# questions

tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-standard-reduction-potentials-for-zn-2-zn-ni-2-ni-and-fe-2-fe-are-076-023-and-044-v-respectively-the-reaction-x-y-2-x-2-y-will-be-spontaneous-when-1

slug:
the-standard-reduction-potentials-for-zn-2-zn-ni-2-ni-and-fe-2-fe-are-076-023-and-044-v-respectively-the-reaction-x-y-2-x-2-y-will-be-spontaneous-when-1-72044

question:
<div class="question">The standard reduction potentials for $\mathrm{Zn}^{2+} / \mathrm{Zn}, \mathrm{Ni}^{2+} / \mathrm{Ni}$, and $\mathrm{Fe}^{2+} / \mathrm{Fe}$ are $-0.76,-0.23$ and $-0.44 \mathrm{~V}$ respectively. The reaction $\mathrm{X}+\mathrm{Y}^{2+} \rightarrow \mathrm{X}^{2+}+\mathrm{Y}$ will be spontaneous when:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$X=Z n, Y=N i$</span> </div>

answer:
<div class="solution">$\begin{aligned}<br/>&amp; \mathrm{Zn}+\mathrm{Fe}^{+2} \rightarrow \mathrm{Zn}^{+2}+\mathrm{Fe} \\<br/>&amp; \mathrm{Fe}+\mathrm{Ni}^{+2} \rightarrow \mathrm{Fe}^{2+}+\mathrm{Ni} \\<br/>&amp; \mathrm{Zn}+\mathrm{Ni}^{2+} \rightarrow \mathrm{Zn}^{+2}+\mathrm{Ni}<br/>\end{aligned}$<br/>All these are spontaneous</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main', 'JEE Main 2012 (Offline)']
source_db: MarksBatch2_P3.db
title:
the-standard-reduction-potentials-for-zn-2-zn-ni-2-ni-and-fe-2-fe-are-076-023-and-044-v-respectively-the-reaction-x-y-2-x-2-y-will-be-spontaneous-when

slug:
the-standard-reduction-potentials-for-zn-2-zn-ni-2-ni-and-fe-2-fe-are-076-023-and-044-v-respectively-the-reaction-x-y-2-x-2-y-will-be-spontaneous-when-42462

question:
<div class="question">The standard reduction potentials for $\mathrm{Zn}^{2+} / \mathrm{Zn}, \mathrm{Ni}^{2+} / \mathrm{Ni}$, and $\mathrm{Fe}^{2+} / \mathrm{Fe}$ are $-0.76,-0.23$ and $-0.44 \mathrm{~V}$ respectively. The reaction $\mathrm{X}+\mathrm{Y}^{2+} \rightarrow \mathrm{X}^{2+}+\mathrm{Y}$ will be spontaneous when:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$X=Z n, Y=N i$</span> </div>

answer:
<div class="solution">$\begin{aligned}<br/>&amp; \mathrm{Zn}+\mathrm{Fe}^{+2} \rightarrow \mathrm{Zn}^{+2}+\mathrm{Fe} \\<br/>&amp; \mathrm{Fe}+\mathrm{Ni}^{+2} \rightarrow \mathrm{Fe}^{2+}+\mathrm{Ni} \\<br/>&amp; \mathrm{Zn}+\mathrm{Ni}^{2+} \rightarrow \mathrm{Zn}^{+2}+\mathrm{Ni}<br/>\end{aligned}$<br/>All these are spontaneous</div>


tags: ['Chemistry', 'Electrochemistry', 'KVPY', 'KVPY 2015 (SB/SX)']
source_db: MarksBatch2_P3.db
title:
the-standard-reduction-potentials-in-v-of-a-few-metal-ionmetal-electrodes-are-given-below-the-reducing-strength-of-the-metals-follows-the-order

slug:
the-standard-reduction-potentials-in-v-of-a-few-metal-ionmetal-electrodes-are-given-below-the-reducing-strength-of-the-metals-follows-the-order-56777

question:
<div class="question">The standard reduction potentials (in V) of a few metal ion/metal electrodes are given below.<br/>The reducing strength of the metals follows the order.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Cr}&gt;\mathrm{Pb}&gt;\mathrm{Cu}&gt;\mathrm{Ag}$</span> </div>

answer:
<div class="solution">Which have low value of reduction potential is a good reducing agent.<br/>$$<br/>\mathrm{Cr}&gt;\mathrm{Pb}&gt;\mathrm{Cu}&gt;\mathrm{Ag}<br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'AP EAMCET', 'AP EAMCET 2006']
source_db: MarksBatch2_P3.db
title:
the-standard-reduction-potentials-of-zn-2-zn-cu-2-cu-and-ag-cu-and-ag-ag-are-respectively-076-034-and-08-v-the-following-cells-were-constructed-1-zn-z-1

slug:
the-standard-reduction-potentials-of-zn-2-zn-cu-2-cu-and-ag-cu-and-ag-ag-are-respectively-076-034-and-08-v-the-following-cells-were-constructed-1-zn-z-1-33670

question:
<div class="question">The standard reduction potentials of $\mathrm{Zn}^{2+}\left|\mathrm{Zn}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}$ and $\mathrm{Ag}^{+} \mid \mathrm{Cu}$ and $\mathrm{Ag}^{+} \mid \mathrm{Ag}$ are respectively $-0.76,0.34$ and $0.8 \mathrm{~V}$. The following cells were constructed :<br/>(1) $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Cu}^{2+}\right| \mathrm{Cu}$<br/>(2) $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag}$<br/>(3) $\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}$<br/>What is the correct order of $E_{\text {cell }}^{\circ}$ of these cells?</div>

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

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

answer:
<div class="solution">Given<br/>$\mathrm{Zn}^{2+} \longrightarrow \mathrm{Zn} \quad E^{\circ}=-0.78 \mathrm{~V}$<br/>$\mathrm{Cu}^{2+} \longrightarrow \mathrm{Cu} \quad E^{\circ}=0.34 \mathrm{~V}$<br/>$\mathrm{Ag}^{+} \longrightarrow \mathrm{Ag} \quad E^{\circ}=0.8 \mathrm{~V}$<br/>Cell reaction of (1) is<br/>$\mathrm{Zn}+\mathrm{Cu}^{2+} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Cu}$<br/>$E_{\text {cell }}^{\circ}=E_{\text {oxidation }}+E_{\text {reduction }}$<br/>$=+0.78+0.34$<br/>$=+1.12 \mathrm{~V}$<br/>Cell reaction of (2) is<br/>$\mathrm{Zn}+\mathrm{Ag}^{+} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Ag}$<br/>$E_{\text {cell }}^{\circ}=0.78+0.8$<br/>$=+1.58 \mathrm{~V}$<br/>Cell reaction of (3) is :<br/>$\mathrm{Cu}+\mathrm{Ag}^{+} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{Ag}$<br/>$E_{\text {cell }}^{\circ}=-0.34+0.8$<br/>$=+0.46$<br/>So, the correct order of $E_{\text {cell }}^{\circ}$ of these cell is -<br/>$\mathrm{b}&gt;\mathrm{a}&gt;\mathrm{c} .$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-standard-reduction-potentials-of-zn-2-zn-cu-2-cu-and-ag-cu-and-ag-ag-are-respectively-076-034-and-08-v-the-following-cells-were-constructed-1-zn-z-2

slug:
the-standard-reduction-potentials-of-zn-2-zn-cu-2-cu-and-ag-cu-and-ag-ag-are-respectively-076-034-and-08-v-the-following-cells-were-constructed-1-zn-z-2-96445

question:
<div class="question">The standard reduction potentials of $\mathrm{Zn}^{2+}\left|\mathrm{Zn}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}$ and $\mathrm{Ag}^{+} \mid \mathrm{Cu}$ and $\mathrm{Ag}^{+} \mid \mathrm{Ag}$ are respectively $-0.76,0.34$ and $0.8 \mathrm{~V}$. The following cells were constructed :<br/>(1) $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Cu}^{2+}\right| \mathrm{Cu}$<br/>(2) $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag}$<br/>(3) $\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}$<br/>What is the correct order of $E_{\text {cell }}^{\circ}$ of these cells?</div>

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

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

answer:
<div class="solution">Given<br/>$\mathrm{Zn}^{2+} \longrightarrow \mathrm{Zn} \quad E^{\circ}=-0.78 \mathrm{~V}$<br/>$\mathrm{Cu}^{2+} \longrightarrow \mathrm{Cu} \quad E^{\circ}=0.34 \mathrm{~V}$<br/>$\mathrm{Ag}^{+} \longrightarrow \mathrm{Ag} \quad E^{\circ}=0.8 \mathrm{~V}$<br/>Cell reaction of (1) is<br/>$\mathrm{Zn}+\mathrm{Cu}^{2+} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Cu}$<br/>$E_{\text {cell }}^{\circ}=E_{\text {oxidation }}+E_{\text {reduction }}$<br/>$=+0.78+0.34$<br/>$=+1.12 \mathrm{~V}$<br/>Cell reaction of (2) is<br/>$\mathrm{Zn}+\mathrm{Ag}^{+} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Ag}$<br/>$E_{\text {cell }}^{\circ}=0.78+0.8$<br/>$=+1.58 \mathrm{~V}$<br/>Cell reaction of (3) is :<br/>$\mathrm{Cu}+\mathrm{Ag}^{+} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{Ag}$<br/>$E_{\text {cell }}^{\circ}=-0.34+0.8$<br/>$=+0.46$<br/>So, the correct order of $E_{\text {cell }}^{\circ}$ of these cell is -<br/>$\mathrm{b}&gt;\mathrm{a}&gt;\mathrm{c} .$</div>


tags: ['Chemistry', 'Electrochemistry', 'TS EAMCET', 'TS EAMCET 2006']
source_db: MarksBatch2_P3.db
title:
the-standard-reduction-potentials-of-zn-2-zn-cu-2-cu-and-ag-cu-and-ag-ag-are-respectively-076-034-and-08-v-the-following-cells-were-constructed-1-zn-z

slug:
the-standard-reduction-potentials-of-zn-2-zn-cu-2-cu-and-ag-cu-and-ag-ag-are-respectively-076-034-and-08-v-the-following-cells-were-constructed-1-zn-z-84444

question:
<div class="question">The standard reduction potentials of $\mathrm{Zn}^{2+}\left|\mathrm{Zn}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}$ and $\mathrm{Ag}^{+} \mid \mathrm{Cu}$ and $\mathrm{Ag}^{+} \mid \mathrm{Ag}$ are respectively $-0.76,0.34$ and $0.8 \mathrm{~V}$. The following cells were constructed :<br/>(1) $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Cu}^{2+}\right| \mathrm{Cu}$<br/>(2) $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag}$<br/>(3) $\mathrm{Cu}\left|\mathrm{Cu}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag}$<br/>What is the correct order of $E_{\text {cell }}^{\circ}$ of these cells?</div>

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

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

answer:
<div class="solution">Given<br/>$\mathrm{Zn}^{2+} \longrightarrow \mathrm{Zn} \quad E^{\circ}=-0.78 \mathrm{~V}$<br/>$\mathrm{Cu}^{2+} \longrightarrow \mathrm{Cu} \quad E^{\circ}=0.34 \mathrm{~V}$<br/>$\mathrm{Ag}^{+} \longrightarrow \mathrm{Ag} \quad E^{\circ}=0.8 \mathrm{~V}$<br/>Cell reaction of (1) is<br/>$\mathrm{Zn}+\mathrm{Cu}^{2+} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Cu}$<br/>$E_{\text {cell }}^{\circ}=E_{\text {oxidation }}+E_{\text {reduction }}$<br/>$=+0.78+0.34$<br/>$=+1.12 \mathrm{~V}$<br/>Cell reaction of (2) is<br/>$\mathrm{Zn}+\mathrm{Ag}^{+} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Ag}$<br/>$E_{\text {cell }}^{\circ}=0.78+0.8$<br/>$=+1.58 \mathrm{~V}$<br/>Cell reaction of (3) is :<br/>$\mathrm{Cu}+\mathrm{Ag}^{+} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{Ag}$<br/>$E_{\text {cell }}^{\circ}=-0.34+0.8$<br/>$=+0.46$<br/>So, the correct order of $E_{\text {cell }}^{\circ}$ of these cell is -<br/>$\mathrm{b}&gt;\mathrm{a}&gt;\mathrm{c} .$</div>


tags: ['Chemistry', 'Electrochemistry', 'COMEDK', 'COMEDK 2013']
source_db: MarksBatch2_P3.db
title:
the-standard-reduction-potentials-of-zn-and-ag-in-water-at-298-k-are-zn-2-2-e-zn-and-ag-e-ag-e-076-v-e-080-v-which-of-the-following-reactions-take-pla

slug:
the-standard-reduction-potentials-of-zn-and-ag-in-water-at-298-k-are-zn-2-2-e-zn-and-ag-e-ag-e-076-v-e-080-v-which-of-the-following-reactions-take-pla-92518

question:
<div class="question">The standard reduction potentials of $\mathrm{Zn}$ and $\mathrm{Ag}$ in water at $298 \mathrm{~K}$ are,<br/>$\begin{aligned}<br/>\mathrm{Zn}^{2+}+2 e^{-} \rightleftharpoons \mathrm{Zn}, &amp; E^{\circ}=-0.76 \mathrm{~V} \\<br/>\text { and } \quad \mathrm{Ag}^{+}+e^{-} \rightleftharpoons \mathrm{Ag} ; &amp; E^{\circ}=+0.80 \mathrm{~V}.<br/>\end{aligned}$<br/>Which of the following reactions take place?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Zn}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+2 \mathrm{Ag}(s)$</span> </div>

answer:
<div class="solution">For reaction to be spontaneous, $E_{\text {cell }}^{\circ}&gt;0$<br/>For option (b),<br/>$$<br/>\begin{aligned}<br/>E_{\text {cell }}^{o} &amp;=\left(E_{\text {red }}^{0}\right)_{\text {Cathode }}-\left(E_{\text {red }}^{0}\right)_{\text {Anode }} \\<br/>&amp;=0.80-(-0.76)=156 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/>$\therefore$ It will be spontaneous reaction<br/>$$<br/>\because E_{\text {cell }}^{a}&gt;0 \text {. }<br/>$$</div>


title: the-standard-temperature-used-in-thermo-chemical-calculations-is
slug: the-standard-temperature-used-in-thermo-chemical-calculations-is-66800
question: <div class="question">The standard temperature used in thermo chemical calculations is</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'COMEDK', 'COMEDK 2019']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$273 \mathrm{~K}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$298 \mathrm{~K}$</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><li class=""> <span class="option-label">C</span> <span class="option-data">$297 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$303 \mathrm{~K}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$298 \mathrm{~K}$</span> </div>

answer:
<div class="solution">The standard temperature used in thermo chemical calculation is $25^{\circ} \mathrm{C}$ or $298 \mathrm{~K}$<br/>$$<br/>K=T+273=25+273=298 \mathrm{~K}<br/>$$</div>


tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-steps-involved-in-spermatogenesis-are-given-below-arrange-them-in-proper-sequence-and-select-the-correct-option-a-primary-spermatocytes-undergo-th

slug:
the-steps-involved-in-spermatogenesis-are-given-below-arrange-them-in-proper-sequence-and-select-the-correct-option-a-primary-spermatocytes-undergo-th-56312

question:
<div class="question">The steps involved in spermatogenesis are given below. Arrange them in proper sequence and select the correct option.<br/> <br/>
A. Primary spermatocytes undergo the first meiotic division.<br/>
B. Spermatogonia multiply by mitotic division.<br/>
C. Transformation of spermatids into sperms.<br/>
D. Secondary spermatocytes undergo the second meiotic division.<br/>
E. Release of sperms from the seminiferous tubules.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">B, A, D, C, E</span> </div>

answer:
<div class="solution">The process of spermatogenesis is as follows:<br/><br/><math><mn>1</mn><mo>.</mo></math> Spermatogonia present in seminiferous tubules multiply by mitotic division and increase in numbers.<br/><br/><math><mn>2</mn><mo>.</mo></math> Few spermatogonia called 'primary spermatocytes' undergo meiotic division to form two equal 'secondary spermatocytes'.<br/><br/><math><mn>3</mn><mo>.</mo></math> Secondary spermatocytes undergo meiotic division to form four haploid spermatids.<br/><br/><math><mn>4</mn><mo>.</mo></math> Spermatids are transformed into sperms by the process of spermiogenesis.<br/><br/><math><mn>5</mn><mo>.</mo></math> Sperms are released from the seminiferous tubules by the process of spermiation.</div>


title: the-straight-line-2-x-3-3-y-4-4-z-5-is-parallel-to-which-one-of-the-following
slug: the-straight-line-2-x-3-3-y-4-4-z-5-is-parallel-to-which-one-of-the-following-87863
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The straight line $\frac{\mathrm{x}-3}{2}=\frac{\mathrm{y}-4}{3}=\frac{\mathrm{z}-5}{4}$ is parallel to which<br/>one of the following ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 x+4 y-5 z=0$</span> </div>

answer:
<div class="solution">A plane ax $+$ by $+\mathrm{cz}=0$ is parallel to, a straight line having direction ratios $\mathrm{a}^{\prime}, \mathrm{b}^{\prime}, \mathrm{c}^{\prime}$.<br/>If $a a^{\prime}+b b^{\prime}+c c^{\prime}=0$<br/>In the given problem, $\mathrm{dr}_{\mathrm{s}}$ of line is $2,3,4$. We check the equations of plane in the given choices, one by one.<br/>(a) $4 \times 2+3 \times 3+(-5) \times 4=8+9-20 \neq 0$<br/>(b) $4 \times 2+5 \times 3+(-4) \times 4=8+15-16 \neq 0$<br/>(c) $4 \times 2+4 \times 3+(-5) \times 4=8+12-20=0$<br/>Further checking is not needed</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-straight-line-a-x-b-y-c-0-and-the-coordinate-axes-form-an-isosceles-triangle-under-which-one-of-the-following-conditions

slug:
the-straight-line-a-x-b-y-c-0-and-the-coordinate-axes-form-an-isosceles-triangle-under-which-one-of-the-following-conditions-52028

question:
<div class="question">The straight line $a x+b y+c=0$ and the coordinate axes form an isosceles triangle under which one of the following conditions?</div>

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

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

answer:
<div class="solution">Co-ordinate axes and straight line ax $+$ by $+c=0$ form an isosceles triangle. This is possible when, the line makes equal intercept on both the axes.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/SDuz_XKlpLxZt79XP61eZZvmqnAgYiDnpgtW4SxjRB8.original.fullsize.png"/><br/><br/>Expressing $a x+b y+c=0$ in intercept form:<br/>$a x+b y=-c$ or $\frac{x}{-\frac{c}{a}}+\frac{y}{-\frac{c}{b}}=1$<br/>So, $x$ -inntercept $=-\frac{\mathrm{c}}{\mathrm{a}}$ and $\mathrm{y}$ -intercept $=-\frac{\mathrm{c}}{\mathrm{b}}$<br/>Since, $-\frac{c}{a}=-\frac{c}{b}$<br/>Hence, $\mathrm{a}=\mathrm{b}$<br/>Intercepts can be on both the sides of axis. So, $|\mathrm{a}|=|\mathrm{b}|$</div>


title: the-straight-lines-x-y-4-0-3-x-y-4-0-and-x-3-y-4-0-form-a-triangle-which-is
slug: the-straight-lines-x-y-4-0-3-x-y-4-0-and-x-3-y-4-0-form-a-triangle-which-is-87527
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The straight lines $\mathrm{x}+\mathrm{y}-4=0,3 \mathrm{x}+\mathrm{y}-4=0$ and $\mathrm{x}+3 \mathrm{y}-4$<br/>$=0$ form a triangle, which is</div>

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

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

answer:
<div class="solution">Given lines: $\mathrm{L}_{1} \equiv \mathrm{x}+\mathrm{y}-4=0$<br/>$\mathrm{L}_{2} \equiv 3 \mathrm{x}+\mathrm{y}-4=0$<br/>$L_{3} \equiv x+3 y-4=0$<br/>Slope of $L_{1}=m_{1}=\frac{-1}{1}=-1$<br/>Slope of $L_{2}=m_{2}=\frac{-3}{1}=-3$<br/>Slope of $L_{3}=m_{3}=\frac{-1}{3}$<br/>Angle between $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$ $\Rightarrow \tan \theta_{1}=\left|\frac{-1-(-3)}{1+(-1)(-3)}\right|=\frac{-1+3}{1+3}=\frac{1}{2}$<br/>Angle between $\mathrm{L}_{2}$ and $\mathrm{L}_{3}$<br/>$\Rightarrow \tan \theta_{3}=\left|\frac{-1-\left(\frac{-1}{3}\right)}{1+(-1)\left(\frac{-1}{3}\right)}\right|=\left|\frac{-3+1}{3+1}\right|=\frac{1}{2}$<br/>The triangle formed is an isosceles triangle.</div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Main', 'JEE Main 2020 (08 Jan Shift 1)']
source_db: MarksBatch2_P3.db
title:
the-strength-of-an-aqueous-n-a-o-h-solution-is-most-accurately-determined-by-titrating-note-consider-that-an-appropriate-indicator-is-used

slug:
the-strength-of-an-aqueous-n-a-o-h-solution-is-most-accurately-determined-by-titrating-note-consider-that-an-appropriate-indicator-is-used-69558

question:
<div class="question">The strength of an aqueous <math><mi mathvariant="normal">N</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi></math> solution is most accurately determined by titrating: (Note: consider that an appropriate indicator is used)</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mi mathvariant="normal">A</mi><mi mathvariant="normal">q</mi><mo>.</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi></math> in a burette and aqueous oxalic acid in a conical flask</span> </div>

answer:
<div class="solution"><p>Oxalic acid is a primary standard solution while H2SO4 is a secondary standard solution.</p><p>Titration is a common laboratory method of quantitative chemical analysis to determine the concentration of an identified analyte. A reagent, termed the titrant or titrator, is prepared as a standard solution of known concentration and volume.</p></div>


title: the-strongest-force-among-the-following-forces-in-nature-is
slug: the-strongest-force-among-the-following-forces-in-nature-is-89556
question: <div class="question">The strongest force among the following forces in nature is</div>
tags: ['Physics', 'Laws of Motion', 'TS EAMCET', 'TS EAMCET 2021 (06 Aug Shift 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">electromagnetic force</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">weak nuclear force</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">gravitational force</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">strong nuclear force</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">According to the fundamental forces in nature, the increasing order of strength of forces is given by<br/>Gravitational force $ &lt; $ Electromagnetic force $ &lt; $ Weak nuclear force $ &lt; $ Strong nuclear force.<br/>Hence, the 'strong nuclear force' is the strongest force in nature.</div>


title: the-structural-feature-which-distinguishes-proline-from-natural-amino-acids-1
slug: the-structural-feature-which-distinguishes-proline-from-natural-amino-acids-1-15739
tags: ['Chemistry', 'Biomolecules', 'JEE Main']
source_db: MarksBatch2_P3.db
question:
<div class="question">The structural feature which distinguishes proline from natural $\alpha$ -amino acids?</div>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/EVjiw_wywOmLBIoma9hdXxh2tjN1bH_um9XjbEc5cT4.original.fullsize.png"/></div>


title: the-structure-of-functional-grouv-of-secondary-amide-is
slug: the-structure-of-functional-grouv-of-secondary-amide-is-91009
question: <div class="question">The structure of functional grouv of secondary amide is:</div>
tags: ['Chemistry', 'General Organic Chemistry', 'MHT CET', 'MHT CET 2023 (10 May Shift 1)']
answer: <div class="solution">Std.11|Ch-14|Subtopic-14.3</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-\mathrm{NH}-$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/Q8lkmtS69Dg0vtRhN19jN_7bGXKF1UiOIpTXE9YbG3E.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/D6kjbAvU5zpf3mU19JKmj-Dh-t6NTZz_Ez5Tr9ohBkE.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"><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/mhDv2xWliunU8SrqmT4CUTd1Tu-iPSZl_hR3Isn6ubI.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/D6kjbAvU5zpf3mU19JKmj-Dh-t6NTZz_Ez5Tr9ohBkE.original.fullsize.png"/><br/></span> </div>


title: the-structure-of-isobutyl-group-in-an-organic-compound-is
slug: the-structure-of-isobutyl-group-in-an-organic-compound-is-49141
question: <div class="question">The structure of isobutyl group in an organic compound is</div>
tags: ['Chemistry', 'Hydrocarbons', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>-</mo><mover><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi></mrow><mrow><mo>|</mo></mrow></mover><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">C</mi><mo>-</mo></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><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> </ul>

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

answer:
<div class="solution"><img alt="N14new1.PNG" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/d8fc58a0-ba01-4a99-ad0f-2a89b8f7a686.png" style="width:1.37708in;height:0.78333in"/> <br/><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>-</mo><mover><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi></mrow><mrow><mo>|</mo></mrow></mover><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub></math> (Secondary butyl) <br/><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>-</mo></math> (Normal butyl) <br/><math><mo>(</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">C</mi><mo>-</mo></math> (Tertiary butyl)</div>


title: the-structure-of-protein-that-is-unaffected-by-heating-is
slug: the-structure-of-protein-that-is-unaffected-by-heating-is-23936
question: <div class="question">The structure of protein that is unaffected by heating is :</div>
tags: ['Chemistry', 'Biomolecules', 'JEE Main', 'JEE Main 2022 (29 Jun Shift 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">secondary structure</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">tertiary structure</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">primary structure</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Quaternary structure</span> </li> </ul>

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

answer:
<div class="solution"><p>Primary structure of proteins: Proteins may have one or more polypeptide chains. Each polypeptide in a protein has amino acids linked with each other in a specific sequence and it is this sequence of amino acids that is said to be the primary structure of that protein.</p><p>Secondary structure of proteins: The secondary structure of protein refers to the shape in which a long polypeptide chain can exist.</p><p>Tertiary structure of proteins: The tertiary structure of proteins represents overall folding of the polypeptide chains i.e., further folding of the secondary structure.</p><p>Quaternary structure of proteins: Some proteins are composed of two or more polypeptide chains referred to as subunits. The spatial arrangement of these subunits with respect to each other is known as quaternary structure.</p><p>During denaturation Quaternary, secondary and tertiary structures are destroyed, but primary structure remains intact.</p></div>


title: the-structure-of-the-protein-that-is-absolutely-necessary-for-its-biological-activity-is
slug: the-structure-of-the-protein-that-is-absolutely-necessary-for-its-biological-activity-is-10319
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The structure of the protein that is absolutely necessary for its biological activity is</div>

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

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

answer:
<div class="solution">In tertiary structure, the polypeptide chain having secondary structure is twisted and folded to produce a stable, three dimensional structure, which may be maintained by three types of bonds e.g. ionic bond, hydrogen bond and disulphide bond. In a large protein like hemoglobin, or in the case of an enzyme, the molecule undergoes further folding and coiling to attain functional conformation and is termed as the tertiary structure. The coils and folds of the protein molecule are so arranged as to hide non-polar amino acid side chains inside and expose the polar side chains and is absolutely necessary for many biological activity. Quaternary structure is most complex structure.</div>


tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-structure-shown-below-is-made-up-of-two-strands-of-long-chains-of-amino-acids-what-does-it-depict

slug:
the-structure-shown-below-is-made-up-of-two-strands-of-long-chains-of-amino-acids-what-does-it-depict-10063

question:
<div class="question">The structure shown below is made up of two strands of long chains of amino acids.<br/> <br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/45_qie_biocaa23.jpeg" style="max-width:100%; object-fit:contain"/><br/> <br/>
What does it depict?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary structure with Î²-pleated sheet</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Tertiary structure with amino acid chains</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Secondary structure with Î²-conformation</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Quaternary structure with Î²-pleated sheet</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Secondary structure with Î²-conformation</span> </div>

answer:
<div class="solution">The given figure depicts a secondary structure with beta confirmation. It represents the manner in which the regions of the protein threads, apart from the helix are folded onto each other. <br/><br/>Tertiary structure is the structure which represents how a long chain protein thread is folded upon itself.<br/><br/>Primary structure is the structure which represents the position of amino acids.<br/><br/>Quaternary structure is the structure which represents how the individual folded polypeptides and subunits are arranged.</div>


title: the-structure-which-holds-the-leaf-blades-and-helps-to-flutter-in-wind-known-as-a
slug: the-structure-which-holds-the-leaf-blades-and-helps-to-flutter-in-wind-known-as-a-14132
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The structure which holds the leaf blades and helps to flutter in wind known as a __________</div>

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

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

answer:
<div class="solution">The petiole is a long thin flexible structure that holds leaf blades and flutter in wind. Sometimes petiole becomes tendril and leaf-like. A stipule is a small leaflike appendage to a leaf, typically borne in pairs at the base of the leaf stalk. Lamina is the leaf blade. The swollen leaf base is known as pulvinus.</div>


title: the-structures-present-in-the-roots-to-absorb-water-and-minerals-is
slug: the-structures-present-in-the-roots-to-absorb-water-and-minerals-is-76259
question: <div class="question">The structures present in the roots to absorb water and minerals is</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'JIPMER', 'JIPMER 2013']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">epidermal extensions</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">hypodermis</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">endodermis</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">epidermal appendages</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">epidermal appendages</span> </div>

answer:
<div class="solution">Epidermal extensions are always unicellular, while epidermal appendages may be uni or multicellular. Root hairs are epidermal extensions formed by outward elongated bulging of wall of epidermal cells.</div>


title: the-structures-that-help-some-bacteria-to-attach-to-rocks-andor-host-tissue-are-1
slug: the-structures-that-help-some-bacteria-to-attach-to-rocks-andor-host-tissue-are-1-57551
tags: ['Biology', 'Cell - The Unit of Life', 'NEET', 'NEET 2015 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The structures that help some bacteria to attach to rocks and/or host tissue are:</div>

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

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

answer:
<div class="solution">Fimbriae: Hollow tubular surface appendages are present in the bacterial cells, which help in an attachment to rocks and/or host tissues.</div>


title: the-structures-that-help-some-bacteria-to-attach-to-rocks-andor-host-tissue-are
slug: the-structures-that-help-some-bacteria-to-attach-to-rocks-andor-host-tissue-are-19041
tags: ['Biology', 'Cell - The Unit of Life', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The structures that help some bacteria to attach to rocks and/or host tissue are</div>

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

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

answer:
<div class="solution">Fimbriae: Hollow tubular surface appendages, present in the bacterial cells, which help in an attachment to rocks and/or host tissues.</div>


title: the-study-of-mutations-is-easy-in-haploids-as-compared-to-diploids-because
slug: the-study-of-mutations-is-easy-in-haploids-as-compared-to-diploids-because-74230
tags: ['Biology', 'Strategies for Enhancement in Food Production', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The study of mutations is easy in haploids as compared to diploids, because</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">All mutations, whether dominant or recessive are expressed in haploids</span> </div>

answer:
<div class="solution">Haploids are the cells which have only one set of the chromosome or can say one of the pair of the alleles of gene. Since haploids are not having the whole pair of allele, thus its allele is not influenced or affected by the counterpart. All allele types gets expressed in a haploid. It is the choice of cell for studying mutations as even the recessive allele will get expressed and not just only the dominant type since the recessive allele is singular and not in pair.</div>


tags: ['Biology', 'Human Reproduction', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">LH</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sudden-increase-in-which-of-the-following-hormone-is-directly-responsible-for-the-release-of-ovum-from-the-graafian-follicle

slug:
the-sudden-increase-in-which-of-the-following-hormone-is-directly-responsible-for-the-release-of-ovum-from-the-graafian-follicle-14537

question:
<div class="question">The sudden increase in which of the following hormone is directly responsible for the release of ovum from the Graafian follicle?</div>

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

answer:
<div class="solution">Luteinising hormone is secreted by the anterior pituitary. It increases suddenly in the middle of the menstrual cycle. This is called LH surge. It stimulates the membrane granulosa cells of the Graafian follicle to release more liquor folliculi. This causes the pressure inside the follicle to increase causing it to rupture. The ovum in the secondary oocycte stage is released along with some follicular cells. This is called ovulation</div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2012 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1 only</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sum-and-product-of-matrices-a-and-b-exist-which-of-the-following-implications-are-necessarily-true-1-a-and-b-are-square-matrices-of-same-order-2-a

slug:
the-sum-and-product-of-matrices-a-and-b-exist-which-of-the-following-implications-are-necessarily-true-1-a-and-b-are-square-matrices-of-same-order-2-a-72202

question:
<div class="question">The sum and product of matrices $\mathrm{A}$ and $\mathrm{B}$ exist. Which of the following implications are necessarily true?<br/>$1.$ $\mathrm{A}$ and $\mathrm{B}$ are square matrices of same order.<br/>$2.$ A and B are non-singular matrices <br/>Select the correct answer using the code given below:</div>

answer:
<div class="solution">(1) Since sum of matrices exist therefore $\mathrm{A}$ and $\mathrm{B}$ are square matrices of same order.<br/>(2) Non-singularity of A and B does not depend on sum and product of $\mathrm{A}$ and $\mathrm{B}$.</div>


tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
the-sum-and-sum-of-the-squares-corresponding-to-length-x-incm-and-weight-y-in-gm-of-50-plant-products-are-given-below-i-1-50-x-i-212-i-1-50-x-i-2-9028

slug:
the-sum-and-sum-of-the-squares-corresponding-to-length-x-incm-and-weight-y-in-gm-of-50-plant-products-are-given-below-i-1-50-x-i-212-i-1-50-x-i-2-9028-56157

question:
<div class="question">The sum and sum of the squares corresponding to length $x$ in(cm) and weight $y$ (in gm) of 50 plant products are given below;<br/>$\begin{aligned}<br/>&amp;\sum_{i=1}^{50} x_i=212, \sum_{i=1}^{50} x_i^2=902.8, \sum_{i=1}^{50} y_i=261 \\<br/>&amp;\sum_{i=1}^{50} y_i^2=1457.6<br/>\end{aligned}$<br/>Which is more varying, the length or weight?</div>

answer:
<div class="solution">For length<br/>$\mathrm{N}=50, \sum_{i=1}^{50} x_i=212, \sum_{i=1}^{50} x_i^2=902.8$<br/>$\bar{x}=\frac{\sum x_i}{N}=\frac{212}{50}=4.24$<br/>Standard deviation $=\sigma$<br/>$=\frac{1}{N}\left[N \sum x_i^2-\left(\sum x_i\right)^2\right]$<br/>$=\frac{1}{50} \sqrt{50 \times 902.8-(212)^2}$<br/>$=\frac{\sqrt{196}}{50}=\frac{14}{50}=0.28$<br/>Coefficients of variation $=\frac{\sigma}{\bar{x}} \times 100$<br/>$=\frac{0.28}{4.24} \times 100=6.6$<br/>For weight, $\mathrm{N}=50, \sum_{i=1}^{50} y_i=261, \sum_{i=1}^{50} y_i^2=1457.6$<br/>Mean $\bar{x}=\frac{\sum y_i}{N}=\frac{261}{50}=5.22 \mathrm{gm}$.<br/>Standard deviation, $\sigma$<br/>$\begin{aligned}<br/>&amp;=\frac{1}{N} \sqrt{N \sum y_i^2-\left(\sum y_i\right)^2} \\<br/>&amp;=\frac{1}{50} \sqrt{50 \times 1457.6-(261)^2}=\frac{\sqrt{4759}}{50}=1.38 \\<br/>&amp;\therefore \text { Coefficients of variation }(\text { C.V })=\frac{\sigma}{\overline{\mathrm{x}}} \times 100 \\<br/>&amp;=\frac{1.38}{5.22} \times 100=26.4<br/>\end{aligned}$<br/>Coefficients of variation of weights is more than that of length<br/>$\therefore$ Weight is more varying than length.</div>


title: the-sum-of-10-values-is-12-and-the-sum-of-their-squares-is-169-then-their-standard-deviation-s-d-is
tags: ['Mathematics', 'Statistics', 'MHT CET', 'MHT CET 2022 (10 Aug Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$0.5$</span> </div>
source_db: MarksBatch2_P3.db
slug:
the-sum-of-10-values-is-12-and-the-sum-of-their-squares-is-169-then-their-standard-deviation-s-d-is-87336

question:
<div class="question">The sum of 10 values is 12 and the sum of their squares is 16.9 , then their standard deviation $(S, D)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.05$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.5$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.005$</span> </li> </ul>

answer:
<div class="solution">Given $\sum x=12, \sum x^2=16.9$ and $n=10$<br/>$$<br/>\begin{aligned}<br/>&amp; \because \text { S.D. }=\sqrt{\frac{\sum x^2}{n}-\left(\frac{\sum x}{n}\right)^2}=\sqrt{\frac{16.9}{10}-\left(\frac{12}{10}\right)^2} \\<br/>&amp; =\sqrt{\frac{169-144}{100}}=\frac{5}{10}=0.5<br/>\end{aligned}<br/>$$</div>


title: the-sum-of-all-real-roots-of-the-equation-x-3-2-x-3-2-0-is
slug: the-sum-of-all-real-roots-of-the-equation-x-3-2-x-3-2-0-is-19021
question: <div class="question">The sum of all real roots of the equation $|x-3|^{2}+$ $|x-3|-2=0$ is</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2017 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">$|x-3|^{2}+|x-3|-2=0$<br/>Let $|x-3|=t$<br/>$\therefore \mathrm{t}^{2}+\mathrm{t}-2=0 \Rightarrow \mathrm{t}^{2}+2 \mathrm{t}-\mathrm{t}-2=0$<br/>$\Rightarrow \mathrm{t}(\mathrm{t}+2)-1(\mathrm{t}+2)=0$<br/>$\Rightarrow(\mathrm{t}+2)(\mathrm{t}-1)=0$<br/>$\Rightarrow \mathrm{t}=-2$ or $\mathrm{t}=1$<br/>Since tis modulus of a number, it cannot be negative. $\therefore \mathrm{t}=1 \Rightarrow|\mathrm{x}-3|=1 \Rightarrow \mathrm{x}-3=1$ or $\mathrm{x}-3=-1$<br/>$\Rightarrow \mathrm{x}=4$ or 2<br/>Sum of roots $=4+2=6$</div>


title: the-sum-of-all-the-twodigit-odd-numbers-is
slug: the-sum-of-all-the-twodigit-odd-numbers-is-78543
question: <div class="question">The sum of all the two-digit odd numbers is</div>
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2475</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2475</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">2530</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4905</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5049</span> </li> </ul>

answer:
<div class="solution">Sum of odd numbers $=\mathrm{n}^{2}$ <br/>Two-digit odd numbers are from $11-99$. <br/>Number of odd numbers from 1 to $99=50$ <br/>Sum of odd numbers from 1 to $99=50^{2}=2500$ <br/>Number of odd numbers from $1+9=5$ <br/>Sum of odd numbers from 1 to $9=5^{2}=25$ <br/>So, Sum of all two digit odd numbers <br/>$=2500-25=2475 .$</div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">70</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sum-of-all-values-of-r-in-leftbeginarrayc-18-r2-endarrayright2leftbeginarrayc-18-r1-endarrayrightleftbeginarrayc-18-r-endarrayright-geqleftbeginar

slug:
the-sum-of-all-values-of-r-in-leftbeginarrayc-18-r2-endarrayright2leftbeginarrayc-18-r1-endarrayrightleftbeginarrayc-18-r-endarrayright-geqleftbeginar-98694

question:
<div class="question">The sum of all values of \( r \) in<br/>\[<br/>\left(\begin{array}{c}<br/>18 \\<br/>r-2<br/>\end{array}\right)+2\left(\begin{array}{c}<br/>18 \\<br/>r-1<br/>\end{array}\right)+\left(\begin{array}{c}<br/>18 \\<br/>r<br/>\end{array}\right) \geq\left(\begin{array}{c}<br/>20 \\<br/>13<br/>\end{array}\right) \text { must be }<br/>\]</div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>18</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mn>2</mn><mfenced><mtable><mtr><mtd><mn>18</mn></mtd></mtr><mtr><mtd><mi>r</mi><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>+</mo><mfenced><mtable><mtr><mtd><mn>18</mn></mtd></mtr><mtr><mtd><mi>r</mi></mtd></mtr></mtable></mfenced><mo>≥</mo><mfenced><mtable><mtr><mtd><mn>20</mn></mtd></mtr><mtr><mtd><mn>13</mn></mtd></mtr></mtable></mfenced></math> it means that</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>C</mi><mrow><mi>r</mi><mo>-</mo><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>18</mn></mmultiscripts><mo>+</mo><mn>2</mn><mmultiscripts><mi>C</mi><mrow><mi>r</mi><mo>-</mo><mn>1</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>18</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mi>r</mi><none></none><mprescripts></mprescripts><none></none><mn>18</mn></mmultiscripts><mo>≥</mo><mmultiscripts><mi>C</mi><mn>13</mn><none></none><mprescripts></mprescripts><none></none><mn>20</mn></mmultiscripts></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfenced><mrow><mmultiscripts><mi>C</mi><mrow><mi>r</mi><mo>-</mo><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>18</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mrow><mi>r</mi><mo>-</mo><mn>1</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>18</mn></mmultiscripts></mrow></mfenced><mo>+</mo><mfenced><mrow><mmultiscripts><mi>C</mi><mrow><mi>r</mi><mo>-</mo><mn>1</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>18</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mprescripts></mprescripts><none></none><mn>18</mn></mmultiscripts><mi>r</mi></mrow></mfenced><mo>≥</mo><mmultiscripts><mi>C</mi><mn>13</mn><none></none><mprescripts></mprescripts><none></none><mn>20</mn></mmultiscripts></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mmultiscripts><mi>C</mi><mrow><mi>r</mi><mo>-</mo><mn>1</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>19</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mi>r</mi><none></none><mprescripts></mprescripts><none></none><mn>19</mn></mmultiscripts><mo> </mo><mo>≥</mo><mmultiscripts><mi>C</mi><mn>13</mn><none></none><mprescripts></mprescripts><none></none><mn>20</mn></mmultiscripts></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mmultiscripts><mi>C</mi><mi>r</mi><none></none><mprescripts></mprescripts><none></none><mn>20</mn></mmultiscripts><mo>≥</mo><mmultiscripts><mi>C</mi><mn>13</mn><none></none><mprescripts></mprescripts><none></none><mn>20</mn></mmultiscripts></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mmultiscripts><mi>C</mi><mi>r</mi><none></none><mprescripts></mprescripts><none></none><mn>20</mn></mmultiscripts><mo>≥</mo><mmultiscripts><mi>C</mi><mn>7</mn><none></none><mprescripts></mprescripts><none></none><mn>20</mn></mmultiscripts></math></p><p>Hence <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mn>13</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>r</mi><mo>=</mo><mn>7</mn><mo>,</mo><mo> </mo><mn>8</mn><mo>,</mo><mo> </mo><mn>9</mn><mo>,</mo><mo> </mo><mn>10</mn><mo>,</mo><mo> </mo><mn>11</mn><mo>,</mo><mo> </mo><mn>12</mn><mo>,</mo><mo> </mo><mn>13</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Required sum</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>7</mn><mo>+</mo><mn>8</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>10</mn><mo>+</mo><mn>11</mn><mo>+</mo><mn>12</mn><mo>+</mo><mn>13</mn><mo>=</mo><mn>70</mn></math></p></div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2010 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9 or 3</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sum-of-an-infinite-geometric-progression-is-6-if-the-sum-of-the-first-two-terms-is-92-then-what-is-the-first-term

slug:
the-sum-of-an-infinite-geometric-progression-is-6-if-the-sum-of-the-first-two-terms-is-92-then-what-is-the-first-term-68436

question:
<div class="question">The sum of an infinite geometric progression is 6 , If the sum of the first two terms is $9 / 2$, then what is the first term?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 / 2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3 or $3 / 2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">9 or 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>

answer:
<div class="solution">Let 'a ' be the first term and 'ar' be the second term of<br/>G.Pwith common ratio 'r'.<br/>Given: $\mathrm{S}_{\infty}=6$ and $a+a r=\frac{9}{2} \Rightarrow \frac{a}{1-r}=6$<br/>$\Rightarrow \quad \mathrm{a}=6(1-\mathrm{r})$ ...(i)<br/>and $a+a r=\frac{9}{2}$<br/>$\Rightarrow \quad 6(1-r)+6 r(1-r)=\frac{9}{2} \quad$ [from (i)]<br/>$\Rightarrow \quad 12-12 \mathrm{r}+12 \mathrm{r}-12 \mathrm{r}^{2}=9$<br/>$\Rightarrow \quad r^{2}=\frac{3}{12}=\frac{1}{4} \Rightarrow r=\frac{1}{2}$ or $\frac{-1}{2} \Rightarrow a=3$ or 9</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-sum-of-an-infinite-gp-is-x-and-the-common-ratio-r-is-such-that-r-1-if-the-first-term-of-the-gp-is-2-then-which-one-of-the-following-is-correct

slug:
the-sum-of-an-infinite-gp-is-x-and-the-common-ratio-r-is-such-that-r-1-if-the-first-term-of-the-gp-is-2-then-which-one-of-the-following-is-correct-82943

question:
<div class="question">The sum of an infinite $G P$ is $x$ and the common ratio $r$ is such that $|r|   &lt; 1$. If the first term of the $G P$ is 2, then which one of the following is correct?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad 1   &lt; x &lt; \infty$</span> </div>

answer:
<div class="solution">$\quad \mathrm{GP}=\mathrm{x}$<br/>$\qquad \frac{\mathrm{a}}{1-\mathrm{r}}=\mathrm{x} \quad$ (where, $\mathrm{a}=$ lst term and $\mathrm{r}=$ common ratio $)$<br/>$\Rightarrow \frac{2}{1-r}=x \quad$...(1) $(\because$ Given $a=2$ and $|r|   &lt; 1)$<br/>$\Rightarrow-1 &lt; \mathrm{r} &lt; 1 \Rightarrow 1&gt;-\mathrm{r}&gt;-1$<br/>$\Rightarrow 1+1&gt;1-r&gt;1-1$<br/>$\Rightarrow 0 &lt; 1-\mathrm{r} &lt; 2$<br/>$\Rightarrow \frac{1}{1-r}&gt;\frac{1}{2}, \frac{2}{1-r}&gt;1$<br/>from equation (i) $x&gt;1$ <br/>Hence, $1 &lt; \mathrm{x} &lt; \infty$</div>


title: the-sum-of-first-10-terms-and-20-terms-of-an-ap-are-120-and-440-respectively-what-is-its-first-term
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2012 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
slug:
the-sum-of-first-10-terms-and-20-terms-of-an-ap-are-120-and-440-respectively-what-is-its-first-term-91738

question:
<div class="question">The sum of first 10 terms and 20 terms of an AP are 120 and 440 respectively.<br/>What is its first term?</div>

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

answer:
<div class="solution">$\mathrm{S}_{10}=\frac{10}{2}[2 \mathrm{a}+9 \mathrm{~d}]$<br/>$120=5(2 \mathrm{a}+9 \mathrm{~d})$<br/>$2 \mathrm{a}+9 \mathrm{~d}=24$ ...(i)<br/>$\mathrm{S}_{20}=\frac{20}{2}[2 \mathrm{a}+19 \mathrm{~d}]$<br/>$440=10[2 \mathrm{a}+19 \mathrm{~d}]$<br/>$2 \mathrm{a}+19 \mathrm{~d}=44$ ...(ii)<br/>Solving (i) \&amp; (11), we get<br/>a = 3</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2012 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sum-of-first-10-terms-and-20-terms-of-an-ap-are-120-and-440-respectively-what-is-the-common-difference

slug:
the-sum-of-first-10-terms-and-20-terms-of-an-ap-are-120-and-440-respectively-what-is-the-common-difference-73548

question:
<div class="question">The sum of first 10 terms and 20 terms of an AP are 120 and 440 respectively.<br/>What is the common difference?</div>

answer:
<div class="solution">put a = 3 in (i) $6+9 \mathrm{~d}=24$<br/>$9 \mathrm{~d}=18 \Rightarrow \mathrm{d}=2$</div>


title: the-sum-of-p-q-th-and-p-q-th-terms-of-an-ap-is-equal-to
slug: the-sum-of-p-q-th-and-p-q-th-terms-of-an-ap-is-equal-to-41700
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The sum of $(p+q)^{\text {th }}$ and $(p-q)^{\text {th }}$ terms of an AP is equal to</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Twice the $\mathrm{p}^{\text {th }}$ term</span> </div>

answer:
<div class="solution">Let the first term of $\mathrm{AP}=\mathrm{a}$ Let the common difference of $\mathrm{AP}=\mathrm{d}$ $(p+q)^{\text {th }}$ term $=\mathrm{T}_{\mathrm{ptq}}=\mathrm{a}+(\mathrm{p}+\mathrm{q}-1) \mathrm{d}$<br/>$(p-q)^{\text {th }}$ term $=T_{p-q}^{p \cdot q}=a+(p-q-1) d$<br/>$\mathrm{T}_{\mathrm{ptq}}+\mathrm{T}_{\mathrm{p-q}}=\mathrm{a}+(\mathrm{p}+\mathrm{q}-1) \mathrm{d}+\mathrm{a}+(\mathrm{p}-\mathrm{q}-1) \mathrm{d}$<br/>$=2 a+(p+q-1+p-q-1) d$<br/>$=2 a+(2 p-2) d=2[a+(p-1) d]=2 T_{p}$</div>


tags: ['Mathematics', 'Application of Derivatives', 'JEE Main', 'JEE Main 2022 (28 Jul Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-sum-of-the-absolute-maximum-and-absolute-minimum-values-of-the-function-f-x-tan-1-sin-x-cos-x-in-the-interval-0-is

slug:
the-sum-of-the-absolute-maximum-and-absolute-minimum-values-of-the-function-f-x-tan-1-sin-x-cos-x-in-the-interval-0-is-35248

question:
<div class="question">The sum of the absolute maximum and absolute minimum values of the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mi>sin</mi><mi>x</mi><mo>-</mo><mi>cos</mi><mi>x</mi></mrow></mfenced></math> in the interval <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>π</mi></mrow></mfenced></math> is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>cos</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac></mfenced><mo>-</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></math></span> </div>

answer:
<div class="solution"><blockquote><p>Given,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mrow><mi>sin</mi><mi>x</mi><mo>-</mo><mi>cos</mi><mi>x</mi></mrow></mfenced></math></p><p>Now differentiating the function we get,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mi>cos</mi><mi>x</mi><mo>+</mo><mi>sin</mi><mi>x</mi></mrow><mrow><msup><mfenced><mrow><mi>sin</mi><mi>x</mi><mo>-</mo><mi>cos</mi><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac></math></p><p>Now equating <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>0</mn></math> to find critical points,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>cos</mi><mi>x</mi><mo>+</mo><mi>sin</mi><mi>x</mi></mrow><mrow><msup><mfenced><mrow><mi>sin</mi><mi>x</mi><mo>-</mo><mi>cos</mi><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>cos</mi><mi>x</mi><mo>+</mo><mi>sin</mi><mi>x</mi><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>tan</mi><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo>  </mo><mi>x</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mn>4</mn></mfrac></math></p><p>Now checking the value of function at critical point and boundary point we get,</p><table border="1" cellpadding="1" cellspacing="1" style="width: 200px;"> <tbody> <tr> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mn>4</mn></mfrac></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi></math></td> </tr> <tr> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msqrt><mn>2</mn></msqrt></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>π</mi><mn>4</mn></mfrac></math></td> </tr> </tbody></table><p>So, we get,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open=""><mtable><mtr><mtd><msub><mfenced><mrow><mi>f</mi><mfenced><mi>x</mi></mfenced></mrow></mfenced><mi>max</mi></msub><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msqrt><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mo>∴</mo><mo> </mo><msub><mfenced><mrow><mi>f</mi><mfenced><mi>x</mi></mfenced></mrow></mfenced><mi>min</mi></msub><mo>=</mo><mo>-</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></math></p><p>So, the sum will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msqrt><mn>2</mn></msqrt><mo>-</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mi>cos</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>-</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></math></p></blockquote></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-sum-of-the-binary-numbers-11011-2-10110110-2-and-10011-0-y-2-is-the-binary-number-101101101-2-what-are-the-values-of-x-and-y

slug:
the-sum-of-the-binary-numbers-11011-2-10110110-2-and-10011-0-y-2-is-the-binary-number-101101101-2-what-are-the-values-of-x-and-y-58147

question:
<div class="question">The sum of the binary numbers $(11011)_{2}(10110110)_{2}$ and $(10011 \times 0 y)_{2}$ is the binary number ( 101101101$)_{2}$. What are the values of $\mathrm{x}$ and $\mathrm{y}$ ?</div>

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

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

answer:
<div class="solution">On substraction, we get<br/>101101101<br/>\begin{array}{r}<br/>-10110110 \\<br/>\hline 10110111 \\<br/>-11011 \\<br/>\hline 10011100<br/>\end{array}<br/>$\Rightarrow x=1, y=0$</div>


title: the-sum-of-the-direction-cosines-of-zaxis-is
slug: the-sum-of-the-direction-cosines-of-zaxis-is-91636
question: <div class="question">The sum of the direction cosines of z-axis is</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2013 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
answer: <div class="solution">Direction cosines of z-axis are $0,0,1$<br/>sum $=0+0+1=1$</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 / 3$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3</span> </li> </ul>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-sum-of-the-first-2-p-1-terms-of-an-apis-p-1-2p-1-which-one-of-the-following-inferences-can-be-drawn

slug:
the-sum-of-the-first-2-p-1-terms-of-an-apis-p-1-2p-1-which-one-of-the-following-inferences-can-be-drawn-42717

question:
<div class="question">The sum of the first $(2 \mathrm{p}+1)$ terms of an APis $\{(\mathrm{p}+1)$. (2p $+1$ )\}. Which one of the following inferences can be<br/>drawn?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The $(p+1)^{\text {th }}$ term of the $\mathrm{AP}$ is $(\mathrm{p}+1)$</span> </div>

answer:
<div class="solution">Let the first term and common difference of an AP be a and d respectively. Then, as given $(p+1)(2 p+1)=\left(\frac{2 p+1}{2}\right)\{2 a+(2 p+1-1) d\}$<br/>$\Rightarrow \quad(p+1)=\frac{1}{2}\{2 a+2 p d\}$<br/>$\Rightarrow(\mathrm{p}+1)=\mathrm{a}+\mathrm{pd}$<br/>$\Rightarrow \quad p+1=a+[(p+1)-1] d=t_{p+1}$<br/>Hence, the inference is: the $(p+1)^{\text {th }}$ term of the $A P$ is $(p+1)$</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-sum-of-the-first-five-terms-and-the-sum-of-the-first-ten-terms-of-an-a-p-are-same-which-one-of-the-following-is-the-correct-statement

slug:
the-sum-of-the-first-five-terms-and-the-sum-of-the-first-ten-terms-of-an-a-p-are-same-which-one-of-the-following-is-the-correct-statement-59839

question:
<div class="question">The sum of the first five terms and the sum of the first ten terms of an $A P$ are same. Which one of the following is the correct statement?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Either the first term or the common difference is negative but not both</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \mathrm{S}_{5}=\mathrm{S}_{10} \\ &amp; \Rightarrow \frac{5}{2}[2 \mathrm{a}+4 \mathrm{~d}]=\frac{10}{2}[2 \mathrm{a}+9 \mathrm{~d}] \\ &amp; \Rightarrow 5 \mathrm{a}+10 \mathrm{~d}=10 \mathrm{a}+45 \mathrm{~d} \\ &amp; \Rightarrow \mathrm{a}=-7 \mathrm{~d} \text { or } \mathrm{d}=\frac{-1}{7} \mathrm{a} \end{aligned}$<br/>We see, If $\mathrm{d}$ is positive, then first term should be negative and common difference should be positive. If $\mathrm{d}$ is negative, then first term should be position and common difference should be negative.</div>


title: the-sum-of-the-first-n-terms-of-the-series-2-1-4-3-8-7-16-15-is-equal-to
slug: the-sum-of-the-first-n-terms-of-the-series-2-1-4-3-8-7-16-15-is-equal-to-49277
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The sum of the first n terms of the series $\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\ldots .$ is equal to</div>

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

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

answer:
<div class="solution">$\begin{aligned} &amp; \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\ldots . . \\ &amp;=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{8}\right)+\left(1-\frac{1}{16}\right)+\ldots \ldots \\ &amp;=(1+1+1+\ldots . \mathrm{n})-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots . .\right) \end{aligned}$<br/>$=n-\left(\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\frac{1}{2^{4}}+\ldots .\right)$<br/>$=n-\frac{\frac{1}{2}\left(1-\frac{1}{2^{n}}\right)}{1-\frac{1}{2}} \quad\left(\because\right.$ G.P. $\left.a=\frac{1}{2}, r=\frac{1}{2}\right)$<br/>$=n-\frac{\frac{1}{2}\left(1-\frac{1}{2^{n}}\right)}{\frac{1}{2}}$<br/>$=n-1+2^{-n}$<br/>$=2^{-n}+n-1$</div>


title: the-sum-of-the-focal-distances-of-a-point-on-an-ellipse-is-constant-and-equal-to-the
slug: the-sum-of-the-focal-distances-of-a-point-on-an-ellipse-is-constant-and-equal-to-the-77707
tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2019 (Phase 1)']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The sum of the focal distances of a point on an ellipse is constant and equal to the</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">length of major axis</span> </div>


title: the-sum-of-the-focal-distances-of-a-point-on-the-ellipse-4-x-2-9-y-2-1-is
slug: the-sum-of-the-focal-distances-of-a-point-on-the-ellipse-4-x-2-9-y-2-1-is-35419
tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The sum of the focal distances of a point on the ellipse<br/>$\frac{\mathrm{x}^{2}}{4}+\frac{\mathrm{y}^{2}}{9}=1$ is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">4 units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6 units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8 units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">10 units</span> </li> </ul>

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

answer:
<div class="solution">Given equation of ellipse is<br/>$\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$<br/>$\Rightarrow \quad \frac{x^{2}}{(2)^{2}}+\frac{y^{2}}{(3)^{2}}=1$<br/>$\Rightarrow \quad a=2$ and $b=3$<br/>Length of major axis $=2 \mathrm{a}=4$<br/>Since, we have Sum of the focal distances of a point on ellipse $=$ length of major axis. Required Ans $=4$ units.</div>


tags: ['Mathematics', 'Functions', 'JEE Main', 'JEE Main 2022 (25 Jul Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">15</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sum-of-the-maximum-and-minimum-values-of-the-function-f-x-5-x-7-x-2-2-x-in-the-interval-5-4-2-where-t-is-the-greatest-integer-t-is

slug:
the-sum-of-the-maximum-and-minimum-values-of-the-function-f-x-5-x-7-x-2-2-x-in-the-interval-5-4-2-where-t-is-the-greatest-integer-t-is-70925

question:
<div class="question">The sum of the maximum and minimum values of the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced close="|" open="|"><mrow><mn>5</mn><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced><mo>+</mo><mfenced close="]" open="["><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced></math> in the interval <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>,</mo><mn>2</mn></mrow></mfenced></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mi>t</mi></mfenced></math> is the greatest integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≤</mo><mi>t</mi></math>, is ______.</div>

answer:
<div class="solution"><blockquote><p>Given,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced close="|" open="|"><mrow><mn>5</mn><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced><mo>+</mo><mfenced close="]" open="["><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced close="|" open="|"><mrow><mn>5</mn><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced><mo>+</mo><mfenced close="]" open="["><mrow><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced close="|" open="|"><mrow><mn>5</mn><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced><mo>+</mo><mfenced close="]" open="["><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mfenced><mo>-</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mtext>as </mtext><mfenced close="]" open="["><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mtext>=</mtext><mfenced close="]" open="["><mi>x</mi></mfenced><mtext>-1 where </mtext><mfenced close="]" open="["><mo>.</mo></mfenced><mtext> is greatest integer function</mtext></mrow></mfenced></math></p><p>Now critical points of</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mn>7</mn><mn>5</mn></mfrac><mo>,</mo><msqrt><mn>5</mn></msqrt><mo>-</mo><mn>1</mn><mo>,</mo><msqrt><mn>6</mn></msqrt><mo>-</mo><mn>1</mn><mo>,</mo><msqrt><mn>7</mn></msqrt><mo>-</mo><mn>1</mn><mo>,</mo><msqrt><mn>8</mn></msqrt><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Maximum or minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> occur at critical points or boundary points.</p><p>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi>f</mi><mfenced><mfrac><mn>5</mn><mn>4</mn></mfrac></mfenced><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>+</mo><mn>4</mn><mo>=</mo><mfrac><mn>19</mn><mn>4</mn></mfrac></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mfrac><mn>7</mn><mn>5</mn></mfrac></mfenced><mo>=</mo><mn>0</mn><mo>+</mo><mn>4</mn><mo>=</mo><mn>4</mn></math></p><p>As both <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mrow><mn>5</mn><mi>x</mi><mo>-</mo><mn>7</mn></mrow></mfenced></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi></math> are increasing in nature after <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>7</mn><mn>5</mn></mfrac></math></p><p>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mn>2</mn></mfenced><mo>=</mo><mfenced close="|" open="|"><mrow><mn>10</mn><mo>-</mo><mn>7</mn></mrow></mfenced><mo>+</mo><mfenced close="]" open="["><mrow><mn>4</mn><mo>+</mo><mn>4</mn></mrow></mfenced><mo>=</mo><mn>3</mn><mo>+</mo><mn>8</mn><mo>=</mo><mn>11</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>f</mi><msub><mfenced><mfrac><mn>7</mn><mn>5</mn></mfrac></mfenced><mi>min</mi></msub><mo>=</mo><mn>4</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><msub><mfenced><mn>2</mn></mfenced><mi>max</mi></msub><mo>=</mo><mn>11</mn></math></p><p>So sum of minimum and maximum value is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>+</mo><mn>11</mn><mo>=</mo><mn>15</mn></math></p></blockquote></div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-sum-of-the-roots-of-the-equation-a-x-2-x-c-0-where-a-and-c-are-nonzero-is-equal-to-the-sum-of-the-reciprocals-of-their-squares-then-a-ca-2-c-2-are

slug:
the-sum-of-the-roots-of-the-equation-a-x-2-x-c-0-where-a-and-c-are-nonzero-is-equal-to-the-sum-of-the-reciprocals-of-their-squares-then-a-ca-2-c-2-are-44653

question:
<div class="question">The sum of the roots of the equation $a x^{2}+x+c=0$ (where a and $\mathrm{c}$ are non-zero) is equal to the sum of the reciprocals of their squares. Then $\mathrm{a}, \mathrm{ca}^{2}, \mathrm{c}^{2}$ are in</div>

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

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

answer:
<div class="solution">Let $\alpha, \beta$ be roots of $a x^{2}+x+c=0$. Given, $\alpha+\beta$<br/>$=\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}=\frac{\alpha^{2}+\beta^{2}}{\alpha^{2} \beta^{2}}=\frac{(\alpha+\beta)^{2}-2 \alpha \beta}{(\alpha \beta)^{2}}$<br/>$\Rightarrow \frac{-1}{a}=\frac{\left(\frac{-1}{a}\right)^{2}-2\left(\frac{c}{a}\right)}{\left(\frac{c}{a}\right)^{2}}$<br/>$\Rightarrow \frac{-1}{a}=\frac{\frac{1}{a^{2}}-\frac{2 c}{a}}{\frac{c^{2}}{a^{2}}}$<br/>$\Rightarrow \frac{-1}{\mathrm{a}}=\frac{1-2 \mathrm{ac}}{\mathrm{c}^{2}} \Rightarrow-\mathrm{c}^{2}=\mathrm{a}-2 \mathrm{a}^{2} \mathrm{c}$<br/>$\Rightarrow 2 \mathrm{a}^{2} \mathrm{c}=\mathrm{a}+\mathrm{c}^{2}$<br/>So, $a, a^{2} c, c^{2}$ are in A.P.</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">HP</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sum-of-the-roots-of-the-equation-x-2-b-x-c-0-where-b-and-c-are-nonzero-is-equal-to-the-sum-of-the-reciprocals-of-their-squares-then-c-1-b-b-c-are-

slug:
the-sum-of-the-roots-of-the-equation-x-2-b-x-c-0-where-b-and-c-are-nonzero-is-equal-to-the-sum-of-the-reciprocals-of-their-squares-then-c-1-b-b-c-are-12614

question:
<div class="question">The sum of the roots of the equation $x^{2}+b x+c=0$ (where $\mathrm{b}$ and $\mathrm{c}$ are non-zero) is equal to the sum of the reciprocals<br/>of their squares. Then $\frac{1}{\mathrm{c}}, \mathrm{b}, \frac{\mathrm{c}}{\mathrm{b}}$ are in</div>

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

answer:
<div class="solution">Let $\alpha, \beta$ be the roots of $x^{2}+b x+c=0$ Given, $\alpha+\beta=\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}$<br/>$\alpha+\beta=-b ; \alpha, \beta=c$<br/>$\alpha+\beta=\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}$<br/>$\Rightarrow \alpha+\beta=\frac{\alpha^{2}}{\alpha^{2}}+\frac{\beta^{2}}{\beta^{2}}=\frac{(\alpha+\beta)^{2}-2 \alpha \beta}{\alpha^{2} \beta^{2}}$<br/>$\Rightarrow-b=\frac{b^{2}-2 c}{c^{2}}$<br/>$\Rightarrow-b c^{2}=b^{2}-2 c \Rightarrow 2 c=b^{2}+b c^{2}$<br/>$\Rightarrow \frac{2 \mathrm{c}}{\mathrm{b}}=\mathrm{b}+\mathrm{c}^{2} \Rightarrow \frac{2}{\mathrm{~b}}=\frac{\mathrm{b}}{\mathrm{c}}+\mathrm{c}$<br/>We know, if $a, b, c$ are in A.P. $2 b=a+c$. <br/>Similarly, we got $\frac{2}{b}=\frac{b}{c}+c$, which means $\frac{b}{c}, \frac{1}{b}, c$ are in A.P.<br/>So, $\frac{\mathrm{c}}{\mathrm{b}}, \mathrm{b}, \frac{1}{\mathrm{c}}$ are in H.P.</div>


title: the-sum-of-the-series-3-1-3-1-9-1-is-equal-to
slug: the-sum-of-the-series-3-1-3-1-9-1-is-equal-to-87691
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The sum of the series $3-1+\frac{1}{3}-\frac{1}{9}+\ldots .$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{20}{9}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{9}{20}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{9}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{4}{9}$</span> </li> </ul>

answer:
<div class="solution">The series is $\frac{3}{3^{0}}-\frac{3}{3^{1}}+\frac{3}{3^{2}}-\frac{3}{3^{3}}+\ldots . \infty$<br/>This is a G.P. with first term $a=3$<br/>and common ratio $r=-\frac{1}{3}$<br/>$\therefore \operatorname{Sum} \mathrm{S}=\frac{3}{1-\left(-\frac{1}{3}\right)}=\frac{3 \times 3}{3+1}=\frac{9}{4}$</div>


title: the-sum-of-the-series-formed-by-the-sequence-3-3-1-upto-infinity-is
slug: the-sum-of-the-series-formed-by-the-sequence-3-3-1-upto-infinity-is-16302
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The sum of the series formed by the sequence $3, \sqrt{3}, 1 \ldots \ldots$ upto infinity is :</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3 \sqrt{3}(\sqrt{3}+1)}{2}$</span> </div>

answer:
<div class="solution">$3, \sqrt{3}, 1, \frac{1}{\sqrt{3}}, \ldots \ldots, \infty$<br/>This is a Geometric Progression with $\mathrm{a}=3, \mathrm{r}=\frac{1}{\sqrt{3}}$<br/>$\begin{aligned} \mathrm{S}_{\infty} &amp;=\frac{\mathrm{a}}{1-\mathrm{r}}=\frac{3}{1-\frac{1}{\sqrt{3}}} \\ &amp;=\frac{3 \sqrt{3}}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1}=\frac{3 \sqrt{3}(\sqrt{3}+1)}{2} \end{aligned}$</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">12,8</span> </div>
source_db: MarksBatch2_P3.db
title:
the-sum-of-twonumbers-is-20-what-are-the-numbers-if-the-product-of-the-square-of-one-and-the-cube-of-the-other-is-maxinmm

slug:
the-sum-of-twonumbers-is-20-what-are-the-numbers-if-the-product-of-the-square-of-one-and-the-cube-of-the-other-is-maxinmm-19179

question:
<div class="question">The sum of twonumbers is 20 . What are the numbers if the product of the square of one and the cube of the other is maxinmm?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">6,14</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">15,5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">12,8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">10,10</span> </li> </ul>

answer:
<div class="solution">Let the numbers are $\mathrm{x}$ and $\mathrm{y}$. So, $x+y=20$; Let $P=x^{2} y^{3} \quad$ (As given) $=x^{2}(20-x)^{3}$<br/>Differentiating w. r. t. $\mathrm{x}$ $\begin{aligned} \frac{d P}{d x} &amp;=x^{2} \cdot 3(20-x)^{2}(-1)+(20-x)^{3} \cdot 2 x \\ &amp;=(20-x)^{2}\left[-3 x^{2}+40 x-2 x^{2}\right] \\ &amp;=(20-x)^{2}\left[40 x-5 x^{2}\right] \\ \frac{d^{2} P}{d x^{2}} &amp;=(20-x)^{2}[40-10 x]+\left(40 x-5 x^{2}\right) 2(20-x)(-1) \end{aligned}$<br/>$\frac{d p}{d x}=0$ for maxima or minima. So, $(20-x)^{2}\left[40 x-5 x^{2}\right]=0$<br/>$\Rightarrow(20-\mathrm{x})^{2} \times(\mathrm{x})(40-5 \mathrm{x})=0 \Rightarrow \mathrm{x}=20,0,8$<br/>We get, $\left(\frac{\mathrm{d}^{2} \mathrm{P}}{\mathrm{dx}^{2}}\right)_{\mathrm{x}=8}   &lt; 0 ;\left(\frac{\mathrm{d}^{2} \mathrm{p}}{\mathrm{dx}^{2}}\right)_{\mathrm{x}=0}&gt;0$ and<br/>$\left(\frac{\mathrm{d}^{2} \mathrm{p}}{\mathrm{dx}^{2}}\right)_{\mathrm{x}=20}=0$<br/>Hence. $\mathrm{P}$ is maximumat $\mathrm{x}=8$<br/>and, Numbers are 12 and 8 .</div>


title: the-supernatant-left-after-sedimentation-of-sewage-water-during-primary-treatment-is-known-as
slug: the-supernatant-left-after-sedimentation-of-sewage-water-during-primary-treatment-is-known-as-81895
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The supernatant left after sedimentation of sewage water during primary treatment is known as</div>

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

answer:
<div class="solution">Primary treatment is a physical process which involves filteration and sedimentation. After sedimentation the part which settles down is called as primary sludge and the water which comes above is called effluent, it contains dissolved organic substance and is transferred to secondary treatment plant.</div>


title: the-suspended-solids-in-sewage-can-be-removed-at-which-step-in-the-process-of-sewage-treatment
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch2_P3.db
slug:
the-suspended-solids-in-sewage-can-be-removed-at-which-step-in-the-process-of-sewage-treatment-26684

question:
<div class="question">The suspended solids in sewage can be removed at which step in the process of sewage treatment?</div>

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

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

answer:
<div class="solution">Before disposal, sewage is treated in sewage treatment plants (STPs) to make it less polluting. The initial steps basically involve the physical removal of particles â large and small â from the sewage through filtration and sedimentation, which is known as the Primary Treatment. These are removed in stages: initially, floating debris is removed by sequential filtration. Then the grit (soil and small pebbles) are removed by sedimentation. All solids that settle form the primary sludge, and the supernatant forms the effluent. The effluent from the primary settling tank is taken for secondary treatment.</div>


title: the-sweet-potato-family-is-included-in-the-order
slug: the-sweet-potato-family-is-included-in-the-order-53887
question: <div class="question">The sweet potato family is included in the order</div>
tags: ['Biology', 'The Living World', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Polymoniales</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Sapindales</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Poales</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Asparagales</span> </li> </ul>

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

answer:
<div class="solution"><i>Ipomoea batatas<i> </i></i>or sweet potato is a plant which belongs to the family Convolvulaceae. It is also called the Morning glory family. Along with the potato family, Solanaceae is included in the order Polymoniales.</div>


title: the-symmetric-part-of-the-matrix-aleftbeginarrayccc1-2-4-6-8-2-2-2-7endarrayright-is
slug: the-symmetric-part-of-the-matrix-aleftbeginarrayccc1-2-4-6-8-2-2-2-7endarrayright-is-50239
tags: ['Mathematics', 'Indefinite Integration', 'KCET', 'KCET 2014']
source_db: MarksBatch2_P3.db
question:
<div class="question">The symmetric part of the matrix \( A=\left(\begin{array}{ccc}1 &amp; 2 &amp; 4 \\ 6 &amp; 8 &amp; 2 \\ 2 &amp; -2 &amp; 7\end{array}\right) \) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\( \left(\begin{array}{lll}1 &amp; 4 &amp; 3 \\ 2 &amp; 8 &amp; 0 \\ 3 &amp; 0 &amp; 7\end{array}\right) \)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\( \left(\begin{array}{lll}1 &amp; 4 &amp; 3 \\ 4 &amp; 8 &amp; 0 \\ 3 &amp; 0 &amp; 7\end{array}\right) \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( \left(\begin{array}{ccc}0 &amp; -2 &amp; -1 \\ -2 &amp; 0 &amp; -2 \\ -1 &amp; -2 &amp; 0\end{array}\right) \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( \left(\begin{array}{ccc}0 &amp; -2 &amp; 1 \\ 2 &amp; 0 &amp; 2 \\ -1 &amp; 2 &amp; 0\end{array}\right) \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( \left(\begin{array}{lll}1 &amp; 4 &amp; 3 \\ 4 &amp; 8 &amp; 0 \\ 3 &amp; 0 &amp; 7\end{array}\right) \)</span> </div>

answer:
<div class="solution">Given that \( A=\left[\begin{array}{ccc}1 &amp; 2 &amp; 4 \\ 6 &amp; 8 &amp; 2 \\ 2 &amp; -2 &amp; 7\end{array}\right] \)<br/>Symmetric part of A matrix is \( \frac{1}{2}\left(A+A^{\prime}\right) \)<br/>\( =\frac{1}{2}\left[\begin{array}{ccc}1 &amp; 2 &amp; 4 \\ 6 &amp; 8 &amp; 2 \\ 2 &amp; -2 &amp; 7\end{array}\right]+\left[\begin{array}{ccc}1 &amp; 6 &amp; 2 \\ 2 &amp; 8 &amp; -2 \\ 4 &amp; 2 &amp; 7\end{array}\right] \)<br/>\( =\left[\begin{array}{lll}1 &amp; 4 &amp; 3 \\ 4 &amp; 8 &amp; 0 \\ 3 &amp; 0 &amp; 7\end{array}\right] \)</div>


title: the-system-of-equation-2-x-y-3-z-5-3-x-2-y-2-z-5-and-5-x-3-y-z-16
slug: the-system-of-equation-2-x-y-3-z-5-3-x-2-y-2-z-5-and-5-x-3-y-z-16-29873
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The system of equation <br/>$2 x+y-3 z=5$<br/>$3 x-2 y+2 z=5$ and<br/>$5 x-3 y-z=16$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">is consistent, with a unique solution</span> </div>

answer:
<div class="solution">Since $\left|\begin{array}{ccc}2 &amp; 1 &amp; -3 \\ 3 &amp; -2 &amp; 2 \\ 5 &amp; -3 &amp; -1\end{array}\right|=26 \neq 0$<br/>$\Rightarrow$ System is consistent with unique solution.</div>


title: the-system-of-equations-k-x-y-z-1-x-k-y-z-k-and-x-y-k-z-k-2-has-no-solution-if-k-equals
slug: the-system-of-equations-k-x-y-z-1-x-k-y-z-k-and-x-y-k-z-k-2-has-no-solution-if-k-equals-16431
tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2017 (Phase 2)']
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 system of equations $k x+y+z=1, x+k y+z=k$ and $x+y+k z=k^{2}$ has no solution if $k$ equals</div>

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

answer:
<div class="solution">$\begin{array}{l}<br/>\mathrm{kx}+\mathrm{y}+\mathrm{z}=1 \\<br/>\mathrm{x}+\mathrm{ky}+\mathrm{z}=\mathrm{k} \\<br/>\mathrm{x}+\mathrm{y}+\mathrm{k} z=\mathrm{k}^{2}<br/>\end{array}$<br/>These equations will have no solution of $\left|\begin{array}{ccc}\mathrm{k} &amp; 1 &amp; 1 \\ 1 &amp; \mathrm{k} &amp; 1 \\ 1 &amp; 1 &amp; \mathrm{k}\end{array}\right|=0$.<br/>$\Rightarrow \mathrm{k}\left(\mathrm{k}^{2}-1\right)-1(\mathrm{k}-1)+(1-\mathrm{k})=0$<br/>$\Rightarrow \mathrm{k}(\mathrm{k}+1)(\mathrm{k}-1)-1(\mathrm{k}-1)-(\mathrm{k}-1)=0$<br/>$\Rightarrow(\mathrm{k}-1)[\mathrm{k}(\mathrm{k}+1)-1-1]=0$<br/>$\Rightarrow(\mathrm{k}-1)\left(\mathrm{k}^{2}+\mathrm{k}-2\right)=0$<br/>$\Rightarrow \mathrm{k}=1$ or $-2$<br/>For $\mathrm{k}=1$, all equations are same and have infinite solution. So, for $\mathrm{k}=-2$, equations have no solution.</div>


tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-system-of-linear-equations-kx-y-z-1-x-ky-z-1-and-x-y-kz-1-has-a-unique-solution-under-which-one-of-the-following-conditions

slug:
the-system-of-linear-equations-kx-y-z-1-x-ky-z-1-and-x-y-kz-1-has-a-unique-solution-under-which-one-of-the-following-conditions-37512

question:
<div class="question">The system of linear equations $\mathrm{kx}+\mathrm{y}+\mathrm{z}=1, \mathrm{x}+\mathrm{ky}+\mathrm{z}=1$ and<br/>$\mathrm{x}+\mathrm{y}+\mathrm{kz}=1$ has a unique solution under which one of the following conditions?</div>

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

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

answer:
<div class="solution">Linear equations $K x+y+z=1$<br/>$x+K y+z=1$<br/>$x+y+K z=1$<br/>$\left[\begin{array}{ccc}K &amp; 1 &amp; 1 \\ 1 &amp; K &amp; 1 \\ 1 &amp; 1 &amp; K\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$<br/>$A X=B$<br/>$X=A^{-1} B$<br/>Linear equantion will have unique solution when $A^{-1}$ exist:<br/>$|A| \neq 0$<br/>$\left[\begin{array}{lll}K &amp; 1 &amp; 1 \\ 1 &amp; K &amp; 1 \\ 1 &amp; 1 &amp; K\end{array}\right] \neq 0$<br/>$K\left(K^{2}-1\right)-1(K-1)+1(1-K) \neq 0$<br/>$\Rightarrow K^{3}-K-K+1+1-K \neq 0$<br/>$\Rightarrow K^{3}-3 K+2 \neq 0$<br/>$(K-1)\left(K^{2}+K-2\right) \neq 0$<br/>$(K-1)(K-1)(K+2) \neq 0$<br/>$K \neq 1, K \neq 1$ and $K \neq-2$<br/>$\Rightarrow K \neq 1$ and $K \neq-2$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2010 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
the-table-below-gives-an-incomplete-frequency-distribution-with-two-missing-frequencies-f-1-and-f-2-beginarraycc-hline-value-of-x-frequency-hline-0-f1-1

slug:
the-table-below-gives-an-incomplete-frequency-distribution-with-two-missing-frequencies-f-1-and-f-2-beginarraycc-hline-value-of-x-frequency-hline-0-f1-1-45438

question:
<div class="question">The table below gives an incomplete frequency distribution with two missing frequencies $f_{1}$ and $f_{2}$ \begin{array}{|c|c|}<br/>\hline Value of x &amp; Frequency \\<br/>\hline 0 &amp; f_{1} \\<br/>1 &amp; f_{2} \\<br/>2 &amp; 4 \\<br/>3 &amp; 4 \\<br/>4 &amp; 3 \\<br/>\hline<br/>\end{array} The total frequency is 18 and the arithmetic mean of $x$ is 2 .<br/>What is the value of $f_{2}$ ?</div>

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

answer:
<div class="solution">\begin{array}{|c|c|c|}<br/>\hlinex &amp; f &amp; x f \\<br/>\hline 0 &amp; f_{1} &amp; 0 \\<br/>1 &amp; f_{2} &amp; f_{2} \\<br/>2 &amp; 4 &amp; 8 \\<br/>3 &amp; 4 &amp; 12 \\<br/>4 &amp; 3 &amp; 12 \\<br/>\hline Total &amp; f_{1}+f_{2}+11 &amp; 32+f_{2} \\<br/>\hline<br/>\end{array} Since, total frequency is 18<br/>$f_{1}+f_{2}+11=18$<br/>$\Rightarrow f_{1}+f_{2}=7$<br/>As we have, Mean $=\frac{\Sigma x f}{\Sigma f}=2$<br/>(i)<br/>$\frac{32+f_{2}}{18}=2 \Rightarrow f_{2}=36-32=4$<br/>On putting the value of $f_{2}$ in Eq. (i), we get $f_{1}=7-4=3$<br/>$f_{2}=4$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-table-below-gives-an-incomplete-frequency-distribution-with-two-missing-frequencies-f-1-and-f-2-beginarraycc-hline-value-of-x-frequency-hline-0-f1-2

slug:
the-table-below-gives-an-incomplete-frequency-distribution-with-two-missing-frequencies-f-1-and-f-2-beginarraycc-hline-value-of-x-frequency-hline-0-f1-2-81666

question:
<div class="question">The table below gives an incomplete frequency distribution with two missing frequencies $f_{1}$ and $f_{2}$ \begin{array}{|c|c|}<br/>\hline Value of x &amp; Frequency \\<br/>\hline 0 &amp; f_{1} \\<br/>1 &amp; f_{2} \\<br/>2 &amp; 4 \\<br/>3 &amp; 4 \\<br/>4 &amp; 3 \\<br/>\hline<br/>\end{array} The total frequency is 18 and the arithmetic mean of $x$ is 2 .<br/>What is the standard deviation? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{5}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{5}}{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{4}{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{16}{9}$</span> </li> </ul>

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

answer:
<div class="solution">\begin{array}{|c|c|c|}<br/>\hlinex &amp; f &amp; x f \\<br/>\hline 0 &amp; f_{1} &amp; 0 \\<br/>1 &amp; f_{2} &amp; f_{2} \\<br/>2 &amp; 4 &amp; 8 \\<br/>3 &amp; 4 &amp; 12 \\<br/>4 &amp; 3 &amp; 12 \\<br/>\hline Total &amp; f_{1}+f_{2}+11 &amp; 32+f_{2} \\<br/>\hline<br/>\end{array} Since, total frequency is 18<br/>$f_{1}+f_{2}+11=18$<br/>$\Rightarrow f_{1}+f_{2}=7$<br/>As we have, Mean $=\frac{\Sigma x f}{\Sigma f}=2$<br/>(i)<br/>$\frac{32+f_{2}}{18}=2 \Rightarrow f_{2}=36-32=4$<br/>On putting the value of $f_{2}$ in Eq. (i), we get $f_{1}=7-4=3$<br/>Since, mean $=\bar{x}=2$ ( given)<br/>\begin{array}{|c|c|c|c|c|}<br/>\hlinex &amp; x-x &amp; (x-x)^{2} &amp; f &amp; f(x-x)^{2} \\<br/>\hline 0 &amp; -2 &amp; 4 &amp; 3 &amp; 12 \\<br/>1 &amp; -1 &amp; 1 &amp; 4 &amp; 4 \\<br/>2 &amp; 0 &amp; 0 &amp; 4 &amp; 0 \\<br/>3 &amp; 1 &amp; 1 &amp; 4 &amp; 4 \\<br/>4 &amp; 2 &amp; 4 &amp; 3 &amp; 12 \\<br/>\hline Total &amp; &amp; &amp; 18 &amp; 32 \\<br/>\hline<br/>\end{array}<br/>Now, $S D=\sqrt{\frac{\sum f(x-\bar{x})^{2}}{N}}$<br/>where $N=$ sum of all frequencies<br/>$=\sqrt{\frac{32}{18}}=\sqrt{\frac{16}{9}}=\frac{4}{3}$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-table-below-gives-an-incomplete-frequency-distribution-with-two-missing-frequencies-f-1-and-f-2-beginarraycc-hline-value-of-x-frequency-hline-0-f1

slug:
the-table-below-gives-an-incomplete-frequency-distribution-with-two-missing-frequencies-f-1-and-f-2-beginarraycc-hline-value-of-x-frequency-hline-0-f1-67766

question:
<div class="question">The table below gives an incomplete frequency distribution with two missing frequencies $f_{1}$ and $f_{2}$ \begin{array}{|c|c|}<br/>\hline Value of x &amp; Frequency \\<br/>\hline 0 &amp; f_{1} \\<br/>1 &amp; f_{2} \\<br/>2 &amp; 4 \\<br/>3 &amp; 4 \\<br/>4 &amp; 3 \\<br/>\hline<br/>\end{array} The total frequency is 18 and the arithmetic mean of $x$ is 2 .<br/>What is the coefficient of variance? $\quad$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{200}{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{50 \sqrt{5}}{9}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{600}{\sqrt{5}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">150</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{200}{3}$</span> </div>

answer:
<div class="solution">\begin{array}{|c|c|c|}<br/>\hlinex &amp; f &amp; x f \\<br/>\hline 0 &amp; f_{1} &amp; 0 \\<br/>1 &amp; f_{2} &amp; f_{2} \\<br/>2 &amp; 4 &amp; 8 \\<br/>3 &amp; 4 &amp; 12 \\<br/>4 &amp; 3 &amp; 12 \\<br/>\hline Total &amp; f_{1}+f_{2}+11 &amp; 32+f_{2} \\<br/>\hline<br/>\end{array} Since, total frequency is 18<br/>$f_{1}+f_{2}+11=18$<br/>$\Rightarrow f_{1}+f_{2}=7$<br/>As we have, Mean $=\frac{\Sigma x f}{\Sigma f}=2$<br/>(i)<br/>$\frac{32+f_{2}}{18}=2 \Rightarrow f_{2}=36-32=4$<br/>On putting the value of $f_{2}$ in Eq. (i), we get $f_{1}=7-4=3$<br/>Coefficient of variance $=\frac{\sigma}{\bar{x}} \times 100$ where $\sigma=S . D$<br/>$=\frac{4}{3} \times \frac{1}{2} \times 100=\frac{200}{3}$</div>


title: the-technique-of-obtaining-large-number-of-plantlets-by-tissue-culture-method-is-called
slug: the-technique-of-obtaining-large-number-of-plantlets-by-tissue-culture-method-is-called-19609
tags: ['Biology', 'Reproduction in Organisms', 'NEET', 'NEET 2004']
source_db: MarksBatch2_P3.db
question:
<div class="question">The technique of obtaining large number of plantlets by tissue culture method is called:</div>

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

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

answer:
<div class="solution">Micropropagation or tissue culture is the practice of rapidly multiplying stock plant material to produce many progeny plants, using modern plant tissue culture methods. It facilitates the growth, storage, and maintenance of a large number of plants in small spaces which makes it a costeffective process. Micropropagation is used for germplasm storage and the protection of endangered species.</div>


tags: ['Physics', 'Thermal Properties of Matter', 'AP EAMCET', 'AP EAMCET 2020 (18 Sep Shift 2)']
source_db: MarksBatch2_P3.db
title:
the-temperature-of-a-body-is-measured-both-in-circ-mathrmc-and-circ-mathrmf-a-graph-is-plotted-with-circ-mathrmf-on-xaxis-and-circ-mathrmc-on-yaxis-th

slug:
the-temperature-of-a-body-is-measured-both-in-circ-mathrmc-and-circ-mathrmf-a-graph-is-plotted-with-circ-mathrmf-on-xaxis-and-circ-mathrmc-on-yaxis-th-39256

question:
<div class="question">The temperature of a body is measured both in \({ }^{\circ} \mathrm{C}\) and \({ }^{\circ} \mathrm{F}\). A graph is plotted with \({ }^{\circ} \mathrm{F}\) on \(X\)-axis and \({ }^{\circ} \mathrm{C}\) on \(Y\)-axis. Then, the cosine of angle between the graph and the \(X\)-axis is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\frac{9}{5}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\frac{5}{\sqrt{106}}\)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">\(\frac{9}{\sqrt{106}}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{9}{\sqrt{106}}\)</span> </div>

answer:
<div class="solution">The relation between celsius scale temperature and fahrenheit scale temperature is given as<br/>\(\begin{aligned}<br/>&amp; &amp; \frac{C}{5} &amp; =\frac{F-32}{9} \\<br/>\Rightarrow &amp; &amp; 9 C &amp; =5 F-160 \\<br/>\Rightarrow &amp; &amp; C &amp; =\frac{5}{9} F-\frac{160}{9} \quad \ldots (i)<br/>\end{aligned}\)<br/>The graph between \(C\) and \(F\) is shown in the figure<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/Y8IVKDUACVqaN-6eqnDav7eRNLU3v_Wm-qB9WzAEWfM.original.fullsize.png"/><br/><br/>Comparing Eq. (i) with line \(y=m x+C\), we get Slope of graph, \(m=\tan \theta=\frac{5}{9}\)<br/>\(\therefore \quad \cos \theta=\frac{9}{\sqrt{106}}\)<img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/J9tlK8fX1pmHxj-xU4oFbWt4Fkm8LV08Sy_FIFnjYGQ.original.fullsize.png"/><br/></div>


title: the-term-bark-refers-to
slug: the-term-bark-refers-to-18738
question: <div class="question">The term 'bark' refers to</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'JIPMER', 'JIPMER 2011']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">phellem, phelloderm and vascular cambium</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">periderm and secondary xylem</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">cork cambium and cork</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">phellogen, phellem, phelloderm and secondary phloem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">phellogen, phellem, phelloderm and secondary phloem</span> </div>

answer:
<div class="solution">All the dead cells lying outside the phellogen constitute the bark of plant. It may include epidermis, cork, hypodermis and even part of cortex depending upon the position of origin of cork cambium or phellogen.</div>


title: the-term-keel-is-used-for-special-type-of
slug: the-term-keel-is-used-for-special-type-of-52010
question: <div class="question">The term 'keel' is used for special type of</div>
tags: ['Biology', 'Morphology of Flowering Plants', 'JIPMER', 'JIPMER 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">petals</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">sepals</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">petals</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">stamens</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">carpels</span> </li> </ul>

answer:
<div class="solution">Keel is a special type of petal found in papilionaceous type of corolla. Papilionaceous type is butterfly like, the corolla has one large posterior standard, two lateral wings, two innermost and smaller keels.</div>


tags: ['Biology', 'Plant - Growth and Development', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-term-used-for-permanent-cells-that-have-reobtain-meristematic-property-to-perform-cell-division-is

slug:
the-term-used-for-permanent-cells-that-have-reobtain-meristematic-property-to-perform-cell-division-is-57953

question:
<div class="question">The term used for permanent cells that have reobtain meristematic property to perform cell division is</div>

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

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

answer:
<div class="solution">Dedifferentiation is the phenomenon by which a permanent mature cell that has lost the power of division becomes meristematic and starts division again. For example during secondary growth in dicot stem fully differentiated parenchyma becomes meristematic to form interfascicular cambium and cork cambium.</div>


tags: ['Physics', 'Units and Dimensions', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-terminal-velocity-vr-of-a-small-steel-ball-of-radius-r-falling-under-gravity-through-a-column-of-a-viscous-liquid-of-coefficient-of-viscosity-eta-

slug:
the-terminal-velocity-vr-of-a-small-steel-ball-of-radius-r-falling-under-gravity-through-a-column-of-a-viscous-liquid-of-coefficient-of-viscosity-eta-15628

question:
<div class="question">The terminal velocity \( v_{r} \) of a small steel ball of radius \( r \) falling under gravity through a column of a viscous liquid of coefficient of viscosity \( \eta \) depends on the mass of the ball \( m \), acceleration due to gravity \( g \), coefficient of viscosity \( \eta \) and radius \( r \). Which of the following relations is dimensionally correct?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( v_{r} \propto \frac{m g}{r \eta} \)</span> </div>

answer:
<div class="solution"><blockquote><p>According to question, terminal velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>v</mi><mi>r</mi></msub></mfenced></math> of ball depends on mass of ball <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>m</mi></mfenced></math>, acceleration due to gravity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>g</mi></mfenced></math>, coefficient of viscosity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>η</mi></mfenced></math> and radius of ball <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>r</mi></mfenced></math>.</p><p>Using Dimensional analysis, we can write</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>r</mi></msub><mo>∝</mo><msup><mi>m</mi><mi>a</mi></msup><msup><mi>g</mi><mi>b</mi></msup><msup><mi>η</mi><mi>c</mi></msup><msup><mi>r</mi><mi>d</mi></msup><mspace linebreak="newline"></mspace><mo>⇒</mo><mfenced close="]" open="["><msub><mi>v</mi><mi>r</mi></msub></mfenced><mo>=</mo><mfenced close="]" open="["><mrow><msup><mi>m</mi><mi>a</mi></msup><msup><mi>g</mi><mi>b</mi></msup><msup><mi>η</mi><mi>c</mi></msup><msup><mi>r</mi><mi>d</mi></msup></mrow></mfenced></math></p><p>Substituting the dimensions of each term in the above expression we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">M</mi><mn>0</mn></msup><msup><mi mathvariant="normal">L</mi><mn>1</mn></msup><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>=</mo><msup><mfenced><mrow><msup><mi mathvariant="normal">M</mi><mn>1</mn></msup><msup><mi mathvariant="normal">L</mi><mn>0</mn></msup><msup><mi mathvariant="normal">T</mi><mn>0</mn></msup></mrow></mfenced><mi mathvariant="normal">a</mi></msup><msup><mfenced><mrow><msup><mi mathvariant="normal">M</mi><mn>0</mn></msup><msup><mi mathvariant="normal">L</mi><mn>1</mn></msup><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced><mi mathvariant="normal">b</mi></msup><msup><mfenced><mrow><msup><mi mathvariant="normal">M</mi><mn>1</mn></msup><msup><mi mathvariant="normal">L</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi mathvariant="normal">T</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced><mi mathvariant="normal">c</mi></msup><msup><mfenced><mrow><msup><mi mathvariant="normal">M</mi><mn>0</mn></msup><msup><mi mathvariant="normal">L</mi><mn>1</mn></msup><msup><mi mathvariant="normal">T</mi><mn>0</mn></msup></mrow></mfenced><mi mathvariant="normal">d</mi></msup></math></p><p>Now equating the exponent of each of the fundamental dimensions, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>1</mn></mfenced><mspace linebreak="newline"></mspace><mi>b</mi><mo>+</mo><mi>d</mi><mo>-</mo><mi>c</mi><mo>=</mo><mn>1</mn><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>2</mn></mfenced><mspace linebreak="newline"></mspace><mo>-</mo><mn>2</mn><mi>b</mi><mo>-</mo><mi>c</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>3</mn></mfenced></math></p><p>Solving above system of equations, we get <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>d</mi><mo>=</mo><mo>-</mo><mn>1</mn></math>.</p><p>Hence, the dimensionally correct relation is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>r</mi></msub><mo>∝</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mrow><mi>η</mi><mi>r</mi></mrow></mfrac></math>.</p></blockquote></div>


title: the-test-that-distinguishes-primary-amines-from-other-amines-is
slug: the-test-that-distinguishes-primary-amines-from-other-amines-is-70108
question: <div class="question">The test that distinguishes primary amines from other amines is</div>
tags: ['Chemistry', 'Amines', 'TS EAMCET', 'TS EAMCET 2021 (05 Aug Shift 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Iodoform test</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Victor Meyer test</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Lucas test</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Carbylamine test</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Carbylamine test</span> </div>

answer:
<div class="solution"><p>The carbylamine reaction is also known as Hoffman isocyanide synthesis. It is the reaction of a primary amine, chloroform and a base to synthesize isocyanides or carbylamines.</p><p>The dichlorocarbene intermediate is very important for this conversion.</p><p>The carbylamine reaction is not given by secondary and tertiary amines, so primary amines can be distinguished from tertiary and secondary amines.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo>-</mo><msub><mi>NH</mi><mn>2</mn></msub><mo>+</mo><msub><mi>CHCl</mi><mn>3</mn></msub><mo>+</mo><mn>3</mn><mi>KOH</mi><mo>→</mo><mi mathvariant="normal">R</mi><mo>-</mo><mi>NC</mi><mo>+</mo><mn>3</mn><mi>KCl</mi><mo>+</mo><mn>3</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math></p></div>


tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-test-that-is-done-for-the-differentiation-of-primary-amines-from-secondary-and-tertiary-amine-is

slug:
the-test-that-is-done-for-the-differentiation-of-primary-amines-from-secondary-and-tertiary-amine-is-73514

question:
<div class="question"><div> <p align="left" style="text-align:left;"><span>The test that is done for the differentiation of primary amines from secondary and tertiary amine is:</span></p> </div> </div>

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

answer:
<div class="solution"><div><p><span>The Carbylamine reaction is a chemical test for detection of primary amines. In this reaction, the analyte is heated with alcoholic potassium hydroxide and chloroform. If a primary amine is present, the isocyanide is formed.</span></p><p><span>For example, the reaction with ethylamine:</span></p><p align="left" style="text-align:left;"><span style="position:relative;top:0.0pt"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtable columnalign="left" equalcolumns="true" equalrows="true"> <mtr columnalign="left"> <mtd columnalign="left"> <mrow> <msub> <mtext>C</mtext> <mn>2</mn> </msub> <msub> <mtext>H</mtext> <mn>5</mn> </msub> <msub> <mrow> <mtext>NH</mtext></mrow> <mn>2</mn> </msub> <mo>+</mo><msub> <mrow> <mtext>CHCl</mtext></mrow> <mn>3</mn> </msub> <mo>+</mo><mn>3</mn><mtext>KOH</mtext><munderover> <mo>→</mo> <mrow></mrow> <mrow></mrow> </munderover> <msub> <mtext>C</mtext> <mn>2</mn> </msub> <msub> <mtext>H</mtext> <mn>5</mn> </msub> <mtext>NC</mtext><mo>+</mo><mn>3</mn><mtext>KCl</mtext><mo>+</mo><mn>3</mn><msub> <mtext>H</mtext> <mn>2</mn> </msub> <mtext>O</mtext></mrow> </mtd> </mtr> <mtr columnalign="left"> <mtd columnalign="left"> <mrow> <mtext>Ethylamine</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>Chloroform</mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>Ethyl</mtext><mtext> </mtext><mtext>isocyanide</mtext></mrow> </mtd> </mtr> </mtable></mrow></math> </span></p></div></div>


title: the-test-to-distinguish-primary-secondary-and-tertiary-amines-is
slug: the-test-to-distinguish-primary-secondary-and-tertiary-amines-is-69733
question: <div class="question">The test to distinguish primary, secondary and tertiary amines is:</div>
tags: ['Chemistry', 'Amines', 'JEE Main', 'JEE Main 2016 (09 Apr Online)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Sandmeyer's reaction</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Carbylamine reaction</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Idoform test</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">S</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">S</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi></math></span> </div>

answer:
<div class="solution"><p>The Hinsberg test, which can distinguish primary, secondary, and tertiary amines, is based upon sulfonamide formation. In the Hinsberg test, an amine is reacted with benzene sulfonyl chloride. If a product forms, the amine is either a primary or secondary amine, because tertiary amines do not form stable sulfonamides. If the sulfonamide that forms dissolves in aqueous sodium hydroxide solution, it is a primary amine. If the sulfonamide is insoluble in aqueous sodium hydroxide, it is a secondary amine</p><p>Benzene sulphonyl chloride is Hinsberg reagent.</p></div>


tags: ['Biology', 'Human Reproduction', 'NEET', 'NEET 2011 (Screening)']
source_db: MarksBatch2_P3.db
title:
the-testes-in-humans-are-situated-outside-the-abdominal-cavity-inside-a-pouch-called-scrotum-the-purpose-served-is-for-1

slug:
the-testes-in-humans-are-situated-outside-the-abdominal-cavity-inside-a-pouch-called-scrotum-the-purpose-served-is-for-1-52762

question:
<div class="question">The testes in humans are situated outside the abdominal cavity inside a pouch called scrotum. The purpose served is for</div>

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

answer:
<div class="solution">The testes in humans are situated outside the abdominal cavity in scrotal sacs. This is because the temperature of scrotal sacs is $25^{\circ} \mathrm{C}$ less than internal body temperature.</div>


tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-testes-in-humans-are-situated-outside-the-abdominal-cavity-inside-a-pouch-called-scrotum-the-purpose-served-is-for

slug:
the-testes-in-humans-are-situated-outside-the-abdominal-cavity-inside-a-pouch-called-scrotum-the-purpose-served-is-for-23430

question:
<div class="question">The testes in humans are situated outside the abdominal cavity, inside a pouch called scrotum. The purpose served is for</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Maintaining the scrotal temperature lower than the internal body temperature</span> </div>

answer:
<div class="solution">The testes are present in the scrotum which maintains the scrotal temperature below 2<sup>o</sup>C of the internal body temperature and is required for the process of spermatogenesis.</div>


title: the-third-term-of-a-gp-is-3-what-is-the-product-of-the-first-five-terms
slug: the-third-term-of-a-gp-is-3-what-is-the-product-of-the-first-five-terms-39940
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">243</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The third term of a GP is 3 . What is the product of the first five terms?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">216</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">226</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">243</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Cannot be determined due to insufficient data</span> </li> </ul>

answer:
<div class="solution">Given, $3^{\text {rd }}$ term of G.P. =3 Let ' $a$ ' be the first term and ' $\mathrm{r}$ ' be the common ratio. $\therefore \mathrm{ar}^{2}=3$<br/>We know, $\mathrm{T}_{1}=\mathrm{a}, \mathrm{T}_{2}=\mathrm{ar}, \mathrm{T}_{3}=\mathrm{ar}^{2}, \mathrm{~T}_{4}=\mathrm{ar}^{3}, \mathrm{~T}_{5}=\mathrm{ar}^{4}$<br/>$\mathrm{T}_{1} \cdot \mathrm{T}_{2} \cdot \mathrm{T}_{3} \cdot \mathrm{T}_{4} \cdot \mathrm{T}_{5}=(\mathrm{a})(\operatorname{ar})\left(\mathrm{ar}^{2}\right)\left(\mathrm{ar}^{3}\right)\left(\mathrm{ar}^{4}\right)$<br/>$=\left(\mathrm{ar}^{2}\right)^{5}$<br/>$=3^{5}$<br/>$=243$</div>


title: the-three-lines-4-x-4-y-1-8-x-3-y-2-y-0-are
slug: the-three-lines-4-x-4-y-1-8-x-3-y-2-y-0-are-67482
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The three lines $4 \mathrm{x}+4 \mathrm{y}=1,8 \mathrm{x}-3 \mathrm{y}=2, \mathrm{y}=0$ are</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/_FChqvJkl4sxYF22sANuS3JpAeARUdnkH30tQFNWWlo.original.fullsize.png"/><br/><br/>So from the figure it is clear that all the three lines are concurrent at point $\mathrm{P}$.</div>


tags: ['Physics', 'Nuclear Physics']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
the-three-stable-isotopes-of-neon-10-20-ne-10-21-ne-and-10-22-ne-have-respective-abundances-of-9051-027-and-922-the-atomic-masses-of-the-three-isotope

slug:
the-three-stable-isotopes-of-neon-10-20-ne-10-21-ne-and-10-22-ne-have-respective-abundances-of-9051-027-and-922-the-atomic-masses-of-the-three-isotope-56432

question:
<div class="question">The three stable isotopes of neon: ${ }_{10}^{20} \mathrm{Ne},{ }_{10}^{21} \mathrm{Ne}$ and ${ }_{10}^{22}$ Ne have respective abundances of $\mathbf{9 0 . 5 1 \%} \% \mathbf{0 . 2 7 \%}$ and $9.22 \%$. The atomic masses of the three isotopes are $19.99 \mathrm{u}, 20.99 \mathrm{u}$ and $21.99 \mathrm{u}$, respectively. Obtain the average atomic mass of neon.</div>

answer:
<div class="solution">The masses of the three isotopes are $19.99 \mathrm{u}, 20.99 \mathrm{u}$ and 21.99u.<br/>Their abundance are $90.51 \%, 0.27 \%$ and $9.22 \%$<br/>$\therefore \quad$ Average atomic mass of neon is<br/>$$<br/>\begin{aligned}<br/>&amp;\frac{90.51 \times 19.99+0.27 \times 20.99+9.22 \times 21.99}{90.51+0.27+9.22} \\<br/>&amp;=\frac{2017.7}{100}=20.17 \mathrm{u} .<br/>\end{aligned}<br/>$$</div>


title: the-tissue-that-will-be-present-in-the-maximum-amount-in-the-stem-of-a-many-years-old-woody-tree-is
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
slug:
the-tissue-that-will-be-present-in-the-maximum-amount-in-the-stem-of-a-many-years-old-woody-tree-is-49659

question:
<div class="question">The tissue that will be present in the maximum amount in the stem of a many years old woody tree is</div>

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

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

answer:
<div class="solution">In an old trunk, increase in thickness occurs due to secondary growth, secondary growth in stellar region occurs due to activity of vascular cambium which forms more amount of secondary xylem and this form heart of the trunk.</div>


title: the-tissue-whose-cells-acts-like-a-diffusion-boundary-is
slug: the-tissue-whose-cells-acts-like-a-diffusion-boundary-is-56162
question: <div class="question">The tissue whose cells acts like a diffusion boundary is:</div>
tags: ['Biology', 'Structural Organisation in Animals', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Simple Cuboidal epithelium</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Simple Columnar epithelium</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Simple Squamous epithelium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">All of the above</span> </li> </ul>

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

answer:
<div class="solution">The squamous epithelium is made up of a single thin layer of flattened cells with irregular boundaries. They are found in the walls of blood vessels and air sacs of lungs and are involved in functions like forming diffusion boundary for efficient diffusion process.</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-top-of-a-hill-observed-from-the-top-and-bottom-of-a-building-of-height-h-is-at-angles-of-elevation-6-and-3-respectively-what-is-the-height-of-the-

slug:
the-top-of-a-hill-observed-from-the-top-and-bottom-of-a-building-of-height-h-is-at-angles-of-elevation-6-and-3-respectively-what-is-the-height-of-the-52640

question:
<div class="question">The top of a hill observed from the top and bottom of a<br/>building of height $\mathrm{h}$ is at angles of elevation $\frac{\pi}{6}$ and $\frac{\pi}{3}$ respectively. What is the height of the hill?</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/TVXW_-hALaB13c8PHZ2OxUfTOIbesUZr8W_s0CZi8Yo.original.fullsize.png"/><br/><br/>From question, In $\Delta$ PQRand $\Delta$ PST.<br/>$$<br/>\begin{aligned}<br/>&amp; \mathrm{B}=\frac{\mathrm{H}}{\tan \frac{\pi}{3}}=\frac{\mathrm{H}-h}{\tan \frac{\pi}{6}} \\<br/>\Rightarrow &amp; \frac{\mathrm{H}}{3}=\mathrm{H}-h \\<br/>\Rightarrow &amp; \frac{2}{3} \mathrm{H}=h \\<br/>\Rightarrow &amp; \mathrm{H}=\frac{3}{2} h<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-top-of-a-hill-observed-from-the-top-and-bottom-of-a-building-of-height-h-is-at-angles-of-elevation-and-respectively-the-height-of-the-hill-is

slug:
the-top-of-a-hill-observed-from-the-top-and-bottom-of-a-building-of-height-h-is-at-angles-of-elevation-and-respectively-the-height-of-the-hill-is-11376

question:
<div class="question">The top of a hill observed from the top and bottom of a building of height $\mathrm{h}$ is at angles of elevation $\alpha$ and $\beta$ respectively. The height of the hill is: $\quad$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{h} \cot \alpha}{\cot \alpha-\cot \beta}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/uaDnItKqXfiqFz9PYl117010y0vFfv9qqsEk99zTjG8.original.fullsize.png"/><br/><br/>$\operatorname{In} \Delta \mathrm{BDC}$,<br/>$\tan \beta=\frac{\mathrm{CD}}{\mathrm{BD}}=\frac{\mathrm{H}}{\mathrm{BD}}$<br/>$\mathrm{BD}=\frac{\mathrm{H}}{\tan \beta}=\mathrm{H} \cot \beta$<br/>In $\triangle$ ALC, $\tan \alpha=\frac{\mathrm{CL}}{\mathrm{AL}}=\frac{\mathrm{H}-\mathrm{h}}{\mathrm{BD}}$<br/>$\mathrm{BD}=(\mathrm{H}-\mathrm{h}) \cot \alpha$<br/>from (i) \&amp; (ii), $(\mathrm{H}-\mathrm{h}) \cot \alpha=\mathrm{H} \cot \beta$<br/>$\mathrm{H} \cot \alpha-\mathrm{h} \cot \alpha=\mathrm{H} \cot \beta$<br/>$\mathrm{H}[\cot \alpha-\cot \beta]=\mathrm{h} \cot \alpha$<br/>$\mathrm{H}=\frac{\mathrm{h} \cot \alpha}{\cot \alpha-\cot \beta}$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
the-top-of-a-hill-when-observed-from-the-top-and-bottom-of-a-building-of-height-h-is-at-angles-of-elevation-p-and-q-respectively-what-is-the-height-of

slug:
the-top-of-a-hill-when-observed-from-the-top-and-bottom-of-a-building-of-height-h-is-at-angles-of-elevation-p-and-q-respectively-what-is-the-height-of-99528

question:
<div class="question">The top of a hill when observed from the top and bottom of a building of height $\mathrm{h}$ is at angles of elevation $\mathrm{p}$ and $\mathrm{q}$ respectively. What is the height of the hill?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\text { hcot } p}{\cot p-\cot q}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/vTUBjVzxRHiRCi2QP00vVQudheV5OZhY5uTnwtQQ82E.original.fullsize.png"/><br/><br/>Let height of hill $=\mathrm{H}$ \&amp; horizontal distance between building \&amp; hill = d<br/>$\tan \mathrm{q}=\frac{\mathrm{H}}{\mathrm{d}} \Rightarrow \mathrm{d}=\frac{\mathrm{H}}{\tan \mathrm{q}}=\mathrm{H} \cot \mathrm{q}$<br/>$\tan \mathrm{p}=\frac{(\mathrm{H}-\mathrm{h})}{\mathrm{d}} \Rightarrow \mathrm{d}=(\mathrm{H}-\mathrm{h}) \cot \mathrm{p}$<br/>$\Rightarrow \mathrm{H} \cot \mathrm{q}=(\mathrm{H}-\mathrm{h}) \cot \mathrm{p}$<br/>$H=\frac{h \cot p}{\cot p-\cot q}$</div>


title: the-total-dry-weight-accessible-to-heterotrophs-in-an-ecosystem-will-form-the
slug: the-total-dry-weight-accessible-to-heterotrophs-in-an-ecosystem-will-form-the-94729
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The total dry weight accessible to heterotrophs in an ecosystem will form the:</div>

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

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

answer:
<div class="solution">Gross primary productivity of an ecosystem is the rate of production of organic matter during photosynthesis. A considerable amount of GPP is utilised by plants in respiration. Gross primary productivity minus respiration losses (R), is the net primary productivity (NPP). It is the available biomass for the consumption to heterotrophs (herbivores and decomposers)</div>


title: the-total-number-of-5-digit-numbers-that-can-be-composed-of-distinct-digits-from-0-to-9-is
slug: the-total-number-of-5-digit-numbers-that-can-be-composed-of-distinct-digits-from-0-to-9-is-20549
tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2018 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">27216</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The total number of 5 -digit numbers that can be composed of distinct digits from 0 to 9 is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">45360</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">30240</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">27216</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">15120</span> </li> </ul>

answer:
<div class="solution">Number of 5 digits numbers with all distinct digit is same as filling of 5 vacent placed out of 10 boxes. First digit of any number can be choosen in 9 ways. Remaining 4 digits can be choosen in remaining 9 digits in ${ }^{9} \mathrm{P}_{4}$ ways. Total number of such number<br/>$=9 \times 9 \times 8 \times 7 \times 6=27216$</div>


tags: ['Chemistry', 'Biomolecules', 'JEE Main', 'JEE Main 2024 (30 Jan Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
the-total-number-of-correct-statements-regarding-the-nucleic-acids-is-a-rna-is-regarded-as-the-reserve-of-genetic-information-b-dna-molecule-selfdupli

slug:
the-total-number-of-correct-statements-regarding-the-nucleic-acids-is-a-rna-is-regarded-as-the-reserve-of-genetic-information-b-dna-molecule-selfdupli-39849

question:
<div class="question">The total number of correct statements, regarding the nucleic acids is _________.<br/>A. RNA is regarded as the reserve of genetic information.<br/>B. DNA molecule self-duplicates during cell division<br/>C. DNA synthesizes proteins in the cell.<br/>D. The message for the synthesis of particular proteins is present in DNA<br/>E. Identical DNA strands are transferred to daughter cells.</div>

answer:
<div class="solution"><blockquote><p>A. RNA (ribonucleic acid) is not typically regarded as the reserve of genetic information in the same way that DNA (deoxyribonucleic acid) is. While RNA does play important roles in gene expression, protein synthesis, and regulation of cellular processes, it is DNA that is traditionally considered the primary repository of genetic information in cells.</p><p>B. DNA molecule self-duplicates during cell division. (True) Â </p><p>DNA (deoxyribonucleic acid) self-duplicates during cell division through a process called DNA replication. DNA replication is a fundamental process that ensures each daughter cell receives an identical copy of the genetic information from the parent cell.</p><p>C. While DNA contains the genetic instructions necessary for synthesizing proteins, it does not directly synthesize proteins itself. Instead, the process by which proteins are synthesized from the genetic information encoded in DNA involves several steps and intermediates, collectively known as the central dogma of molecular biology.Â </p><p>D. The message for the synthesis of particular proteins is present in DNA. (True) Â </p><p>The message for the synthesis of particular proteins is present in DNA in the form of a specific sequence of nucleotide bases. This sequence is transcribed into mRNA, which carries the genetic information to the ribosomes for translation into a specific sequence of amino acids, ultimately leading to the synthesis of a particular protein.</p><p>E. Identical DNA strands are transferred to daughter cells. (True)</p><p>Identical DNA strands are transferred to daughter cells through the processes of DNA replication, chromosome segregation, and cell division. These processes ensure that each daughter cell receives a complete and identical set of genetic information from the parent cell.</p></blockquote></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2009 (Phase 1)']
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-subsets-of-a-finite-set-a-has-56-more-elements-than-the-total-number-of-subsets-of-another-finite-set-b-what-is-the-number-of-elem

slug:
the-total-number-of-subsets-of-a-finite-set-a-has-56-more-elements-than-the-total-number-of-subsets-of-another-finite-set-b-what-is-the-number-of-elem-15432

question:
<div class="question">The total number of subsets of a finite set $A$ has 56 more elements than the total number of subsets of another finite set $B$. What is the number of elements in the set A ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">Let sets $A$ and $B$ have $m$ and $n$ elements respectively. The set made by subsets of a finite sets $A$ and $B_{\underline{1}}$ s known as power set i.e. $\mathrm{P}(\mathrm{A})$ and $\mathrm{P}(\mathrm{B})$ We know, if set $\mathrm{A}$ has $n$ elements then $\mathrm{P}(\mathrm{A})$ has $2^{n}$ elements. Thus, The total no. of subsets of a finite set $\mathrm{A}=2^{m}$<br/>and set $B=2^{n}$<br/>So, According to the question $2^{m}-2^{n}=56$<br/>$\Rightarrow 2^{n}\left(2^{m-n}-1\right)=8 \times 7=2^{3} \times\left(2^{3}-1\right)$<br/>On comparing the powers, both side $n=3$ and $m-n=3$<br/>$\Rightarrow m=6$ and $n=3$</div>


tags: ['Physics', 'Ray Optics', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-transparent-media-a-and-b-are-separated-by-a-plane-boundary-the-speed-of-light-in-the-medium-a-is-2-10-8-m-s-1-and-in-the-medium-b-is-2-5-10-8-m-s

slug:
the-transparent-media-a-and-b-are-separated-by-a-plane-boundary-the-speed-of-light-in-the-medium-a-is-2-10-8-m-s-1-and-in-the-medium-b-is-2-5-10-8-m-s-27353

question:
<div class="question">The transparent media <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> are separated by a plane boundary. The speed of light in the medium <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>Ã</mo><msup><mn>10</mn><mn>8</mn></msup><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> and in the medium <math><mi>B</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.5</mo><mo>Ã</mo><msup><mn>10</mn><mn>8</mn></msup><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. The critical angle for which a ray of light going from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> is totally internally reflected is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mn>2</mn></msqrt></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>90</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </div>

answer:
<div class="solution">Refractive index of the medium <math><mi>A</mi></math> relative <math><mi>B</mi></math> is given by<br/><br/><math><msub><mrow><mi> </mi></mrow><mrow><mi>B</mi></mrow></msub><msup><mrow><mi>Î¼</mi></mrow><mrow><mi>A</mi></mrow></msup><mo>=</mo><mfrac><mrow><msub><mrow><mi>Î¼</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow><mrow><msub><mrow><mi>Î¼</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>A</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2.5</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math><br/><br/>Since, critical angle for the light ray going from medium <math><mi>A</mi></math> to <math><mi>B</mi></math> is given by<br/><br/><math><mi>C</mi><mo>=</mo><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi> </mi></mrow><mrow><mi>B</mi></mrow></msub><msup><mrow><mi>Î¼</mi></mrow><mrow><mi>A</mi></mrow></msup></mrow></mfrac></mrow></mfenced></mrow></mrow><mo>=</mo><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2017 (26 Apr Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">81 N</span> </div>
source_db: MarksBatch2_P3.db
title:
the-transverse-displacement-of-a-string-of-a-linear-density-001-kg-m-1-clamped-at-its-ends-is-given-by-y-x-t-003-sin-3-2-x-cos-60-t-where-x-and-y-are-

slug:
the-transverse-displacement-of-a-string-of-a-linear-density-001-kg-m-1-clamped-at-its-ends-is-given-by-y-x-t-003-sin-3-2-x-cos-60-t-where-x-and-y-are-96855

question:
<div class="question">The transverse displacement of a string of a linear density $0.01 \mathrm{~kg} \mathrm{~m}^{-1}$, clamped at its ends is given by $Y_{(x, t)}=0.03 \sin \left(\frac{2 \pi x}{3}\right) \cos (60 \pi t)$, where $x$ and $y$ are in metres and time $t$ is in seconds. Tension in the string is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">9 N</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">36 N</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">162 N</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">81 N</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Transverse displacement<br/>$$<br/>y_{(x, t)}=0.03 \sin \left(\frac{2 \pi x}{3}\right) \cos 60 \pi t \text {. }<br/>$$<br/>This is equation of standing wave.<br/>The standard equation of standing wave is $y=a \sin k x \cos \omega t$<br/>Here, $\omega=60 \pi, k=2 \pi / 3$<br/>So, $V=\frac{60 \pi}{2 \pi} \times 3=90$<br/>So, $\sqrt{\frac{T}{\mu}}=90$<br/>$$<br/>\Rightarrow \quad T=90^2 \mu \Rightarrow T=90^2 \times 10=81 \mathrm{~N}<br/>$$</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2020 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-transverse-section-of-a-plant-shows-following-anatomical-features-a-large-number-of-scattered-vascular-bundles-surrounded-by-bundle-sheath-b-large

slug:
the-transverse-section-of-a-plant-shows-following-anatomical-features-a-large-number-of-scattered-vascular-bundles-surrounded-by-bundle-sheath-b-large-27474

question:
<div class="question"><p>The transverse section of a plant shows following anatomical features:</p><p>(a) Large number of scattered vascular bundles surrounded by bundle sheath<br/>(b) Large conspicuous parenchymatous ground tissue<br/>(c) Vascular bundles conjoint and closed<br/>(d) Phloem parenchyma absent</p><p>Identify the category of plant and its part:</p></div>

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

answer:
<div class="solution"><blockquote><p><strong>MONOCOT STEM:</strong></p><p>a.<strong> </strong>Epidermis is uniseriate with compactly arranged barrel shaped cells covered with thick cuticle trichomes are absent.<br/>b. Hypodermis<strong>:</strong> It is made up of a few layers of compactly arranged sclerenchyma cells. It provides mechanical support.<br/>c. Ground tissue is the major component and is formed by an undifferentiated mass of loosely arranged parenchyma cells<strong> </strong>enclosing intercellular spaces. It is not differentiated into cortex or pith.<br/>d. Many vascular bundles are found scattered in the ground tissue and this condition is called attactostele. From periphery to center there is a gradual decrease in the number of vascular bundles and increase in size. The vascular bundles are conjoint, collateral and closed with endarch xylem. Water filled lysigenous cavity present in association with the protoxylem. It is formed by the breakdown of inner protoxylem during earlier stages of growth. Phloem parenchyma is absent. The protophloem forms a thin layer above the functional metaphloem present towards the metaxylem. Each vascular bundle has a prominent bundle sheath made up of sclerenchyma fibres.</p></blockquote></div>


title: the-trophic-level-of-cuscuta-orobanche-and-albugo-is
slug: the-trophic-level-of-cuscuta-orobanche-and-albugo-is-55001
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The trophic level of <em>Cuscuta, Orobanche, </em>and <em>Albugo</em> is</div>

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

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

answer:
<div class="solution"><div style="text-align: justify;">A parasitic plant is a plant that derives some or all of its nutritional requirement from another living plant. They make up about 1% of angiosperms and are in almost every biome in the world. All parasitic plants have modified roots, named haustoria (singular: haustorium), which penetrates the host plants, connecting them to the conductive system â either the xylem, the phloem, or both. This provides them with the ability to extract water and nutrients from the host. <i>All these plants are parasitic.</i></div></div>


title: the-twave-of-a-standard-ecg-represents
slug: the-twave-of-a-standard-ecg-represents-71679
question: <div class="question">The T-wave of a standard ECG represents:</div>
tags: ['Biology', 'Body Fluids and Circulation', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Repolarisation of both ventricles</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Returning of ventricles from excited to normal state</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Ends of T-wave marks the end of systole</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">In an standard ECG, the T-wave represents the repolarisation of both ventricles means repolarisation of the ventricles or returning of ventricles from excited to normal state. The end of the T-wave marks the end of systole.</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
the-two-circles-x-2-y-2-r-2-and-x-2-y-2-10-x-16-0-intersect-at-two-distinct-points-then-which-one-of-the-following-is-correct

slug:
the-two-circles-x-2-y-2-r-2-and-x-2-y-2-10-x-16-0-intersect-at-two-distinct-points-then-which-one-of-the-following-is-correct-30192

question:
<div class="question">The two circles $x^{2}+y^{2}=r^{2}$ and $x^{2}+y^{2}-10 x+16=0$ intersect at two distinct points. Then which one of the following is correct?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad 2   &lt; \mathrm{r} &lt; 8$</span> </div>

answer:
<div class="solution">For the circle, $\mathrm{x}^{2}+\mathrm{y}^{2}=\mathrm{r}^{2}$, centre $(0,0)$ radius $=\mathrm{r}$ If the circle $x^{2}+y^{2}-10 x+16=0$ is compared with general form $x^{2}+y^{2}+2 g+2 f y+c=0$, we get<br/>$2 \mathrm{~g}=-10,2 \mathrm{f}=0, \mathrm{c}=16$<br/>$\Rightarrow \mathrm{g}=-5, \mathrm{f}=0$<br/>$\therefore$ centre $=(+5,0)$<br/>radius $=\sqrt{g^{2}+f^{2}-c}=\sqrt{25+0-16}=\sqrt{9}=3$<br/>Given, two circles intersect at two distinct points,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/dik6vDeD0isitTWeXHM-dga4tr8LYIxtNc9RRZQ9CZw.original.fullsize.png"/><br/><br/>To interset at two points, $\mathrm{r}$ should be greater than 2 So, $2 &lt; \mathrm{r} &lt; 8$</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-two-electrons-have-the-following-set-of-quantum-numbers-beginarrayl-p322frac12-q300frac12-endarray-which-of-the-following-statement-is-true-1

slug:
the-two-electrons-have-the-following-set-of-quantum-numbers-beginarrayl-p322frac12-q300frac12-endarray-which-of-the-following-statement-is-true-1-47602

question:
<div class="question">The two electrons have the following set of quantum numbers :<br/>\[<br/>\begin{array}{l}<br/>P=3,2,-2,+\frac{1}{2} \\<br/>Q=3,0,0,+\frac{1}{2}<br/>\end{array}<br/>\]<br/>Which of the following statement is true?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( P \) has greater energy than \( Q \)</span> </div>

answer:
<div class="solution">For electron $P$, the values of quantum numbers are $n=3, I=2, m l=-2$ and $s=+1 / 2$. For electron $Q$ quantum numbers are $n=3, I=0, m l=0$ and $s=+1 / 2$. Therefore, from the quantum number values, electron $P$ belongs to $3 d-$ orbital and electron $Q$ to $3 s$ - orbital. Energy of the orbital is $s &lt; p &lt; d &lt; f$.<br/>Hence, energy of electron $P$ is higher than electron $Q$.</div>


tags: ['Chemistry', 'Structure of Atom', 'KCET', 'KCET 2015']
source_db: MarksBatch2_P3.db
title:
the-two-electrons-have-the-following-set-of-quantum-numbers-beginarrayl-p322frac12-q300frac12-endarray-which-of-the-following-statement-is-true

slug:
the-two-electrons-have-the-following-set-of-quantum-numbers-beginarrayl-p322frac12-q300frac12-endarray-which-of-the-following-statement-is-true-68013

question:
<div class="question">The two electrons have the following set of quantum numbers :<br/>\[<br/>\begin{array}{l}<br/>P=3,2,-2,+\frac{1}{2} \\<br/>Q=3,0,0,+\frac{1}{2}<br/>\end{array}<br/>\]<br/>Which of the following statement is true?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( P \) has greater energy than \( Q \)</span> </div>

answer:
<div class="solution">For electron $P$, the values of quantum numbers are $n=3, I=2, m l=-2$ and $s=+1 / 2$. For electron $Q$ quantum numbers are $n=3, I=0, m l=0$ and $s=+1 / 2$. Therefore, from the quantum number values, electron $P$ belongs to $3 d-$ orbital and electron $Q$ to $3 s$ - orbital. Energy of the orbital is $s &lt; p &lt; d &lt; f$.<br/>Hence, energy of electron $P$ is higher than electron $Q$.</div>


tags: ['Chemistry', 'General Organic Chemistry', 'AP EAMCET', 'AP EAMCET 2010']
source_db: MarksBatch2_P3.db
title:
the-two-enantiomers-of-secondary-butyl-chloride-differ-from-each-other-in-which-one-of-the-following-properties-1

slug:
the-two-enantiomers-of-secondary-butyl-chloride-differ-from-each-other-in-which-one-of-the-following-properties-1-66044

question:
<div class="question">The two enantiomers of secondary butyl chloride differ from each other in which one of the following properties?</div>

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

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

answer:
<div class="solution">Enantiomers have same physical properties but differ in specific rotation. Thus, the two enantiomers of secondary butyl chloride differ in specific rotation.</div>


tags: ['Chemistry', 'General Organic Chemistry', 'TS EAMCET', 'TS EAMCET 2010']
source_db: MarksBatch2_P3.db
title:
the-two-enantiomers-of-secondary-butyl-chloride-differ-from-each-other-in-which-one-of-the-following-properties

slug:
the-two-enantiomers-of-secondary-butyl-chloride-differ-from-each-other-in-which-one-of-the-following-properties-35537

question:
<div class="question">The two enantiomers of secondary butyl chloride differ from each other in which one of the following properties?</div>

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

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

answer:
<div class="solution">Enantiomers have same physical properties but differ in specific rotation. Thus, the two enantiomers of secondary butyl chloride differ in specific rotation.</div>


tags: ['Chemistry', 'Electrochemistry', 'WBJEE', 'WBJEE 2014']
source_db: MarksBatch2_P3.db
title:
the-two-halfcell-reactions-of-an-electrochemical-cell-is-given-as-ag-e-ag-e-ax-ag-03995-v-fe-3-fe-3-e-e-fe-3-fv-2-07120-v-the-value-of-cell-emf-will-b

slug:
the-two-halfcell-reactions-of-an-electrochemical-cell-is-given-as-ag-e-ag-e-ax-ag-03995-v-fe-3-fe-3-e-e-fe-3-fv-2-07120-v-the-value-of-cell-emf-will-b-12630

question:
<div class="question">$\begin{array}{lllll}\text {The two } &amp; \text { half-cell } &amp; \text { reactions } &amp; \text { of } &amp; \text { an }\end{array}$ electrochemical cell is given as $\mathrm{Ag}^{+}+e^{-} \longrightarrow \mathrm{Ag} ; \quad E_{\mathrm{Ax}^{+} / \mathrm{Ag}}^{\circ}=-0.3995 \mathrm{V}$ $\mathrm{Fe}^{3+} \longrightarrow \mathrm{Fe}^{3 *}+e^{-} ; E_{\mathrm{Fe}^{3+} \mathrm{Fv}^{2+}}=-0.7120 \mathrm{V}$. The value of cell EMF will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-0.3125 \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.3125 \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.114 \mathrm{V}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-1.114 \mathrm{V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.3125 \mathrm{V}$</span> </div>

answer:
<div class="solution">Species with more negative $E^{\circ}$ (standard reduction potential) generally acts as reducing agent while with less negative $E^{\circ}$ acts as oxidising agent. Thus, the overall reaction is
<br/>$\begin{aligned} \mathrm{Ag}^{+}+\mathrm{Fe}^{2+} &amp; \longrightarrow \mathrm{Fe}^{3+}+\mathrm{Ag} \\ \Delta E^{\circ} &amp;=E_{\mathrm{OA}}^{\circ}-E_{\mathrm{RA}}^{\circ} \\ &amp;=-0.3995-(-0.7120) \mathrm{V} \\ &amp;=-0.3995+0.7120 \mathrm{V} \\ &amp;=+0.3125 \mathrm{V} \end{aligned}$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2010 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
the-two-lines-of-regression-are-8-x-10-y-66-and-40-x-18-y-214-and-variance-of-x-series-is-9-what-is-the-standard-deviation-of-y-series

slug:
the-two-lines-of-regression-are-8-x-10-y-66-and-40-x-18-y-214-and-variance-of-x-series-is-9-what-is-the-standard-deviation-of-y-series-85927

question:
<div class="question">The two lines of regression are $8 x-10 y=66$ and $40 x-18 y=214$ and variance of $x$ series is 9 . What is the standard deviation of y series? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">Let us consider lines $\begin{array}{lll} &amp; 8 x-10 y=66 &amp; \text { and } &amp; 40 x-18 y=214 \\ 10 y=8 x-66 &amp; \Rightarrow &amp; 40 x=18 y+214\end{array}$<br/>$\Rightarrow \quad b_{y x}=\frac{8}{10}=\frac{4}{5} \quad \Rightarrow \quad b_{x y}=\frac{18}{40}=\frac{9}{20}$<br/>Thus, $r=\pm \sqrt{\frac{4}{5} \times \frac{9}{20}}=\frac{3}{5}$<br/>Also, $\sigma_{x}=\sqrt{9}=3$<br/>$\therefore \sigma_{y}=\frac{b y x \times \sigma_{x}}{r}=\frac{\frac{4}{5} \times 3}{r}=\frac{12}{5 r}=\frac{12}{5} \times \frac{5}{3}=4$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">20 Hz</span> </div>
source_db: MarksBatch2_P3.db
title:
the-two-nearest-harmonics-of-a-tube-closed-at-one-end-and-open-at-other-end-are-220-hz-and-260-hz-what-is-the-fundamental-frequency-of-the-system-1

slug:
the-two-nearest-harmonics-of-a-tube-closed-at-one-end-and-open-at-other-end-are-220-hz-and-260-hz-what-is-the-fundamental-frequency-of-the-system-1-19962

question:
<div class="question">The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">10 Hz</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">20 Hz</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">30 Hz</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">40 Hz</span> </li> </ul>

answer:
<div class="solution">Two successive frequencies of closed pipe<br/><br/> <math><mfrac><mrow><mi>n</mi><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>220</mn></math>             ....(i)<br/><br/> <math><mfrac><mrow><mfenced separators="|"><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>260</mn></math>             ......(ii)<br/><br/>Dividing (ii) by (i), we get<br/><br/> <math><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>260</mn></mrow><mrow><mn>220</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>13</mn></mrow><mrow><mn>11</mn></mrow></mfrac></math> <br/><br/> <math><mn>11</mn><mi>n</mi><mo>+</mo><mn>22</mn><mo>=</mo><mn>13</mn><mi>n</mi></math> <br/><br/> <math><mi>n</mi><mo>=</mo><mn>11</mn></math> <br/><br/>So,  <math><mn>11</mn><mfrac><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>220</mn></math> <br/><br/> <math><mfrac><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>20</mn></math> <br/><br/>So fundamental frequency is 20 Hz.</div>


tags: ['Physics', 'Waves and Sound', 'NEET', 'NEET 2017']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">20 Hz</span> </div>
source_db: MarksBatch2_P3.db
title:
the-two-nearest-harmonics-of-a-tube-closed-at-one-end-and-open-at-other-end-are-220-hz-and-260-hz-what-is-the-fundamental-frequency-of-the-system

slug:
the-two-nearest-harmonics-of-a-tube-closed-at-one-end-and-open-at-other-end-are-220-hz-and-260-hz-what-is-the-fundamental-frequency-of-the-system-78195

question:
<div class="question">The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">10 Hz</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">20 Hz</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">30 Hz</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">40 Hz</span> </li> </ul>

answer:
<div class="solution">Two successive frequencies of closed pipe<br/><br/> <math><mfrac><mrow><mi>n</mi><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>220</mn></math>             ....(i)<br/><br/> <math><mfrac><mrow><mfenced separators="|"><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>260</mn></math>             ......(ii)<br/><br/>Dividing (ii) by (i), we get<br/><br/> <math><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>260</mn></mrow><mrow><mn>220</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>13</mn></mrow><mrow><mn>11</mn></mrow></mfrac></math> <br/><br/> <math><mn>11</mn><mi>n</mi><mo>+</mo><mn>22</mn><mo>=</mo><mn>13</mn><mi>n</mi></math> <br/><br/> <math><mi>n</mi><mo>=</mo><mn>11</mn></math> <br/><br/>So,  <math><mn>11</mn><mfrac><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>220</mn></math> <br/><br/> <math><mfrac><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mn>4</mn><mi>l</mi></mrow></mfrac><mo>=</mo><mn>20</mn></math> <br/><br/>So fundamental frequency is 20 Hz.</div>


title: the-two-parabolas-y-2-4-a-x-and-x-2-4-ay-intersect
slug: the-two-parabolas-y-2-4-a-x-and-x-2-4-ay-intersect-39161
question: <div class="question">The two parabolas $y^{2}=4 a x$ and $x^{2}=4$ ay intersect</div>
tags: ['Mathematics', 'Parabola', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">at two points on the line $y=x$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">only at the origin</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">at three points one of which lies on $y+x=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">only at $(4 a, 4 a)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">at two points on the line $y=x$</span> </div>

answer:
<div class="solution">The parabolas $\mathrm{y}^{2}=4 \mathrm{ax}$ and $\mathrm{x}^{2}=4$ ay They intersect at $(0,0)$ and $(4 a, 4 a)$ These points lie on $\mathrm{y}=\mathrm{x}$</div>


title: the-two-planes-a-x-b-y-cz-d-0-and-a-x-b-y-cz-d-1-0-where-d-d-1-have
slug: the-two-planes-a-x-b-y-cz-d-0-and-a-x-b-y-cz-d-1-0-where-d-d-1-have-56355
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The two planes $a x+b y+c z+d=0$ and $a x+b y+c z+d_{1}$ $=0$, where $d \neq d_{1}$, have</div>

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

answer:
<div class="solution">Two planes $a x+b y+c z+d=0$ and $a x+b y+c z+d_{1}$ $=0$ are parallel to each other.<br/>They have no common point.</div>


tags: ['Chemistry', 'Surface Chemistry', 'JEE Main', 'JEE Main 2017 (02 Apr)']
source_db: MarksBatch2_P3.db
title:
the-tyndall-effect-is-observed-only-when-the-following-conditions-are-satisfied-i-the-diameter-of-the-dispersed-particles-is-much-smaller-than-the-wav-1

slug:
the-tyndall-effect-is-observed-only-when-the-following-conditions-are-satisfied-i-the-diameter-of-the-dispersed-particles-is-much-smaller-than-the-wav-1-94569

question:
<div class="question">The Tyndall effect is observed only when the following conditions are satisfied,<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">i</mi></mfenced></math> The diameter of the dispersed particles is much smaller than the wavelength of the light used.<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>ii</mi></mfenced></math> The diameter of the dispersed particle is not much smaller than the wavelength of the light used.<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>iii</mi></mfenced></math> The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude.<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>iv</mi></mfenced></math> The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.</div>

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

answer:
<div class="solution">The Tyndall effect is an easy way of determining whether a mixture is colloidal or not. When light is shined through a true solution, the light passes cleanly through the solution, however when light is passed through a colloidal solution, the substance in the dispersed phases scatters the light in all directions, making it readily seen.<br/>The Tyndall effect is observed only when,<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>ii</mi></mfenced></math> The diameter of the dispersed particle is not much smaller than the wavelength of the light used.<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>iv</mi></mfenced></math> The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.</div>


tags: ['Chemistry', 'Surface Chemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-tyndall-effect-is-observed-only-when-the-following-conditions-are-satisfied-i-the-diameter-of-the-dispersed-particles-is-much-smaller-than-the-wav

slug:
the-tyndall-effect-is-observed-only-when-the-following-conditions-are-satisfied-i-the-diameter-of-the-dispersed-particles-is-much-smaller-than-the-wav-48022

question:
<div class="question">The Tyndall effect is observed only when the following conditions are satisfied,<br/>(i) The diameter of the dispersed particles is much smaller than the wavelength of the light used.<br/>(ii) The diameter of the dispersed particle is not much smaller than the wavelength of the light used.<br/>(iii) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude.<br/>(iv) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(ii) and (iv)</span> </div>

answer:
<div class="solution">The Tyndall effect is an easy way of determining whether a mixture is colloidal or not. When light is shined through a true solution, the light passes cleanly through the solution, however when light is passed through a colloidal solution, the substance in the dispersed phases scatters the light in all directions, making it readily seen.<br/>The Tyndall effect is observed only when,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>ii</mi></mfenced></math> The diameter of the dispersed particle is not much smaller than the wavelength of the light used.<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>iv</mi></mfenced></math> The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-type-of-a-battery-in-which-the-reaction-occurs-only-once-and-then-battery-becomes-dead-over-a-period-of-time-is-known-as

slug:
the-type-of-a-battery-in-which-the-reaction-occurs-only-once-and-then-battery-becomes-dead-over-a-period-of-time-is-known-as-17395

question:
<div class="question">The type of a battery, in which the reaction occurs only once and then battery becomes dead over a period of time is known as</div>

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

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

answer:
<div class="solution"><blockquote><p>By definition:</p><p>The type of a battery, in which the reaction occurs only once and then battery becomes dead over a period of time is known as primary cell/batteries.</p><p>eg. clock cell, remote cell, etc.</p></blockquote></div>


title: the-type-of-bond-that-is-most-important-in-maintaining-secondary-structure-of-a-protein-is
slug: the-type-of-bond-that-is-most-important-in-maintaining-secondary-structure-of-a-protein-is-58914
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The type of bond that is most important in maintaining secondary structure of a protein is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Hydrogen bonding within the backbone</span> </div>

answer:
<div class="solution">Secondary structure of a protein is generally maintained by hydrogen bonding between the <math><mo>-</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi></math> group of one amide and the <math><mi mathvariant="normal">C</mi><mo>=</mo><mi mathvariant="normal">O</mi></math> group of another amide.<br/><br/><img alt="" height="90" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/Q_102755_soln.jpg" style="max-width:100%; object-fit:contain" width="208"/></div>


tags: ['Biology', 'Structural Organisation in Animals', 'AIIMS', 'AIIMS 2009']
source_db: MarksBatch2_P3.db
title:
the-type-of-epithelial-cells-which-line-the-inner-surface-of-fallopian-tubes-bronchioles-and-small-bronchi-are-known-as-1

slug:
the-type-of-epithelial-cells-which-line-the-inner-surface-of-fallopian-tubes-bronchioles-and-small-bronchi-are-known-as-1-73148

question:
<div class="question">The type of epithelial cells which line the inner surface of Fallopian tubes, bronchioles and small bronchi are known as</div>

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

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

answer:
<div class="solution">Ciliated epithelium is a region of epithelium consisting of columnar or cuboidal cells bearing hairlike appendages that are capable of beating rapidly. Ciliated epithelium performs the functions of moving particles of fluids over the epithelial surface. Cuboidal ciliated epithelium occurs in certain parts of uriniferous tubules whereas columnar ciliated epithelium occurs in fallopian tubules, nasal passages, bronchioles, small bronchi and buccopharyngeal cavity of frog. It often occurs in the vicinity of mucus secreting goblet cells.</div>


tags: ['Biology', 'Structural Organisation in Animals', 'AIIMS', 'AIIMS 2006']
source_db: MarksBatch2_P3.db
title:
the-type-of-epithelial-cells-which-line-the-inner-surface-of-fallopian-tubes-bronchioles-and-small-bronchi-are-known-as

slug:
the-type-of-epithelial-cells-which-line-the-inner-surface-of-fallopian-tubes-bronchioles-and-small-bronchi-are-known-as-15471

question:
<div class="question">The type of epithelial cells which line the inner surface of Fallopian tubes, bronchioles and small bronchi are known as</div>

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

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

answer:
<div class="solution">Ciliated epithelium is a region of epithelium consisting of columnar or cuboidal cells bearing hairlike appendages called cilia, that are capable of beating rapidly. Ciliated epithelium performs the functions of moving particles of fluids over the epithelial surface. Cubical ciliated epithelium occurs in certain parts of uriniferous tubules whereas columnar ciliated epithelium occurs in fallopian tubules, nasal passages, bronchioles, small bronchi and buccopharyngeal cavity of frog. It often occurs in the vicinity of mucus secreting goblet cells.<br/>Squamous epithelium are found in linning of alveoli in the lungs and Bowman's capsule in the kidney. Columnar epithelium are found in the lining layer of gastrointestinal tract, gall bladder, uterus etc. and cubical or cuboidal epithelium lines the salivary ducts, pancreated ducts, gastric glands, thyroid follicles, germinal epithelium of ovary, proximal part of uriniferous tubules etc.</div>


title: the-type-of-placentation-in-which-ovary-is-syncarpous-unilocular-and-ovules-on-sutures-is-called
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
slug:
the-type-of-placentation-in-which-ovary-is-syncarpous-unilocular-and-ovules-on-sutures-is-called-59634

question:
<div class="question">The type of placentation in which ovary is syncarpous, unilocular and ovules on sutures is called</div>

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

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

answer:
<div class="solution">Screw pine (<em>Pandanus</em>) bear stilt roots. <em>Trapa</em> bears assimilatory roots. <em>Orchid</em> bear clinging roots.</div>


tags: ['Biology', 'Animal Kingdom', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-typical-body-plan-of-a-chordate-is-given-in-the-following-diagram-given-labellings-a-and-b-respectively-are

slug:
the-typical-body-plan-of-a-chordate-is-given-in-the-following-diagram-given-labellings-a-and-b-respectively-are-27053

question:
<div class="question">The typical body plan of a chordate is given in the following diagram. Given labellings A and B, respectively, are:<br/> <br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/33_bioC_ADd.JPG" style="max-width:100%; object-fit:contain"/></div>

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

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

answer:
<div class="solution">Members of Chordata possess 3 fundamental characters at any stage of life:<br/><br/><math><mn>1</mn><mo>.</mo></math> Notochord - Solid, mesodermal and later on develop into vertebral column.<br/><math><mn>2</mn><mo>.</mo></math> Dorsal hollow nerve cord (or dorsal tubular nerve cord or neural tube)<br/><math><mn>3</mn><mo>.</mo></math> Pharyngeal gill slits.<br/><br/>Post anal tail may or may not be present.</div>


title: the-unit-of-energy-if-fundamental-units-are-taken-as-force-f-acceleration-a-and-time-t-is
slug: the-unit-of-energy-if-fundamental-units-are-taken-as-force-f-acceleration-a-and-time-t-is-67482
tags: ['Physics', 'Units and Dimensions', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">The unit of energy if fundamental units are taken as force <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">F</mi></mfenced></math>, acceleration <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">A</mi></mfenced></math> and time <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">T</mi></mfenced></math> is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfenced close="]" open="[" separators="|"><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">A</mi><msup><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></math></span> </div>

answer:
<div class="solution"><math><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">Â </mi><mo>=</mo><mi mathvariant="normal">Â </mi><mi mathvariant="normal">W</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">Â </mi><mo>=</mo><mi mathvariant="normal">Â </mi><mfenced close="}" open="{" separators="|"><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">Â </mi><mo>Ã</mo><mi mathvariant="normal">Â </mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow></mfenced><mo>Ã</mo><mi mathvariant="normal">Â </mi><mfrac><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mi mathvariant="normal">Â </mi></math> <br/><br/> <math><mo>=</mo><mfenced close="]" open="[" separators="|"><mrow><msup><mrow><mi mathvariant="normal">F</mi></mrow><mrow><mn>1</mn></mrow></msup><msup><mrow><mi mathvariant="normal">A</mi></mrow><mrow><mn>1</mn></mrow></msup><msup><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></math></div>


tags: ['Biology', 'Biotechnology and Its Applications', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-use-of-bioresources-by-multinational-companies-and-other-organisation-without-proper-authorisation-from-the-countries-and-people-concerned-without

slug:
the-use-of-bioresources-by-multinational-companies-and-other-organisation-without-proper-authorisation-from-the-countries-and-people-concerned-without-70376

question:
<div class="question">"The use of bio-resources by multinational companies and other organisation, without proper authorisation from the countries and people concerned, without compensatory payment"  will be termed as</div>

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

answer:
<div class="solution">Bioethics may be viewed as a set of standards that may be used to regulate our activities in relation to the biological world. Patents which are being granted for biological entities and for products derived from them are known as biopatents.</div>


tags: ['Biology', 'Biotechnology and Its Applications', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-use-of-bioresources-by-multinational-companies-and-other-organisations-without-proper-authorisation-from-the-countries-and-people-concerned-is-kno

slug:
the-use-of-bioresources-by-multinational-companies-and-other-organisations-without-proper-authorisation-from-the-countries-and-people-concerned-is-kno-14176

question:
<div class="question">The use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned, is known as:</div>

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

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

answer:
<div class="solution">Biopiracy is exploitation of bioresources of any company. This is done by other companies for commercial use with or without patent rights. Bioresouces mean organisms that can provide benefits commercially. These are abundant in developing countries but less in developed countries. But the developed countries have an advantage as they have good technologies. Developing countries have resources and also traditional methods and these are used by developed countries and with the help of their rich technology these countries get patent rights easily without proper laws.</div>


title: the-value-of-0-4-tan-x-d-x-0-4-cot-x-d-x-is-equal-to
slug: the-value-of-0-4-tan-x-d-x-0-4-cot-x-d-x-is-equal-to-19863
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $\int_{0}^{\frac{\pi}{4}} \sqrt{\tan x} d x+\int_{0}^{\frac{\pi}{4}} \sqrt{\cot x} d x$ is equal to</div>

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

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

answer:
<div class="solution">$\int_{0}^{\frac{\pi}{4}} \sqrt{\tan x} d x+\int_{0}^{\frac{\pi}{4}} \sqrt{\cot x} \cdot \mathrm{dx}$<br/>$=\int_{0}^{\frac{\pi}{4}}(\sqrt{\tan x}+\sqrt{\cot x}) \mathrm{dx}$<br/>$=\int_{0}^{\frac{\pi}{4}}\left(\frac{\sqrt{\sin x}}{\sqrt{\cos x}}+\frac{\sqrt{\cos x}}{\sqrt{\sin x}}\right) \mathrm{dx}$<br/>$=\sqrt{2} \int_{0}^{\frac{\pi}{4}} \frac{(\sin x+\cos x)}{\left(\sqrt{1-\left(\sin ^{2} x+\cos ^{2} x-2 \sin x \cos x\right)}\right)} \cdot d x$<br/>$\quad=\int_{0}^{4} \frac{\sin x+\cos x}{\sqrt{\sin x} \cdot \sqrt{\cos x}} \cdot \mathrm{dx}$<br/>$\quad$ Put $\sin x-\cos x=t \Rightarrow(\cos x+\sin x) d x=d t$<br/>When $x=0, \mathrm{t}=-1$ and $\mathrm{x}=\frac{\pi}{4}, \mathrm{t}=0 .$<br/>$=\sqrt{2} \int_{-1}^{0} \frac{1}{\sqrt{1-\mathrm{t}^{2}}} \cdot \mathrm{dt}=\sqrt{2}\left(\sin ^{-1} \mathrm{t}\right)_{-1}^{0}$<br/>$=\sqrt{2}\left[\sin ^{-1}(0)-\sin ^{-1}(-1)\right]$<br/>$=\sqrt{2}\left[0-\left(\frac{-\pi}{2}\right)\right]$<br/>$=\frac{\pi}{\sqrt{2}} .$</div>


title: the-value-of-1-1-1-1-1-x-1-1-1-1-y-is
slug: the-value-of-1-1-1-1-1-x-1-1-1-1-y-is-79267
tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$x y$</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of<br/>$\left|\begin{array}{ccc}1 &amp; 1 &amp; 1 \\ 1 &amp; 1+x &amp; 1 \\ 1 &amp; 1 &amp; 1+y\end{array}\right|$ is</div>

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

answer:
<div class="solution">$\left|\begin{array}{ccc}1 &amp; 1 &amp; 1 \\ 1 &amp; 1+x &amp; 1 \\ 1 &amp; 1 &amp; 1+y\end{array}\right|$<br/>$=[(1+x)(1+y)-1]-1(1+y-1)+1(1-1-x)$<br/>$=1+x+y+x y-1-y-x$<br/>$=x y$<br/>$\therefore$ Option (c) is correct.</div>


title: the-value-of-1-mole-of-any-pure-gas-at-standard-temperature-and-pressure-is-always-equal-to
slug: the-value-of-1-mole-of-any-pure-gas-at-standard-temperature-and-pressure-is-always-equal-to-23199
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'MHT CET', 'MHT CET 2019 (Shift 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of 1 mole of any pure gas at standard temperature and pressure is always equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mn>0.022414</mn><mi></mi><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>22.414</mn><mi></mi><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>2.2414</mn><mi></mi><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>0.22414</mn><mi></mi><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>0.022414</mn><mi></mi><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> </div>

answer:
<div class="solution">The value of 1 mole of any pure gas at standard and pressure (STP) is equal to 22.414 L <math><mn>1</mn><mi>L</mi><mo>=</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></msup><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></math> <br/><math><mo>â´</mo><mtext>ââââââ</mtext><mn>22.4</mn><mi>L</mi><mo>=</mo><mn>0.022414</mn><msup><mrow><mi>m</mi></mrow><mrow><mn>3</mn></mrow></msup></math> <br/>So, from Eq. (i), we get <br/><math><mi>p</mi><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>R</mi></mrow></mfrac></math> or <math><mtext>â</mtext><mi>p</mi><mo>â</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></div>


title: the-value-of-2-1-i-3-n-2-1-i-3-n-where-n-is-not-a-multiple-of-3-and-i-1-is
slug: the-value-of-2-1-i-3-n-2-1-i-3-n-where-n-is-not-a-multiple-of-3-and-i-1-is-12094
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">-1</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of <br/>$\left(\frac{-1+\mathrm{i} \sqrt{3}}{2}\right)^{\mathrm{n}}+\left(\frac{-1-\mathrm{i} \sqrt{3}}{2}\right)^{\mathrm{n}}$<br/>where $\mathrm{n}$ is not a multiple of 3 and $i=\sqrt{-1}$, is</div>

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

answer:
<div class="solution">$\left(\frac{-1+\mathrm{i} \sqrt{3}}{2}\right)^{\mathrm{n}}+\left(\frac{-1-\mathrm{i} \sqrt{3}}{2}\right)^{\mathrm{n}}$<br/>we know that cube roots of a unit use $1, \omega, \omega^{2}$ $\omega=\frac{-1+\mathrm{i} \sqrt{3}}{2}, \omega^{2}=\frac{-1-\mathrm{i} \sqrt{3}}{2}$<br/>So, $\left(\frac{-1+i \sqrt{3}}{2}\right)^{n}+\left(\frac{-1-i \sqrt{3}}{2}\right)^{n}=\omega^{n}+\omega^{2 n}$<br/>Given, $\mathrm{n}$ is not multiple of $3 .$ So, $\mathrm{n}=1,2,4,5 \ldots$ In any case, $\omega^{\mathrm{n}}+\omega^{2 \mathrm{n}}=\omega+\omega^{2}=-1$</div>


title: the-value-of-2-2-a-x-3-b-x-c-d-x-depends-on-which-of-the-following
slug: the-value-of-2-2-a-x-3-b-x-c-d-x-depends-on-which-of-the-following-30351
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x$ depends on which of the following? $\quad\mathrm{}$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Value of $c$ only</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \int_{-2}^{2}\left(a x^{3}+b x+c\right) d x \\ &amp;=\left[\frac{a x^{4}}{4}+\frac{b x^{2}}{2}+\frac{c x}{1}\right]_{-2}^{2} \\ &amp;=\left[\frac{a(16)}{4}+\frac{b(4)}{2}+2 c\right]-\left[\frac{a(16)}{4}+\frac{b(4)}{2}-2 c\right]=4 c \end{aligned}$<br/>So, the value of given integral depends on the value of $c$ only</div>


title: the-value-of-3-cosec-2-0-sec-2-0-is-equal-to
slug: the-value-of-3-cosec-2-0-sec-2-0-is-equal-to-17173
question: <div class="question">The value of $\sqrt{3}$ cosec $20^{\circ}-\sec 20^{\circ}$ is equal to</div>
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2017 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-4$</span> </li> </ul>

answer:
<div class="solution">&amp; \sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}=\frac{\sqrt{3}}{\sin 20^{\circ}}-\frac{1}{\cos 20^{\circ}} \\ &amp;=\frac{\sqrt{3} \cos 20^{\circ}-\sin 20^{\circ}}{\sin 20^{\circ} \cos 20^{\circ}} \\ &amp;=\frac{2\left(\frac{\sqrt{3}}{2} \cos 20^{\circ}-\frac{1}{2} \sin 20^{\circ}\right)}{\sin 20^{\circ} \cos 20^{\circ}} \end{aligned}$<br/>$=\frac{2\left(\cos 30^{\circ} \cos 20^{\circ}-\sin 30^{\circ} \sin 20^{\circ}\right)}{\left(\frac{2 \sin 20^{\circ} \cos 20^{\circ}}{2}\right)}$<br/>$=\frac{4\left[\cos \left(30^{\circ}+20^{\circ}\right)\right]}{\sin 40^{\circ}}$<br/>$=\frac{4 \cos 50^{\circ}}{\sin 40^{\circ}}=\frac{4 \cos \left(90^{\circ}-40^{\circ}\right)}{\sin 40^{\circ}}=\frac{4 \sin 40^{\circ}}{\sin 40^{\circ}}=4 .$</div>


title: the-value-of-a-b-c-o-s-x-x-7-s-i-n-x-d-x-where-a-b-0-is
slug: the-value-of-a-b-c-o-s-x-x-7-s-i-n-x-d-x-where-a-b-0-is-12794
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of<br/>$\int_{a}^{b} \frac{x^{7}+\sin x}{\cos x} d x$ where $a+b=0$ is</div>

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

answer:
<div class="solution">$a+b=0 \Rightarrow a=-b$<br/>$I=\int_{-b}^{b} \frac{x^{7}+\sin x}{\cos x}$<br/>Using property<br/>$\int_{-a}^{a} f(x) d x=\left\{\begin{array}{l}\int_{0}^{2 a} f(x) d x ; \text { if } f(x) \text { is even } \\ 0 &amp; ; \text { if } f(x) \text { is odd }\end{array}\right.$<br/>$f(x)=\frac{x^{7}+\sin x}{\cos x}$<br/>$f(-x)=\frac{(-x)^{7}+\sin (-x)}{\cos (-x)}=\frac{-x^{7}-\sin x}{\cos x}$<br/>$=-\left[\frac{x^{7}+\sin x}{\cos x}\right]$<br/>$=-\mathrm{f}(\mathrm{x})$<br/>So $\mathrm{f}(\mathrm{x})$ is odd hence<br/>$\mathrm{I}=0$</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">-1</span> </div>
source_db: MarksBatch2_P3.db
title:
the-value-of-a-is-consider-the-function-f-x-2-sin-x-a-sin-x-b-cos-x-if-x-2-if-2-x-2-if-x-2-which-is-continuous-everywhere

slug:
the-value-of-a-is-consider-the-function-f-x-2-sin-x-a-sin-x-b-cos-x-if-x-2-if-2-x-2-if-x-2-which-is-continuous-everywhere-75984

question:
<div class="question">The value of $\mathrm{A}$ is<br/>Consider the function<br/>$f(x)=\left\{\begin{array}{cc}-2 \sin x &amp; \text { if } x \leq-\frac{\pi}{2} \\ A \sin x+B &amp; \text { if }-\frac{\pi}{2}   &lt; x &lt; \frac{\pi}{2} \\ \cos x &amp; \text { if } x \geq \frac{\pi}{2}\end{array}\right.$<br/>which is continuous everywhere.</div>

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

answer:
<div class="solution">$\because \mathrm{f}(\mathrm{x})=\left\{\begin{array}{ccc}-2 \sin \mathrm{x} &amp; \text { if } &amp; \mathrm{x} \leq-\pi / 2 \\ \mathrm{~A} \sin \mathrm{x}+\mathrm{B} &amp; \text { if } &amp; -\pi / 2   &lt; \mathrm{x} &lt; \pi / 2 \\ \cos \mathrm{x} &amp; \text { if } &amp; \mathrm{x} \geq \pi / 2\end{array}\right.$<br/>$\because \mathrm{f}(\mathrm{x})$ is continuous every where :<br/>$\therefore \lim _{x \rightarrow \pi / 2^{+}} f(x)=\lim _{x \rightarrow \pi / 2} f(x)$<br/>$\Rightarrow \lim _{x \rightarrow \pi / 2} \cos x=\lim _{x \rightarrow \pi / 2} A \sin x+B$<br/>$\Rightarrow A+B=0$<br/>Also; $\lim _{x \rightarrow-\pi / 2} f(x)=\lim _{x \rightarrow-\pi / 2^{-}} f(x)$<br/>$\Rightarrow \lim _{x \rightarrow-\pi / 2} A \sin x+B=\lim _{x \rightarrow-\pi / 2}-2 \sin x$<br/>$\Rightarrow-A+B=2$<br/>is from eq $(1) \&amp;(2)$ we get,<br/>$A=-1$</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2015 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
answer: <div class="solution">Put the value of A in eq. (2) we get:<br/>$\Rightarrow \mathrm{B}=1$</div>
source_db: MarksBatch2_P3.db
title:
the-value-of-b-is-consider-the-function-f-x-2-sin-x-a-sin-x-b-cos-x-if-x-2-if-2-x-2-if-x-2-which-is-continuous-everywhere

slug:
the-value-of-b-is-consider-the-function-f-x-2-sin-x-a-sin-x-b-cos-x-if-x-2-if-2-x-2-if-x-2-which-is-continuous-everywhere-60654

question:
<div class="question">The value of B is<br/>Consider the function<br/>$f(x)=\left\{\begin{array}{cc}-2 \sin x &amp; \text { if } x \leq-\frac{\pi}{2} \\ A \sin x+B &amp; \text { if }-\frac{\pi}{2}   &lt; x &lt; \frac{\pi}{2} \\ \cos x &amp; \text { if } x \geq \frac{\pi}{2}\end{array}\right.$<br/>which is continuous everywhere.</div>

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


title: the-value-of-c-7-0-c-7-1-c-7-1-c-7-2-c-7-6-c-7-7-is
slug: the-value-of-c-7-0-c-7-1-c-7-1-c-7-2-c-7-6-c-7-7-is-80457
tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">254</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of $[\mathrm{C}(7,0)+\mathrm{C}(7,1)]+[\mathrm{C}(7,1)+\mathrm{C}(7,2)]+\ldots .+$<br/>$[\mathrm{C}(7,6)+\mathrm{C}(7,7)]$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">254</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">255</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">256</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">257</span> </li> </ul>

answer:
<div class="solution">$\left(7 \mathrm{c}_{0}+7 \mathrm{c}_{1}\right)+\left(7 \mathrm{c}_{1}+7 \mathrm{c}_{2}\right)+\ldots+\left(7 \mathrm{c}_{6}+7 \mathrm{c}_{7}\right)$<br/>We know, $\mathrm{n}_{\mathrm{c}_{\mathrm{r}}}+\mathrm{n}_{\mathrm{c}_{\mathrm{r}-1}}={ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}}$<br/>$=8_{\mathrm{c}_{1}}+8_{\mathrm{c}_{2}}+\ldots . .+8_{\mathrm{c}_{7}}$<br/>$=\left(8_{\mathrm{c}_{0}}+8_{\mathrm{c}_{1}}+8_{\mathrm{c}_{2}}+\ldots . .+8_{\mathrm{c}_{7}}+8_{\mathrm{c}_{8}}\right)-\left(8_{\mathrm{c}_{0}}+8_{\mathrm{c}_{8}}\right)$<br/>$=2^{8}-(1+1)$<br/>$\left[\right.$ Since,$\left.n_{c_{0}}+n_{c_{1}}+n_{c_{2}}+\ldots+n_{c_{n}}=2^{n}\right]$<br/>$=256-2$<br/>$=254$</div>


title: the-value-of-determinant-leftbeginarraycccab-bc-a-ba-ca-b-ca-ab-cendarrayright-is
slug: the-value-of-determinant-leftbeginarraycccab-bc-a-ba-ca-b-ca-ab-cendarrayright-is-86961
tags: ['Mathematics', 'Determinants', 'KCET', 'KCET 2018']
source_db: MarksBatch2_P3.db
question:
<div class="question">The value of determinant \( \left|\begin{array}{ccc}a-b &amp; b+c &amp; a \\ b-a &amp; c+a &amp; b \\ c-a &amp; a+b &amp; c\end{array}\right| \) is</div>

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

answer:
<div class="solution">Given that, \( \left|\begin{array}{ccc}a-b &amp; b+c &amp; a \\ b-c &amp; c+a &amp; b \\ c-a &amp; a+b &amp; c\end{array}\right| \)<br/>\( C_{3} \rightarrow C_{2}+C_{3} \)<br/>\( \left|\begin{array}{lll}a-b &amp; b+c &amp; a+b+c \\ b-c &amp; c+a &amp; a+b+c \\ c-a &amp; a+b &amp; a+b+c\end{array}\right| \)<br/>\( =a+b+c)\left|\begin{array}{ccc}a-b &amp; b+c &amp; 1 \\ b-c &amp; c+a &amp; 1 \\ c-a &amp; a+b &amp; 1\end{array}\right| \)<br/>\( =(a+b+c)((c+a)(c-a)-(a+b)(b-c) \)<br/>\( -(b+c)(c-a)-(a+b)(a-b) \)<br/>\( +(b+c)(b-c)-(c+a)(a-b)) \)<br/>\( =(a+b+c)\left(c^{2}-a^{2}-a b+a c-b^{2}+b c\right) \)<br/>\( -b c+a b-c^{2}+a c-a^{2}+b^{2} \)<br/>\( \left.+b^{2}-c^{2}-a c+b c-a^{2}+a b\right) \)<br/>\( =(a+b+c)\left(-c^{2}-3 a^{2}+a b+a c+b^{2}+b c\right) \)<br/>\( =a\left(-c^{2}-3 a^{2}+a b+a c+b^{2}+b c\right) \)<br/>\( +b\left(-c^{2}-3 a^{2}+a b+a c+b^{2}+b c\right) \)<br/>\( +c\left(-c^{2}-3 a^{2}+a b+a c+b^{2}+b c\right) \)<br/>\( =-a c^{2}-3 a^{3}+a^{2} b+a^{2} c+a b^{2}+a b c \)<br/>\( -b c^{2}-3 a^{2} b+a b^{2}+a b c+b^{3}+b^{2} c \)<br/>\( -c^{3}-3 a^{2} c+a b c+a c^{2}+b^{2} c+b c^{2} \)</div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P3.db
title:
the-value-of-e-m-m-o-of-four-metals-a-b-c-and-d-are-1-2-v-0-6-v-0-85-v-and-0-76-v-respectively-the-order-of-tendency-of-their-unipositive-cations-gett

slug:
the-value-of-e-m-m-o-of-four-metals-a-b-c-and-d-are-1-2-v-0-6-v-0-85-v-and-0-76-v-respectively-the-order-of-tendency-of-their-unipositive-cations-gett-40102

question:
<div class="question">The value of <math> <mrow> <mfenced close=")" open="(" separators=","> <mrow> <msubsup> <mtext>E</mtext> <mrow> <msup> <mtext>M</mtext> <mo>+</mo> </msup> <mo>/</mo> <mtext>M</mtext> </mrow> <mtext>o</mtext> </msubsup> </mrow> </mfenced> </mrow> </math> of four metals <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">B</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">D</mi></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>6</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>85</mn><mo> </mo><mi mathvariant="normal">V</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>76</mn><mo> </mo><mi mathvariant="normal">V</mi></math>, respectively. The order of tendency of their unipositive cations getting deposited at the cathode during electrolysis of the respective salts is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>&gt;</mo><mi mathvariant="normal">B</mi><mo>&gt;</mo><mi mathvariant="normal">D</mi><mo>&gt;</mo><mi mathvariant="normal">A</mi></math>.</span> </div>

answer:
<div class="solution"><p>During electrolysis, the species having higher reduction potential is preferably reduced at the cathode.</p><p>As per the data given in the question, the standard reduction potential of the metals are in the order-</p><p><math> <mrow> <msubsup> <mtext>E</mtext> <mtext>C</mtext> <mo>∘</mo> </msubsup> <mo>&gt;</mo> <msubsup> <mtext>E</mtext> <mtext>B</mtext> <mo>∘</mo> </msubsup> <mo>&gt;</mo> <msubsup> <mtext>E</mtext> <mtext>D</mtext> <mo>∘</mo> </msubsup> <mo>&gt;</mo> <msubsup> <mtext>E</mtext> <mtext>A</mtext> <mo>∘</mo> </msubsup> </mrow> </math></p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>&gt;</mo><mi mathvariant="normal">B</mi><mo>&gt;</mo><mi mathvariant="normal">D</mi><mo>&gt;</mo><mi mathvariant="normal">A</mi></math> will be the preference of deposition of these metals on the cathode.</p></div>


