4-s-is

slug:
the-x-t-graph-of-a-particle-undergoing-simple-harmonic-motion-is-shown-below-the-acceleration-of-the-particle-at-t-3-4-s-is-98992

question:
<div class="question">The $x-t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=\frac{4}{3} \mathrm{~s}$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U6hJmmO4R4N41xZzVh1AYNPenYB5HABlK_NaZjcprJU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{\sqrt{3}}{32} \pi^2 \mathrm{cms}^{-2}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{-\pi^2}{32} \mathrm{cms}^{-2}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{\pi^2}{32} \mathrm{cms}^{-2}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$-\frac{\sqrt{3}}{32} \pi^2 \mathrm{cms}^{-2}$</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"><br/>$-\frac{\sqrt{3}}{32} \pi^2 \mathrm{cms}^{-2}$</span> </div>

answer:
<div class="solution">$T=8 \mathrm{~s}, \omega=\frac{2 \pi}{T}=\left(\frac{\pi}{4}\right) \operatorname{rads}^{-1}$<br/>$$<br/>\begin{aligned}<br/>x &amp; =A \sin \omega t \\<br/>\therefore \quad a=-\omega^2 x &amp; =-\left(\frac{\pi^2}{16}\right) \sin \left(\frac{\pi}{4} t\right)<br/>\end{aligned}<br/>$$<br/>Substituting $t=\frac{4}{3} \mathrm{~s}$, we get<br/>$$<br/>a=-\left(\frac{\sqrt{3}}{32} \pi^2\right) \mathrm{cms}^{-2}<br/>$$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: MarksBatch2_P3.db
title:
there-is-a-rectangular-plate-of-mass-m-kg-of-dimensions-a-b-the-plate-is-held-in-horizontal-position-by-striking-n-small-balls-each-of-mass-m-per-unit-1

slug:
there-is-a-rectangular-plate-of-mass-m-kg-of-dimensions-a-b-the-plate-is-held-in-horizontal-position-by-striking-n-small-balls-each-of-mass-m-per-unit-1-77400

question:
<div class="question">There is a rectangular plate of mass $M \mathrm{~kg}$ of dimensions $(a \times b)$. The plate is held in horizontal position by striking $n$ small balls each of mass $m$ per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity $v$. What is $v$ ? It is given $n=100, M=3 \mathrm{~kg}, m=0.01 \mathrm{~kg}$; $b=2 \mathrm{~m} ; a=1 \mathrm{~m} ; g=10 \mathrm{~m} / \mathrm{s}^2$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vJSVNXoaYPf1U_0F5xfgHLe_kp2hDDhISVHsCGlvQiI.original.fullsize.png"/><br/></div>

answer:
<div class="solution">$F=\frac{\Delta p}{\Delta t}=n \times\left(a \times \frac{b}{2}\right) \times(2 m v)$<br/>Equating the torque about hinge side, we have<br/>$$<br/>n \times\left(a \times \frac{b}{2}\right) \times(2 m v) \times \frac{3 b}{4}=M g \times \frac{b}{2}<br/>$$<br/>Substituting the given values we get,<br/>$$<br/>v=10 \mathrm{~m} / \mathrm{s}<br/>$$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Advanced', 'JEE Advanced 2006']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: MarksBatch2_P3.db
title:
there-is-a-rectangular-plate-of-mass-m-kg-of-dimensions-a-b-the-plate-is-held-in-horizontal-position-by-striking-n-small-balls-each-of-mass-m-per-unit

slug:
there-is-a-rectangular-plate-of-mass-m-kg-of-dimensions-a-b-the-plate-is-held-in-horizontal-position-by-striking-n-small-balls-each-of-mass-m-per-unit-71896

question:
<div class="question">There is a rectangular plate of mass $M \mathrm{~kg}$ of dimensions $(a \times b)$. The plate is held in horizontal position by striking $n$ small balls each of mass $m$ per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity $v$. What is $v$ ? It is given $n=100, M=3 \mathrm{~kg}, m=0.01 \mathrm{~kg}$; $b=2 \mathrm{~m} ; a=1 \mathrm{~m} ; g=10 \mathrm{~m} / \mathrm{s}^2$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vJSVNXoaYPf1U_0F5xfgHLe_kp2hDDhISVHsCGlvQiI.original.fullsize.png"/><br/></div>

answer:
<div class="solution">$F=\frac{\Delta p}{\Delta t}=n \times\left(a \times \frac{b}{2}\right) \times(2 m v)$<br/>Equating the torque about hinge side, we have<br/>$$<br/>n \times\left(a \times \frac{b}{2}\right) \times(2 m v) \times \frac{3 b}{4}=M g \times \frac{b}{2}<br/>$$<br/>Substituting the given values we get,<br/>$$<br/>v=10 \mathrm{~m} / \mathrm{s}<br/>$$</div>


title: thermococcus-methanococcus-and-methanobacterium-are-groups-of
slug: thermococcus-methanococcus-and-methanobacterium-are-groups-of-96355
question: <div class="question">Thermococcus, Methanococcus and Methanobacterium are groups of</div>
tags: ['Biology', 'Biological Classification', 'JIPMER', 'JIPMER 2015']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">bacteria containing a cytoskeleton and all membrane bound organelles</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">archaebacteria with peptidoglycan in their cell wall</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">archaebacteria that consists of protein homologous to eukaryotic core histones</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">most advanced type of bacteria</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">archaebacteria that consists of protein homologous to eukaryotic core histones</span> </div>

answer:
<div class="solution">Archaebacteria are the most primitive and ancient bacterial species.<br/>Key characteristic features are<br/>(i) Lack of peptidoglycan in cell wall instead pseudomurein is present.<br/>(ii) Lipids in cell membrane have different structure than in all other organisms.<br/>(iii) They lack membrane bound organelles.</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
three-concentric-metallic-spherical-shells-of-radii-r-2-r-3-r-are-given-charges-q-1-q-2-q-3-respectively-it-is-found-that-the-surface-charge-densities

slug:
three-concentric-metallic-spherical-shells-of-radii-r-2-r-3-r-are-given-charges-q-1-q-2-q-3-respectively-it-is-found-that-the-surface-charge-densities-30785

question:
<div class="question">Three concentric metallic spherical shells of radii $R, 2 R, 3 R$ are given charges $Q_1, Q_2, Q_3$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $Q_1: Q_2: Q_3$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$1: 2: 3$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$1: 3: 5$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$1: 4: 9$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$1: 8: 18$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1: 3: 5$<br/></span> </div>

answer:
<div class="solution">$Q_1=\sigma\left(4 \pi R^2\right)=4 \pi \sigma R^2$<br/>$$<br/>\begin{aligned}<br/>&amp; Q_2=16 \pi \sigma R^2-Q_1=12 \pi \sigma R^2 \\<br/>&amp; Q_3=36 \pi \sigma R^2-16 \pi \sigma R^2=20 \pi \sigma R^2 \\<br/>&amp; Q_1: Q_2: Q_3=1: 3: 5<br/>\end{aligned}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Jz5mCEist3pR1NMXu_D_hDCaSA1XV59ytfACfkSpAiA.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
three-objects-a-b-and-c-are-kept-in-a-straight-line-on-a-frictionless-horizontal-surface-these-have-masses-m-2-m-and-m-respectively-the-object-a-moves-1

slug:
three-objects-a-b-and-c-are-kept-in-a-straight-line-on-a-frictionless-horizontal-surface-these-have-masses-m-2-m-and-m-respectively-the-object-a-moves-1-25348

question:
<div class="question">Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m, 2 m$ and $m$, respectively. The object $A$ moves towards $B$ with a speed $9 \mathrm{~ms}^{-1}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in $\mathrm{ms}^{-1}$ ) of the object $C$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zW9SGWwq_1moP5kJ51ynQVnFY0Fpenyy15farrFIcl0.original.fullsize.png"/><br/></div>

answer:
<div class="solution">After elastic collision,<br/>$$<br/>\begin{aligned}<br/>v_A^{\prime} &amp; =\left(\frac{m-2 m}{m+2 m}\right)(9)+\frac{2(2 m)}{m+2 m}(0) \\<br/>&amp; =-3 \mathrm{~ms}^{-1}<br/>\end{aligned}<br/>$$<br/>Now from conservation of linear momentum after all collisions are complete,<br/>$$<br/>\begin{array}{rlrl}<br/>m\left(+9 \mathrm{~ms}^{-1}\right) &amp; =m\left(-3 \mathrm{~ms}^{-1}\right)+3 m\left(v_C\right) \\<br/>&amp; \text { or } \quad v_C &amp; =4 \mathrm{~ms}^{-1}<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
three-objects-a-b-and-c-are-kept-in-a-straight-line-on-a-frictionless-horizontal-surface-these-have-masses-m-2-m-and-m-respectively-the-object-a-moves-2

slug:
three-objects-a-b-and-c-are-kept-in-a-straight-line-on-a-frictionless-horizontal-surface-these-have-masses-m-2-m-and-m-respectively-the-object-a-moves-2-34935

question:
<div class="question">Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m, 2 m$ and $m$, respectively. The object $A$ moves towards $B$ with a speed $9 \mathrm{~ms}^{-1}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in $\mathrm{ms}^{-1}$ ) of the object $C$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zW9SGWwq_1moP5kJ51ynQVnFY0Fpenyy15farrFIcl0.original.fullsize.png"/><br/></div>

answer:
<div class="solution">After elastic collision,<br/>$$<br/>\begin{aligned}<br/>v_A^{\prime} &amp; =\left(\frac{m-2 m}{m+2 m}\right)(9)+\frac{2(2 m)}{m+2 m}(0) \\<br/>&amp; =-3 \mathrm{~ms}^{-1}<br/>\end{aligned}<br/>$$<br/>Now from conservation of linear momentum after all collisions are complete,<br/>$$<br/>\begin{array}{rlrl}<br/>m\left(+9 \mathrm{~ms}^{-1}\right) &amp; =m\left(-3 \mathrm{~ms}^{-1}\right)+3 m\left(v_C\right) \\<br/>&amp; \text { or } \quad v_C &amp; =4 \mathrm{~ms}^{-1}<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Motion In Two Dimensions', 'JEE Advanced', 'JEE Advanced 2017 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
three-vectors-p-q-and-r-are-shown-in-the-figure-let-s-be-any-point-on-the-vector-r-the-distance-between-the-points-p-and-s-is-b-r-the-general-relation

slug:
three-vectors-p-q-and-r-are-shown-in-the-figure-let-s-be-any-point-on-the-vector-r-the-distance-between-the-points-p-and-s-is-b-r-the-general-relation-63268

question:
<div class="question"><p>Three vectors <math><mover accent="true"><mrow><mi>P</mi></mrow><mo>â</mo></mover><mo>,</mo><mi>Â </mi><mover accent="true"><mrow><mi>Q</mi></mrow><mo>â</mo></mover></math> and <math><mover accent="true"><mrow><mi>R</mi></mrow><mo>â</mo></mover></math> are shown in the figure. Let, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> be any point on the vector <math><mover accent="true"><mrow><mi>R</mi></mrow><mo>â</mo></mover></math> . The distance between the points <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mfenced close="|" open="|" separators="|"><mover><mi>R</mi><mo>â</mo></mover></mfenced></math>. The general relation among vectors <math><mover accent="true"><mrow><mi>P</mi></mrow><mo>â</mo></mover><mo>,</mo><mi>Â </mi><mover accent="true"><mrow><mi>Q</mi></mrow><mo>â</mo></mover></math> and <math><mover accent="true"><mrow><mi>S</mi></mrow><mo>â</mo></mover></math> are<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fxvjotshlvejqksysmtytynwyqgfburynvsnjqnidlmxhiijui.jpeg"/></p></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mover accent="true"><mrow><mi>S</mi></mrow><mo>→</mo></mover><mo>=</mo><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mi>b</mi></mrow></mfenced><mover accent="true"><mrow><mi>P</mi></mrow><mo>→</mo></mover><mo>+</mo><mi>b</mi><mover accent="true"><mrow><mi>Q</mi></mrow><mo>→</mo></mover></math></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fxvjotshlvejqksysmtytynwyqgfburynvsnjqnidlmxhiijui.jpeg"/><p>Let, vector from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> to point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> beÂ <math><mover accent="true"><mrow><mi>C</mi></mrow><mo>â</mo></mover></math>,Â </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mi>Â </mi><mover><mi>C</mi><mo>â</mo></mover><mo>=</mo><mi>b</mi><mfenced close="|" open="|" separators="|"><mover><mi>R</mi><mo>â</mo></mover></mfenced><mi>Â </mi><mover><mi>R</mi><mo>^</mo></mover><mo>=</mo><mi>b</mi><mfenced close="|" open="|" separators="|"><mover><mi>R</mi><mo>â</mo></mover></mfenced><mi>Â </mi><mfenced separators="|"><mfrac><mover><mi>R</mi><mo>â</mo></mover><mfenced close="|" open="|" separators="|"><mover><mi>R</mi><mo>â</mo></mover></mfenced></mfrac></mfenced><mo>=</mo><mi>b</mi><mover><mi>R</mi><mo>â</mo></mover><mo>=</mo><mi>b</mi><mfenced separators="|"><mrow><mover><mi>Q</mi><mo>â</mo></mover><mo>-</mo><mi>Â </mi><mover><mi>P</mi><mo>â</mo></mover></mrow></mfenced></math></p><p>From triangle rule of vector addition,Â </p><p><math><mover accent="true"><mrow><mi>P</mi></mrow><mo>â</mo></mover><mo>+</mo><mi>Â </mi><mover accent="true"><mrow><mi>C</mi></mrow><mo>â</mo></mover><mo>=</mo><mi>Â </mi><mover accent="true"><mrow><mi>S</mi></mrow><mo>â</mo></mover></math></p><p><math><mover accent="true"><mrow><mi>P</mi></mrow><mo>â</mo></mover><mo>+</mo><mi>b</mi><mfenced separators="|"><mrow><mover accent="true"><mrow><mi>Q</mi></mrow><mo>â</mo></mover><mo>-</mo><mi>Â </mi><mover accent="true"><mrow><mi>P</mi></mrow><mo>â</mo></mover></mrow></mfenced><mo>=</mo><mi>Â </mi><mover accent="true"><mrow><mi>S</mi></mrow><mo>â</mo></mover></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mi>Â </mi><mover><mi>S</mi><mo>â</mo></mover><mo>=</mo><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mi>b</mi></mrow></mfenced><mover><mi>P</mi><mo>â</mo></mover><mo>+</mo><mi>b</mi><mover><mi>Q</mi><mo>â</mo></mover></math></p></div>


tags: ['Physics', 'Thermal Properties of Matter', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
three-very-large-plates-of-same-area-are-kept-parallel-and-close-to-each-other-they-are-considered-as-ideal-black-surfaces-and-have-very-high-thermal-

slug:
three-very-large-plates-of-same-area-are-kept-parallel-and-close-to-each-other-they-are-considered-as-ideal-black-surfaces-and-have-very-high-thermal-84099

question:
<div class="question">Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2 T$ and $3 T$ respectively. The temperature of the middle (i.e. second) plate under steady state condition is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(\frac{65}{2}\right)^{1 / 4} T$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\frac{97}{4}\right)^{1 / 4} T$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(\frac{97}{2}\right)^{1 / 4} T$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$(97)^{1 / 4} T$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{97}{2}\right)^{1 / 4} T$</span> </div>

answer:
<div class="solution">Under steady conditions, the heat gained per second by a plate is equal to the heat released per second by the plate.
<br/> <br/>$\begin{array}{l}
<br/> <br/>\frac{\text { Heat gained }}{\text { Second }}[\text { by }(2) \text { from }(1)]+\frac{\text { Heat gained }}{\text { Second }} \\
<br/> <br/>{\left[\left(\text { by }((2) \text { from }(3)]=\frac{\text { Heat gained }}{\text { Second }} \text { (by } 2\right)\right.}
<br/> <br/>\end{array}$
<br/> <br/>$\begin{array}{ll}\therefore \quad &amp; \sigma A(2 T)^{4}+\sigma A(3 T)^{4} \\ &amp; =\sigma(2 A)(T)^{4} \\ \therefore \quad &amp; T=\left[\frac{97}{2}\right]^{1 / 4} T\end{array}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/CU3UHsWLck3S_PsQWHmTDkId9HzReLFaovVG6Io1GJs.original.fullsize.png"/></div>


tags: ['Chemistry', 'States of Matter', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P3.db
title:
to-an-evacuated-vessel-with-movable-piston-under-external-pressure-of-1-atm-01-mole-of-he-and-10-mole-of-an-unknown-compound-vapour-pressure-068-ma-t-

slug:
to-an-evacuated-vessel-with-movable-piston-under-external-pressure-of-1-atm-01-mole-of-he-and-10-mole-of-an-unknown-compound-vapour-pressure-068-ma-t-28084

question:
<div class="question">To an evacuated vessel with movable piston under external pressure of $1 \mathrm{~atm}$, $0.1$ mole of He and $1.0$ mole of an unknown compound (vapour pressure $0.68 mathrm{~atm}$ at $0^{\circ} \mathrm{C}$ ) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at $0^{\circ} \mathrm{C}$ is close to</div>

answer:
<div class="solution">Since, the external pressure is $1.0 \mathrm{~atm}$, the gas pressure is also $1.0 \mathrm{~atm}$ as piston is movable. Out of this $1.0 \mathrm{~atm}$ partial pressure due to unknown compound is $0.68 \mathrm{~atm}$. Therefore, partial pressure of $\mathrm{He}=1.00-0.68=0.32 \mathrm{~atm}$.<br/>$$<br/>\begin{aligned}<br/>&amp; \Rightarrow \quad \text { Volume }=\frac{n(\mathrm{He}) \mathrm{RT}}{r(\mathrm{He})}=\frac{0.1 \times 0.082 \times 273}{0.32}=7 \mathrm{~L} \\<br/>&amp; \Rightarrow \text { Volume of container }=\text { Volume of } \mathrm{He} .<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P3.db
title:
to-determine-the-halflife-of-a-radioactive-element-a-student-plots-a-graph-of-ln-d-t-d-n-t-versust-here-d-t-d-n-t-is-the-rate-of-radioactive-decay-at-

slug:
to-determine-the-halflife-of-a-radioactive-element-a-student-plots-a-graph-of-ln-d-t-d-n-t-versust-here-d-t-d-n-t-is-the-rate-of-radioactive-decay-at-65724

question:
<div class="question">To determine the half-life of a radioactive element, a student plots a graph of $\ln \left|\frac{d N(t)}{d t}\right|$ versust. Here $\frac{d N(t)}{d t}$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element decreases by a factor of $p$ after $4.16 \mathrm{yr}$, the value of $p$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/cVWnejtFcY6cljXBHxMmON746JdsX22aYXuq-g9-vyg.original.fullsize.png"/><br/></div>

answer:
<div class="solution">$\left|\frac{d N}{d t}\right|=\mid$ Activity of radioactive substance|<br/>$$<br/>=\lambda N=\lambda N_0 e^{-\lambda t}<br/>$$<br/>Taking log both sides<br/>$$<br/>\ln \left|\frac{d N}{d t}\right|=\ln \left(\lambda N_0\right)-\lambda t<br/>$$<br/>Hence, $\ln \left|\frac{d N}{d t}\right|$ versus $t$ graph is a straight line with slope $-\lambda$<br/>From the graph we can see that,<br/>$$<br/>\lambda=\frac{1}{2}=0.5 \mathrm{yr}^{-1}<br/>$$<br/>Now applying the equation,<br/>$$<br/>\begin{aligned}<br/>N &amp; =N_0 e^{-\lambda t} \\<br/>&amp; =N_0 e^{-0.5 \times 4.16} \\<br/>&amp; =N_0 e^{-2.08}=0.125 N_0 \\<br/>&amp; =\frac{N_0}{8}<br/>\end{aligned}<br/>$$<br/>ie, nuclei decreases by a factor of 8 . Hence the answer is 8 .</div>


tags: ['Physics', 'Current Electricity', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
to-verify-ohms-law-a-student-is-provided-with-a-test-resistor-r-t-a-high-resistance-r-1-a-small-resistance-r-2-two-identical-galvanometers-g-1-and-g-2-1

slug:
to-verify-ohms-law-a-student-is-provided-with-a-test-resistor-r-t-a-high-resistance-r-1-a-small-resistance-r-2-two-identical-galvanometers-g-1-and-g-2-1-63583

question:
<div class="question">To verify Ohm's law, a student is provided with a test resistor $R_T$, a high resistance $R_1$, a small resistance $R_2$, two identical galvanometers $G_1$ and $G_2$, and a variable voltage source $V$. The correct circuit to carry out the experiment is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NTfm4R3CESuRYWjdLwkM5mLtReWptl3E9O19YO_mNcU.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/w4-0tdmb_lC8pItkWVuInxDcK1iOf9Lq0LrFuSOxxQ0.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IKwaHmR5G8DBZTEgscDMeB4PFuCvF_bW1PvTz9qpCM8.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/GZroKs7fZUBze7YQXg4QQsRUbOiZRO9AdqjRhos0sdI.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IKwaHmR5G8DBZTEgscDMeB4PFuCvF_bW1PvTz9qpCM8.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">We will require a voltmeter, an ammeter, a test resistor and a variable battery to verify Ohm's law.<br/>Voltmeter which is made by connecting a high resistance with a galvanometer is connected in parallel with the test resistor.<br/>Further, an ammeter which is formed by connecting a low resistance in parallel with galvanometer is required to measure the current through test resistor.<br/>The correct option is (c).</div>


tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
to-verify-ohms-law-a-student-is-provided-with-a-test-resistor-r-t-a-high-resistance-r-1-a-small-resistance-r-2-two-identical-galvanometers-g-1-and-g-2-2

slug:
to-verify-ohms-law-a-student-is-provided-with-a-test-resistor-r-t-a-high-resistance-r-1-a-small-resistance-r-2-two-identical-galvanometers-g-1-and-g-2-2-19287

question:
<div class="question">To verify Ohm's law, a student is provided with a test resistor $R_T$, a high resistance $R_1$, a small resistance $R_2$, two identical galvanometers $G_1$ and $G_2$, and a variable voltage source $V$. The correct circuit to carry out the experiment is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NTfm4R3CESuRYWjdLwkM5mLtReWptl3E9O19YO_mNcU.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/w4-0tdmb_lC8pItkWVuInxDcK1iOf9Lq0LrFuSOxxQ0.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IKwaHmR5G8DBZTEgscDMeB4PFuCvF_bW1PvTz9qpCM8.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/GZroKs7fZUBze7YQXg4QQsRUbOiZRO9AdqjRhos0sdI.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IKwaHmR5G8DBZTEgscDMeB4PFuCvF_bW1PvTz9qpCM8.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">We will require a voltmeter, an ammeter, a test resistor and a variable battery to verify Ohm's law.<br/>Voltmeter which is made by connecting a high resistance with a galvanometer is connected in parallel with the test resistor.<br/>Further, an ammeter which is formed by connecting a low resistance in parallel with galvanometer is required to measure the current through test resistor.<br/>The correct option is (c).</div>


title: total-number-of-geometrical-isomers-for-the-complex-rhcl-co-pph-3-nh-3-is
slug: total-number-of-geometrical-isomers-for-the-complex-rhcl-co-pph-3-nh-3-is-44794
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">Total number of geometrical isomers for the complex $\left[\mathrm{RhCl}(\mathrm{CO})\left(\mathrm{PPh}_3\right)\left(\mathrm{NH}_3\right)\right]$ is</div>

answer:
<div class="solution">$[M(a b c d)]$ complex is square planar so will have 3 geometrical isomers.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/CLJT1LSnf5AAyDbyf-jy3K8z0ZrWX4IDQrgeYvzaCEw.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Vector Algebra', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-adjacent-sides-of-a-parallelogram-a-bc-d-are-given-by-ab-2-i-10-j-11-k-and-ad-i-2-j-2-k-the-side-a-d-is-rotated-by-an-acute-angle-in-the-plane-of-

slug:
two-adjacent-sides-of-a-parallelogram-a-bc-d-are-given-by-ab-2-i-10-j-11-k-and-ad-i-2-j-2-k-the-side-a-d-is-rotated-by-an-acute-angle-in-the-plane-of-84287

question:
<div class="question">Two adjacent sides of a parallelogram $A B C D$ are given by $\overrightarrow{\mathbf{A B}}=2 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}$ and $\overrightarrow{\mathbf{A D}}=-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$. The side $A D$ is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that $A D$ becomes $A D^{\prime}$. If $A D^{\prime}$ makes a right angle with the side $A B$, then the cosine of the angle $\alpha$ is given by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{8}{9}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{\sqrt{17}}{9}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{9}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{4 \sqrt{5}}{9}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{\sqrt{17}}{9}$<br/></span> </div>

answer:
<div class="solution">$$<br/>\overrightarrow{\mathbf{A B}}=2 \hat{\mathbf{i}}+10 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}<br/>$$<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IeHV7ImfTIKMoDZunV5T_tkgnXw6g11G59YmpbR-u4k.original.fullsize.png"/><br/><br/><br/>$$<br/>\overrightarrow{\mathbf{A D}}=-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}<br/>$$<br/>Angle ' $\theta$ ' between $\overrightarrow{\mathbf{A B}}$ and $\overrightarrow{\mathbf{A D}}$ is<br/>$$<br/>\begin{aligned}<br/>&amp; \cos (\theta)=\left|\begin{array}{l}<br/>\overrightarrow{\mathbf{A B}} \cdot \overrightarrow{\mathbf{A D}} \\<br/>\mid \overrightarrow{\mathbf{A B}}\|\overrightarrow{\mathbf{A D}}\|<br/>\end{array}\right| \\<br/>&amp; =\left|\frac{-2+20+22}{(15)(3)}\right|=\frac{8}{9} \\<br/>&amp; \Rightarrow \quad \sin (\theta)=\frac{\sqrt{17}}{9} \\<br/>&amp; \text { Since, } \quad \alpha+\theta=90^{\circ} \\<br/>&amp; \therefore \quad \cos (\alpha)=\cos \left(90^{\circ}-\theta\right) \\<br/>&amp; =\sin (\theta)=\frac{\sqrt{17}}{9} \\<br/>&amp;<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
two-balls-having-linear-momenta-p-1-p-i-and-p-2-p-i-undergo-a-collision-in-free-space-there-is-no-external-force-acting-on-the-balls-let-p-1-and-p-2-b

slug:
two-balls-having-linear-momenta-p-1-p-i-and-p-2-p-i-undergo-a-collision-in-free-space-there-is-no-external-force-acting-on-the-balls-let-p-1-and-p-2-b-80423

question:
<div class="question">Two balls, having linear momenta $\overrightarrow{\mathbf{p}}_1=p \hat{\mathbf{i}}$ and $\overrightarrow{\mathbf{p}}_2=-p \hat{\mathbf{i}}$, undergo a collision in free space. There is no external force acting on the balls. Let $\overrightarrow{\mathbf{p}}_1^{\prime}$ and $\overrightarrow{\mathbf{p}}_2^{\prime}$ be their final momenta. The following option(s) is/are NOT ALLOWED for any non-zero value of $p, a_1, a_2, b_1, b_2, c_1$ and $c_2$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\overrightarrow{\mathbf{p}}_1^{\prime}=a_1 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}+c_1 \hat{\mathbf{k}}, \overrightarrow{\mathbf{p}}_2^{\prime}=a_2 \hat{\mathbf{i}}+b_2 \hat{\mathbf{j}}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\overrightarrow{\mathbf{p}}_1^{\prime}=c_1 \hat{\mathbf{k}}, \overrightarrow{\mathbf{p}}_2^{\prime}=c_2 \hat{\mathbf{k}}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\overrightarrow{\mathbf{p}}_1^{\prime}=a_1 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}+c_1 \hat{\mathbf{k}}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\overrightarrow{\mathbf{p}}_1^{\prime}=a_1 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}$<br/>$\overrightarrow{\mathbf{p}}_2^{\prime}=a_2 \hat{\mathbf{i}}+b_2 \hat{\mathbf{j}}-c_1 \hat{\mathbf{k}}$<br/>$\overrightarrow{\mathbf{p}}_2^{\prime}=a_2 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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"><br/>$\overrightarrow{\mathbf{p}}_1^{\prime}=a_1 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}+c_1 \hat{\mathbf{k}}, \overrightarrow{\mathbf{p}}_2^{\prime}=a_2 \hat{\mathbf{i}}+b_2 \hat{\mathbf{j}}$<br/>, <br/>$\overrightarrow{\mathbf{p}}_1^{\prime}=a_1 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}$<br/>$\overrightarrow{\mathbf{p}}_2^{\prime}=a_2 \hat{\mathbf{i}}+b_2 \hat{\mathbf{j}}-c_1 \hat{\mathbf{k}}$<br/>$\overrightarrow{\mathbf{p}}_2^{\prime}=a_2 \hat{\mathbf{i}}+b_1 \hat{\mathbf{j}}$</span> </div>

answer:
<div class="solution">Initial momentum of the system $\overrightarrow{\mathbf{p}_1}+\overrightarrow{\mathbf{p}_2}=0$<br/>$\therefore$ Final momentum $\overrightarrow{\mathbf{p}_1^{\prime}}+\overrightarrow{\mathbf{p}_2^{\prime}}$ should also be zero.<br/>Option (b) is allowed because if we putc $c_1=-c_2 \neq 0, \overrightarrow{\mathbf{p}_1^{\prime}}+\overrightarrow{\mathbf{p}_2^{\prime}}$ will be zero. Similarly, we can check other options.<br/>$\therefore$ correct options are (a) and (d).</div>


tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
two-bars-of-radius-r-and-2-r-are-kept-in-contact-as-shown-an-electric-current-i-is-passed-through-the-bars-which-one-of-the-following-is-correct-1

slug:
two-bars-of-radius-r-and-2-r-are-kept-in-contact-as-shown-an-electric-current-i-is-passed-through-the-bars-which-one-of-the-following-is-correct-1-13318

question:
<div class="question">Two bars of radius ' $r$ ' and ' $2 r$ ' are kept in contact as shown. An electric current $I$ is passed through the bars. Which one of the following is correct?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/3BJ3ax4_H0x5tjzPE6zxTmxBgcNfjjyHZfX_fLKfU5k.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Heat produced in bar $B C$ is 4 times the heat produced in bar $A B$<br/></span> </div>

answer:
<div class="solution">Current flowing through both the bars is equal. Now, the heat produced is given by<br/>$$<br/>\begin{aligned}<br/>H &amp; =I^2 R t \text { or } H \propto R \text { or } \frac{H_{A B}}{H_{B C}}=\frac{R_{A B}}{R_{B C}} \\<br/>&amp; =\frac{\left(\frac{1}{2 r}\right)^2}{\left(\frac{1}{r}\right)^2} \\<br/>&amp; =\frac{1}{4} \text { or } H_{B C}=4 H_{A B}<br/>\end{aligned}<br/>$$<br/>$$<br/>\left(\text { as } R \propto \frac{1}{A} \propto \frac{1}{r^2}\right)<br/>$$</div>


tags: ['Physics', 'Current Electricity', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P3.db
title:
two-bars-of-radius-r-and-2-r-are-kept-in-contact-as-shown-an-electric-current-i-is-passed-through-the-bars-which-one-of-the-following-is-correct

slug:
two-bars-of-radius-r-and-2-r-are-kept-in-contact-as-shown-an-electric-current-i-is-passed-through-the-bars-which-one-of-the-following-is-correct-99753

question:
<div class="question">Two bars of radius ' $r$ ' and ' $2 r$ ' are kept in contact as shown. An electric current $I$ is passed through the bars. Which one of the following is correct?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/3BJ3ax4_H0x5tjzPE6zxTmxBgcNfjjyHZfX_fLKfU5k.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Heat produced in bar $B C$ is 4 times the heat produced in bar $A B$<br/></span> </div>

answer:
<div class="solution">Current flowing through both the bars is equal. Now, the heat produced is given by<br/>$$<br/>\begin{aligned}<br/>H &amp; =I^2 R t \text { or } H \propto R \text { or } \frac{H_{A B}}{H_{B C}}=\frac{R_{A B}}{R_{B C}} \\<br/>&amp; =\frac{\left(\frac{1}{2 r}\right)^2}{\left(\frac{1}{r}\right)^2} \\<br/>&amp; =\frac{1}{4} \text { or } H_{B C}=4 H_{A B}<br/>\end{aligned}<br/>$$<br/>$$<br/>\left(\text { as } R \propto \frac{1}{A} \propto \frac{1}{r^2}\right)<br/>$$</div>


tags: ['Physics', 'Current Electricity', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
title:
two-batteries-of-different-emfs-and-different-internal-resistances-are-connected-as-shown-the-voltage-across-a-b-in-volt-is

slug:
two-batteries-of-different-emfs-and-different-internal-resistances-are-connected-as-shown-the-voltage-across-a-b-in-volt-is-43703

question:
<div class="question">Two batteries of different emfs and different internal resistances are connected as shown. The voltage across $A B$ in volt is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/W2cdpJKmwYYphVd0NTggoakyZDVjRGpVU8m5_97fO6Y.original.fullsize.png"/><br/></div>

answer:
<div class="solution">$V_{A B}=$ Equivalent emf of two batteries in parallel.<br/>$$<br/>\begin{aligned}<br/>&amp; =\frac{E_1 / r_1+E_1 / r_2}{1 / r_1+1 / r_2} \\<br/>&amp; =\frac{(6 / 1)+(3 / 2)}{(1 / 1)+(1 / 2)}=5 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/>$\therefore$ Answer is 5 .<br/>Analysis of Question<br/>(i) In my opinion this is the simplest question of JEE 2011.<br/>(ii) When no current is drawn from this equivalent battery, then<br/>$$<br/>V_{A B}=V=E<br/>$$<br/>Otherwise, $V=E \pm$ ir<br/>(iii) Similar type of question was asked in JEE 1981 and cancelled paper of JEE 1997.</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
two-beams-of-red-and-violet-colours-are-made-to-pass-separately-through-a-prism-angle-of-the-prism-is-6-0-in-the-position-of-minimum-deviation-the-ang

slug:
two-beams-of-red-and-violet-colours-are-made-to-pass-separately-through-a-prism-angle-of-the-prism-is-6-0-in-the-position-of-minimum-deviation-the-ang-46422

question:
<div class="question">Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is $60^{\circ}$ ). In the position of minimum deviation, the angle of refraction will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$30^{\circ}$ for both the colours<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>greater for the violet colour<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>greater for the red colour<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>equal but not $30^{\circ}$ for both the colours</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$30^{\circ}$ for both the colours<br/></span> </div>

answer:
<div class="solution">At minimum deviation $\left(\delta=\delta_m\right)$ :<br/>$$<br/>r_1=r_2=\frac{A}{2}=\frac{60^{\circ}}{2}=30^{\circ}<br/>$$<br/>(For both colours)<br/>$\therefore$ correct answer is (a).</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-identical-discs-of-same-radius-r-are-rotating-about-their-axes-in-opposite-directions-with-the-same-constant-angular-speed-the-discs-are-in-the-sa

slug:
two-identical-discs-of-same-radius-r-are-rotating-about-their-axes-in-opposite-directions-with-the-same-constant-angular-speed-the-discs-are-in-the-sa-69724

question:
<div class="question">Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The discs are in the same horizontal plane. At time $t=0$, the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ is $v_{r}$. In one time period $(T)$ of rotation of the discs, $v_{r}$ as a function of time is best represented by
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/KFcBPQUQTOd87psqK-4OIMdktsT-38YSuG1_LHfgmD4.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/KkZ_El7bykdh0VQ_GQ0XyktTNz7J3uSqgINO8K3FAlo.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">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/du1TYMRJqpQ7seZYBFg02paxVU21wfOjkxX4JrXrOvk.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ViXw-Cm2vuVInN2SnD6_CBhq-3k9kvvTyT6ldPWQqxE.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/jee_advanced/iSIY08YzFM8YciIAw4yZVKMYIcocyt-cpVe1BmBpDdA.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/jee_advanced/KkZ_El7bykdh0VQ_GQ0XyktTNz7J3uSqgINO8K3FAlo.original.fullsize.png"/></span> </div>

answer:
<div class="solution">At $t=0, t=\frac{T}{2}$ and $t=T$ therelative velocity will bezero. At $t=\frac{T}{4}$ and $t=\frac{3 T}{4}$, the relative velocity will be maximum in magnitude
<br/> <br/>Hence graph (a) correctly depicts $v_{r}$ versus $t$ graph.</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2015 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P3.db
title:
two-identical-uniform-discs-roll-without-slipping-on-two-different-surfaces-a-b-and-c-d-see-figure-starting-at-a-and-c-with-linear-speeds-1-and-2-resp

slug:
two-identical-uniform-discs-roll-without-slipping-on-two-different-surfaces-a-b-and-c-d-see-figure-starting-at-a-and-c-with-linear-speeds-1-and-2-resp-34459

question:
<div class="question"><p>Two identical uniform discs roll without slipping on two different surfaces <math><mi mathvariant="normal">A</mi><mi mathvariant="normal">B</mi></math> and <math><mi mathvariant="normal">C</mi><mi mathvariant="normal">D</mi></math> (see figure) starting at <math><mi mathvariant="normal">A</mi></math> and <math><mi mathvariant="normal">C</mi></math> with linear speeds <math><msub><mrow><mi mathvariant="normal">Ï</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mi mathvariant="normal">Ï</mi></mrow><mrow><mn>2</mn></mrow></msub></math> , respectively, and always remain in contact with the surfaces. If they reach <math><mi mathvariant="normal">B</mi></math> and <math><mi mathvariant="normal">D</mi></math> with the same linear speed and <math><msub><mrow><mi mathvariant="normal">Ï</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>3</mn><mi mathvariant="normal">Â </mi></math> m/s, then <math><msub><mrow><mi mathvariant="normal">Ï</mi></mrow><mrow><mn>2</mn></mrow></msub></math> in m/s is <math><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi><mo>=</mo><mn>10</mn><mi mathvariant="normal">Â </mi><mfrac><mrow><mi mathvariant="normal">m</mi></mrow><mrow><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mfenced></math><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/image5-4c0aca5f-f276-4e40-b0c6-ce9b5bb384d0.png"/></p></div>

answer:
<div class="solution"><p><math><mi mathvariant="normal">K</mi><mo>.</mo><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi mathvariant="normal">d</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">K</mi><mo>.</mo><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi mathvariant="normal">T</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">K</mi><mo>.</mo><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi></mrow></msub></math><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/image5-4c0aca5f-f276-4e40-b0c6-ce9b5bb384d0.png"/><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi mathvariant="normal">m</mi><msup><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></mrow></msub><msup><mrow><mi mathvariant="normal">w</mi></mrow><mrow><mn>2</mn></mrow></msup></math><br/><math><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi mathvariant="normal">m</mi><msup><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">m</mi><msup><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup></math><br/><math><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mi mathvariant="normal">m</mi><msup><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>2</mn></mrow></msup></math><br/><math><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">A</mi></mrow></msub><mo>+</mo><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi mathvariant="normal">g</mi></mrow></msub><mo>=</mo><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><msubsup><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">v</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">g</mi><mo>Ã</mo><mn>30</mn><mo>=</mo><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub></math><br/><math><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow></msub><mo>+</mo><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi mathvariant="normal">g</mi></mrow></msub><mo>=</mo><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">D</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mi mathvariant="normal">m</mi><msubsup><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">g</mi><mo>Ã</mo><mn>27</mn><mo>=</mo><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">D</mi></mrow></msub></math><br/><math><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">B</mi></mrow></msub><mo>=</mo><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">D</mi></mrow></msub></math> (Conversation of energy)<br/><math><mo>â</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mi mathvariant="normal">m</mi><msup><mrow><mfenced separators="|"><mrow><mn>3</mn></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mi mathvariant="normal">m</mi><msubsup><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><mn>3</mn><mi mathvariant="normal">m</mi><mi mathvariant="normal">g</mi><mo>=</mo><mn>0</mn></math><br/><math><mo>â</mo><msubsup><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>49</mn></math><br/><math><mo>â</mo><mi mathvariant="normal">v</mi><mo>=</mo><mn>7</mn></math></p></div>


tags: ['Physics', 'Laws of Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
two-large-vertical-and-parallel-metal-plates-having-a-separation-of-1-cm-are-connected-to-a-dc-voltage-source-of-potential-difference-x-a-proton-is-re

slug:
two-large-vertical-and-parallel-metal-plates-having-a-separation-of-1-cm-are-connected-to-a-dc-voltage-source-of-potential-difference-x-a-proton-is-re-32349

question:
<div class="question">Two large vertical and parallel metal plates having a separation of $1 \mathrm{~cm}$ are connected to a DC voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at $45^{\circ}$ to the vertical JUST after release. Then $X$ is nearly</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \times 10^{-5} \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 \times 10^{-7} V$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1 \times 10^{-9} V$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 \times 10^{-10} V$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \times 10^{-9} V$</span> </div>

answer:
<div class="solution">According to the question, a proton is released at rest mid-way between the two plates and is found to move at $45^{\circ}$, so net force is at $45^{\circ}$ from vertical and two forces acting on the proton just after the release are as shown in the figure.
<br/> <br/>$q E=m g$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PA2626pPIkCW70kNiLtlWmKMaBUca5V-vIIUOz1ALI0.original.fullsize.png"/><br/> <br/> <br/>$\therefore \quad V=\frac{m g d}{q}=\frac{1.67 \times 10^{-27} \times 10 \times 10^{-2}}{1.6 \times 10^{-19}}=10^{-9} \mathrm{~V}$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-metallic-rings-a-and-b-identical-in-shape-and-size-but-having-different-resistivities-a-and-b-are-kept-on-top-of-two-identical-solenoids-as-shown-

slug:
two-metallic-rings-a-and-b-identical-in-shape-and-size-but-having-different-resistivities-a-and-b-are-kept-on-top-of-two-identical-solenoids-as-shown-34705

question:
<div class="question">Two metallic rings $A$ and $B$, identical in shape and size but having different resistivities $\rho_A$ and $\rho_B$, are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in identical manner, the rings $A$ and $B$ jump to heights $h_A$ and $h_B$, respectively, with $h_A&gt;h_B$. The possible relation(s) between their resistivities and their masses $m_A$ and $m_B$ is(are)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/cAWt44w_vRNo7N_FM9HAQIkbCi01R15BSkltLk_Bh9g.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\rho_A&gt;\rho_B$ and $m_A=m_B$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\rho_A &lt; \rho_B$ and $m_A=m_B$</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">C</span> <span class="option-data"><br/>$\rho_A&gt;\rho_B$ and $m_A&gt;m_B$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\rho_A &lt; \rho_B$ and $m_A &lt; m_B$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\rho_A &lt; \rho_B$ and $m_A=m_B$, <br/>$\rho_A &lt; \rho_B$ and $m_A &lt; m_B$</span> </div>

answer:
<div class="solution">Induced emf $e=-\frac{d \phi}{d t}$. For identical rings induced emf will be same. But currents will be different. Given $h_A&gt;h_B$. Hence, $v_A&gt;v_B$ as $\left(h=\frac{v^2}{2 g}\right)$.<br/>If $\rho_A&gt;\rho_B$, then, $I_A &lt; I_B$. In this case given condition can be fulfilled if $m_A &lt; m_B$.<br/>If $\rho_A &lt; \rho_B$, then $I_A&gt;I_B$. In this case given condition can be fulfilled of $m_A \leq m_B$.</div>


tags: ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-moles-of-ideal-helium-gas-are-in-a-rubber-balloon-at-3-0-c-the-balloon-is-fully-expandable-and-can-be-assumed-to-require-no-energy-in-its-expansio

slug:
two-moles-of-ideal-helium-gas-are-in-a-rubber-balloon-at-3-0-c-the-balloon-is-fully-expandable-and-can-be-assumed-to-require-no-energy-in-its-expansio-17073

question:
<div class="question">Two moles of ideal helium gas are in a rubber balloon at $30^{\circ} \mathrm{C}$. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $35^{\circ} \mathrm{C}$. The amount of heat required in raising the temperature is nearly (take $R=8.31 \mathrm{~J} / \mathrm{mol} . \mathrm{K}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$62 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$104 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$124 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$208 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$208 \mathrm{~J}$</span> </div>

answer:
<div class="solution">The heat is supplied at constant pressure. i.e., the process is isobaric
<br/> <br/>$\begin{array}{l}
<br/> <br/>\therefore Q=n C_{p} \Delta t \\
<br/> <br/>=2\left[\frac{5}{2} R\right] \times \Delta t=2 \times \frac{5}{2} \times 8.31 \times 5=208 \mathrm{~J} \\
<br/> <br/>\left(\because C_{p}=\frac{5}{2} R \text { for mono-atomic gas }\right)
<br/> <br/>\end{array}$</div>


tags: ['Mathematics', 'Circle', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
two-parallel-chords-of-a-circle-of-radius-2-are-at-a-distance-3-1-apart-if-the-chords-subtend-at-the-centre-angles-of-k-and-k-2-where-k-0-then-the-val-1

slug:
two-parallel-chords-of-a-circle-of-radius-2-are-at-a-distance-3-1-apart-if-the-chords-subtend-at-the-centre-angles-of-k-and-k-2-where-k-0-then-the-val-1-22459

question:
<div class="question">Two parallel chords of a circle of radius 2 are at a distance $\sqrt{3}+1$ apart. If the chords subtend at the centre, angles of $\frac{\pi}{k}$ and $\frac{2 \pi}{k}$, where $k&gt;0$, then the value of $[k]$ is<br/>[Note : $[k]$ denotes the largest integer less than or equal to $k$ ]</div>

answer:
<div class="solution">Let $\theta=\frac{\pi}{2 k}$<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/nsyCMwfdsSgoA4eN35QoPJm706I-Z4eMkUQz8O6WHAQ.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \cos \theta=\frac{x}{2} \\<br/>&amp; \Rightarrow \quad \cos 2 \theta=\frac{\sqrt{3}+1-x}{2} \\<br/>&amp; \Rightarrow 2 \cos ^2 \theta-1=\frac{\sqrt{3}+1-x}{2} \\<br/>&amp; \Rightarrow 2\left(\frac{x^2}{4}\right)-1=\frac{\sqrt{3}+1-x}{2} \\<br/>&amp; \Rightarrow \quad x^2+x-3-\sqrt{3}=0 \\<br/>&amp; \Rightarrow \quad x=\frac{-1 \pm \sqrt{1+12+4 \sqrt{3}}}{2} \\<br/>&amp; =\frac{-1 \pm \sqrt{13+4 \sqrt{3}}}{2} \\<br/>&amp; =\frac{-1+2 \sqrt{3}+1}{2}=\sqrt{3} \\<br/>&amp; \therefore \quad \cos \theta=\frac{\sqrt{3}}{2} \Rightarrow \theta=\frac{\pi}{6} \\<br/>&amp; \therefore \quad \text { Required angle }=\frac{\pi}{k}=2 \theta=\frac{\pi}{3} \\<br/>&amp; \Rightarrow \quad k=3 \\<br/>&amp;<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
two-parallel-chords-of-a-circle-of-radius-2-are-at-a-distance-3-1-apart-if-the-chords-subtend-at-the-centre-angles-of-k-and-k-2-where-k-0-then-the-val

slug:
two-parallel-chords-of-a-circle-of-radius-2-are-at-a-distance-3-1-apart-if-the-chords-subtend-at-the-centre-angles-of-k-and-k-2-where-k-0-then-the-val-93121

question:
<div class="question">Two parallel chords of a circle of radius 2 are at a distance $\sqrt{3}+1$ apart. If the chords subtend at the centre, angles of $\frac{\pi}{k}$ and $\frac{2 \pi}{k}$, where $k&gt;0$, then the value of $[k]$ is<br/>[Note : $[k]$ denotes the largest integer less than or equal to $k$ ]</div>

answer:
<div class="solution">Let $\theta=\frac{\pi}{2 k}$<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/nsyCMwfdsSgoA4eN35QoPJm706I-Z4eMkUQz8O6WHAQ.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \cos \theta=\frac{x}{2} \\<br/>&amp; \Rightarrow \quad \cos 2 \theta=\frac{\sqrt{3}+1-x}{2} \\<br/>&amp; \Rightarrow 2 \cos ^2 \theta-1=\frac{\sqrt{3}+1-x}{2} \\<br/>&amp; \Rightarrow 2\left(\frac{x^2}{4}\right)-1=\frac{\sqrt{3}+1-x}{2} \\<br/>&amp; \Rightarrow \quad x^2+x-3-\sqrt{3}=0 \\<br/>&amp; \Rightarrow \quad x=\frac{-1 \pm \sqrt{1+12+4 \sqrt{3}}}{2} \\<br/>&amp; =\frac{-1 \pm \sqrt{13+4 \sqrt{3}}}{2} \\<br/>&amp; =\frac{-1+2 \sqrt{3}+1}{2}=\sqrt{3} \\<br/>&amp; \therefore \quad \cos \theta=\frac{\sqrt{3}}{2} \Rightarrow \theta=\frac{\pi}{6} \\<br/>&amp; \therefore \quad \text { Required angle }=\frac{\pi}{k}=2 \theta=\frac{\pi}{3} \\<br/>&amp; \Rightarrow \quad k=3 \\<br/>&amp;<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Laws of Motion', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
two-particles-of-mass-m-each-are-tied-at-the-ends-of-a-light-string-of-length-2-a-the-whole-system-is-kept-on-a-frictionless-horizontal-surface-with-t

slug:
two-particles-of-mass-m-each-are-tied-at-the-ends-of-a-light-string-of-length-2-a-the-whole-system-is-kept-on-a-frictionless-horizontal-surface-with-t-78077

question:
<div class="question">Two particles of mass $m$ each are tied at the ends of a light string of length $2 a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result, the particles move towards each other on the surface.<br/>The magnitude of acceleration, when the separation between them becomes $2 x$, is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Q_K7C81tVdzEH0oCE0tZ6FId-Hb5SBLzFb6esDvD5mM.original.fullsize.png"/><br/></div>

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

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

answer:
<div class="solution">6.<br/>$$<br/>\begin{aligned}<br/>&amp; 2 T \cos \theta=F \\<br/>&amp; \therefore T=\frac{F}{2} \sec \theta \\<br/>&amp; \text { Acceleration of particle }=\frac{T \sin \theta}{m}=\frac{F \tan \theta}{2 m}=\frac{F}{2 m} \frac{x}{\sqrt{a^2-x^2}}<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\therefore \text { Option (b) is correct. }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/czDNFTSOTpo3yxad4winPks0pMRQkvnS2fZ-aupjRsk.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
two-small-particles-of-equal-masses-start-moving-in-opposite-directions-from-a-point-a-in-a-horizontal-circular-orbit-their-tangential-velocities-are--1

slug:
two-small-particles-of-equal-masses-start-moving-in-opposite-directions-from-a-point-a-in-a-horizontal-circular-orbit-their-tangential-velocities-are-1-83688

question:
<div class="question">Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$ respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$, these two particles will again reach the point $A$ ?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LUO-op-gg-4W6HlSrRymYXOiQJSCK6F9HDghvhO5mxg.original.fullsize.png"/><br/></div>

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

answer:
<div class="solution">At first collision one particle having speed $2 v$ will rotate $240^{\circ}\left(\right.$ or $\left.\frac{4 \pi}{3}\right)$ while other particle having speed $v$ will rotate $120^{\circ}$ (or $\left.\frac{2 \pi}{3}\right)$. At first collision they will exchange their velocities. Now as shown in figure, after two collisions they will again reach at point $A$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Bricntb7-F7VumJnUzIQRhEPzq2XkCY8sAliWPDZJdc.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
two-small-particles-of-equal-masses-start-moving-in-opposite-directions-from-a-point-a-in-a-horizontal-circular-orbit-their-tangential-velocities-are-

slug:
two-small-particles-of-equal-masses-start-moving-in-opposite-directions-from-a-point-a-in-a-horizontal-circular-orbit-their-tangential-velocities-are-13922

question:
<div class="question">Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$ respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$, these two particles will again reach the point $A$ ?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LUO-op-gg-4W6HlSrRymYXOiQJSCK6F9HDghvhO5mxg.original.fullsize.png"/><br/></div>

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

answer:
<div class="solution">At first collision one particle having speed $2 v$ will rotate $240^{\circ}\left(\right.$ or $\left.\frac{4 \pi}{3}\right)$ while other particle having speed $v$ will rotate $120^{\circ}$ (or $\left.\frac{2 \pi}{3}\right)$. At first collision they will exchange their velocities. Now as shown in figure, after two collisions they will again reach at point $A$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Bricntb7-F7VumJnUzIQRhEPzq2XkCY8sAliWPDZJdc.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
title:
two-soap-bubbles-a-and-b-are-kept-in-a-closed-chamber-where-the-air-is-maintained-at-pressure-8-nm-2-the-radii-of-bubbles-a-and-b-are-2-cm-respectivel

slug:
two-soap-bubbles-a-and-b-are-kept-in-a-closed-chamber-where-the-air-is-maintained-at-pressure-8-nm-2-the-radii-of-bubbles-a-and-b-are-2-cm-respectivel-25040

question:
<div class="question">Two soap bubbles $A$ and $B$ are kept in a closed chamber where the air is maintained at pressure $8 \mathrm{Nm}^{-2}$. The radii of bubbles $A$ and $B$ are $2 \mathrm{~cm}$, respectively. Surface tension of the soap-water used to make bubbles is $0.04$ $\mathrm{Nm}^{-1}$. Find the ratio $\frac{n_B}{n_A}$, where $n_A$ and $n_B$ are the number of moles of air in bubbles $A$ and $B$, respectively. [Neglect the effect of gravity]</div>

answer:
<div class="solution">Although not given in the question but we will have to assume that temperatures of $A$ and $B$ are same.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/R_nXQKXsgRU_Yf6edoVvo3Mol9x3Nj68X29tjGHUZ_Q.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \frac{n_B}{n_A}=\frac{p_B V_B / R T}{p_A V_A / R T}=\frac{p_B V_B}{p_A V_A} \\<br/>&amp;= \frac{p+4 s / r_A \times 4 / 3 \pi\left(r_A\right)^3}{\left(p+4 s / r_B\right) \times 4 / 3 \pi\left(r_B\right)^3} \\<br/>&amp;(s=\text { surface tension) }<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-solid-cylinders-p-and-q-of-same-mass-and-same-radius-start-rolling-down-a-fixed-inclined-plane-from-the-same-height-at-the-same-time-cylinder-p-ha

slug:
two-solid-cylinders-p-and-q-of-same-mass-and-same-radius-start-rolling-down-a-fixed-inclined-plane-from-the-same-height-at-the-same-time-cylinder-p-ha-17597

question:
<div class="question">Two solid cylinders $P$ and $Q$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $P$ has most of its mass concentrated near its surface, while $Q$ has most of its mass concentrated near the axis. Which statement(s) is(are) correct?</div>

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

answer:
<div class="solution">As we know, acceleration of the center of mass of cylinder rolling down an inclined plane
<br/> <br/>$a_{c}=\frac{g \sin \theta}{1+\frac{I}{M R^{2}}}$
<br/> <br/>In case of $P$ the mass is concentrated away from the axis, So $I_{P}&gt;I_{Q}$
<br/> <br/>$\therefore \quad a_{P} &lt; a_{Q} \Rightarrow v_{\mathrm{P}} &lt; v_{\mathrm{Q}} \Rightarrow \omega_{\mathrm{P}} &lt; \omega_{\mathrm{Q}}$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ANENaTvUCAd2VYC6vCTFI7UrvJHtVD1BadiNHQTQ598.original.fullsize.png"/></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-solid-spheres-a-and-b-of-equal-volumes-but-of-different-densities-d-a-and-d-b-are-connected-by-a-string-they-are-fully-immersed-in-a-fluid-of-dens

slug:
two-solid-spheres-a-and-b-of-equal-volumes-but-of-different-densities-d-a-and-d-b-are-connected-by-a-string-they-are-fully-immersed-in-a-fluid-of-dens-86291

question:
<div class="question">Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/yEAAJCJIdANjAiDe-9oOygBsemXz7jvUKEY5LffhBUs.original.fullsize.png"/><br/></div>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/euBn6cAUoeqMELNqoHx0YpWVMQQ5bPSOBfCkJDYBYyk.original.fullsize.png"/><br/><br/>Equilibrium of $A$<br/>$$<br/>\begin{aligned}<br/>V d_F g &amp; =T+W_A \\<br/>&amp; =T+V d_A g<br/>\end{aligned}<br/>$$<br/>Equilibrium of $B$,<br/>$$<br/>T+V d_F g=V d_B g<br/>$$<br/>Adding Eqs. (i) and (ii), we get $2 d_f=d_A+d_B$<br/>$\therefore$ Option (d) is correct. From Eq. (i), we can see that<br/>$$<br/>d_F&gt;d_A \quad \text { [as } T&gt;0 \text { ] }<br/>$$<br/>$\therefore$ Option (a) is correct.<br/>From Eq. (ii) we can see that,<br/>$$<br/>d_B&gt;d_F<br/>$$<br/>$\therefore$ Option (a) is correct.<br/>$\therefore$ Correct options are (a), (b) and (d).<br/>Analysis of Question<br/>Question is moderately difficult but conceptwise it is good.</div>


tags: ['Physics', 'Thermal Properties of Matter', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch2_P3.db
title:
two-spherical-bodies-a-radius-6-cm-and-b-radius-18-cm-are-at-temperatures-t-1-and-t-2-respectively-the-maximum-intensity-in-the-emission-spectrum-of-a

slug:
two-spherical-bodies-a-radius-6-cm-and-b-radius-18-cm-are-at-temperatures-t-1-and-t-2-respectively-the-maximum-intensity-in-the-emission-spectrum-of-a-98563

question:
<div class="question">Two spherical bodies $A$ (radius $6 \mathrm{~cm}$ ) and $B$ (radius $18 \mathrm{~cm}$ ) are at temperatures $T_1$ and $T_2$, respectively. The maximum intensity in the emission spectrum of $A$ is at $500 \mathrm{~nm}$ and in that of $B$ is at $1500 \mathrm{~nm}$. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by $A$ to that of $B$ ?</div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { } \lambda_m \propto \frac{1}{T} \\<br/>&amp; \therefore \frac{\lambda_A}{\lambda_B}=\frac{T_B}{T_A}=\frac{500}{1500}=\frac{1}{3} \\<br/>&amp; E \propto T^4 A \text { (where } A=\text { surface area } \\<br/>&amp; =4 \pi R^2 \text { ) } \\<br/>&amp; \therefore E \propto T^4 R^2 \\<br/>&amp; \frac{E_A}{E_B}=\left(\frac{T_A}{T_B}\right)^4\left(\frac{R_A}{R_B}\right)^2 \\<br/>&amp; =(3)^4\left(\frac{6}{18}\right)^2=9<br/>\end{aligned}<br/>$$<br/>$\therefore$ Answer is 9 .</div>


tags: ['Physics', 'Gravitation', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-spherical-planets-p-and-q-have-the-same-uniform-density-masses-m-p-and-m-q-and-surface-areas-a-and-4a-respectively-a-spherical-planet-r-also-has-u

slug:
two-spherical-planets-p-and-q-have-the-same-uniform-density-masses-m-p-and-m-q-and-surface-areas-a-and-4a-respectively-a-spherical-planet-r-also-has-u-45094

question:
<div class="question">Two spherical planets $P$ and $Q$ have the same uniform density $\rho$, masses $M_{P}$ and $M_{Q}$ and surface areas $A$ and 4A respectively. A spherical planet $R$ also has uniform density $\rho$ and its mass is $\left(M_{P}+M_{Q}\right)$. The escape velocities from the planets $P, Q$ and $R$ are $V_{P}, V_{Q}$ and $V_{R}$, respectively. Then</div>

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

answer:
<div class="solution">Here Planets $P$ and $Q$ have the same uniform density ' $\rho$ ' and surface areas $A$ and $4 A$ respectively. Let the mass of $P, M_{P}$ be $m$.
<br/> <br/>Then $m=\rho \times \frac{4}{3} \pi r^{3}=\rho \times \frac{4}{3} \pi\left[\frac{A}{4 \pi}\right]^{3 / 2}$
<br/> <br/>The mass of $M_{Q}=\rho \times \frac{4}{3} \pi\left[\frac{4 A}{4 \pi}\right]^{3 / 2}=8 \mathrm{~m}$
<br/> <br/>$\therefore \quad$ The mass of Planet $R=8 \mathrm{~m}+\mathrm{m}=9 \mathrm{~m}$
<br/> <br/>If the radius of $P=r$
<br/> <br/>Then the radius of $Q=2 r$
<br/> <br/>$\left[\because r_{Q}=\left(\frac{4 A}{4 \pi}\right)^{3 / 2}=2\left(\frac{A}{4 \pi}\right)^{3 / 2}\right]$
<br/> <br/>and radius of $R=9^{1 / 3} r$
<br/> <br/>$\left[\begin{array}{l}
<br/> <br/>\because M_{R}=M_{P}+M_{Q} \\
<br/> <br/>r_{R}^{3}=r^{3}+(2 r)^{3}=9 r^{3}
<br/> <br/>\end{array}\right]$
<br/> <br/>As we know, escape velocity from the planet
<br/> <br/>$\begin{aligned} V_{e}=\sqrt{\frac{2 G M}{R}} &amp; \therefore v_{P}=\sqrt{\frac{2 G M_{P}}{R_{p}}}=\sqrt{\frac{2 G m}{r}} \\ v_{Q} &amp;=\sqrt{\frac{2 G M_{Q}}{R_{Q}}}=\sqrt{\frac{2 G(8 \mathrm{~m})}{2 r}}=2 v_{P} \\ v_{R} &amp;=\sqrt{\frac{2 G(9 \mathrm{~m})}{9^{1 / 3} r}}=9^{1 / 3} v_{P} \end{aligned}$</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-transparent-media-of-refractive-indices-1-and-3-have-a-solid-lens-shaped-transparent-material-of-refractive-index-2-between-them-as-shown-in-figur

slug:
two-transparent-media-of-refractive-indices-1-and-3-have-a-solid-lens-shaped-transparent-material-of-refractive-index-2-between-them-as-shown-in-figur-24407

question:
<div class="question">Two transparent media of refractive indices $\mu_1$ and $\mu_3$ have a solid lens shaped transparent material of refractive index $\mu_2$ between them as shown in figures in Column II. A ray traversing these media is also shown in the figures. In Column I different relationships between $\mu_1, \mu_2$ and $\mu_3$ are given. Match them to the ray diagram shown in Column II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/n4koPUPns0Duo43JAwnK2kyG7ieDaj7HgCUz0wUkeCc.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) P,R, (B) Q,S,T, (C) P,R,T, (D) Q,S<br/></span> </div>

answer:
<div class="solution">(A) $\rightarrow$ since $\mu_1 &lt; \mu_2$, the ray of light will bend towards normal after first refraction.<br/>(B) $\rightarrow \mu_1&gt;\mu_2$, the ray of light will bend away from the normal after first refraction.<br/>(C) $\rightarrow$ since $\mu_2=\mu_3$ means in second refraction there will be no change in the path of ray of light.<br/>(D) $\rightarrow$ Since $\mu_2&gt;\mu_3$, ray of light will bend away from the normal after second refraction.<br/>Therefore the correct options are as under.<br/>(A) $\rightarrow$ P, R<br/>(B) $\rightarrow$ Q, S, T<br/>(C) $\rightarrow$ P, R, T<br/>(D) $\rightarrow$ Q, $S$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P3.db
title:
two-wires-each-carrying-a-steady-current-i-are-shown-in-four-configurations-in-column-i-some-of-the-resulting-effects-are-described-in-column-ii-match-1

slug:
two-wires-each-carrying-a-steady-current-i-are-shown-in-four-configurations-in-column-i-some-of-the-resulting-effects-are-described-in-column-ii-match-1-34654

question:
<div class="question">Two wires each carrying a steady current $I$ are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/10VY3wvCE3mi0B4Xwl5xqOCTrSZ6crG8OyCxIhCMnbk.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-q, r; B-p; C-q, r; D-q, s</span> </div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P3.db
title:
two-wires-each-carrying-a-steady-current-i-are-shown-in-four-configurations-in-column-i-some-of-the-resulting-effects-are-described-in-column-ii-match

slug:
two-wires-each-carrying-a-steady-current-i-are-shown-in-four-configurations-in-column-i-some-of-the-resulting-effects-are-described-in-column-ii-match-33892

question:
<div class="question">Two wires each carrying a steady current $I$ are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/10VY3wvCE3mi0B4Xwl5xqOCTrSZ6crG8OyCxIhCMnbk.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-q, r; B-p; C-q, r; D-q, s</span> </div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
under-the-influence-of-the-coulomb-field-of-charge-q-a-charge-q-is-moving-around-it-in-an-elliptical-orbit-find-out-the-correct-statements

slug:
under-the-influence-of-the-coulomb-field-of-charge-q-a-charge-q-is-moving-around-it-in-an-elliptical-orbit-find-out-the-correct-statements-37565

question:
<div class="question">Under the influence of the coulomb field of charge $+Q$, a charge $-q$ is moving around it in an elliptical orbit. Find out the correct statement(s).</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>The angular momentum of the charge $-q$ is constant<br/></span> </div>

answer:
<div class="solution">Net torque on $(-q$ ) about a point (say $P$ ) lying over $+Q$ is zero. Therefore, angular momentum of $(-q)$ about point $P$ should remain constant.</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
under-the-same-reaction-conditions-initial-concentration-of-1386-mol-dm-3-of-a-substance-becomes-half-in-40-s-and-20-s-through-firstorder-and-zeroorde-1

slug:
under-the-same-reaction-conditions-initial-concentration-of-1386-mol-dm-3-of-a-substance-becomes-half-in-40-s-and-20-s-through-firstorder-and-zeroorde-1-39993

question:
<div class="question">Under the same reaction conditions, initial concentration of $1.386 \mathrm{~mol} \mathrm{dm}^{-3}$ of a substance becomes half in 40 s and 20 s through first-order and zero-order kinetics, respectively. Ratio $\left(\frac{k_1}{k_0}\right)$ of the rate constants for first order $\left(k_1\right)$ and zero $\operatorname{order}\left(k_0\right)$ of the reaction is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$0.5 \mathrm{~mol}^{-1} \mathrm{dm}^3$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$1.0 \mathrm{~mol} \mathrm{dm}^3$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$1.5 \mathrm{~mol} \mathrm{dm}^3$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$2.0 \mathrm{~mol}^{-1} \mathrm{dm}^3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$0.5 \mathrm{~mol}^{-1} \mathrm{dm}^3$<br/></span> </div>

answer:
<div class="solution">First order kinetics, $k_1=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{40} \mathrm{~s}^{-1}$<br/>Zero order kinetics, $k_1=\frac{C_0}{2 t_{1 / 2}}=\frac{1.386}{2 \times 20}$<br/>Hence, $\frac{k_1}{k_0}=\frac{0.693}{1.386}=0.5$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">815</span> </div>
source_db: MarksBatch2_P3.db
title:
using-the-data-provided-calculate-the-multiple-bond-energy-kj-mol-1-of-a-c-c-bond-in-c-2-h-2-that-energy-is-take-the-bond-energy-of-a-c-h-bond-as-350-

slug:
using-the-data-provided-calculate-the-multiple-bond-energy-kj-mol-1-of-a-c-c-bond-in-c-2-h-2-that-energy-is-take-the-bond-energy-of-a-c-h-bond-as-350-45183

question:
<div class="question">Using the data provided, calculate the multiple bond energy $\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ of a $\mathrm{C} \equiv \mathrm{C}$ bond in $\mathrm{C}_{2} \mathrm{H}_{2}$. That energy is (take the bond energy of a $\mathrm{C}-\mathrm{H}$ bond as $350 \mathrm{~kJ} \mathrm{~mol}^{-1}$ ) $2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{HC}=\mathrm{CH}(\mathrm{g}) ; \Delta \mathrm{H}=225 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) ; \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}$ $\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}(\mathrm{g}) ; \Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1165</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">837</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">865</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">815</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">(i) $2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{H}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}(\mathrm{g})$
<br/> <br/>$\Delta \mathrm{H}=225 \mathrm{~kJ} \mathrm{~mol}^{-1}$
<br/> <br/>(ii) $2 \mathrm{C}(\mathrm{s}) \longrightarrow 2 \mathrm{C}(\mathrm{g}) \Delta \mathrm{H}=1410 \mathrm{~kJ} \mathrm{~mol}^{-1}$
<br/> <br/>(iii) $\mathrm{H}_{2}$ (g) $\longrightarrow 2 \mathrm{H}$ (g) $\Delta \mathrm{H}=330 \mathrm{~kJ} \mathrm{~mol}^{-1}$
<br/> <br/>From equation (i) :
<br/> <br/>$\begin{array}{l}
<br/> <br/>225=\left[2 \times \Delta \mathrm{H}_{\mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{C}(\mathrm{g})}+1 \times \mathrm{BE}_{\mathrm{H}-\mathrm{H}}\right] \\
<br/> <br/>-\left[2 \times \mathrm{BE}_{\mathrm{C}-\mathrm{H}}+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
<br/> <br/>225=[1410+1 \times 330]-\left[2 \times 350+1 \times \mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
<br/> <br/>225=[1410+330]-\left[700+\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}\right] \\
<br/> <br/>225=1740-700-\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}} \\
<br/> <br/>\mathrm{BE}_{\mathrm{C} \equiv \mathrm{C}}=815 \mathrm{~kJ} \mathrm{~mol}^{-1}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
water-is-filled-up-to-a-height-h-in-a-beaker-of-radius-r-as-shown-in-the-figure-the-density-of-water-is-the-surface-tension-of-water-is-t-and-the-atmo-1

slug:
water-is-filled-up-to-a-height-h-in-a-beaker-of-radius-r-as-shown-in-the-figure-the-density-of-water-is-the-surface-tension-of-water-is-t-and-the-atmo-1-31252

question:
<div class="question">Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$, the surface tension of water is $T$ and the atmospheric pressure is $p_0$. Consider a vertical section $A B C D$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U9L6A5gFosJxDI2DolDICI2XIMxNUvXy__El6qT0wVI.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left|2 p_0 R h+\pi R^2 \rho g h-2 R T\right|$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\left|2 p_0 R h+R \rho g h^2-2 R T\right|$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\left|p_0 \pi R^2+R \rho g h^2-2 R T\right|$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left|p_0 \pi R^2+R \rho g h^2+2 R T\right|$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left|2 p_0 R h+R \rho g h^2-2 R T\right|$<br/></span> </div>

answer:
<div class="solution">Force from right hand side liquid on left hand side liquid.<br/>(i) Due to surface tension force $=2 R T$ (towards right)<br/>(ii) Due to liquid pressure force<br/>$$<br/>\begin{aligned}<br/>&amp; =\int_{x=0}^{x=h}\left(p_0+\rho g h\right)(2 R \cdot x) d x \\<br/>&amp; =\left(2 p_0 R h+R \rho g h^2\right) \text { (towards left) }<br/>\end{aligned}<br/>$$<br/>$\therefore$ Net force is $\left|2 p_0 R h+R \rho g h^2-2 R T\right|$ Correct option is (b).</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
water-with-refractive-index-3-4-in-a-tank-is-18-cm-deep-oil-of-refractive-index-4-7-lies-on-water-making-a-convex-surface-of-radius-of-curvature-r-6-c

slug:
water-with-refractive-index-3-4-in-a-tank-is-18-cm-deep-oil-of-refractive-index-4-7-lies-on-water-making-a-convex-surface-of-radius-of-curvature-r-6-c-72704

question:
<div class="question">Water (with refractive index $=\frac{4}{3}$ ) in a tank is $18 \mathrm{~cm}$ deep. Oil of refractive index $\frac{7}{4}$ lies on water making a convex surface of radius of curvature $R=6 \mathrm{~cm}$ as shown. Consider oil to act as a thin lens. An object $S$ is placed $24 \mathrm{~cm}$ above water surface. The location of its image is at $x \mathrm{~cm}$ above the bottom of the tank. Then, $x$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/mKmOXjj29zhkmQK3XlN_hAMfYUgpycKMqHhLndIqnRA.original.fullsize.png"/><br/></div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/rSJNjUb0wdB89rx4-vZfch8RceDmysbdQmtVOKpuukA.original.fullsize.png"/><br/><br/>Two refractions will take place, first from spherical surface and the other from the plane surface.<br/>So, applying<br/>$$<br/>\frac{\mu_2}{v}-\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R}<br/>$$<br/>two times with proper sign convention. Ray of light is travelling downwards. Therefore, downward direction is taken as positive direction.<br/>$$<br/>\begin{gathered}<br/>\frac{7 / 4}{v}-\frac{1.0}{-24}=\frac{7 / 4-1.0}{+6} \\<br/>\frac{4 / 3}{(18-x)}-\frac{7 / 4}{v}=\frac{4 / 3-7 / 4}{\propto}<br/>\end{gathered}<br/>$$<br/>Solving these equations, we get<br/>$$<br/>x=2 \mathrm{~cm}<br/>$$<br/>$\therefore$ Answer is 2 .<br/>Analysis of Question<br/>(i) Question is moderately difficult from calculation point of view, otherwise it is simple.<br/>(ii) $\frac{\mu_2}{v}-\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R}$ can be applied for<br/>plane surface also with $R=\propto$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2006']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">55</span> </div>
source_db: MarksBatch2_P3.db
title:
we-have-taken-a-saturated-solution-of-agbr-k-sp-is-12-1-0-14-if-1-0-7-mole-of-agno-3-are-added-to-1-litre-of-this-solution-find-conductivity-specific-

slug:
we-have-taken-a-saturated-solution-of-agbr-k-sp-is-12-1-0-14-if-1-0-7-mole-of-agno-3-are-added-to-1-litre-of-this-solution-find-conductivity-specific-56273

question:
<div class="question">We have taken a saturated solution of $\mathrm{AgBr}, K_{\mathrm{sp}}$ is $12 \times 10^{-14}$. If $10^{-7}$ mole of $\mathrm{AgNO}_3$ are added to 1 litre of this solution, find conductivity (specific conductance) of this solution in terms of $10^{-7} \mathrm{Sm}^{-1}$ units.<br/>$$<br/>\text { Given, } \begin{aligned}<br/>\lambda_{\left(\mathrm{Ag}^{+}\right)}^{\circ} &amp; =6 \times 10^{-3} \mathrm{Sm}^2 \mathrm{~mol}^{-1}, \lambda_{\left(\mathrm{Br}^{-}\right)}^{\circ}=8 \times 10^{-3} \mathrm{Sm}^2 \mathrm{~mol}^{-1}, \\<br/>\lambda_{\left(\mathrm{NO}_3^{-}\right)} &amp; =7 \times 10^{-3} \mathrm{Sm}^2 \mathrm{~mol}^{-1},<br/>\end{aligned}<br/>$$</div>

answer:
<div class="solution">Suppose the solubility of $\mathrm{AgBr}$ in $10^{-7} \mathrm{MAgNO}_3$ is $\mathrm{mol} / \mathrm{L}$<br/>$$<br/>\begin{aligned}<br/>&amp; \underset{s \mathrm{~mol} / \mathrm{L}}{\mathrm{AgBr}} \rightleftharpoons \mathrm{Ag}^{+}+\mathrm{Br}^{-} \\<br/>&amp; \mathrm{AgNO}_3 \rightleftharpoons \mathrm{Ag}^{+}+\mathrm{NO}_3^{-} \\<br/>&amp; 10^{-7} \mathrm{M} \quad 10^{-7} \mathrm{M} \times 10^{-7} \mathrm{M} \\<br/>&amp; \text { Total }\left[\mathrm{Ag}^{+}\right]=\left(s+10^{-7}\right) \mathrm{M} \\<br/>&amp; K_{\mathrm{sp}} \text { of } \mathrm{AgBr}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{Br}^{-}\right] \\<br/>&amp; 12 \times 10^{-14}=\left(s+10^{-7}\right)(s)=s^2+10^{-7} s \\<br/>&amp; s^2+10^{-7} s-12 \times 10^{-14}=0 \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>On solving $s=3 \times 10^{-7} \mathrm{M}$<br/>Hence, $\left[\mathrm{Br}^{-}\right]=3 \times 10^{-7} \mathrm{M}=3 \times 10^{-7} \times 10^3 \mathrm{~m}^3=3 \times 10^{-4} \mathrm{~m}^3$<br/>$$<br/>\left[\mathrm{Ag}^{+}\right]=\left(3 \times 10^{-7}+10^{-7}\right) \mathrm{M}=4 \times 10^{-7} \times 10^3 \mathrm{~m}^3=4 \times 10^{-4} \mathrm{~m}^3<br/>$$<br/>$$<br/>\left[\mathrm{NO}_3^{-}\right]=10^{-7} \mathrm{M}=10^{-7} \times 10^{+3}=1 \times 10^{-4} \mathrm{~m}^3<br/>$$<br/>$$<br/>\because \quad \lambda=\frac{k}{C} \text { or } k=\lambda \times C<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>\therefore \quad k_{\mathrm{Br}^{-}} &amp; =3 \times 10^{-4} \times 8 \times 10^{-3} \mathrm{Sm}^{-1}=24 \times 10^{-7} \mathrm{Sm}^{-1} \\<br/>k_{\mathrm{Ag}^{+}} &amp; =4 \times 10^{-4} \times 6 \times 10^{-3} \mathrm{Sm}^{-1}=24 \times 10^{-7} \mathrm{Sm}^{-1} \\<br/>k_{\mathrm{NO}_3^{-}} &amp; =1 \times 10^{-4} \times 7 \times 10^{-3}=7 \times 10^{-7} \mathrm{Sm}^{-1} \\<br/>k_{\text {Total }} &amp; =k_{\mathrm{Br}^{-}}+k_{\mathrm{Ag}^{+}}+k_{\mathrm{NO}_3^{-}} \\<br/>&amp; =\left(24 \times 10^{-7}+24 \times 10^{-7}+7 \times 10^{-7} \mathrm{Sm}^{-1}\right. \text { ) } \\<br/>&amp; =55 \times 10^{-7} \mathrm{Sm}^{-1} \\<br/>&amp; \left.=\mathbf{5 5} \mathbf{S m}^{-1} \text { (in term of } 10^{-7} \mathrm{Sm}^{-1}\right)<br/>\end{aligned}<br/>$$</div>


title: what-are-n-and-m-1
slug: what-are-n-and-m-1-45932
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P3.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/JMS_gxyfnfGLHwrLd6kj2A5sBnQa76NPsAQVCvhDcHA.original.fullsize.png"/><br/><br/>$$<br/>\text { What are } N \text { and } M \text { ? }<br/>$$</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/cxJRp0KMs5knAbgnNw2AdaOxvnfNf1qjOWmwnvBCqo4.original.fullsize.png"/><br/><br/>In these, (iii) and (iv) are enantiomers and (v) and (vi) are also enantiomers to each other. Thus total six isomers will be possible for $N$. In these only four isomers will be obtained on fractional distillation without resolution because $d$ and $l$ isomers (i.e., (iii) \&amp; (iv) and (v) \&amp; (vi)) cannot be separated by fractional distillation. Hence $N=6$ and $M=4$.</div>


tags: ['Biology', 'Evolution']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
what-are-we-referring-to-when-we-say-simple-organisms-or-complex-organismswhat-are-we-referring-to-when-we-say-simple-organisms-or-complex-organisms

slug:
what-are-we-referring-to-when-we-say-simple-organisms-or-complex-organismswhat-are-we-referring-to-when-we-say-simple-organisms-or-complex-organisms-13469

question:
<div class="question">What are we referring to when we say 'simple organisms' or 'complex organisms'?What are we referring to when we say 'simple organisms' or 'complex organisms'?</div>

answer:
<div class="solution">The organisms that have simple structural and functional organisation and are considered primitive are simple organisms. Whereas organisms that have higher and complex levels of structural and functional organisation are complex organisms. These are more advanced and said to have arisen from simple organisms.</div>


title: what-is-the-advancement-in-ex-situ-conservation
slug: what-is-the-advancement-in-ex-situ-conservation-31189
question: <div class="question">What is the advancement in ex situ conservation?</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Keeping threatened species in enclosures</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Gametes preservation through cryopreservation techniques</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Fertilization of eggs in vivo</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Propagation of plants using tissue culture methods</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Gametes preservation through cryopreservation techniques</span> </div>

answer:
<div class="solution">In recent years, ex situ conservation has advanced beyond keeping threatened species in enclosures to include the preservation of gametes of threatened species through cryopreservation techniques.</div>


title: what-is-the-limitation-of-treatments-using-metal-salts-like-aluminium-and-magnesium-hydroxide
slug: what-is-the-limitation-of-treatments-using-metal-salts-like-aluminium-and-magnesium-hydroxide-37559
tags: ['Chemistry', 'Chemistry in Everyday Life', 'NEET']
answer: <div class="solution">Treatments with metal salts control only symptoms and not the cause.</div>
source_db: MarksBatch2_P3.db
question:
<div class="question">What is the limitation of treatments using metal salts like aluminium and magnesium hydroxide?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">They control symptoms and not the cause.</span> </div>


tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P4.db
title:
what-is-the-term-for-cryopreservation-of-gametes-of-threatened-species-in-viable-and-fertile-conditions

slug:
what-is-the-term-for-cryopreservation-of-gametes-of-threatened-species-in-viable-and-fertile-conditions-51570

question:
<div class="question">What is the term for cryopreservation of gametes of threatened species in viable and fertile conditions?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Advanced Ex-situ conservation of biodiversity.</span> </div>

answer:
<div class="solution">In recent years, Ex-situ conservation has advanced beyond keeping threatened species in enclosures. Now gametes of threatened species can be preserved in viable and fertile condition for long periods using cryo preservation techniques.</div>


tags: ['Chemistry', 'Solutions', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P4.db
title:
when-20-g-of-naphthoic-acid-c-11-h-8-o-2-is-dissolved-in-50-g-of-benzene-k-f-172-k-kg-mol-1-a-freezing-point-depression-of-2-k-is-observed-the-vant-ho

slug:
when-20-g-of-naphthoic-acid-c-11-h-8-o-2-is-dissolved-in-50-g-of-benzene-k-f-172-k-kg-mol-1-a-freezing-point-depression-of-2-k-is-observed-the-vant-ho-29596

question:
<div class="question">When $20 \mathrm{~g}$ of naphthoic acid $\left(\mathrm{C}_{11} \mathrm{H}_8 \mathrm{O}_2\right)$ is dissolved in $50 \mathrm{~g}$ of benzene $\left(K_f=1.72 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$, a freezing point depression of $2 \mathrm{~K}$ is observed. The van't Hoff factor $(i)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$0.5$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>1<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>2<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>3</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$0.5$<br/></span> </div>

answer:
<div class="solution">Actual molecular weight of napthoic acid $\left(\mathrm{C}_{11} \mathrm{H}_8 \mathrm{O}_2\right)=172$<br/>$$<br/>\begin{aligned}<br/>\text { Molecular mass (calculated ) } &amp; =\frac{1000 . K_f \cdot w}{W . \Delta T_f} \\<br/>&amp; =\frac{1000 \times 1.72 \times 20}{50 \times 2} \\<br/>&amp; =344<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch2_P4.db
title:
when-benzene-sulphonic-acid-and-p-nitrophenol-are-treated-with-nahco-3-the-gases-released-respectively-are-1

slug:
when-benzene-sulphonic-acid-and-p-nitrophenol-are-treated-with-nahco-3-the-gases-released-respectively-are-1-82503

question:
<div class="question">When benzene sulphonic acid and $p$-nitrophenol are treated with $\mathrm{NaHCO}_3$, the gases released respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{SO}_2, \mathrm{NO}_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{SO}_2, \mathrm{NO}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{SO}_2, \mathrm{CO}_2$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{CO}_2, \mathrm{CO}_2$</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"><br/>$\mathrm{CO}_2, \mathrm{CO}_2$</span> </div>

answer:
<div class="solution">$$<br/>\text { Benzene sulphonic acid and p-nitrophenol react with } \mathrm{NaHCO}_3 \text { and evolve } \mathrm{CO}_2 \text { gas. }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VYAE7Q7eQIqgFrITxHedCdwWvz6pLzQ0SOd5pTlVftE.original.fullsize.png"/><br/><br/>Because benezene sulphonic acid and $p$-nitro phenol are stronger acids with $\mathrm{H}_2 \mathrm{CO}_3$ (i.e., $\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2$ ) so, they are capable to evolve $\mathrm{CO}_2$ with $\mathrm{NaHCO}_3$.<br/>$$<br/>\mathrm{HCO}_3^{-}+\underset{\text { Acid }}{\mathrm{H}^{+}} \rightarrow \mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2 \uparrow<br/>$$</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P4.db
title:
when-benzene-sulphonic-acid-and-p-nitrophenol-are-treated-with-nahco-3-the-gases-released-respectively-are

slug:
when-benzene-sulphonic-acid-and-p-nitrophenol-are-treated-with-nahco-3-the-gases-released-respectively-are-89996

question:
<div class="question">When benzene sulphonic acid and $p$-nitrophenol are treated with $\mathrm{NaHCO}_3$, the gases released respectively are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{SO}_2, \mathrm{NO}_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{SO}_2, \mathrm{NO}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{SO}_2, \mathrm{CO}_2$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{CO}_2, \mathrm{CO}_2$</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"><br/>$\mathrm{CO}_2, \mathrm{CO}_2$</span> </div>

answer:
<div class="solution">$$<br/>\text { Benzene sulphonic acid and p-nitrophenol react with } \mathrm{NaHCO}_3 \text { and evolve } \mathrm{CO}_2 \text { gas. }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VYAE7Q7eQIqgFrITxHedCdwWvz6pLzQ0SOd5pTlVftE.original.fullsize.png"/><br/><br/>Because benezene sulphonic acid and $p$-nitro phenol are stronger acids with $\mathrm{H}_2 \mathrm{CO}_3$ (i.e., $\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2$ ) so, they are capable to evolve $\mathrm{CO}_2$ with $\mathrm{NaHCO}_3$.<br/>$$<br/>\mathrm{HCO}_3^{-}+\underset{\text { Acid }}{\mathrm{H}^{+}} \rightarrow \mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2 \uparrow<br/>$$</div>


tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P4.db
title:
when-the-following-aldohexose-exists-in-its-dconfiguration-the-total-number-of-stereoisomers-in-its-pyranose-form-is-cho-ch-2-choh-choh-choh-ch-2-oh

slug:
when-the-following-aldohexose-exists-in-its-dconfiguration-the-total-number-of-stereoisomers-in-its-pyranose-form-is-cho-ch-2-choh-choh-choh-ch-2-oh-80543

question:
<div class="question">When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is :
<br/> <br/>$\mathrm{CHO}-\mathrm{CH}_{2}-\mathrm{CHOH}-\mathrm{CHOH}-\mathrm{CHOH}-\mathrm{CH}_{2} \mathrm{OH}$</div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/KyWlZsicRYTj_rfw35_zDvgQtgvHykOdM0o0zUk-dhc.original.fullsize.png"/><br/> <br/> <br/>Thus, total number of stereoisomers in pyranose form of D-configuration $=2^{3}=8$</div>


tags: ['Physics', 'Current Electricity', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P4.db
title:
when-two-identical-batteries-of-internal-resistance-1-each-are-connected-in-series-across-a-resistor-r-the-rate-of-heat-produced-in-r-is-j-1-when-the-

slug:
when-two-identical-batteries-of-internal-resistance-1-each-are-connected-in-series-across-a-resistor-r-the-rate-of-heat-produced-in-r-is-j-1-when-the-11677

question:
<div class="question">When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $R$, the rate of heat produced in $R$ is $J_1$. When the same batteries are connected in parallel across $R$, the rate is $J_2$. If $J_1=2.25 J_2$ then the value of $R$ in $\Omega$ is</div>

answer:
<div class="solution">In series, $i=\frac{2 E}{2+R}$<br/>$$<br/>\therefore J_1=i^2 R=\left(\frac{2 E}{2+R}\right)^2 \cdot R<br/>$$<br/>In parallel, $i=\frac{E}{0.5+R}$<br/>$$<br/>\begin{aligned}<br/>\therefore \quad J_2 &amp; =i^2 R=\left(\frac{E}{0.5+R}\right)^2 \cdot R \\<br/>\frac{J_1}{J_2} &amp; =2.25=\frac{4(0.5+R)^2}{(2+R)^2}<br/>\end{aligned}<br/>$$<br/>or $1.5=\frac{2(0.5+R)}{(2+R)}$<br/>Solving we get, $R=4 \Omega$<br/>$\therefore$ The answer is 4 .</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P4.db
title:
when-two-progressive-waves-y-1-4-sin-2-x-6-t-and-y-2-3-sin-2-x-6-t-2-are-superimposed-the-amplitude-of-the-resultant-wave-is

slug:
when-two-progressive-waves-y-1-4-sin-2-x-6-t-and-y-2-3-sin-2-x-6-t-2-are-superimposed-the-amplitude-of-the-resultant-wave-is-55880

question:
<div class="question">When two progressive waves $y_1=4 \sin (2 x-6 t) \quad$ and $y_2=3 \sin \left(2 x-6 t-\frac{\pi}{2}\right) \quad$ are superimposed, the amplitude of the resultant wave is</div>

answer:
<div class="solution">Phase difference between the two waves is $90^{\circ}$. Amplitudes are added by vector method.<br/>$\therefore$ Answer is 5 .</div>


title: which-is-correct-statement-if-n-2-is-added-at-equilibrium-condition
slug: which-is-correct-statement-if-n-2-is-added-at-equilibrium-condition-83400
tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P4.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/mDD0jGXX6OV1AR-ZiUfP1pQsYDLICFAUyr4BWER6He8.original.fullsize.png"/><br/><br/>Which is correct statement if $\mathrm{N}_2$ is added at equilibrium condition?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>The equilibrium will shift to forward direction because according to IInd law of thermodynamics the entropy must increases in the direction of spontaneous reaction.<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>The condition for equilibrium is $G_{\mathrm{N}_2}+3 G_{\mathrm{H}_2}=2 G_{\mathrm{NH}_3}$ where $G$ is Gibbs free energy per mole of the gaseous species measured at the partial pressure. The condition of equilibrium is unaffected by the use of catalyst, which increases the rate of both the forward and backward reactions to the same extent.<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>The catalyst will increase the rate of forward reaction by $\alpha$ and that of backward reaction by $\beta$.<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Catalyst will not alter the rate of either of the reaction.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>The condition for equilibrium is $G_{\mathrm{N}_2}+3 G_{\mathrm{H}_2}=2 G_{\mathrm{NH}_3}$ where $G$ is Gibbs free energy per mole of the gaseous species measured at the partial pressure. The condition of equilibrium is unaffected by the use of catalyst, which increases the rate of both the forward and backward reactions to the same extent.<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/USmQlSPUj1K_-DRsZdEIV5xKkcnpjajwJ3M-vY850tY.original.fullsize.png"/><br/><br/>$K_p$ or $K_c$ remains constant for above reaction at constant temperature.<br/>Although in presence of catalyst rate of forward and backward reaction is increased in same order (extent) due to decreasing the activation energy of both reaction. So the equilibrium is established in short time i.e., catalyst is able to increase the concentration of reactants and products in same order, so the value of $K_C$ or $K_p$ remains constant. Hence equilibrium state is not effected in presence of catalyst. Hence, at equilibrium $\Delta G=0$<br/>$$<br/>\begin{aligned}<br/>&amp; \because \quad \Delta G=2 G \text { of } \mathrm{NH}_3-\left(\mathrm{G} \text { of } \mathrm{H}_2+3 \times G \text { of } \mathrm{NH}_3\right) \\<br/>&amp; \therefore G_{\mathrm{N}_2}+3 G_{\mathrm{H}_2}=2 G_{\mathrm{NH}_3}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Electromagnetic Induction', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P4.db
title:
which-of-the-field-patterns-given-in-the-figure-is-valid-for-electric-field-as-well-as-for-magnetic-field

slug:
which-of-the-field-patterns-given-in-the-figure-is-valid-for-electric-field-as-well-as-for-magnetic-field-71304

question:
<div class="question">Which of the field patterns given in the figure is valid for electric field as well as for magnetic field?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PvXG5u85HXYPikpmJCG0Dyb9XLSnjaulKAjw6YYBM8Q.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8sAGjXi2E27EMRrmB8p4jNzjcPrulhkKE0jI6HTNJ0g.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vB6wiKRN6J5Veh7UeXiZol7mOzgMVULyI16yyFEu8Hw.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iEBS_GWoOypMxmFZtVPC3y0Rvs0ctlO9FwT931vvo78.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vB6wiKRN6J5Veh7UeXiZol7mOzgMVULyI16yyFEu8Hw.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">Correct answer is (c), because induced electric field lines (produced by change in magnetic field) and magnetic field lines form closed loops.<br/>Analysis of Question<br/>Question is simple, provided you have an idea of induced electric field lines.</div>


title: which-of-the-following-complexe-is-used-in-cencer-treatment
slug: which-of-the-following-complexe-is-used-in-cencer-treatment-59091
question: <div class="question">Which of the following complexe is used in cencer treatment?</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mtext>N</mtext><msub><mrow><mtext>a</mtext></mrow><mrow><mn>2</mn></mrow></msub><mtext>CoC</mtext><msub><mrow><mtext>l</mtext></mrow><mrow><mn>4</mn></mrow></msub></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">cis- <math><mo>[</mo><mtext>PtC</mtext><msub><mrow><mtext>l</mtext></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mtext>N</mtext><msub><mrow><mtext>H</mtext></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">mer- <math><mo>[</mo><mtext>Co</mtext><mo>(</mo><mtext>N</mtext><msub><mrow><mtext>H</mtext></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msub><mtext>C</mtext><msub><mrow><mtext>l</mtext></mrow><mrow><mn>3</mn></mrow></msub><mo>]</mo></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">cis- <math><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced close="]" open="[" separators="|"><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">B</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">cis- <math><mo>[</mo><mtext>PtC</mtext><msub><mrow><mtext>l</mtext></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mtext>N</mtext><msub><mrow><mtext>H</mtext></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></math></span> </div>

answer:
<div class="solution">Cis-platin is used as an anticancer unit in treatment of advanced bladder cancer, metastatic ovarian cancer, andmetastatic testicular cancer. Testicular, ovarian, bladder, head and neck, esophageal, small and non-small cell lung, breast, cervical, stomach and prostate cancers.</div>


tags: ['Chemistry', 'Practical Chemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P4.db
title:
which-of-the-following-halides-reacts-with-agno-3-aq-to-give-a-precipitate-that-dissolves-in-na-2-s-2-o-3-aq

slug:
which-of-the-following-halides-reacts-with-agno-3-aq-to-give-a-precipitate-that-dissolves-in-na-2-s-2-o-3-aq-37136

question:
<div class="question">Which of the following halides react(s) with $\mathrm{AgNO}_{3}(\mathrm{aq})$ to give a precipitate that dissolves in $\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(\mathrm{aq})$ ?</div>

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

answer:
<div class="solution">$\begin{array}{l}
<br/> <br/>\mathrm{HX}+\mathrm{AgNO}_{3} \longrightarrow \mathrm{AgX} \downarrow+\mathrm{HNO}_{3}(\mathrm{X}=\mathrm{Cl}, \mathrm{Br}, \mathrm{I}) \\
<br/> <br/>\mathrm{AgX}+2 \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} \longrightarrow \mathrm{Na}_{3}\left[\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}\right]+\mathrm{NaX}
<br/> <br/>\end{array}$</div>


title: which-of-the-following-molecules-in-pure-form-is-are-unstable-at-room-temperature
slug: which-of-the-following-molecules-in-pure-form-is-are-unstable-at-room-temperature-46617
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
answer: <div class="solution">(b) and (c) being antiaromatic, are unstable at room temperature.</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following molecules, in pure form, is (are) unstable at room temperature ?</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/jee_advanced/q_G7MXO8c1gTTHi4SSgtPquWGNRwoPGHWaNJ0Hkavdc.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/jee_advanced/TnMQXzV-4nBO0lG5drYsT9nm53VLR-ElBhP3CtBE_9E.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="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QpYAc1R_u96fs_-WRhJ7FV0NJiUexLwFGkAS3MXfDhM.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/elyCAV3Laj8Q_lUkQwso3U5cPCROSdt8W1PeMwfuyic.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/TnMQXzV-4nBO0lG5drYsT9nm53VLR-ElBhP3CtBE_9E.original.fullsize.png"/>, <img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QpYAc1R_u96fs_-WRhJ7FV0NJiUexLwFGkAS3MXfDhM.original.fullsize.png"/></span> </div>


title: which-of-the-following-pairs-is-not-correctly-matched
slug: which-of-the-following-pairs-is-not-correctly-matched-54815
question: <div class="question">Which of the following pairs is not correctly matched?</div>
tags: ['Biology', 'Digestion and Absorption', 'NEET']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Vitamin B3-Pellagra</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Vitamin B12-Pernicious anemia</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Vitamin C-Scurvy</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Vitamin B6-Beriberi</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Vitamin B6-Beriberi</span> </div>

answer:
<div class="solution">Vitamin B1 is also called thiamine<span style="white-space: pre;">. The d</span>eficiency causes beriberi. Symptoms of this disease of the nervous system include weight loss, emotional disturbances, Wernicke's encephalopathy (impaired sensory perception), weakness and pain in the limbs, periods of irregular heartbeat, and edema (swelling of bodily tissues).<br/><br/>Vitamin B3<span style="white-space:pre"> </span>is also called niacin. The<span style="white-space:pre"> d</span>eficiency, along with a deficiency of tryptophan causes pellagra. Symptoms include aggression, dermatitis, insomnia, weakness, mental confusion, and diarrhea. In advanced cases, pellagra may lead to dementia and death.<br/><br/>Vitamin C also called as ascorbic acid. The deficiency leads to a condition called scurvy and it is characterised by general weakness, anaemia, gingivitis (gum disease), and skin hemorrhages.<br/><br/>Vitamin B12<span style="white-space:pre"> is also known as </span>cobalamin. The<span style="white-space:pre"> d</span>eficiency results in macrocytic anemia, elevated homocysteine, peripheral neuropathy, memory loss, and other cognitive deficits. It is most likely to occur among elderly people, as absorption through the gut declines with age; the autoimmune disease pernicious anemia is another common cause. It can also cause symptoms of mania and psychosis. In rare extreme cases, paralysis can result.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P4.db
title:
which-of-the-following-reactants-on-reaction-with-conc-naoh-followed-by-acidification-gives-following-lactone-as-the

slug:
which-of-the-following-reactants-on-reaction-with-conc-naoh-followed-by-acidification-gives-following-lactone-as-the-13247

question:
<div class="question">Which of the following reactants on reaction with conc. $\mathrm{NaOH}$ followed by acidification gives following lactone as the<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/hFIUuuQhoOoSESiay5SP2om-L-EmxmEoV5XRY7OgMd0.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/9QEJjVaao_ODXnMLq-NbDu_hiNobnIpRr2AFWlNY3_E.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0be_OEXARO8cnZ0jmr4xLa5gaVty6MJTPQo0YnyS5Mw.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/uhD6edI0Yz-nrLKaB6K5a2dKGZjvRoWLDnVs4wOzOBQ.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/7GJIagcoHPNjp3bhAwaFkBDWBr9GAP8dgYdPx2hb_ac.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/uhD6edI0Yz-nrLKaB6K5a2dKGZjvRoWLDnVs4wOzOBQ.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fcSTR95uq9_Lgsv8MZQyYbU7Z40gfA4l9Jfacsr5G3E.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/xpJNaP9uXVg1uti1kjWTIKT7xQWuo6venAg_aAjscuU.original.fullsize.png"/><br/><br/>This compound on acidification to give a compound which have $-\mathrm{CH}_2 \mathrm{OH}$ and $-\mathrm{COOH}$ group, such groups on dehydration to give lactone.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FbAethDSj0BVdyEnSzK3q-mtcam9_7Z_adfRfG5Ra-g.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P4.db
title:
which-of-the-following-statement-is-correct-in-infinitely-long-wire-kept-perpendicular-to-the-paper-carrying-current-inwards-the-given-figure

slug:
which-of-the-following-statement-is-correct-in-infinitely-long-wire-kept-perpendicular-to-the-paper-carrying-current-inwards-the-given-figure-59519

question:
<div class="question">$$<br/>\text { Which of the following statement is correct in Infinitely long wire kept perpendicular }<br/>$$<br/>to the paper carrying current inwards the given figure?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SYLXFKpBfOd_SpVt4Ekr8sCl2_H1MJuM584PMrnE7yU.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>net force on the loop is zero<br/>, <br/>loop will rotate clockwise about axis $\mathrm{OO}^{\prime}$ when seen from $O$<br/></span> </div>

answer:
<div class="solution">$\mathbf{F}_{B A}=0$, because magnetic lines are parallel to this wire.<br/>$\mathbf{F}_{C D}=0$, because magnetic lines are antiparallel to this wire.<br/>$\mathbf{F}_{C B}$ is perpendicular to paper inwards and $\mathbf{F}_{A D}$ is perpendicular to paper outwards. These two forces (although calculated by integration) cancel each other but produce a torque which tend to rotate the loop in clockwise direction about an axis $O O^{\prime}$.</div>


title: which-of-the-following-statements-is-not-true-11
slug: which-of-the-following-statements-is-not-true-11-83364
question: <div class="question">Which of the following statements is not true?</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'AIIMS', 'AIIMS 2014']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The biodiversity decreases with increasing latitude.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The biodiversity decreases with increasing altitude.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The fishes show greatest biodiversity <br/>among vertebrates</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The biodiversity of bryophytes is greater <br/>than that of angiosperms.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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 biodiversity of bryophytes is greater <br/>than that of angiosperms.</span> </div>

answer:
<div class="solution">The biodiversity of bryophytes is less than that of angiosperms. Bryophytes are plants that can live in soil but are dependent on water for sexual reproduction.<br/>Angiosperms are much advanced plant species which consist of male sex organ (stamen) and female sex organ (pistil) borne in a flower.</div>


title: which-of-the-following-statements-isare-correct
slug: which-of-the-following-statements-isare-correct-22646
question: <div class="question">Which of the following statement(s) is/are correct?</div>
tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then the Gauss's law will still be valid<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>The Gauss's law can be used to calculate the field distribution around an electric dipole<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same<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="correct"> <span class="option-label">D</span> <span class="option-data"><br/>The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $\left(V_B-V_A\right)$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same<br/>, <br/>The work done by the external force in moving a unit positive charge from point $A$ at potential $V_A$ to point $B$ at potential $V_B$ is $\left(V_B-V_A\right)$</span> </div>

answer:
<div class="solution">If charges are of opposite signs, then the two fields are along the same direction. So, they cannot be zero. Hence, the charges should be of same sign.<br/>Therefore, option (c) is correct.<br/>Further, work done by external force = change in potential energy<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore \quad W_{A \rightarrow B}=q(\Delta V) \\<br/>&amp; =(+1)\left(V_B-V_A\right) \\<br/>&amp; \text { or } \quad W_{A \rightarrow B}=V_B-V_A \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Therefore, option (d) is also correct.<br/>$\therefore$ Correct options are (c) and (d).<br/>Analysis of Question<br/>(i) Question is simple.<br/>(ii) $W=\Delta U$ (by external force)<br/>If charge is just moved, without changing the kinetic energy. If nothing is mentioned in the question regarding the kinetic energy then we take $W=\Delta U$.</div>


title: which-of-the-given-statements-about-n-o-p-and-q-with-respect-to-m-is-are-correct
slug: which-of-the-given-statements-about-n-o-p-and-q-with-respect-to-m-is-are-correct-48451
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the given statement(s) about $\mathbf{N}, \mathbf{O}, \mathbf{P}$ and $\mathbf{Q}$ with respect to $\mathbf{M}$ is (are) correct?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SZDMS4f1Uiss5dxX0H5SIuyEDMhH2xcNxLMB-alL7ao.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\mathbf{M}$ and $\mathbf{N}$ are non-mirror image stereoisomers, $\mathbf{M}$ and $\mathbf{O}$ are identical, $\mathbf{M}$ and $\mathbf{P}$ are enantiomers</span> </div>

answer:
<div class="solution">The given conformation are of the following compound
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/BkNxOIAtxhe0FIUxcm3-iSohhglpAkYs5r8ywpE7uLM.original.fullsize.png"/><br/> <br/> <br/>Note : Fisher conformation always show the eclipsed form of molecule. Thus, we have to convert the given staggered conformation of 'O' to an eclipsed conformation.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/H1wE3LQDmoqiPus0uIrgTvx5VJLVxkBs1cKkYXYVYaM.original.fullsize.png"/><br/> <br/> <br/>Based on the above structures, we can say that
<br/> <br/>(a) $\mathrm{M}$ and $\mathrm{N}$ are diastereomers or non-mirror image stereoisomers.
<br/> <br/>(b) $\mathrm{M}$ and $\mathrm{O}$ are identical.
<br/> <br/>(c) $\mathrm{M}$ and $\mathrm{P}$ are enantiomers.
<br/> <br/>(d) $\mathrm{M}$ and $\mathrm{Q}$ are diastereomers and therefore not identical.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2022 (Paper 2)']
source_db: MarksBatch2_P4.db
title:
which-one-of-the-following-options-represents-the-magnetic-field-b-at-o-due-to-the-current-flowing-in-the-given-wire-segments-lying-on-the-x-y-plane

slug:
which-one-of-the-following-options-represents-the-magnetic-field-b-at-o-due-to-the-current-flowing-in-the-given-wire-segments-lying-on-the-x-y-plane-98296

question:
<div class="question"><p>Which one of the following options represents the magnetic field <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo>→</mo></mover></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> due to the current flowing in the given wire segments lying on the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi></math> plane?</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/315eac39-9614-4744-940b-a5694b59d1b9-1.jpg" style="width: 400px; height: 220px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo>→</mo></mover><mo>=</mo><mfrac><mrow><mo>-</mo><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><msqrt><mn>2</mn></msqrt><mi>π</mi></mrow></mfrac></mrow></mfenced><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo>→</mo></mover><mo>=</mo><mfrac><mrow><mo>-</mo><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt><mi>π</mi></mrow></mfrac></mrow></mfenced><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo>→</mo></mover><mo>=</mo><mfrac><mrow><mo>-</mo><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><msqrt><mn>2</mn></msqrt><mi>π</mi></mrow></mfrac></mrow></mfenced><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo>→</mo></mover><mo>=</mo><mfrac><mrow><mo>-</mo><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi></mrow></mfrac></mrow></mfenced><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>B</mi><mo>→</mo></mover><mo>=</mo><mfrac><mrow><mo>-</mo><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><msqrt><mn>2</mn></msqrt><mi>π</mi></mrow></mfrac></mrow></mfenced><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></math></span> </div>

answer:
<div class="solution"><blockquote><p><img alt="" src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/b3f41a6a-b29f-4091-9ea2-9307e3a3a657-1.jpg" style="width: 400px; height: 220px;"/></p><p>Magnetic field due to a straight wire will be zero if the line of the wire passes through the point of interest. Therefore, In the above figure,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mrow><mi>B</mi><mi>C</mi></mrow></msub><mo>+</mo><msub><mi>B</mi><mrow><mi>D</mi><mi>E</mi></mrow></msub><mo>+</mo><msub><mi>B</mi><mrow><mi>F</mi><mi>G</mi></mrow></msub><mo>=</mo><mn>0</mn></math></p><p>Therefore,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>B</mi><mo>→</mo></mover><mrow><mi>net</mi><mo> </mo></mrow></msub><mo>=</mo><msub><mover><mi>B</mi><mo>→</mo></mover><mrow><mi>A</mi><mi>B</mi></mrow></msub><mo>+</mo><msub><mover><mi>B</mi><mo>→</mo></mover><mrow><mi>C</mi><mi>D</mi><mo> </mo></mrow></msub><mo>+</mo><msub><mover><mi>B</mi><mo>→</mo></mover><mrow><mi>E</mi><mi>F</mi></mrow></msub></math></p><p>Magnetic field due to a finite wire is given by,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>4</mn><mi>π</mi><mi>d</mi></mrow></mfrac><mfenced><mrow><mi>sin</mi><mi>α</mi><mo>+</mo><mi>sin</mi><mi>β</mi></mrow></mfenced></math></p><p>Using above formula,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>B</mi><mo>→</mo></mover><mrow><mi>A</mi><mi>B</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>4</mn><mi>π</mi><mi>L</mi></mrow></mfrac><mo>×</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mfenced><mrow><mo>-</mo><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></mrow></mfenced></math></p><p>Magnetic field due to a circular arc is,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>2</mn><mi>R</mi></mrow></mfrac><mo>×</mo><mfrac><mi>θ</mi><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></math></p><p>Therefore,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>B</mi><mo>→</mo></mover><mrow><mi>C</mi><mi>D</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>4</mn><mfenced><mfrac><mi>L</mi><mn>2</mn></mfrac></mfenced></mrow></mfrac><mfenced><mrow><mo>-</mo><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>B</mi><mo>→</mo></mover><mrow><mi>E</mi><mi>F</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>8</mn><mo>×</mo><mfenced><mfrac><mi>L</mi><mn>4</mn></mfrac></mfenced></mrow></mfrac><mfenced><mrow><mo>-</mo><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></mrow></mfenced></math></p><p>Therefore, net magnetic field</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mover><mi>B</mi><mo>→</mo></mover><mi>net</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>4</mn><mi>π</mi><mo>×</mo><mi>L</mi></mrow></mfrac><mfenced><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac></mfenced><mo>+</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>4</mn><mfenced><mfrac><mi>L</mi><mn>2</mn></mfrac></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>8</mn><mo>×</mo><mfenced><mfrac><mi>L</mi><mn>4</mn></mfrac></mfenced></mrow></mfrac><mfenced><mrow><mo>-</mo><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mover><mi>B</mi><mo>→</mo></mover><mi>net</mi></msub><mo>=</mo><mfenced><mrow><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>2</mn><mi>L</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mrow><mn>4</mn><msqrt><mn>2</mn></msqrt><mi>π</mi><mi>L</mi></mrow></mfrac></mrow></mfenced><mfenced><mrow><mo>-</mo><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mover><mi>B</mi><mo>→</mo></mover><mi>net</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>I</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>4</mn><msqrt><mn>2</mn></msqrt><mi>π</mi></mrow></mfrac></mrow></mfenced><mfenced><mrow><mo>-</mo><mover><mi mathvariant="normal">k</mi><mo>^</mo></mover></mrow></mfenced></math></p></blockquote></div>


title: which-one-of-the-following-statement-is-wrong-in-the-context-of-xrays-generated-from-xray-tube
tags: ['Physics', 'Electromagnetic Waves', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P4.db
slug:
which-one-of-the-following-statement-is-wrong-in-the-context-of-xrays-generated-from-xray-tube-58472

question:
<div class="question">Which one of the following statement is WRONG in the context of X-rays generated from X-ray tube?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Cut-off wavelength of the continuous X-rays depends on the atomic number of the target<br/></span> </div>

answer:
<div class="solution">Cut-off wavelength depends on the applied voltage not on the atomic number of the target. Characteristic wavelengths depend on the atomic number of target.</div>


title: which-ordering-of-compounds-is-according-to-the-decreasing-order-of-the-oxidation-state-of-nitrogen
source_db: MarksBatch2_P4.db
slug:
which-ordering-of-compounds-is-according-to-the-decreasing-order-of-the-oxidation-state-of-nitrogen-41881

question:
<div class="question">Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{HNO}_{3}, \mathrm{NO}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{N}_{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{HNO}_{3}, \mathrm{NO}, \mathrm{N}_{2}, \mathrm{NH}_{4} \mathrm{Cl}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\mathrm{HNO}_{3}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{NO}, \mathrm{N}_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{NO}, \mathrm{HNO}_{3}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{N}_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{HNO}_{3}, \mathrm{NO}, \mathrm{N}_{2}, \mathrm{NH}_{4} \mathrm{Cl}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/5uMr3OWtv4gIlYFa331LZHI9LGHFboDuNrZkFwIydD8.original.fullsize.png"/></div>


title: why-does-ozone-hole-forms-over-antarctica-how-will-enhanced-ultraviolet-radiation-affect-us
slug: why-does-ozone-hole-forms-over-antarctica-how-will-enhanced-ultraviolet-radiation-affect-us-64909
tags: ['Biology', 'Environmental Issues']
options: None
correct_option: None
source_db: MarksBatch2_P4.db
question:
<div class="question">Why does ozone hole forms over Antarctica? How will enhanced ultraviolet radiation affect us?</div>

answer:
<div class="solution">A large amount of ODS (Ozone Depleting Sub-stances) like $\mathrm{CFCs}, \mathrm{N}_2 \mathrm{O}$, halons, $\mathrm{SO}_2, \mathrm{CH}_4, \mathrm{Cl}^{-}$are released by advanced countries like USA, Japan, European countries. These are released in stratosphere, drift towards poles and reach there before the coming of winter. During winter (temp. $85^{\circ} \mathrm{C}$ ) ice clouds are formed over Antarctica and no sunrise is received in polar areas. It catalyses release of $\mathrm{Cl}$ from CFCs. With the coming of spring season, $\mathrm{Cl}$ reacts with ozone in the presence of sunlight and converts $\mathrm{O}_3$ into $\mathrm{O}_2$ causing ozone depletion/thining of ozone shield in stratosphere called ozone hole. This hole disappears in summer due to free mixing of air of Antarctica with the rest of the global air.<br/>Effect of Enhanced UV Radiation. (i) Snow blindness or inflammation of cornea (ii) Damage of skin cells and development of skin cancer. (iii) Damage to nucleic acids and proteins. (iv) Reduced immunity (v) Higher number of cataracts in humans.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P4.db
title:
with-reference-to-the-scheme-given-below-which-of-the-given-statements-about-t-u-v-and-w-is-are-correct

slug:
with-reference-to-the-scheme-given-below-which-of-the-given-statements-about-t-u-v-and-w-is-are-correct-13132

question:
<div class="question">With reference to the scheme given below, which of the given statement(s) about $\mathrm{T}, \mathrm{U}, \mathrm{V}$ and $\mathrm{W}$ is (are) correct?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/YcEuYDm0VDjB3nm3oKWss0DYEArArPyi9uK2phG0688.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{T}$ is soluble in hot aqueous $\mathrm{NaOH}$</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">B</span> <span class="option-data">$\mathrm{U}$ is optically active</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Molecular formula of $\mathrm{W}$ is $\mathrm{C}_{10} \mathrm{H}_{18} \mathrm{O}_{4}$</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="correct"> <span class="option-label">D</span> <span class="option-data">V gives effervescence on treatment with aqueous $\mathrm{NaHCO}_{3}$.</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 answers are:
<span class="option-value">$\mathrm{T}$ is soluble in hot aqueous $\mathrm{NaOH}$, Molecular formula of $\mathrm{W}$ is $\mathrm{C}_{10} \mathrm{H}_{18} \mathrm{O}_{4}$, V gives effervescence on treatment with aqueous $\mathrm{NaHCO}_{3}$.</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/B4fLnn98z9ChszMBWHI9rnpchU7GH3h0pepdswTiRFo.original.fullsize.png"/></div>


title: with-respect-to-graphite-and-diamond-which-of-the-statements-given-below-is-are-correct
slug: with-respect-to-graphite-and-diamond-which-of-the-statements-given-below-is-are-correct-75753
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">With respect to graphite and diamond, which of the statement(s) given below is (are) correct?</div>

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

answer:
<div class="solution">(a) Diamond is harder than graphite.
<br/> <br/>(b) Graphite is good conductor of electricity as each carbon is attached to three C-atoms leaving one valency free, which is responsible for electrical conduction, while in diamond, all the four valencies of carbon are satisfied, hence insulator.
<br/> <br/>(c) Diamond is better thermal conductor than graphite. Whereas electrical conduction is due to availability of free electrons; thermal conduction is due to transfer of thermal vibrations from atom to atom. A compact and precisely aligned crystal like diamond thus facilitates fast movement of heat.
<br/> <br/>(d) In graphite, $\mathrm{C}-\mathrm{C}$ bond acquires double bond character, hence higher bond order than in diamond.</div>


