# questions

tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-following-statements-with-regard-to-correlation-coefficient-r-between-random-variables-x-and-y-i-r-1-or-1-means-there-is-a-linear-relatio

slug:
consider-the-following-statements-with-regard-to-correlation-coefficient-r-between-random-variables-x-and-y-i-r-1-or-1-means-there-is-a-linear-relatio-60232

question:
<div class="question">Consider the following statements with regard to correlation coefficient $r$ between random variables $x$ and $y$.<br/>I. $\quad r=+1$ or $-1$ means there is a linear relationship between the variables.<br/>II. $-1 \leq r \leq 1$ and $r^{2}$ is a measure of the linear relationship between the variables. Which of the statements given above is/are correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Only I</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Only II</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Both I and II</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither Inor II</span> </li> </ul>

answer:
<div class="solution">Both the given statements which is related to correlation coefficient $r$ between variables $x$ and $y$ are correct.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-following-three-methods-of-collecting-data-1-collecting-data-from-government-offices-2-collecting-data-from-public-libraries-3-collecting

slug:
consider-the-following-three-methods-of-collecting-data-1-collecting-data-from-government-offices-2-collecting-data-from-public-libraries-3-collecting-97828

question:
<div class="question">Consider the following three methods of collecting data<br/>(1) collecting data from government offices $\quad$<br/>(2) collecting data from public libraries<br/>(3) collecting data by telephonic interview Select the correct answer using the code given below</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">1 and 2 give secondary and 3 gives primary data</span> </div>

answer:
<div class="solution">Collecting data from government offices is secondary. collecting data from public libraries is also secondary but collecting data by telephonic interview is primary data.</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2023 (Manipur)']
source_db: MarksBatch1_P2.db
title:
consider-the-following-tissues-in-the-stelar-region-of-a-stem-showing-secondary-growth-a-primary-xylem-b-secondary-xylem-c-primary-phloem-d-secondary-

slug:
consider-the-following-tissues-in-the-stelar-region-of-a-stem-showing-secondary-growth-a-primary-xylem-b-secondary-xylem-c-primary-phloem-d-secondary-66689

question:
<div class="question">Consider the following tissues in the stelar region of a stem showing secondary growth.<br/>(A) Primary xylem<br/>(B) Secondary xylem<br/>(C) Primary phloem<br/>(D) Secondary phloem<br/>Arrange these in the correct sequence of their position from pith towards cortex.</div>

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

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

answer:
<div class="solution">The correct sequence of tissues in the stelar region of the stem showing secondary growth from pith towards cortex is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/yiXEyW1nm4nAEyZdRr6HuYg7d5RrmcdwmXaK-7ZMrDM.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2018 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3 only</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-the-following-values-of-x-1-8-2-4-3-6-1-4-4-1-which-of-the-above-values-of-x-isare-the-solutions-of-the-equation-tan-1-2-x-tan-1-3-x-4

slug:
consider-the-following-values-of-x-1-8-2-4-3-6-1-4-4-1-which-of-the-above-values-of-x-isare-the-solutions-of-the-equation-tan-1-2-x-tan-1-3-x-4-90469

question:
<div class="question">Consider the following values of $\mathrm{x}$ :<br/>1)$8$<br/>2) $-4$<br/>3) $\frac{1}{6}$<br/>4) $-\frac{1}{4}$<br/>Which of the above values of $\mathrm{x}$ is/are the solutions of the<br/>equation $\tan ^{-1}(2 \mathrm{x})+\tan ^{-1}(3 \mathrm{x})=\frac{\pi}{4}$</div>

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

answer:
<div class="solution">$\tan ^{-1}\left(\frac{2 x+3 x}{1-2 x .3 x}\right)=\frac{\pi}{4}$<br/>$\tan ^{-1} \frac{5 x}{1-6 x^{2}}=\frac{\pi}{4}$<br/>$\frac{5 x}{1-6 x^{2}}=1$<br/>$1-6 x^{2}=5 x$<br/>$6 x^{2}+5 x-1=0$<br/>$(6 x-1)(x+1)=0$<br/>$\Rightarrow \quad x=\frac{1}{6},-1$<br/>$\Rightarrow \quad x=\frac{1}{6}$<br/>Here $x=-1$ rejected.</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-following-with-regard-to-a-relation-r-on-a-set-of-real-numbers-defined-by-x-r-y-if-and-only-if-3-x-4-y-5-i-0-r-1-ii-1-r-2-1-iii-3-2-r-4-3

slug:
consider-the-following-with-regard-to-a-relation-r-on-a-set-of-real-numbers-defined-by-x-r-y-if-and-only-if-3-x-4-y-5-i-0-r-1-ii-1-r-2-1-iii-3-2-r-4-3-73173

question:
<div class="question">Consider the following with regard to a relation $R$ on a set of real numbers defined by $x R y$ if and only if $3 x+4 y=5$<br/>I. $\quad 0 R 1$<br/>II. $\quad 1 R \frac{1}{2}$<br/>III. $\frac{2}{3} \mathrm{R} \frac{3}{4}$<br/>Which of the above are correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{I}$ and $\mathrm{II}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">I and III</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">II and III 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">I, II and III</span> </li> </ul>

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

answer:
<div class="solution">Let on the setof real numbers, $R$ is a relation defined by $x R y$ if and only if $3 x+4 y=5$ Consider, $3 x+4 y=5$<br/>(I) Put $x=0$ and $y=1$, we get $\mathrm{LHS}=3(0)+4(1)=4 \neq 5(=\mathrm{RHS})$<br/>Hence 0 is not related to 1<br/>(II) Now, Put $x=1$ and $y=\frac{1}{2}$, we get<br/>$\mathrm{LHS}=3(1)+4 \times \frac{1}{2}=5=5(=\mathrm{RHS})$<br/>Hence 1 is related to $\frac{1}{2}$<br/>(III) Similarly, $\frac{2}{3}$ is related to $\frac{3}{4}$. Hence, both statements II and III are correct</div>


tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-function-f-r-0-1-such-that-2010-ii-f-x-1-if-x-is-rational-0-if-x-is-irrational-which-one-of-the-following-is-correct

slug:
consider-the-function-f-r-0-1-such-that-2010-ii-f-x-1-if-x-is-rational-0-if-x-is-irrational-which-one-of-the-following-is-correct-24776

question:
<div class="question">Consider the function $f: R \rightarrow\{0,1\}$ such that $[2010-I I]$ $f(x)=\left\{\begin{array}{l}1, \text { if } x \text { is rational } \\ 0, \text { if } x \text { is irrational }\end{array}\right.$<br/>Which one of the following is correct?</div>

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

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

answer:
<div class="solution">Since, on taking a straight line parallel to $\mathrm{x}$ -axis, the group of given function intersect it at one point. $\therefore \quad \mathrm{f}(\mathrm{x})$ is one-one.<br/>and as range of $\mathrm{f}(\mathrm{x})=\mathrm{Co}$ -domain $\therefore \mathrm{f}(\mathrm{x})$ is onto.<br/>Hence, $\mathrm{f}(\mathrm{x})$ is one-one onto.</div>


tags: ['Mathematics', 'Application of Derivatives', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-the-function-f-r-rightarrow-r-defined-by-fxleftbeginarraycleft2sin-leftfrac1xrightrightx-x-neq-0-0endarray-x0-right-then-f-is

slug:
consider-the-function-f-r-rightarrow-r-defined-by-fxleftbeginarraycleft2sin-leftfrac1xrightrightx-x-neq-0-0endarray-x0-right-then-f-is-89657

question:
<div class="question">Consider the function \( f: R \rightarrow R \) defined by \( f(x)=\left\{\begin{array}{c}\left(2-\sin \left(\frac{1}{x}\right)\right)|x|, x \neq 0 \\ 0\end{array}, x=0 .\right. \) Then \( f \) is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">monotonic on \( (-\infty, 0) \cup(0, \infty) \)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">not monotonic on \( (-\infty, 0) \) and \( (0, \infty) \)</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">C</span> <span class="option-data">monotonic on \( (0, \infty) \) only</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">monotonic on \( (-\infty, 0) \) only</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">not monotonic on \( (-\infty, 0) \) and \( (0, \infty) \)</span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfenced close="" open="{"><mtable><mtr><mtd><mo>-</mo><mi>x</mi><mfenced><mrow><mn>2</mn><mo>-</mo><mi>sin</mi><mfenced><mfrac><mn>1</mn><mi>x</mi></mfrac></mfenced></mrow></mfenced></mtd><mtd><mi>x</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>x</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></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><mfenced close="" open="{"><mtable columnalign="left"><mtr><mtd><mo>-</mo><mfenced><mrow><mn>2</mn><mo>-</mo><mi>sin</mi><mfrac><mn>1</mn><mi mathvariant="normal">x</mi></mfrac></mrow></mfenced><mo>-</mo><mi mathvariant="normal">x</mi><mfenced><mrow><mo>-</mo><mi>cos</mi><mfrac><mn>1</mn><mi mathvariant="normal">x</mi></mfrac><mo>·</mo><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mfrac></mrow></mfenced></mrow></mfenced></mtd><mtd><mi mathvariant="normal">x</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mfenced><mrow><mn>2</mn><mo>-</mo><mi>sin</mi><mfrac><mn>1</mn><mi mathvariant="normal">x</mi></mfrac></mrow></mfenced><mo>+</mo><mi mathvariant="normal">x</mi><mfenced><mrow><mo>-</mo><mi>cos</mi><mfrac><mn>1</mn><mi mathvariant="normal">x</mi></mfrac><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mfrac></mrow></mfenced></mrow></mfenced></mtd><mtd><mi mathvariant="normal">x</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></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><mfenced close="" open="{"><mtable columnalign="left"><mtr><mtd><mo>-</mo><mn>2</mn><mo>+</mo><mi>sin</mi><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>-</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mi>cos</mi><mfrac><mn>1</mn><mi>x</mi></mfrac><mo> </mo><mo>,</mo><mo> </mo><mi>x</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>-</mo><mi>sin</mi><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mi>cos</mi><mfrac><mn>1</mn><mi>x</mi></mfrac><mo> </mo><mo>,</mo><mo> </mo><mi>x</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mo>'</mo></msup><mo>(</mo><mi>x</mi><mo>)</mo></math> is an oscillating function which is non-monotonic in <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mo>∞</mo><mo>,</mo><mn>0</mn><mo>)</mo><mo>∪</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math>.</p></div>


title: consider-the-function-f-x-4-27-x-23-x-how-many-solutions-does-the-function-f-x-1-have-1
slug: consider-the-function-f-x-4-27-x-23-x-how-many-solutions-does-the-function-f-x-1-have-1-40719
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">One</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the function $f(x)=\frac{27\left(x^{2 / 3}-x\right)}{4}$<br/>How many solutions does the function $\mathrm{f}(\mathrm{x})=-1$ have?</div>

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

answer:
<div class="solution">Similarly for $f(x)=-1$ we will get $27 y^{3}-27 y^{2}-4=0$ and after solving it we will find that it has one real solution. $y_{0}=1.1184$<br/>$x=\left(\mathrm{y}_{0}\right)^{3}=(1.1184)^{3}=1.4$</div>


title: consider-the-function-f-x-4-27-x-23-x-how-many-solutions-does-the-function-f-x-1-have
slug: consider-the-function-f-x-4-27-x-23-x-how-many-solutions-does-the-function-f-x-1-have-83798
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Two</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the function $f(x)=\frac{27\left(x^{2 / 3}-x\right)}{4}$<br/>How many solutions does the function $\mathrm{f}(\mathrm{x})=1$ have?</div>

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

answer:
<div class="solution">For $f(x)=1$<br/>$\frac{27}{4}\left(\left(x^{2}\right)^{1 / 3}-x\right)=1$<br/>$\left(x^{1 / 3}\right)^{2}-x=\frac{4}{27}$<br/>Put $x^{1 / 3}=y$<br/>$x=y^{3}$<br/>$y^{2}-y^{3}=\frac{4}{27}$<br/>$\Rightarrow y^{3}-y^{2}+\frac{4}{27}=0$<br/>$\Rightarrow 27 y^{3}-27 y^{2}+4=0$<br/>This is a cubic equation.<br/>If we put $y=-\frac{1}{3}$ then $(3 y+1)=0$ is a factor of cubic equation.<br/>$3 y+1$ ) $27 y^{3}-27 y^{2}+4\left(9 y^{2}-12 y+4\right.$<br/>$\frac{-27 y^{3}+9 y^{2}}{-36 y^{2}+4}$<br/>$\frac{\mp^{-36 y^{2}} \mp^{12 y}}{12 y+4}$<br/>$\frac{12 y+4}{x}$<br/>$(3 y+1)\left(9 y^{2}-12 y+4\right)=0$<br/>$(3 y+1)(3 y-2)^{2}=0$<br/>Hence $y=-\frac{1}{3}, \frac{2}{3}$<br/>Thus $f(x)=1$ has two solutions.</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-function-f-x-5-x-s-i-n-2-x-if-x-0-15-2-if-x-0-which-one-of-the-following-is-correct-in-respect-of-the-function

slug:
consider-the-function-f-x-5-x-s-i-n-2-x-if-x-0-15-2-if-x-0-which-one-of-the-following-is-correct-in-respect-of-the-function-77621

question:
<div class="question">Consider the function<br/>$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{l}\frac{\sin 2 \mathrm{x}}{5 \mathrm{x}} \text { if } \mathrm{x} \neq 0 \\ \frac{2}{15} \text { if } \mathrm{x}=0\end{array}\right.$<br/>Which one of the following is correct in respect of the function?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It is not continuous at $x=0$</span> </div>

answer:
<div class="solution">$\lim _{x \rightarrow 0} \frac{\sin (2 x)}{5 x}=\lim _{x \rightarrow 0} \frac{\sin (2 x)(2)}{5 \cdot(2 x)}=\frac{2}{5}$<br/>But at $x=0, f(x)=\frac{2}{15}$<br/>Hence, $f(x)$ is not continuous at $x=0$.</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: MarksBatch1_P2.db
title:
consider-the-function-f-x-a-x-2-1-a-2-x-1-2-for-for-for-2-x-1-1-x-1-1-x-2-what-is-the-value-of-a-for-which-f-x-is-continuous-at-x-1-and-x-1

slug:
consider-the-function-f-x-a-x-2-1-a-2-x-1-2-for-for-for-2-x-1-1-x-1-1-x-2-what-is-the-value-of-a-for-which-f-x-is-continuous-at-x-1-and-x-1-81138

question:
<div class="question">Consider the function<br/>$f(x)=\left\{\begin{array}{ccc}a x-2 &amp; \text { for } &amp; -2   &lt; x &lt; -1 \\ -1 &amp; \text { for } &amp; -1 \leq x \leq 1 \\ a+2(x-1)^{2} &amp; \text { for } &amp; 1 &lt; x &lt; 2\end{array}\right.$<br/>What is the value of a for which $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=-1$ $\operatorname{and} \mathrm{x}=1$ ?</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">1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\mathrm{ax}-2 &amp; -2   &lt; \mathrm{x} &lt; -1 \\ -1 &amp; -1 \leq \mathrm{x} \leq 1 \\ \mathrm{a}+2(\mathrm{x}-1)^{2} &amp; 1 &lt; \mathrm{x} &lt; 2\end{array}\right.$<br/>if $f(x)$ is continuous at $x=-1$<br/>then, $\lim _{x \rightarrow-1}(a x-2)=\lim _{x \rightarrow-1}(-1)$<br/>$\Rightarrow a(-1)-2=-1$<br/>$\Rightarrow a=-1$<br/>if $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=1$<br/>then, $\lim _{x \rightarrow 1} a+2(x-1)^{2}=\lim _{x \rightarrow 1}-1$<br/>$\Rightarrow \mathrm{a}+2(1-1)^{2}=-1$<br/>$\Rightarrow \mathrm{a}=-1$</div>


title: consider-the-function-f-x-sec-4-4-with-f-0-0-and-f-0-0-what-is-f-x-equal-to-1
slug: consider-the-function-f-x-sec-4-4-with-f-0-0-and-f-0-0-what-is-f-x-equal-to-1-66557
tags: ['Mathematics', 'Indefinite Integration', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the function $\mathrm{f}^{\prime \prime}(\mathrm{x})=\sec ^{4} \times+4$ with $\mathrm{f}(0)=0$ and $\mathrm{f}^{\prime}(0)=0$.<br/>What is $f^{\prime}(x)$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\tan x-\frac{\tan ^{3} x}{3}+4 x$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\tan x+\frac{\tan ^{3} x}{3}+4 x$</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">C</span> <span class="option-data">$\tan x-\frac{\sec ^{3} x}{3}+4 x$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-\tan x-\frac{\tan ^{3} x}{3}+4 x$</span> </li> </ul>

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

answer:
<div class="solution">$\mathrm{f}^{\prime}(\mathrm{x})=\int \mathrm{f}^{\prime \prime}(\mathrm{x}) \mathrm{d} \mathrm{x}+\mathrm{C}_{1}$<br/>$=\int\left(\sec ^{4} \mathrm{x}+4\right) \mathrm{d} \mathrm{x}+\mathrm{C}_{1}$<br/>$=\int \sec ^{2} \mathrm{x} \sec ^{2} \mathrm{x} \mathrm{d} \mathrm{x}+\int 4 \mathrm{~d} \mathrm{x}+\mathrm{C}_{1}$<br/>$=\int\left(1+\tan ^{2} \mathrm{x}\right) \sec ^{2} \mathrm{x} \mathrm{d} \mathrm{x}+4 \mathrm{x}+\mathrm{C}_{1}=\mathrm{I}_{1}+4 \mathrm{x}+\mathrm{C}_{1}$<br/>Put $\tan \mathrm{x}=\mathrm{t}$ in the integral $\mathrm{I}_{1}$, then<br/>$\sec ^{2} \mathrm{x} \mathrm{d} \mathrm{x}=\mathrm{dt}$<br/>$\therefore \mathrm{I}_{1}=\int\left(1+\mathrm{t}^{2}\right) \mathrm{dt}=\mathrm{t}+\frac{\mathrm{t}^{3}}{3}+\mathrm{C}^{\prime}$<br/>$=\tan \mathrm{x}+\frac{\tan ^{3} \mathrm{x}}{3}+\mathrm{C}^{\prime}$<br/>$\therefore \mathrm{f}^{\prime}(\mathrm{x})=\tan \mathrm{x}+\frac{\tan ^{3} \mathrm{x}}{3}+4 \mathrm{x}+\mathrm{C}^{\prime}$<br/>where, $\mathrm{C}=\mathrm{C}_{1}+\mathrm{C}^{\prime}$<br/>$\because \mathrm{f}^{\prime}(0)=0 \Rightarrow \mathrm{C} 0$<br/>Thus, $\mathrm{f}^{\prime}(\mathrm{x})=\tan \mathrm{x}+\frac{\tan ^{3} \mathrm{x}}{3}+4 \mathrm{x}$</div>


title: consider-the-function-f-x-sec-4-4-with-f-0-0-and-f-0-0-what-is-f-x-equal-to
slug: consider-the-function-f-x-sec-4-4-with-f-0-0-and-f-0-0-what-is-f-x-equal-to-36608
tags: ['Mathematics', 'Indefinite Integration', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the function $\mathrm{f}^{\prime \prime}(\mathrm{x})=\sec ^{4} \times+4$ with $\mathrm{f}(0)=0$ and $\mathrm{f}^{\prime}(0)=0$.<br/>What is $f(x)$ equal to?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2 \ln \sec x}{3}+\frac{\tan ^{2} x}{6}+2 x^{2}$</span> </div>

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\int \mathrm{f}^{\prime}(\mathrm{x}) \mathrm{d} \mathrm{x}+\mathrm{C}_{2}$<br/>$=\int\left(\tan \mathrm{x}+\frac{\tan ^{3} \mathrm{x}}{3}+4 \mathrm{x}\right) \mathrm{d} \mathrm{x}+\mathrm{C}_{2}$<br/>$=\int \tan \mathrm{x} \mathrm{d} \mathrm{x}+\frac{1}{3} \int \tan ^{3} \mathrm{x} \mathrm{dx}+4 \int \mathrm{x} \mathrm{d} \mathrm{x}+\mathrm{C}_{2}$<br/>$=\int \tan \mathrm{x} \mathrm{d} \mathrm{x}+\frac{1}{3} \int \tan \mathrm{x}\left(\sec ^{2} \mathrm{x}-1\right) \mathrm{d} \mathrm{x}+4 \cdot \frac{\mathrm{x}^{2}}{2}+\mathrm{C}_{2}$<br/>$=\frac{2}{3} \int \tan \mathrm{x} \mathrm{d} \mathrm{x}+\frac{1}{3} \int \tan \mathrm{x} \cdot \sec ^{2} \mathrm{x} \mathrm{d} \mathrm{x}+2 \mathrm{x}^{2}+\mathrm{C}_{2}$<br/>$=\frac{2}{3} \ln (\sec \mathrm{x})+\frac{1}{3} \mathrm{I}_{2}+2 \mathrm{x}^{2}+\mathrm{C}_{2}$<br/>Consider $\mathrm{I}_{2}=\int \tan \mathrm{x} \sec ^{2} \mathrm{x} \mathrm{dx}$<br/>Put $\tan \mathrm{x}=\mathrm{t} \Rightarrow \sec ^{2} \mathrm{x} \mathrm{d} \mathrm{x}=\mathrm{dt}$<br/>$\Rightarrow 1_{2}=\int \mathrm{t} \mathrm{dt}=\frac{\mathrm{t}^{2}}{2}+\mathrm{C}_{3}=\frac{\tan ^{2} \mathrm{x}}{2}+\mathrm{C}_{3}$<br/>$\therefore \mathrm{f}(\mathrm{x})=\frac{2}{3} \ln (\sec \mathrm{x})+\frac{1}{6} \tan ^{2} \mathrm{x}+2 \mathrm{x}^{2}+\mathrm{C}_{4}$<br/>Here, $\mathrm{C}_{4}=\mathrm{C}_{2}+\left(\frac{\mathrm{C}_{3}}{3}\right)$<br/>$\because \mathrm{f}(0)=0$<br/>$\Rightarrow 0=\frac{2}{3} \ln (1)+0+0+\mathrm{C}_{4}$<br/>$\Rightarrow \mathrm{C}_{4}=0$<br/>$\therefore \mathrm{f}(\mathrm{x})=\frac{2}{3} \ln (\sec \mathrm{x})+\frac{1}{6} \tan ^{2} \mathrm{x}+2 \mathrm{x}^{2}$</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-function-f-x-x-2-3-x-2-x-2-x-2-which-one-of-the-following-statements-is-correct-in-respect-of-the-above-function

slug:
consider-the-function-f-x-x-2-3-x-2-x-2-x-2-which-one-of-the-following-statements-is-correct-in-respect-of-the-above-function-26573

question:
<div class="question">Consider the function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cl}\mathrm{x}^{2}, &amp; \mathrm{x}&gt;2 \\ 3 \mathrm{x}-2, &amp; \mathrm{x} \leq 2\end{array}\right.$. <br/>Which one of the following statements is correct in respect of the above function?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{f}(\mathrm{x})$ is derivable but not continuous at $\mathrm{x}=2$.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{f}(\mathrm{x})$ is continuous but not derivable at $\mathrm{x}=2$.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{f}(\mathrm{x})$ is neither continuous nor derivable at $\mathrm{x}=2$.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{f}(\mathrm{x})$ is continuous as well as derivable at $\mathrm{x}=2$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{f}(\mathrm{x})$ is continuous but not derivable at $\mathrm{x}=2$.</span> </div>

answer:
<div class="solution">First we check continuity at $\mathrm{x}=2$<br/>L. H. $L=\lim _{h \rightarrow 0} f(2-h)=\lim _{h \rightarrow 0} 3(2-h)-2$<br/>$=\lim _{h \rightarrow 0} 4-3 h=4$<br/>R. H. L. $=\lim _{h \rightarrow 0} f(2+h)=\lim _{h \rightarrow 0}(2+h)^{2}=4$<br/>Also, $\mathrm{f}(2)=(2)^{2}=4$<br/>Since, $\mathrm{L} . \mathrm{H} \cdot \mathrm{L}=\mathrm{R} . \mathrm{H} \cdot \mathrm{L}=\mathrm{f}(2)$<br/>$\therefore \mathrm{f}(\mathrm{x})$ is continuous at $2 .$<br/>Now, we check for differentiability $\begin{array}{ll}\text { L. H. Dat } x=2 &amp; \text { R. H. Dat } x=2\end{array}$<br/>$\mathrm{f}(\mathrm{x})=3 \mathrm{x}-2 \quad \mathrm{f}(\mathrm{x})=\mathrm{x}^{2}$<br/>$\mathrm{f}^{\prime}(\mathrm{x})=3 \quad \mathrm{f}^{\prime}(\mathrm{x})=2 \mathrm{x}$<br/>$\left.\mathrm{f}^{\prime}(\mathrm{x})\right|_{\mathrm{x}=2}=\left.3 \quad \mathrm{f}^{\prime}(\mathrm{x})\right|_{\mathrm{x}=2}=4$<br/>Since L. H. $\mathrm{D} \neq \mathrm{R}$ H. $\mathrm{D}$ $\therefore \mathrm{f}(\mathrm{x})$ is not derivable at $\mathrm{x}=2$</div>


title: consider-the-function-f-x-x-2-ln-x-0-x-0-x-0-what-is-f-0-equal-to
slug: consider-the-function-f-x-x-2-ln-x-0-x-0-x-0-what-is-f-0-equal-to-15223
tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\mathrm{x}^{2} \ln |\mathrm{x}| &amp; \mathrm{x} \neq 0 \\ 0 &amp; \mathrm{x}=0\end{array}\right.$. What is<br/>$\begin{array}{cc}\mathrm{f}^{\prime}(0) \text { equal to? } &amp;\end{array}$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">0</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">It does not exist</span> </li> </ul>

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\mathrm{x}^{2} \ell \mathrm{n}|\mathrm{x}| &amp; \mathrm{x} \neq 0 \\ 0 &amp; \mathrm{x}=0 .\end{array}\right.$<br/>$f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{\mathrm{f}(\mathrm{h})-\mathrm{f}(0)}{\mathrm{h}}$<br/>$=\lim _{\mathrm{h} \rightarrow 0} \frac{\mathrm{h}^{2} \cdot \ln |\mathrm{h}|-0}{\mathrm{~h}}$<br/>$=\lim _{\mathrm{h} \rightarrow 0} \mathrm{~h} . \ell \mathrm{n}|\mathrm{h}|$<br/>$=0$</div>


tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-function-f-x-x-3-6-p-sin-x-1-p-2-cos-x-0-p-3-where-p-is-a-constant-what-is-the-value-of-f-0

slug:
consider-the-function-f-x-x-3-6-p-sin-x-1-p-2-cos-x-0-p-3-where-p-is-a-constant-what-is-the-value-of-f-0-21007

question:
<div class="question">Consider the function<br/>$\mathrm{f}(\mathrm{x})=\left|\begin{array}{ccc}\mathrm{x}^{3} &amp; \sin \mathrm{x} &amp; \cos \mathrm{x} \\ 6 &amp; -1 &amp; 0 \\ \mathrm{p} &amp; \mathrm{p}^{2} &amp; \mathrm{p}^{3}\end{array}\right|$ where $\mathrm{p}$ is a constant.<br/>What is the value of $\mathrm{f}^{\prime}(0) ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-6 \mathrm{p}^{3}$</span> </div>

answer:
<div class="solution">$f(x)=\left|\begin{array}{ccc}x^{3} &amp; \sin x &amp; \cos x \\ 6 &amp; -1 &amp; 0 \\ p &amp; p^{2} &amp; p^{3}\end{array}\right|$<br/>$f^{\prime}(x)=\left|\begin{array}{ccc}3 x^{2} &amp; \cos x &amp; -\sin x \\ 6 &amp; -1 &amp; 0 \\ p &amp; p^{2} &amp; p^{3}\end{array}\right|+\left|\begin{array}{ccc}x^{3} &amp; \sin x &amp; \cos x \\ 6 &amp; -1 &amp; 0 \\ 0 &amp; 0 &amp; 0\end{array}\right|$ $+\left|\begin{array}{ccc}x^{3} &amp; \sin x &amp; \cos x \\ 0 &amp; 0 &amp; 0 \\ p &amp; p^{2} &amp; p^{3}\end{array}\right|$<br/>$\begin{aligned} f^{\prime}(x) &amp;=\left|\begin{array}{ccc}3 x^{2} &amp; \cos x &amp; -\sin x \\ 6 &amp; -1 &amp; 0 \\ p &amp; p^{2} &amp; p^{3}\end{array}\right| \\ f^{\prime}(0) &amp;=\left|\begin{array}{ccc}0 &amp; \cos 0 &amp; -\sin 0 \\ 6 &amp; -1 &amp; 0 \\ p &amp; p^{2} &amp; p^{3}\end{array}\right| \\ &amp;=-6 p^{3} \end{aligned}$</div>


tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-function-f-x-x-3-6-p-sin-x-1-p-2-cos-x-0-p-3-where-p-is-a-constant-what-is-the-value-of-p-for-which-f-0-0

slug:
consider-the-function-f-x-x-3-6-p-sin-x-1-p-2-cos-x-0-p-3-where-p-is-a-constant-what-is-the-value-of-p-for-which-f-0-0-72355

question:
<div class="question">Consider the function<br/>$\mathrm{f}(\mathrm{x})=\left|\begin{array}{ccc}\mathrm{x}^{3} &amp; \sin \mathrm{x} &amp; \cos \mathrm{x} \\ 6 &amp; -1 &amp; 0 \\ \mathrm{p} &amp; \mathrm{p}^{2} &amp; \mathrm{p}^{3}\end{array}\right|$ where $\mathrm{p}$ is a constant.<br/>What is the value of p for which $\mathrm{f}^{\prime \prime}(0)=0$ ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-\frac{1}{6}$ or 0</span> </div>

answer:
<div class="solution">$f^{\prime \prime}(x)=\left|\begin{array}{ccc}6 x &amp; -\sin x &amp; -\cos x \\ 6 &amp; -1 &amp; 0 \\ p &amp; p^{2} &amp; p^{3}\end{array}\right|$<br/>$f^{\prime \prime}(0)=\left|\begin{array}{ccc}0 &amp; 0 &amp; -\cos 0 \\ 6 &amp; -1 &amp; 0 \\ p &amp; p^{2} &amp; p^{3}\end{array}\right|$<br/>$\quad=-1\left(6 p^{2}+p\right)$<br/>$f^{\prime \prime}(0)=0$<br/>$-\left(6 p^{2}+p\right)=0$<br/>$p(6 p+1)=0$<br/>$p=0$ or $p=-\frac{1}{6}$</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-function-f-x-x-t-a-n-k-x-3-x-2-k-2-x-0-x-0-wha-t-i-s-t-h-e-n-o-n-zero-v-a-l-u-eo-f-k-f-or-w-hi-c-h-t-h-e-f-u-n-c-t-i-o-ni-sco-n-t-in-u-o-

slug:
consider-the-function-f-x-x-t-a-n-k-x-3-x-2-k-2-x-0-x-0-wha-t-i-s-t-h-e-n-o-n-zero-v-a-l-u-eo-f-k-f-or-w-hi-c-h-t-h-e-f-u-n-c-t-i-o-ni-sco-n-t-in-u-o-17772

question:
<div class="question">Consider the function<br/>$$<br/>f(x)=\left\{\begin{array}{cc}<br/>\frac{\tan k x}{x}, &amp; x   &lt; 0 \\<br/>3 x+2 k^{2}, &amp; x \geq 0<br/>\end{array}\right.<br/>$$<br/>What is the non-zero value of $k$ for which the function is continuous at $x=0$ ?</div>

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

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

answer:
<div class="solution">Given, $f(x)=\left\{\begin{array}{ll}\frac{\tan \mathrm{kx}}{x}, &amp; x   &lt; 0 \\ 3 x+2 \mathrm{k}^{2}, &amp; x \geq 0\end{array}\right.$<br/>When function is continuous at $\mathrm{x}=0$, then<br/>$\lim _{x-0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x)=f(0)$<br/>$\therefore \lim _{x \rightarrow 0-h}\left(\frac{\tan k x}{x}\right)=\lim _{x \rightarrow 0+h}\left(3 x+2 k^{2}\right)=3(0)+2 k^{2}$<br/>$\Rightarrow \lim _{x \rightarrow 0-h}\left[\frac{\tan k(0-h)}{(0-h)}\right]=\lim _{x \rightarrow 0+h}\left[3(0+h)+2 k^{2}\right]=2 k^{2}$<br/>Therefore, $\lim _{h \rightarrow 0}\left(\frac{\tan \mathrm{kh}}{\mathrm{h}}\right)=2 \mathrm{k}^{2}$<br/>$\mathrm{k}=2 \mathrm{k}^{2}$<br/>$\left[\because \lim _{x \rightarrow 0} \frac{\tan x}{x}=1\right]$<br/>Hence, $\mathrm{k}=\frac{1}{2}$</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-functions-f-x-xg-x-and-g-x-x-1-where-is-the-greatest-integer-function-what-is-3-1-1-f-x-dx-equal-to

slug:
consider-the-functions-f-x-xg-x-and-g-x-x-1-where-is-the-greatest-integer-function-what-is-3-1-1-f-x-dx-equal-to-97013

question:
<div class="question">Consider the functions<br/>$\mathrm{f}(\mathrm{x})=\mathrm{xg}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})=\left[\frac{1}{\mathrm{x}}\right]$<br/>Where $[\cdot]$ is the greatest integer function.<br/>What is $\int_{\frac{1}{3}}^{1} \mathrm{f}(\mathrm{x}) \mathrm{dx}$ equal to ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{37}{72}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2}{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{17}{72}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{37}{144}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{37}{72}$</span> </div>

answer:
<div class="solution">$\int_{1 / 3}^{1} f(x) d x=\int_{1 / 3}^{1 / 2} f(x) d x+\int_{1 / 2}^{1} f(x) d x$<br/>$f(x)=x g(x)$<br/>$g\left(\frac{1}{3}\right)=3 \quad g\left(\frac{1}{2}\right)=2 g(1)=1$<br/>The value of $g(x)$ in value $\left(\frac{1}{2}, \frac{1}{3}\right)$ will be 2 and in range $\left(\frac{1}{2}, 1\right)$ it will be 1 form(1)<br/>$\int_{1 / 3}^{1} f(x) d x=\int_{1 / 3}^{1 / 2} x g(x) d x+\int_{1 / 2}^{1} x g(x) d x$<br/>$=\int_{1 / 3}^{1 / 2} x \cdot 2 d x+\int_{1 / 2}^{1} x \times 1 d x .$<br/>$=\left[x^{2}\right]_{1 / 3}^{1 / 2}+\left[\frac{x^{2}}{2}\right]_{1 / 2}^{1}$<br/>$=\left[\frac{1}{4}-\frac{1}{9}\right]+\frac{1}{2}\left[1-\frac{1}{4}\right]$<br/>$=\frac{5}{36}+\frac{3}{8}=\frac{37}{72}$</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-functions-f-x-xg-x-and-g-x-x-1-where-is-the-greatest-integer-function-what-is-3-1-2-1-g-x-dx-equal-to

slug:
consider-the-functions-f-x-xg-x-and-g-x-x-1-where-is-the-greatest-integer-function-what-is-3-1-2-1-g-x-dx-equal-to-39515

question:
<div class="question">Consider the functions<br/>$\mathrm{f}(\mathrm{x})=\mathrm{xg}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})=\left[\frac{1}{\mathrm{x}}\right]$<br/>Where $[\cdot]$ is the greatest integer function.<br/>What is $\int_{\frac{1}{3}}^{\frac{1}{2}} \mathrm{~g}(\mathrm{x}) \mathrm{dx}$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{6}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{5}{18}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{5}{36}$</span> </li> </ul>

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

answer:
<div class="solution">$\int_{1 / 3}^{1 / 2} \mathrm{~g}(x) \mathrm{d} x$<br/>$$<br/>\mathrm{~g}(\mathrm{x})=\left\{\begin{array}{ll}2, &amp; \text { if } \frac{1}{3}   &lt; x \leq \frac{1}{2} \\ 3, &amp; \text { if } x=\frac{1}{3}\end{array}\right.<br/>$$<br/>As $\mathrm{g}(\mathrm{x})$ is a gretest integer function so value of $\mathrm{g}(\mathrm{x})$ in integral limit will be<br/>So $\int_{1 / 3}^{1 / 2} g(x) d x=\int_{1 / 3}^{1 / 2} 2 d x$<br/>$=2[x]_{1 / 3}^{1 / 2}=2\left[\frac{1}{2}-\frac{1}{3}\right]=\frac{1}{3}$</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-the-given-compounds-1-c-h-3-c-h-2-n-h-2-2-c-h-3-c-h-n-h-3-c-h-3-c-n-4-c-2-h-5-n-h-c-2-h-5-arrange-basicity-of-these-compounds-in-decreasing-o

slug:
consider-the-given-compounds-1-c-h-3-c-h-2-n-h-2-2-c-h-3-c-h-n-h-3-c-h-3-c-n-4-c-2-h-5-n-h-c-2-h-5-arrange-basicity-of-these-compounds-in-decreasing-o-73170

question:
<div class="question">Consider the given compounds<br/> <math><mo>(</mo><mn>1</mn><mo>)</mo></math> <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>â</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>â</mo><mi mathvariant="normal">N</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></math><br/> <math><mo>(</mo><mn>2</mn><mo>)</mo></math> <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>â</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi><mo>=</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi></math><br/> <math><mo>(</mo><mn>3</mn><mo>)</mo></math> <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>â</mo><mi mathvariant="normal">C</mi><mo>â¡</mo><mi mathvariant="normal">N</mi></math><br/> <math><mo>(</mo><mn>4</mn><mo>)</mo></math> <math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>â</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">H</mi><mo>â</mo><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub></math><br/>
Arrange basicity of these compounds in decreasing order:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">4 &gt; 1 &gt; 2 &gt; 3</span> </div>

answer:
<div class="solution">Here the correct order of basic nature is as follows<br/><math> <mrow> <msub> <mtext>C</mtext> <mtext>2</mtext> </msub> <msub> <mtext>H</mtext> <mtext>5</mtext> </msub> <mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>NH</mtext><mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><msub> <mtext>C</mtext> <mtext>2</mtext> </msub> <msub> <mtext>H</mtext> <mtext>5</mtext> </msub> <mtext>â</mtext><mtext>&gt;</mtext><mtext>â</mtext><msub> <mrow> <mtext>CH</mtext></mrow> <mtext>3</mtext> </msub> <mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><msub> <mrow> <mtext>CH</mtext></mrow> <mtext>2</mtext> </msub> <mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><msub> <mrow> <mtext>NH</mtext></mrow> <mtext>2</mtext> </msub> <mtext>â</mtext><mtext>&gt;</mtext><mtext>â</mtext><msub> <mrow> <mtext>CH</mtext></mrow> <mtext>3</mtext> </msub> <mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>CH</mtext><mtext>â</mtext><mtext>=</mtext><mtext>â</mtext><mtext>NH</mtext><mtext>â</mtext><mtext>&gt;</mtext><mtext>â</mtext><msub> <mrow> <mtext>CH</mtext></mrow> <mtext>3</mtext> </msub> <mtext>â</mtext><mtext>â</mtext><mtext>â</mtext><mtext>C</mtext><mo>â¡</mo><mtext>N</mtext></mrow> </math><br/><math><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo></math> Secondary amine is more basic than primary amine.<br/><math><mo>(</mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">i</mi><mo>)</mo></math> <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>â</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi><mo>=</mo><munder><mrow><mi mathvariant="normal">N</mi></mrow><mrow><mi mathvariant="normal">s</mi><msup><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></munder><mi mathvariant="normal">H</mi></math><br/><math> <mrow> <mfenced> <mrow> <mtext>iii</mtext></mrow> </mfenced><mtext>â</mtext><msub> <mrow> <mtext>CH</mtext></mrow> <mtext>3</mtext> </msub> <mo>â</mo><mtext>CÂ¹</mtext><mo>â¡</mo><munder> <mtext>N</mtext> <mrow> <mtext>sp</mtext></mrow> </munder> </mrow> </math></div>


tags: ['Mathematics', 'Linear Programming', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-the-given-problem-5-x-y-100-x-y-60-x-0-y-0-if-we-solve-the-above-linear-equations-by-the-graphical-method-of-linear-programming-then-the-foll

slug:
consider-the-given-problem-5-x-y-100-x-y-60-x-0-y-0-if-we-solve-the-above-linear-equations-by-the-graphical-method-of-linear-programming-then-the-foll-22668

question:
<div class="question">Consider the given problem:<br/>$\begin{aligned}<br/>&amp; 5 x+y \leq 100 \\<br/>&amp; x+y \leq 60 \\<br/>&amp; x \geq 0 \\<br/>&amp; y \geq 0<br/>\end{aligned}$<br/>If we solve the above linear equations by the graphical method of Linear Programming, then the following point will not form the the boundary of the feasible region.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$(60,0)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(20,0)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(0,60)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(10,50)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(60,0)$</span> </div>

answer:
<div class="solution">After equating each constraint to zero (0) we get the equations of lines on cartesian coordinate.<br/>On comparing the inequality with $(0,0)$ and shading the common area we get the feasible region as follows,<br/><img src="https://cdn-question-pool.getmarks.app/modules/qc/ePiD0DImwJ3y2dgUQZlIweSVkqBAKmLSmLKERKdOyRw.original.fullsize.png"/><br/><br/>Hence we can easily conclude that point $(60,0)$ and $(0,100)$ are outside the feasible region.</div>


title: consider-the-integral-i-0-ln-sin-x-d-x-what-is-0-2-ln-cos-x-d-x-equal-to
slug: consider-the-integral-i-0-ln-sin-x-d-x-what-is-0-2-ln-cos-x-d-x-equal-to-54880
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the integral $I=\int_{0}^{\pi} \ln (\sin x) d x$<br/>What is $\int_{0}^{\pi / 2} \ln (\cos x) d x$ equal to ?</div>

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

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

answer:
<div class="solution">From eq. (ii), we have<br/>$\mathrm{I}=2 \int_{0}^{\frac{\pi}{2}} \ln (\cos \mathrm{x}) \mathrm{d} \mathrm{x}$<br/>$\Rightarrow \int_{0}^{\frac{\pi}{2}} \ln (\cos x) \mathrm{d} x=\frac{1}{2} I$<br/>\begin{array}{l}<br/>\text { Consider } \mathrm{I}=\int_{0}^{\pi} \ln (\sin \mathrm{x}) \mathrm{d} \mathrm{x}\\<br/>\mathrm{I}=\int_{0}^{\pi} \ln (\sin \mathrm{x}) \mathrm{d} \mathrm{x}\\<br/>=2 \int_{0}^{\frac{\pi}{2}} \ln (\sin x) \mathrm{d} x\\<br/>\left[\because \int_{0}^{2 a} f(x) d x=2 \int_{0}^{a} f(x) d x, \text { if } f(2 a-x)=f(x)\right]\\<br/>=2 \int_{0}^{\frac{\pi}{2}} \ln \left[\sin \left(\frac{\pi}{2}-\mathrm{x}\right)\right] \mathrm{d} \mathrm{x}\\<br/>\left(\because \int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x\right)\\<br/>=2 \int_{0}^{\frac{\pi}{2}} \ln (\cos x) \mathrm{d} x<br/>\end{array}</div>


title: consider-the-integral-i-0-ln-sin-x-d-x-what-is-0-2-ln-sin-x-d-x-equal-to
slug: consider-the-integral-i-0-ln-sin-x-d-x-what-is-0-2-ln-sin-x-d-x-equal-to-15996
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the integral $I=\int_{0}^{\pi} \ln (\sin x) d x$<br/>What is $\int_{0}^{\pi / 2} \ln (\sin x) d x$ equal to ?</div>

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

answer:
<div class="solution">(d) From eq. (i),<br/>$\mathrm{I}=2 \int_{0}^{\frac{\pi}{2}} \ln (\sin \mathrm{x}) \mathrm{d} \mathrm{x}$<br/>$\Rightarrow \int_{0}^{\frac{\pi}{2}} \ln (\sin \mathrm{x}) \mathrm{d} \mathrm{x}=\frac{1}{2} \mathrm{I}$<br/>Consider $\mathrm{I}=\int_{0}^{\pi} \ln (\sin \mathrm{x}) \mathrm{d} \mathrm{x}$<br/>$\mathrm{I}=\int_{0}^{\pi} \ln (\sin \mathrm{x}) \mathrm{d} \mathrm{x}$<br/>$=2 \int_{0}^{\frac{\pi}{2}} \ln (\sin x) \mathrm{d} x$<br/>$\left[\because \int_{0}^{2 a} f(x) d x=2 \int_{0}^{a} f(x) d x\right.$, if $\left.f(2 a-x)=f(x)\right]$<br/>$=2 \int_{0}^{\frac{\pi}{2}} \ln \left[\sin \left(\frac{\pi}{2}-\mathrm{x}\right)\right] \mathrm{d} \mathrm{x}$<br/>$\left(\because \int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x\right)$<br/>$=2 \int_{0}^{\frac{\pi}{2}} \ln (\cos x) \mathrm{d} x$</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1 only</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-consider-the-following-1-i-m-i-m-1-is-equal-to-0-2-i-2-m-i-m-which-o

slug:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-consider-the-following-1-i-m-i-m-1-is-equal-to-0-2-i-2-m-i-m-which-o-16004

question:
<div class="question">Consider the integral $I_{m}=\int_{0}^{\pi \sin 2 m x} \frac{\sin x} d x$, where $m$ is a positive<br/>integer.<br/>Consider the following:<br/> 1 . $I_{m}-I_{m-1}$ is equal to 0 .<br/> 2 . $\quad I_{2 m}&gt;I_{m}$<br/>Which of the above is/are correct?</div>

answer:
<div class="solution">$\mathrm{I}_{2 \mathrm{~m}}&gt;\mathrm{I}_{\mathrm{m}}$ is wrong statement<br/>Because, $\mathrm{I}_{\mathrm{m}}=\mathrm{I}_{\mathrm{m}-1}=\ldots . .=\mathrm{I}_{\mathrm{n}}$<br/>Thus, $\mathrm{I}_{\mathrm{m}}-\mathrm{I}_{\mathrm{m}-1}=0$ is the only correct statement.</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-what-is-i-1-equal-to

slug:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-what-is-i-1-equal-to-56800

question:
<div class="question">Consider the integral $I_{m}=\int_{0}^{\pi \sin 2 m x} \frac{\sin x} d x$, where $m$ is a positive<br/>integer.<br/>What is $I_{1}$ equal to?</div>

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

answer:
<div class="solution">$\begin{array}{ll} &amp; I_{m}=\int_{0}^{\pi} \frac{\sin 2 m x}{\sin x} d x \\ \therefore \quad &amp; I_{1}=\int_{0}^{\pi} \frac{\sin 2 x}{\sin x} d x=\int_{0}^{\pi} \frac{2 \sin x \cos x}{\sin x} d x \\ &amp; =2 \int_{0}^{\pi} \cos x d x=2[\sin x]_{0}^{\pi}=2[\sin \pi-\sin 0] \\ &amp; =2(0)=0\end{array}$</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-what-is-i-2-i-3-equal-to

slug:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-what-is-i-2-i-3-equal-to-27702

question:
<div class="question">Consider the integral $I_{m}=\int_{0}^{\pi \sin 2 m x} \frac{\sin x} d x$, where $m$ is a positive<br/>integer.<br/>What is $I_{2}+I_{3}$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</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">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">$\mathrm{I}_{2}=\int_{0}^{\pi} \frac{\sin 4 \mathrm{x}}{\sin \mathrm{x}} \mathrm{dx}=\int_{0}^{\pi} \frac{2 \sin 2 \mathrm{x} \cos 2 \mathrm{x}}{\sin \mathrm{x}} \mathrm{dx}$<br/>$=2 \int_{0}^{\pi} \frac{2 \sin \mathrm{x} \cos \mathrm{x} \cos 2 \mathrm{x}}{\sin \mathrm{x}} \mathrm{dx}$<br/>$=4 \int_{0}^{\pi} \cos \mathrm{x}\left(1-2 \sin ^{2} \mathrm{x}\right) \mathrm{dx}$<br/>$=4 \int_{0}^{\pi} \cos x d x-8 \int_{0}^{\pi} \cos x \sin ^{2} x d x=0$<br/>Let $\sin x=t$<br/>$\cos x d x=d t$<br/>$=4(\sin \pi-\sin 0)-0=0$<br/>$I_{3}=\int_{0}^{\pi} \frac{\sin 6 x}{\sin x} d x$<br/>$=\int_{0}^{\pi} \frac{2\left[3 \sin x-4 \sin ^{3} x\right] \cos 3 x}{\sin x} d x$<br/>$=\int_{0}^{\pi} 2\left(3-4 \sin ^{2} x\right) \cos 3 x d x$<br/>$=\int_{0}^{\pi} 6 \cos 3 x d x-\int_{0}^{\pi} 8 \sin ^{2} x \cos 3 x d x$<br/>$=\frac{6 \sin 3 x}{3} \int_{0}^{\pi}-8 \cdot \frac{1}{2}\left[\int_{0}^{\pi} \sin x(\sin 4 x-\sin 2 x) d x\right]$<br/>$=6-\frac{8}{2}\left[\int_{0}^{\pi}(\sin x \sin 4 x-\sin x \cdot \sin 2 x) d x\right]$<br/>$=\frac{-8}{2}\left[\frac{1}{2} \int_{0}^{\pi} \cos 3 x-\cos 5 x-\cos x+\cos 3 x d x\right]$<br/>Hence, $I_{2}+I_{3}=0+0=0$</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-what-is-i-m-equal-to

slug:
consider-the-integral-i-m-0-s-i-n-2-m-x-d-s-i-n-x-x-where-m-is-a-positive-integer-what-is-i-m-equal-to-95265

question:
<div class="question">Consider the integral $I_{m}=\int_{0}^{\pi \sin 2 m x} \frac{\sin x} d x$, where $m$ is a positive<br/>integer.<br/>What is $I_{m}$ equal to?</div>

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

answer:
<div class="solution">$\begin{aligned} &amp; I_{m}=\int_{0}^{\pi} \frac{\sin 2 m x}{\sin x} d x \\ &amp;=\int_{0}^{\pi} \frac{\sin 2 m(\pi-x)}{\sin (\pi-x)} d x \\ &amp;=\int_{0}^{\pi} \frac{\sin (2 m \pi-2 m x)}{\sin x} d x \\ &amp;=\int_{0}^{\pi-\sin 2 m x}{\sin x} d x \\ &amp; I_{m}=-\int_{0}^{\pi} \frac{\sin 2 m x}{\sin x} d x \\ &amp; 2 I_{m}=0 \Rightarrow I_{m}=0 \end{aligned}$</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-integrals-a-0-s-i-n-x-c-o-s-x-s-i-n-x-dx-and-b-0-s-i-n-x-c-o-s-x-s-i-n-xdx-what-is-the-value-of-b

slug:
consider-the-integrals-a-0-s-i-n-x-c-o-s-x-s-i-n-x-dx-and-b-0-s-i-n-x-c-o-s-x-s-i-n-xdx-what-is-the-value-of-b-64062

question:
<div class="question">Consider the integrals<br/>$\mathrm{A}=\int_{0}^{\pi} \frac{\sin \mathrm{x} \mathrm{dx}}{\sin \mathrm{x}+\cos \mathrm{x}}$ and $\overline{\mathrm{B}}=\int_{0}^{\pi} \frac{\sin \mathrm{x} \mathrm{d} \mathrm{x}}{\sin \mathrm{x}-\cos \mathrm{x}}$<br/>What is the value of $\mathrm{B}$ ?</div>

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

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

answer:
<div class="solution">$\begin{aligned} &amp; \mathrm{B}=\int_{0}^{\pi} \frac{\sin \mathrm{x}}{\sin \mathrm{x}-\cos \mathrm{x}} \times \frac{(\sin \mathrm{x}+\cos \mathrm{x})}{(\sin \mathrm{x}+\cos \mathrm{x})} \mathrm{dx} \\ &amp;=-\int_{0}^{\pi} \frac{\sin ^{2} \mathrm{x}+\sin \mathrm{x} \cos \mathrm{x}}{\cos 2 \mathrm{x}} \mathrm{dx} \\ &amp;=\frac{-1}{2} \int_{0}^{\pi} \frac{2 \sin ^{2} \mathrm{x}}{\cos 2 \mathrm{x}} \mathrm{dx}-\frac{1}{2} \int_{0}^{\pi} \frac{2 \sin \mathrm{x} \cos \mathrm{x}}{\cos 2 \mathrm{x}} \mathrm{dx} \\ &amp;=\frac{-1}{2} \int_{0}^{\pi} \frac{1-\cos 2 \mathrm{x}}{\cos 2 \mathrm{x}} \mathrm{dx}-\frac{1}{2} \int_{0}^{\pi} \tan 2 \mathrm{x} \mathrm{dx} \\ &amp;=\frac{-1}{2} \int_{0}^{\pi} \sec 2 \mathrm{x} \mathrm{dx}+\frac{1}{2} \int_{0}^{\pi} \mathrm{dx}-\frac{1}{2} \int_{0}^{\pi} \tan 2 \mathrm{x} \mathrm{d} \mathrm{x} \\ &amp;=\frac{-1}{2}\left[\frac{\log |\sec 2 \mathrm{x}+\tan 2 \mathrm{x}|}{2}\right]_{0}^{\pi}+\frac{1}{2}[\mathrm{x}]_{0}^{\pi}-\frac{1}{2}\left[\frac{\log |\sec 2 \mathrm{x}|}{2}\right]_{0}^{\pi} \\ &amp;=\frac{-1}{4}[\log (1+0)-\log (1+0)]+\frac{1}{2}[\pi+0]-\frac{1}{4}[\log (1)-\log (1)] \\ &amp;=0+\pi / 2-0=\pi / 2 \end{aligned}$</div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-integrals-a-0-s-i-n-x-c-o-s-x-s-i-n-x-dx-and-b-0-s-i-n-x-c-o-s-x-s-i-n-xdx-which-one-of-the-follwing-is-correct

slug:
consider-the-integrals-a-0-s-i-n-x-c-o-s-x-s-i-n-x-dx-and-b-0-s-i-n-x-c-o-s-x-s-i-n-xdx-which-one-of-the-follwing-is-correct-23851

question:
<div class="question">Consider the integrals<br/>$\mathrm{A}=\int_{0}^{\pi} \frac{\sin \mathrm{x} \mathrm{dx}}{\sin \mathrm{x}+\cos \mathrm{x}}$ and $\overline{\mathrm{B}}=\int_{0}^{\pi} \frac{\sin \mathrm{x} \mathrm{d} \mathrm{x}}{\sin \mathrm{x}-\cos \mathrm{x}}$<br/>Which one of the follwing is correct?</div>

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

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

answer:
<div class="solution">$\mathrm{A}=\int_{0}^{\pi} \frac{\sin x}{\sin x+\cos x} \mathrm{dx}$<br/>Using property<br/>$A=\int_{0}^{\pi} \frac{\sin (\pi-x)}{\sin (\pi-x)+\cos (\pi-x)} d x$<br/>$A=\int_{0}^{\pi} \frac{\sin x}{\sin x-\cos x} d x=B$<br/>$A=B$</div>


tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-line-x-3-y-and-the-circle-x-2-y-2-4-what-is-the-area-of-the-region-in-the-first-quadrant-enclosed-by-the-x-axis-the-line-x-3-and-the-circ

slug:
consider-the-line-x-3-y-and-the-circle-x-2-y-2-4-what-is-the-area-of-the-region-in-the-first-quadrant-enclosed-by-the-x-axis-the-line-x-3-and-the-circ-58128

question:
<div class="question">Consider the line $x=\sqrt{3} y$ and the circle $x^{2}+y^{2}=4$<br/>What is the area of the region in the first quadrant enclosed by the $x$ -axis, the line $x=\sqrt{3}$ and the circle?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{3}-\frac{\sqrt{3}}{2}$</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">$\frac{\pi}{2}-\frac{\sqrt{3}}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{3}-\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

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

answer:
<div class="solution">$x^{2}+y^{2}=4$ and $x=\sqrt{3} y$<br/>$P(\sqrt{3}, 1)=$ First quadrant<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/41ozDgYnQKip1OyFewMiIwztYfhmcC0wYpHOsYWCe6g.original.fullsize.png"/><br/><br/>The point of intersection of the line and the circle in the first<br/>quadrant is $(\sqrt{3}, 1)$. Area of $\Delta$ OPA $=$ Area of $\Delta$ OPB $+$ Area of PAB<br/>$=\frac{1}{2} \times \mathrm{OB} \times \mathrm{PB}=\frac{1}{2} \times \sqrt{3} \times 1=\frac{\sqrt{3}}{2}$<br/>Area of $\mathrm{PAB} \int_{\sqrt{3}}^{2} \mathrm{ydx}$<br/>$=\int_{\sqrt{3}}^{2} \sqrt{4-x^{2}} \mathrm{~d} x=\left[\frac{x}{2} \sqrt{4-x^{2}}+\frac{4}{2} \sin ^{-1} \frac{x}{2}\right]_{\sqrt{3}}^{2}$<br/>$\left[2 \times \frac{\pi}{2}-\frac{\sqrt{3}}{2}[\sqrt{4-3}]-2 \sin ^{-1} \frac{\sqrt{3}}{2}\right]$<br/>$=\pi-\frac{\sqrt{3}}{2}-\frac{2 \pi}{3}=\frac{\pi}{3}-\frac{\sqrt{3}}{2}$</div>


tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-line-x-3-y-and-the-circle-x-2-y-2-4-what-is-the-area-of-the-region-in-the-first-quadrant-enclosed-by-the-x-axis-the-line-x-3-y-and-the-ci

slug:
consider-the-line-x-3-y-and-the-circle-x-2-y-2-4-what-is-the-area-of-the-region-in-the-first-quadrant-enclosed-by-the-x-axis-the-line-x-3-y-and-the-ci-83995

question:
<div class="question">Consider the line $x=\sqrt{3} y$ and the circle $x^{2}+y^{2}=4$<br/>What is the area of the region in the first quadrant enclosed by the $x$ -axis, the line $x=\sqrt{3} y$ and the circle?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{3}$</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">$\frac{\pi}{6}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{3}-\frac{\sqrt{3}}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

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

answer:
<div class="solution">Area enclosed by $x$ -axis, the line $x=\sqrt{3}$.y, and the circle $x^{2}+y^{2}=4$ in the first quadrant $=\frac{\sqrt{3}}{2}+\frac{\pi}{3}-\frac{\sqrt{3}}{2}=\frac{\pi}{3}$<br/>$x^{2}+y^{2}=4$ and $x=\sqrt{3} y$<br/>$P(\sqrt{3}, 1)=$ First quadrant<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/41ozDgYnQKip1OyFewMiIwztYfhmcC0wYpHOsYWCe6g.original.fullsize.png"/><br/><br/>The point of intersection of the line and the circle in the first<br/>quadrant is $(\sqrt{3}, 1)$. Area of $\Delta$ OPA $=$ Area of $\Delta$ OPB $+$ Area of PAB<br/>$=\frac{1}{2} \times \mathrm{OB} \times \mathrm{PB}=\frac{1}{2} \times \sqrt{3} \times 1=\frac{\sqrt{3}}{2}$<br/>Area of $\mathrm{PAB} \int_{\sqrt{3}}^{2} \mathrm{ydx}$<br/>$=\int_{\sqrt{3}}^{2} \sqrt{4-x^{2}} \mathrm{~d} x=\left[\frac{x}{2} \sqrt{4-x^{2}}+\frac{4}{2} \sin ^{-1} \frac{x}{2}\right]_{\sqrt{3}}^{2}$<br/>$\left[2 \times \frac{\pi}{2}-\frac{\sqrt{3}}{2}[\sqrt{4-3}]-2 \sin ^{-1} \frac{\sqrt{3}}{2}\right]$<br/>$=\pi-\frac{\sqrt{3}}{2}-\frac{2 \pi}{3}=\frac{\pi}{3}-\frac{\sqrt{3}}{2}$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-lines-y-3-x-y-6-x-and-y-9-the-centroid-of-the-triangle-is-at-which-one-of-the-following-points

slug:
consider-the-lines-y-3-x-y-6-x-and-y-9-the-centroid-of-the-triangle-is-at-which-one-of-the-following-points-47789

question:
<div class="question">Consider the lines $\mathrm{y}=3 \mathrm{x}, \mathrm{y}=6 \mathrm{x}$ and $\mathrm{y}=9$<br/>The centroid of the triangle is at which one of the following points?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(3,6)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left(\frac{3}{2}, 6\right)$</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">$(3,3)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(\frac{3}{2}, 9\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{3}{2}, 6\right)$</span> </div>

answer:
<div class="solution">Coordinates of $O, A, B$ are $(0,0)\left(\frac{3}{2}, 9\right),(3,9)$ respectively.<br/>Centroid $C=\left[\left(\frac{0+\frac{3}{2}+3}{3}\right),\left(\frac{0+9+9}{3}\right)\right]=\left(\frac{3}{2}, 6\right)$</div>


title: consider-the-lines-y-3-x-y-6-x-and-y-9-what-is-the-area-of-the-triangle-formed-by-these-lines
slug: consider-the-lines-y-3-x-y-6-x-and-y-9-what-is-the-area-of-the-triangle-formed-by-these-lines-35796
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the lines $\mathrm{y}=3 \mathrm{x}, \mathrm{y}=6 \mathrm{x}$ and $\mathrm{y}=9$<br/>What is the area of the triangle formed by these lines?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{27}{4}$ square 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">$\frac{27}{2}$ square units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{19}{4}$ square units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{19}{2}$ square units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{27}{4}$ square units</span> </div>

answer:
<div class="solution">$O A B$ is triangle.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Qal47vTeWWYspsEepGfRM12uHxEdj6b3CEk12ILC_o0.original.fullsize.png"/><br/><br/>$\begin{aligned} \text { Area of triangle } &amp;=\frac{1}{2} \times \text { base } \times \text { height }=\frac{1}{2} \times \mathrm{AB} \times \mathrm{OP} \\ &amp;=\frac{1}{2} \times \frac{3}{2} \times 9=\frac{27}{4} \end{aligned}$<br/>Area of triangle $=\frac{27}{4}$ square units</div>


tags: ['Mathematics', 'Parabola', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-parabola-y-x-2-7-x-2-and-the-straight-line-y-3-x-3-what-are-thecoordinates-of-the-point-on-the-parabola-which-is-closest-to-the-straight-

slug:
consider-the-parabola-y-x-2-7-x-2-and-the-straight-line-y-3-x-3-what-are-thecoordinates-of-the-point-on-the-parabola-which-is-closest-to-the-straight-68136

question:
<div class="question">Consider the parabola $y=x^{2}+7 x+2$ and the straight line $y=3x-3$ <br/>What are thecoordinates of the point on the parabola which is closest to the straight line?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(0,2)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(-2,-8)$</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">C</span> <span class="option-data">$(-7,2)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(1,10)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(-2,-8)$</span> </div>

answer:
<div class="solution">Parabola Eq: $y=x^{2}+7 x+2$ Line eq. : $y=3 x-3$ Since all the points given in the options lie on the parabola Thus we will calculate the distance from the given line to these points :<br/>for $(0,2):$ distance $==\frac{|3(0)-(2)-3|}{\sqrt{(3)^{2}+(-1)^{2}}}=\frac{5}{\sqrt{10}}$<br/>for $(-2,-8):$ distance $=\frac{|3(-2)-(-8)-3|}{\sqrt{10}}=\frac{1}{\sqrt{10}}$<br/>for $(-7,2):$ distance $=\frac{|3(-7)-2-3|}{\sqrt{10}}=\frac{26}{\sqrt{10}}$<br/>for $(1,10):$ distance $=\frac{|3(1)-10-3|}{\sqrt{10}}=\frac{10}{\sqrt{10}}$<br/>$(-2,-8)$ is the given point.</div>


tags: ['Mathematics', 'Parabola', 'NDA', 'NDA 2016 (Phase 2)']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch1_P2.db
title:
consider-the-parabola-y-x-2-7-x-2-and-the-straight-line-y-3-x-3-what-is-the-shortest-distance-from-the-above-point-on-the-parabola-to-the-line

slug:
consider-the-parabola-y-x-2-7-x-2-and-the-straight-line-y-3-x-3-what-is-the-shortest-distance-from-the-above-point-on-the-parabola-to-the-line-46984

question:
<div class="question">Consider the parabola $y=x^{2}+7 x+2$ and the straight line $y=3 x-3$<br/>What is the shortest distance from the above point on the parabola to the line?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{10}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{10}}{5}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{\sqrt{10}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\sqrt{5}}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{\sqrt{10}}$</span> </div>


title: consider-the-parabolas-s-1-y-2-4-a-x-0-and-s-2-y-2-4-b-x-0-s-2-will-contain-s-1-if
slug: consider-the-parabolas-s-1-y-2-4-a-x-0-and-s-2-y-2-4-b-x-0-s-2-will-contain-s-1-if-96018
tags: ['Mathematics', 'Parabola', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the parabolas $S_{1}=y^{2}-4 a x=0$ and<br/>$S_{2}=y^{2}-4 b x=0, S_{2}$ will contain $S_{1}$, if</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$a&gt;b&gt;0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$b&gt;a&gt;0$</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">$a&gt;0, b   &lt; 0$ but $|b|&gt;a$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$a   &lt; 0, b&gt;0$ but $b&gt;|a|$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$b&gt;a&gt;0$</span> </div>

answer:
<div class="solution">If a and $b&gt;0$, then graphic representation would be as follows<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/MqUx77QXoeG8EaNB7dqFjLMGdgeZBjw8rHe7EvcdQ6c.original.fullsize.png"/><br/><br/>$S_{2}$ will contain $S_{1}$, if latusrectum of $S_{2}&gt;$ latusrectum of $S$ $\Rightarrow 4 b&gt;4 a$<br/>$\therefore b&gt;a&gt;0$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-plane-passing-through-the-points-a-2-2-1-b-3-4-2-and-c-7-0-6-what-are-the-direction-ratios-of-the-normal-to-the-plane

slug:
consider-the-plane-passing-through-the-points-a-2-2-1-b-3-4-2-and-c-7-0-6-what-are-the-direction-ratios-of-the-normal-to-the-plane-18766

question:
<div class="question">Consider the plane passing through the points $\mathrm{A}(2,2,1), \mathrm{B}(3,4,2)$ and $\mathrm{C}(7,0,6)$<br/>What are the direction ratios of the normal to the plane?</div>

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

answer:
<div class="solution">Direction ratios of the nomal to the plane $\mathrm{x}-\mathrm{z}=1$ are $(1,0,-1)$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-plane-passing-through-the-points-a-2-2-1-b-3-4-2-and-c-7-0-6-which-one-of-the-following-points-lines-on-the-plane

slug:
consider-the-plane-passing-through-the-points-a-2-2-1-b-3-4-2-and-c-7-0-6-which-one-of-the-following-points-lines-on-the-plane-70330

question:
<div class="question">Consider the plane passing through the points $\mathrm{A}(2,2,1), \mathrm{B}(3,4,2)$ and $\mathrm{C}(7,0,6)$<br/>Which one of the following points lines on the plane?</div>

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

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

answer:
<div class="solution">We know that, equation of plane passing through three non-collinear points $\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right),\left(\mathrm{x}_{2}, \mathrm{y}_{2}, \mathrm{z}_{2}\right)$ and $\left(\mathrm{x}_{3}, \mathrm{y}_{3}, \mathrm{z}_{3}\right)$ is<br/>$\left|\begin{array}{lll}\mathrm{x}-\mathrm{x}_{1} &amp; \mathrm{y}-\mathrm{y}_{1} &amp; \mathrm{z}-\mathrm{z}_{1} \\ \mathrm{x}_{2}-\mathrm{x}_{1} &amp; \mathrm{y}_{2}-\mathrm{y}_{1} &amp; \mathrm{z}_{2}-\mathrm{z}_{1} \\ \mathrm{x}_{3}-\mathrm{x}_{1} &amp; \mathrm{y}_{3}-\mathrm{y}_{1} &amp; \mathrm{z}_{3}-\mathrm{z}_{1}\end{array}\right|=0$<br/>Put the value of $\left(x_{1}, y_{1}, z_{1}\right),\left(x_{2}, y_{2}, z_{2}\right)$ and $\left(x_{3}, y_{3}, z_{3}\right)$<br/>we get<br/>$\left|\begin{array}{ccc}\mathrm{x}-2 &amp; \mathrm{y}-2 &amp; \mathrm{z}-1 \\ 1 &amp; 2 &amp; 1 \\ 5 &amp; -2 &amp; 5\end{array}\right|=0$<br/>$\Rightarrow(x-2)(10+2)-(y-2)(5-5)+(z-1)(-2-10)=0$<br/>$\Rightarrow 12 x-12 z=12 \Rightarrow x-z=1$<br/>Hence the equation of plane parses through $(1,0,0)$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-points-a-1-a-a-1-a-a-1-a-1-and-a-1-a-1-a-1-these-points-always-form-the-vertices-of-an-equilateral-triangle-for-any-real-value-of-a-2-the

slug:
consider-the-points-a-1-a-a-1-a-a-1-a-1-and-a-1-a-1-a-1-these-points-always-form-the-vertices-of-an-equilateral-triangle-for-any-real-value-of-a-2-the-11021

question:
<div class="question">Consider the points $(a-1, a, a+1),(a, a+1, a-1)$ and $(a+1, a-1, a)$<br/> 1 . These points always form the vertices of an equilateral triangle for any real value of a<br/> 2 . The area of the triangle formed by these points is independent of a. Which of the statement(s) given above is/are correct?</div>

answer:
<div class="solution">Let $\mathrm{A}(\mathrm{a}-1, \mathrm{a}, \mathrm{a}+1), \mathrm{B}(\mathrm{a}, \mathrm{a}+1, \mathrm{a}-1)$ and<br/>a) be the vertices of a triangle $\mathrm{ABC}$. $\mathrm{C}(\mathrm{a}+1, \mathrm{a}-1$<br/>Length of $A B=\sqrt{(a-a+1)^{2}+(a+1-a)^{2}+(a-1-a-1)^{2}}$<br/>$=\sqrt{1+1+4}=\sqrt{6}$<br/>Length of $\begin{aligned} \mathrm{BC} &amp;=\sqrt{(\mathrm{a}+\mathrm{l}-\mathrm{a})^{2}+(\mathrm{a}-1-\mathrm{a}-1)^{2}+(\mathrm{a}-\mathrm{a}+1)^{2}} \\ &amp;=\sqrt{1+4+1}=\sqrt{6} \\ \text { and } \mathrm{CA}=\sqrt{(\mathrm{a}-1-\mathrm{a}-1)^{2}+(\mathrm{a}-\mathrm{a}+1)^{2}+(\mathrm{a}+1-\mathrm{a})^{2}} \end{aligned}$<br/>$=\sqrt{4+1+1}=\sqrt{6}$<br/>$\mathrm{AB}=\mathrm{BC}=\mathrm{CA}$<br/>Triangle $\mathrm{ABC}$ is an equilateral triangle and these given points are vertices of an equilateral triangle for any real value of a.<br/>Position vector of $\mathrm{A}, \overrightarrow{\mathrm{OA}}=(\mathrm{a}-1) \hat{\mathrm{i}}+\hat{\mathrm{a}}+(\mathrm{a}+1) \hat{\mathrm{k}}$<br/>Position vector of $\mathrm{B}, \overrightarrow{\mathrm{OB}}=\mathrm{a} \hat{\mathrm{i}}+(\mathrm{a}+1) \hat{\mathrm{j}}+(\mathrm{a}-1) \hat{\hat{k}}$<br/>Position vector of $\mathrm{C}, \overrightarrow{\mathrm{OC}}=(\mathrm{a}+1) \hat{\mathrm{i}}+(\mathrm{a}-1) \hat{\mathrm{j}}+\mathrm{a} \hat{k}$<br/>$\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{OB}}-\overrightarrow{\mathrm{OA}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$<br/>$\overrightarrow{\mathrm{AC}}=\overrightarrow{\mathrm{OC}}-\overrightarrow{\mathrm{OA}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$<br/>Now, area of a triangle $\Delta \mathrm{ABC}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/TJx9xxHuL1UXOuyWzB3IcFK0Dr15CxDD93udhkxCHuQ.original.fullsize.png"/><br/><br/>$=\frac{1}{2}|\mathrm{~A} \overline{\mathrm{B}} \times \mathrm{A} \overrightarrow{\mathrm{C}}|$<br/>$=\frac{1}{2}\left|\begin{array}{ccc}\hat{1} &amp; \hat{\mathrm{j}} &amp; \hat{\mathrm{k}} \\ 1 &amp; 1 &amp; -2 \\ 2 &amp; -1 &amp; -1\end{array}\right|$<br/>$=\frac{1}{2}|-3 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}|=\frac{1}{2} \sqrt{9+9+9}=\frac{\sqrt{27}}{2} \mathrm{sq}$ units.<br/>Since, a does not appear so, area of triangle formed by these points is independent of a.</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P2.db
title:
consider-the-propagating-sound-with-velocity-330-m-s-1-in-a-pipe-of-length-1-5-m-with-one-end-closed-and-the-other-open-the-frequency-associated-with-

slug:
consider-the-propagating-sound-with-velocity-330-m-s-1-in-a-pipe-of-length-1-5-m-with-one-end-closed-and-the-other-open-the-frequency-associated-with-89818

question:
<div class="question">Consider the propagating sound (with velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>330</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>) in a pipe of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.5 </mo><mi mathvariant="normal">m</mi></math> with one end closed and the other open. The frequency associated with the fundamental mode 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>11</mn><mi mathvariant="normal"> </mi><mi>Hz</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn><mi mathvariant="normal"> </mi><mi>Hz</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>110</mn><mi mathvariant="normal"> </mi><mi>Hz</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>165</mn><mi mathvariant="normal"> </mi><mi>Hz</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn><mi mathvariant="normal"> </mi><mi>Hz</mi></math></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/lkivxzyqymvrzpahflrpcxxneedeaqryiacihgqdrktvwvzbwr.jpeg" style="max-width:100%; object-fit:contain"/><br/><br/>Given,<br/><br/>Velocity of sound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>330</mn><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/><br/>Length of closed pipe <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>15</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi></math><br/><br/>In a closed pipe for the fundamental mode<br/><br/><math><mfrac><mrow><mi>λ</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mi>l</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>4</mn><mo>×</mo><mn>15</mn><mo>=</mo><mn>6</mn><mo> </mo><mi mathvariant="normal">m</mi></math><br/><br/><math><mi>v</mi><mo>=</mo><mi>n</mi><mi>λ</mi></math><br/><br/><math><mi>n</mi><mo>=</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mi>λ</mi></mrow></mfrac></math><br/><br/><math><mo>=</mo><mfrac><mrow><mn>330</mn></mrow><mrow><mn>6</mn></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>55</mn><mi mathvariant="normal"> </mi><mi>Hz</mi></math></div>


tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-set-a-of-all-matrices-of-order-3-3-with-entries-0-or-1-only-let-b-be-the-subset-of-a-consisting-of-all-matrices-whose-determinant-is-1-le

slug:
consider-the-set-a-of-all-matrices-of-order-3-3-with-entries-0-or-1-only-let-b-be-the-subset-of-a-consisting-of-all-matrices-whose-determinant-is-1-le-30092

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{B}$ has as many elements as $\mathrm{C}$</span> </div>

answer:
<div class="solution">determinant of $\mathrm{B}=1$<br/>Let ' $\mathrm{B}$ ' be identity matrix<br/>So, $B=\left|\begin{array}{lll}1 &amp; 0 &amp; 0 \\ 0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 1\end{array}\right|$<br/>If we interchange any 2 rows, determinant will be $-1$<br/>Let, $\mathrm{C}=\left|\begin{array}{lll}1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; 1 \\ 0 &amp; 1 &amp; 0\end{array}\right|,|\mathrm{C}|=-1$<br/>Here, number of elements in $\mathrm{B}$ and $\mathrm{C}$ are equal.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-spheres-x-2-y-2-z-2-4-y-3-0-and-x-2-y-2-z-2-2-x-4-z-4-0-consider-the-following-statements-1-the-two-spheres-intersect-each-other-2-the-ra

slug:
consider-the-spheres-x-2-y-2-z-2-4-y-3-0-and-x-2-y-2-z-2-2-x-4-z-4-0-consider-the-following-statements-1-the-two-spheres-intersect-each-other-2-the-ra-43895

question:
<div class="question">Consider the spheres $x^{2}+y^{2}+z^{2}-4 y+3=0$ and $x^{2}+y^{2}+z^{2}+2 x$ $+4 z-4=0$<br/>Consider the following statements:<br/> 1 . The two spheres intersect each other.<br/> 2 . The radius of first sphere is less than that of second sphere. Which of the above statements is/are correct?</div>

answer:
<div class="solution">$x^{2}+y^{2}+z^{2}-4 y+3=0$<br/>$x^{2}+y^{2}-4 y+4-4+z^{2}+3=0$<br/>$x^{2}+(y-2)^{2}+z^{2}=1$<br/>Sphere with centre $(0,2,0)$ and radius 1 unit. $x^{2}+y^{2}+z^{2}+2 x+4 z-4=0$<br/>$x^{2}+2 x+1-1+y^{2}+z^{2}+4 z+4-4-4=0$<br/>$(x+1)^{2}+y^{2}+(z+2)^{2}=3^{2}$<br/>Sphere with centre $(-1,0,-2)$ and radius 3 units.<br/>$\mathrm{r}_{1}+\mathrm{r}_{2}=3+1=4$<br/>$\mathrm{C}_{1} \mathrm{C}_{2}   &lt; \mathrm{r}_{1}+\mathrm{r}_{2}$<br/>$\therefore$ Two spheres intersect each other.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-spheres-x-2-y-2-z-2-4-y-3-0-and-x-2-y-2-z-2-2-x-4-z-4-0-what-is-the-distance-between-the-centres-of-the-two-spheres

slug:
consider-the-spheres-x-2-y-2-z-2-4-y-3-0-and-x-2-y-2-z-2-2-x-4-z-4-0-what-is-the-distance-between-the-centres-of-the-two-spheres-36168

question:
<div class="question">Consider the spheres $x^{2}+y^{2}+z^{2}-4 y+3=0$ and $x^{2}+y^{2}+z^{2}+2 x$ $+4 z-4=0$<br/>What is the distance between the centres of the two spheres?</div>

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

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

answer:
<div class="solution">$x^{2}+y^{2}+z^{2}-4 y+3=0$<br/>$x^{2}+y^{2}-4 y+4-4+z^{2}+3=0$<br/>$x^{2}+(y-2)^{2}+z^{2}=1$<br/>Sphere with centre $(0,2,0)$ and radius 1 unit. $x^{2}+y^{2}+z^{2}+2 x+4 z-4=0$<br/>$x^{2}+2 x+1-1+y^{2}+z^{2}+4 z+4-4-4=0$<br/>$(x+1)^{2}+y^{2}+(z+2)^{2}=3^{2}$<br/>Sphere with centre $(-1,0,-2)$ and radius 3 units.<br/>$\quad C_{1} C_{2}=\sqrt{(0+1)^{2}+(2-0)^{2}+(0+2)^{2}}=3$ units</div>


tags: ['Mathematics', 'Circle', 'TS EAMCET', 'TS EAMCET 2021 (06 Aug Shift 2)']
source_db: MarksBatch1_P2.db
title:
consider-the-system-of-circles-x-2-y-2-2-f-y-x-2-y-2-2-gx-k-0-where-g-0-f-0-and-a-parameter-if-a-and-b-are-the-point-circles-of-this-system-such-that-

slug:
consider-the-system-of-circles-x-2-y-2-2-f-y-x-2-y-2-2-gx-k-0-where-g-0-f-0-and-a-parameter-if-a-and-b-are-the-point-circles-of-this-system-such-that-77127

question:
<div class="question">Consider the system of circles $x^2+y^2+2 f y+\lambda\left(x^2+y^2+2 g x+k\right)=0$, where $g \neq 0, f \neq 0$ and $\lambda$ a parameter. If $A$ and $B$ are the point circles of this system such that $\angle A O B=\frac{\pi}{2}$, then $g^2$ is equal to</div>

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

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

answer:
<div class="solution">Given, system of family of circles is<br/>$$<br/>x^2+y^2+2 f y+\lambda\left(x^2+y^2+2 g x+k\right)=0<br/>$$<br/>$\begin{aligned} &amp; \Rightarrow \quad(1+\lambda) x^2+(1+\lambda) y^2+2 g \lambda x+2 f y+\lambda k=0 \\ &amp; \Rightarrow \quad x^2+y^2+2 \cdot\left(\frac{g \lambda}{1+\lambda}\right) x+2\left(\frac{f}{1+\lambda}\right) y+\frac{\lambda k}{1+\lambda}=0\end{aligned}$<br/>For point circle, radius should be zero.<br/>$$<br/>\begin{array}{ll}<br/>\therefore &amp; \frac{g^2 \lambda^2}{(1+\lambda)^2}+\frac{f^2}{(1+\lambda)^2}=\frac{\lambda k}{1+\lambda} \\<br/>\Rightarrow &amp; g^2 \lambda^2+f^2=k\left(\lambda+\lambda^2\right)<br/>\end{array}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/Dc8nE1wfi5NxXKwGeaxoJlY_tc5V87QZ-PJ9706CmjM.original.fullsize.png"/><br/><br/>Let the quadratic Eq. (i) has roots $\lambda_1$ and $\lambda_2$, then the coordinates of point circles are<br/>$$<br/>c_1\left(\frac{-g \lambda_1}{1+\lambda_1}, \frac{f}{1+\lambda_1}\right) \text { and } c_2\left(\frac{-g \lambda_2}{1+\lambda_2}, \frac{f}{1+\lambda_2}\right)<br/>$$<br/>$\because$ Lines $O C_1$ and $O C_2$ are perpendicular to each other.<br/>So,<br/>$$<br/>\frac{\frac{f}{1+\lambda_2}}{\frac{g \lambda_2}{1+\lambda_2}} \times \frac{\frac{f}{1+\lambda_1}}{\frac{g \lambda_1}{1+\lambda_1}}=-1<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/peQXbqoUxUiNDAqat80dagvaU0jbT3SrbRhTJByHNtg.original.fullsize.png"/><br/><br/>$\because$ Product of roots of Eq. (i), we get<img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/4TTYJ8I6ec67eRi2AQLxOhkGvKYDeYBwpzHJDPWgGgU.original.fullsize.png"/><br/><br/>From Eqs. (ii) and (iii), we get<br/>$$<br/>\begin{array}{rlrl}<br/>g^2\left(\frac{f^2}{g^2-k}\right) &amp; =-f^2 \\<br/>\Rightarrow &amp; &amp; g^2 &amp; =-g^2+k \\<br/>\Rightarrow &amp; 2 g^2 &amp; =k \Rightarrow g^2=\frac{k}{2}<br/>\end{array}<br/>$$</div>


tags: ['Mathematics', 'Linear Programming', 'WBJEE', 'WBJEE 2013']
source_db: MarksBatch1_P2.db
title:
consider-the-system-of-equations-beginarraycc-xyz-0-alpha-xbeta-ygamma-z-0-alpha2-xbeta2-ygamma2-z-0-endarray-then-the-system-of-equations-has

slug:
consider-the-system-of-equations-beginarraycc-xyz-0-alpha-xbeta-ygamma-z-0-alpha2-xbeta2-ygamma2-z-0-endarray-then-the-system-of-equations-has-25126

question:
<div class="question">Consider the system of equations
<br/>\(\begin{array}{cc}
<br/>x+y+z &amp; =0 \\
<br/>\alpha x+\beta y+\gamma z &amp; =0 \\
<br/>\alpha^{2} x+\beta^{2} y+\gamma^{2} z &amp; =0
<br/>\end{array}\)
<br/>Then the system of equations has</div>

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

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">infinite number of solutions, if any two of $\alpha, \bar{\beta},$ yare equal., a unique solution, if $\alpha, \beta$ and $\gamma$ are distinct.</span> </div>

answer:
<div class="solution">Given system of equations is $x+y+z=0$<br/>$\begin{array}{l}<br/>\alpha x+\beta y+\gamma z=0 \\<br/>\alpha^{2} x+\beta^{2} y+\gamma^{2} z=0<br/>\end{array}$<br/>The coefficient matrix, $A=\left[\begin{array}{ccc}1 &amp; 1 &amp; 1 \\ \alpha &amp; \beta &amp; \gamma \\ \alpha^{2} &amp; \beta^{2} &amp; \gamma^{2}\end{array}\right]$<br/>Now, $|A|=\left|\begin{array}{ccc}1 &amp; 1 &amp; 1 \\ \alpha &amp; \beta &amp; \gamma \\ \alpha^{2} &amp; \beta^{2} &amp; \gamma^{2}\end{array}\right|=(\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)$<br/>(i) The system of equations has a unique solution, if $\alpha, \beta$ and $\gamma$ are distinct<br/>i.e. $|A| \neq 0$<br/>(ii) The system of equations has infinite number of solutions, if any two of $\alpha, \beta$ and $\gamma$ ar equal.<br/>i.e. $|A|=0$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-triangle-a-bc-with-vertices-a-2-3-b-2-1-and-c-1-2-what-is-the-centroid-of-the-tirnalge-a-bc

slug:
consider-the-triangle-a-bc-with-vertices-a-2-3-b-2-1-and-c-1-2-what-is-the-centroid-of-the-tirnalge-a-bc-69082

question:
<div class="question">Consider the triangle $A B C$ with vertices $A(-2,3), B(2,1)$ and $C(1,2)$.<br/>What is the centroid of the tirnalge $A B C$ ?</div>

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

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

answer:
<div class="solution">Centroid of the triangle<br/>$=\left(\frac{\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}}{3}, \frac{\mathrm{y}_{1}+\mathrm{y}_{2}+\mathrm{y}_{3}}{3}\right)$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/tf3y8ZkxCpakff1jv6vodI3DNe9CPpYGcMnsfW1oZSs.original.fullsize.png"/><br/><br/>$=\left(\frac{-2+2+1}{3}, \frac{3+1+2}{3}\right)=\left(\frac{1}{3}, 2\right)$<br/>$\therefore \quad$ Option (b) is correct.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-triangle-a-bc-with-vertices-a-2-3-b-2-1-and-c-1-2-what-is-the-circumcentre-of-the-triangle-abc

slug:
consider-the-triangle-a-bc-with-vertices-a-2-3-b-2-1-and-c-1-2-what-is-the-circumcentre-of-the-triangle-abc-48084

question:
<div class="question">Consider the triangle $A B C$ with vertices $A(-2,3), B(2,1)$ and $C(1,2)$.<br/>What is the circumcentre of the triangle $\mathrm{ABC} ?$</div>

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

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

answer:
<div class="solution">A circumcentre is a point at which perpendicular bisectors meet each other. <br/>Here, ' $\mathrm{E}$ ' represents circumcentre<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/HlUOMoi2uoYNLNHEF02ggriZ8dzizCkT0pdauHXQsqM.original.fullsize.png"/><br/><br/>Mid-point of $\mathrm{BC}=\left(\frac{2+1}{2}, \frac{1+2}{2}\right)=\left(\frac{3}{2}, \frac{3}{2}\right)$<br/>Slope of $\mathrm{BC}=\frac{2-1}{1-2}=-1$<br/>$\therefore \quad$ Slope of $\mathrm{DE}=1$<br/>Now, equation of $\overline{E D}$ is $\left(y-\frac{3}{2}\right)=1\left(x-\frac{3}{2}\right)$<br/>$2 y-3=2 x-3$<br/>$\mathrm{x}=\mathrm{y}$ ...(i)<br/>Now, mid-point of $\mathrm{AC}=\left(\frac{-2+1}{2}, \frac{3+2}{2}\right)=\left(-\frac{1}{2}, \frac{5}{2}\right)$<br/>Slope of $\mathrm{AC}=\frac{3-2}{-2-1}=-\frac{1}{3}$<br/>Slope of $\mathrm{EF}=3$<br/>Now, equation of $\overrightarrow{\mathrm{EF}}$ is $\left(\mathrm{y}-\frac{5}{2}\right)=3\left(\mathrm{x}+\frac{1}{2}\right)$<br/>$2 y-5=6 x+3$ ...(ii)<br/>From equations (i) and (ii), $\mathrm{x}=-2$ and $\mathrm{y}=-2$<br/>Hence, circumcentre of $\Delta \mathrm{ABC}$ is $(\mathrm{x}, \mathrm{y})=(-2,-2)$<br/>Option (a) is correct.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-triangle-a-bc-with-vertices-a-2-3-b-2-1-and-c-1-2-what-is-the-foot-of-the-altitude-from-the-vertex-a-of-the-triangle-a-bc

slug:
consider-the-triangle-a-bc-with-vertices-a-2-3-b-2-1-and-c-1-2-what-is-the-foot-of-the-altitude-from-the-vertex-a-of-the-triangle-a-bc-11845

question:
<div class="question">Consider the triangle $A B C$ with vertices $A(-2,3), B(2,1)$ and $C(1,2)$.<br/>What is the foot of the altitude from the vertex $A$ of the triangle $A B C ?$</div>

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

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

answer:
<div class="solution">Slope of $\mathrm{BC}=\frac{2-1}{1-2}=-1$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/vMLtKC9Fs6Mi91x3v6A_6uZmpGSKFQPH7N63239d_JU.original.fullsize.png"/><br/><br/>Slope of $\mathrm{AD}=1$<br/>Now, equation of $\overrightarrow{B C}$ is $y-2=-1(x-1)$<br/>$\therefore \quad y-2=-x+1$<br/>$\therefore \quad x+y-3=0$ ...(i)<br/>and equation of $\mathrm{AD}$ is $(\mathrm{y}-3)=1(\mathrm{x}+2)$<br/>$\therefore \quad \mathrm{x}-\mathrm{y}+5=0$...(ii)<br/>From equations (i) and (ii), $\mathrm{x}=-1$ and $\mathrm{y}=4$<br/>$\therefore$ Foot of altitude from the vertex A of the triangle $\mathrm{ABC}$ is $(-1,4)$<br/>$\therefore$ Option (d) is correct.</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-two-circles-x-1-2-y-3-2-r-2-and-x-2-y-2-8-x-2-y-8-0-if-the-circles-intersect-at-two-distinct-points-then-which-one-of-the-following-is-co

slug:
consider-the-two-circles-x-1-2-y-3-2-r-2-and-x-2-y-2-8-x-2-y-8-0-if-the-circles-intersect-at-two-distinct-points-then-which-one-of-the-following-is-co-47795

question:
<div class="question">Consider the two circles $(x-1)^{2}+(y-3)^{2}=r^{2}$ and $\mathrm{x}^{2}+\mathrm{y}^{2}-8 \mathrm{x}+2 \mathrm{y}+8=0$<br/>If the circles intersect at two distinct points, 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">$\mathrm{r}=1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad 1   &lt; \mathrm{r} &lt; 2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad r=2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2   &lt; \mathrm{r} &lt; 8$</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> </ul>

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

answer:
<div class="solution">Given equation of circles $(x-1)^{2}+(y-3)^{2}=r^{2}$<br/>$\left(h_{1}, k_{1}\right) \equiv$ coordinates of centre $\equiv(1,3)$<br/>$$<br/>\begin{array}{l}<br/>\therefore x^{2}+y^{2}-8 x+2 y+8=0 \\<br/>\Rightarrow(x-4)^{2}+(y+1)^{2}=(3)^{2}<br/>\end{array}<br/>$$<br/>$\left(h_{2}, k_{2}\right) \equiv$ coordinates of centre $\equiv(4,-1)$<br/>Radius of circle one $=r_{1}=r$<br/>Radius of circle two $=r_{2}=3$ ". Circle intersects at two points so distance between<br/>circle is $d   &lt; r_{1}+r_{2}$<br/>$5 &lt; r+3$<br/>$r&gt;2$ also $\mathrm{r} \leq 5+2$. Hence, $2 &lt; \mathrm{r} &lt; 8$</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-two-circles-x-1-2-y-3-2-r-2-and-x-2-y-2-8-x-2-y-8-0-what-is-the-distance-between-the-centres-of-the-two-circles

slug:
consider-the-two-circles-x-1-2-y-3-2-r-2-and-x-2-y-2-8-x-2-y-8-0-what-is-the-distance-between-the-centres-of-the-two-circles-88373

question:
<div class="question">Consider the two circles $(x-1)^{2}+(y-3)^{2}=r^{2}$ and $\mathrm{x}^{2}+\mathrm{y}^{2}-8 \mathrm{x}+2 \mathrm{y}+8=0$<br/>What is the distance between the centres of the two circles?</div>

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

answer:
<div class="solution">Given equation of circles $(x-1)^{2}+(y-3)^{2}=r^{2}$<br/>$\left(h_{1}, k_{1}\right) \equiv$ coordinates of centre $\equiv(1,3)$<br/>$$<br/>\begin{array}{l}<br/>\therefore x^{2}+y^{2}-8 x+2 y+8=0 \\<br/>\Rightarrow(x-4)^{2}+(y+1)^{2}=(3)^{2}<br/>\end{array}<br/>$$<br/>$\left(h_{2}, k_{2}\right) \equiv$ coordinates of centre $\equiv(4,-1)$<br/>Distance between centres of two circles<br/>$d=\sqrt{\left(h_{1}-h_{2}\right)^{2}+\left(k_{1}-k_{2}\right)^{2}}$<br/>$\Rightarrow d=\sqrt{(1-4)^{2}+(3+1)^{2}}$<br/>$\Rightarrow d=\sqrt{25}$<br/>$d=5$ units</div>


tags: ['Physics', 'Magnetic Properties of Matter']
source_db: MarksBatch1_P2.db
title:
consider-the-two-idealised-systems-i-a-parallel-plate-capacitor-with-large-plates-and-small-separation-and-ii-a-long-solenoid-of-length-l-r-radius-of-

slug:
consider-the-two-idealised-systems-i-a-parallel-plate-capacitor-with-large-plates-and-small-separation-and-ii-a-long-solenoid-of-length-l-r-radius-of-81194

question:
<div class="question">Consider the two idealised systems (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid $\quad$ of $\quad$ length $\mathrm{L}&gt;\mathrm{R}$, radius of cross-section. In (i) $\mathrm{E}$ is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>case (ii) contradicts Gauss' law for magnetic fields<br/></span> </div>

answer:
<div class="solution">The electric field lines, do not form a continuous path while the magnetic field lines form the closed paths.<br/>Gauss's law states that, $\oint_{\mathrm{s}}$ E.ds $=\frac{\mathrm{q}}{\varepsilon_0}$ for electrostatic field. So, it does not contradict for electrostatic fields as the electric field lines do not form closed continuous path.<br/>According to Gauss' law in magnetic field, $\oint E \mathrm{ds}=0$<br/>It contradicts for magnetic field, because there is a magnetic field inside the solenoid and no field outside the solenoid carrying current but the magnetic field lines form the closed path.<br/>According to Gauss' law in magnetic field,<br/>$$<br/>\oint_{\mathrm{s}} \mathrm{E} . \mathrm{ds}=0<br/>$$<br/>It contradicts for magnetic field, because there is a magnetic field inside the solenoid and no field outside the solenoid carrying current but the magnetic field lines form the closed path.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-two-lines-x-y-1-0-and-3-x-2-y-1-0-what-is-the-equation-of-the-line-passing-through-the-point-of-intersection-of-the-given-lines-and-paral-1

slug:
consider-the-two-lines-x-y-1-0-and-3-x-2-y-1-0-what-is-the-equation-of-the-line-passing-through-the-point-of-intersection-of-the-given-lines-and-paral-1-97358

question:
<div class="question">Consider the two lines $x+y+1=0$ and $3 x+2 y+1=0$ <br/>What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis? $[2016-I]$</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/IjWGZsaQfUyvv4MdSTvETD5qNYknjAaxHzoOPkBn6pc.original.fullsize.png"/><br/><br/>Equation of $y$ -axis $x=0$<br/>Equation of line parallel to $y$ -axis is $x=k$<br/>If this line passes through $(1,-2$ then $)$ $x=1$<br/>Hence equation of line which passes through point of intersection of given line $(1,-2)$ and parallel to $y$ -axis $x=1$<br/>$\Rightarrow x-1=0$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-two-lines-x-y-1-0-and-3-x-2-y-1-0-what-is-the-equation-of-the-line-passing-through-the-point-of-intersection-of-the-given-lines-and-paral

slug:
consider-the-two-lines-x-y-1-0-and-3-x-2-y-1-0-what-is-the-equation-of-the-line-passing-through-the-point-of-intersection-of-the-given-lines-and-paral-19545

question:
<div class="question">Consider the two lines $x+y+1=0$ and $3 x+2 y+1=0$ <br/>What is the equation of the line passing through the point of intersection of the given lines and parallel to $\mathrm{x}$ -axis?</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/IjWGZsaQfUyvv4MdSTvETD5qNYknjAaxHzoOPkBn6pc.original.fullsize.png"/><br/><br/>Equation of $x$ -axi $y=0$<br/>Line parallel to $x$ axis is $y=k$<br/>If this line passes through $(1,-2)$ then $k=-2$<br/>$\Rightarrow y=-2$<br/>$\Rightarrow y+2=0$<br/>Equation of line passing through $(1,-2)$ and parallel to $x$ -axis is $y+2=0$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-two-series-of-observations-aand-b-as-follows-beginarrayllllll-hline-series-a-1019-1008-1015-1006-1002-hline-series-b-19-08-15-06-02-hline

slug:
consider-the-two-series-of-observations-aand-b-as-follows-beginarrayllllll-hline-series-a-1019-1008-1015-1006-1002-hline-series-b-19-08-15-06-02-hline-18121

question:
<div class="question">Consider the two series of observations Aand B as follows:<br/>\begin{array}{l|l|l|l|l|l}<br/>\hline Series A &amp; 1019 &amp; 1008 &amp; 1015 &amp; 1006 &amp; 1002 \\<br/>\hline Series B &amp; 1.9 &amp; 0.8 &amp; 1.5 &amp; 0.6 &amp; 0.2 \\<br/>\hline<br/>\end{array}<br/>If the standard deviation of the Series A is $\sqrt{38,}$ then what is the standard deviation of the Series $\mathrm{B}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3.8$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{0.38}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.38$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{38}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{0.38}$</span> </div>

answer:
<div class="solution">Standard deviation (series B)<br/>$=\sqrt{\left(\frac{1.9+0.8+1.5+0.6+0.2}{5}\right)^{2}}$<br/>$=\sqrt{\frac{6.9}{5}-1}=\sqrt{1.38-1}$<br/>$=\sqrt{0.38}$</div>


title: consider-the-vectors-a-i-2-j-k-and-b-4-i-4-j-7-k-what-is-the-scalar-projection-of-a-on-b
slug: consider-the-vectors-a-i-2-j-k-and-b-4-i-4-j-7-k-what-is-the-scalar-projection-of-a-on-b-27483
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider the vectors $\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$ and $\bar{b}=4 \hat{i}-4 \hat{j}+7 \hat{k}$.<br/>What is the scalar projection of $\bar{a}$ on $\bar{b}$ ?</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">$19 / 9$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$17 / 9$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$23 / 9$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$19 / 9$</span> </div>

answer:
<div class="solution">Projection of $\vec{a}$ on $\overrightarrow{\mathrm{b}}=\frac{\overrightarrow{\mathrm{a}} \overrightarrow{\vec{b}}}{|\overrightarrow{\mathrm{b}}|}=\frac{(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}) \cdot(4 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+7 \hat{\mathrm{k}})}{\left|\sqrt{4^{2}+(-4)^{2}+7^{2}}\right|}$<br/>$=\frac{19}{9}$</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
consider-the-vectors-a-i-2-j-k-and-b-4-i-4-j-7-k-what-is-the-vector-perpendicular-to-both-the-vectors

slug:
consider-the-vectors-a-i-2-j-k-and-b-4-i-4-j-7-k-what-is-the-vector-perpendicular-to-both-the-vectors-43364

question:
<div class="question">Consider the vectors $\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$ and $\bar{b}=4 \hat{i}-4 \hat{j}+7 \hat{k}$.<br/>What is the vector perpendicular to both the vectors?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\quad-10 \hat{i}-3 \hat{j}+4 \hat{k}$</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">B</span> <span class="option-data">$-10 \hat{i}+3 \hat{j}+4 \hat{k}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \hat{i}-3 \hat{j}+4 \hat{k}$</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">$\quad-10 \hat{i}-3 \hat{j}+4 \hat{k}$</span> </div>

answer:
<div class="solution">Vector perpendicular to $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$<br/>$=\left|\begin{array}{ccc}\hat{i} &amp; \hat{j} &amp; \hat{k} \\ 1 &amp; -2 &amp; 1 \\ 4 &amp; -4 &amp; 7\end{array}\right|=\hat{i}(-14+4)-j(7-4)+\hat{k}(-4+8)$<br/>$=-10 \hat{i}-3 \hat{j}+4 \hat{k}$</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-three-observations-a-b-and-c-such-that-b-a-c-if-the-standard-deviation-of-a-2-c-2-is-d-then-which-of-the-following-is-true-1

slug:
consider-three-observations-a-b-and-c-such-that-b-a-c-if-the-standard-deviation-of-a-2-c-2-is-d-then-which-of-the-following-is-true-1-83520

question:
<div class="question">Consider three observations <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>c</mi></math>. If the standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>c</mi><mo>+</mo><mn>2</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>, then which of the following is true?</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"><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>+</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></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>b</mi><mn>2</mn></msup><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><msup><mi>d</mi><mn>2</mn></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>+</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></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> </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>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></math></span> </div>

answer:
<div class="solution"><p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></p><p>mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mn>3</mn></mfrac><mfenced><mrow><mo>=</mo><mover><mi>x</mi><mo>¯</mo></mover></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mover><mi>x</mi><mo>¯</mo></mover><mo>=</mo><mfrac><mrow><mn>2</mn><mi>b</mi></mrow><mn>3</mn></mfrac></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mn>1</mn><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">S</mi><mo>.</mo><mi mathvariant="normal">D</mi><mo>.</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>b</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>c</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mi mathvariant="normal">S</mi><mo>.</mo><mi mathvariant="normal">D</mi><mo>.</mo><mfenced><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced><mo>=</mo><mi>d</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>d</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>-</mo><msup><mfenced><mover><mi>x</mi><mo>¯</mo></mover></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>d</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mn>4</mn><msup><mi>b</mi><mn>2</mn></msup></mrow><mn>9</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>4</mn><msup><mi>b</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></math></p></div>


tags: ['Mathematics', 'Statistics', 'JEE Main', 'JEE Main 2021 (16 Mar Shift 1)']
source_db: MarksBatch1_P2.db
title:
consider-three-observations-a-b-and-c-such-that-b-a-c-if-the-standard-deviation-of-a-2-c-2-is-d-then-which-of-the-following-is-true

slug:
consider-three-observations-a-b-and-c-such-that-b-a-c-if-the-standard-deviation-of-a-2-c-2-is-d-then-which-of-the-following-is-true-23614

question:
<div class="question">Consider three observations <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>c</mi></math>. If the standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>c</mi><mo>+</mo><mn>2</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math>, then which of the following is true?</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"><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>+</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></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>b</mi><mn>2</mn></msup><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><msup><mi>d</mi><mn>2</mn></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>+</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></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> </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>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></math></span> </div>

answer:
<div class="solution"><p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></p><p>mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow><mn>3</mn></mfrac><mfenced><mrow><mo>=</mo><mover><mi>x</mi><mo>¯</mo></mover></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mover><mi>x</mi><mo>¯</mo></mover><mo>=</mo><mfrac><mrow><mn>2</mn><mi>b</mi></mrow><mn>3</mn></mfrac></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mn>1</mn><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">S</mi><mo>.</mo><mi mathvariant="normal">D</mi><mo>.</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>b</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>c</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mi mathvariant="normal">S</mi><mo>.</mo><mi mathvariant="normal">D</mi><mo>.</mo><mfenced><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced><mo>=</mo><mi>d</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>d</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>-</mo><msup><mfenced><mover><mi>x</mi><mo>¯</mo></mover></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>d</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mn>4</mn><msup><mi>b</mi><mn>2</mn></msup></mrow><mn>9</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>4</mn><msup><mi>b</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>3</mn><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfenced><mo>-</mo><mn>9</mn><msup><mi>d</mi><mn>2</mn></msup></math></p></div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P2.db
title:
consider-two-identical-tubes-a-and-b-tube-a-has-both-ends-open-while-tube-b-has-one-end-closed-the-ratio-of-the-fundamental-frequency-of-tube-a-and-b-

slug:
consider-two-identical-tubes-a-and-b-tube-a-has-both-ends-open-while-tube-b-has-one-end-closed-the-ratio-of-the-fundamental-frequency-of-tube-a-and-b-41504

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mo>:</mo><mo> </mo><mn>1</mn></math></span> </div>

answer:
<div class="solution">In tube <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>,  <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Î»</mi><mtext>A</mtext></msub><mo>=</mo><mn>2</mn><mtext mathvariant="italic">l</mtext></math><br/><br/>In tube <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>B</mtext></math>,  <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Î»</mi><mtext>B</mtext></msub><mo>=</mo><mn>4</mn><mtext mathvariant="italic">l</mtext></math><br/><br/><math> <mrow> <mo>â´</mo> </mrow> </math>  <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Ï</mi><mtext>A</mtext></msub><mo>=</mo><mfrac><mi>Î½</mi><msub><mi>Î»</mi><mtext>A</mtext></msub></mfrac><mo>=</mo><mfrac><mi>Î½</mi><mrow><mn>2</mn><mtext mathvariant="italic">l</mtext></mrow></mfrac></math><br/><br/><math> <mrow> <mo>â´</mo> </mrow> </math>  <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Ï</mi><mtext>B</mtext></msub><mo>=</mo><mfrac><mi>Î½</mi><msub><mi>Î»</mi><mtext>B</mtext></msub></mfrac><mo>=</mo><mfrac><mi>Î½</mi><mrow><mn>4</mn><mtext mathvariant="italic">l</mtext></mrow></mfrac></math><br/><br/><math> <mrow> <mo>â´</mo> </mrow> </math>  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>Ï</mi><mtext>A</mtext></msub><msub><mi>Ï</mi><mtext>B</mtext></msub></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>1</mn></mfrac></math>.<br/><br/><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/0002554_solu.JPG" style="width: 250px; height: 211px;"/></div>


title: consider-two-matrices-a-1-2-1-2-1-1-and-b-1-2-2-1-4-4-which-one-of-the-following-is-correct
slug: consider-two-matrices-a-1-2-1-2-1-1-and-b-1-2-2-1-4-4-which-one-of-the-following-is-correct-40546
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider two matrices $A=\left[\begin{array}{ll}1 &amp; 2 \\ 2 &amp; 1 \\ 1 &amp; 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 &amp; 2 &amp; -4 \\ 2 &amp; 1 &amp; -4\end{array}\right]$.<br/>Which one of the following is correct?</div>

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

answer:
<div class="solution">I. <br/>$\mathrm{AB}=\left|\begin{array}{cc}1 &amp; 2 \\ 2 &amp; 1 \\ 1 &amp; 1\end{array}\right|_{3 \times 2}\left|\begin{array}{ccc}1 &amp; 2 &amp; -4 \\ 2 &amp; 1 &amp; -4\end{array}\right|_{2 \times 3}$<br/>$=\left|\begin{array}{rrr}5 &amp; 4 &amp; -12 \\ 4 &amp; 5 &amp; -12 \\ 3 &amp; 3 &amp; -8\end{array}\right|_{3 \times 3}$<br/>II. <br/>$\begin{aligned} \mathrm{BA} &amp;=\left|\begin{array}{lll}1 &amp; 2 &amp; -4 \\ 2 &amp; 1 &amp; -4\end{array}\right|_{2 \times 3}\left|\begin{array}{cc}1 &amp; 2 \\ 2 &amp; 1 \\ 1 &amp; 1\end{array}\right|_{3 \times 2} \\ &amp;=\left|\begin{array}{ll}1 &amp; 0 \\ 0 &amp; 1\end{array}\right|_{2 \times 2} \end{aligned}$<br/>Here, $\mathrm{B}$ is not the right inverse of $\mathrm{A}$ but $\mathrm{B}$ is the left inverse of $\mathrm{A}$.</div>


title: consider-x-4-tan-1-5-1-y-tan-1-70-1-and-z-tan-1-99-1-what-is-x-equal-to
slug: consider-x-4-tan-1-5-1-y-tan-1-70-1-and-z-tan-1-99-1-what-is-x-equal-to-13564
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider $x=4 \tan ^{-1}\left(\frac{1}{5}\right), y=\tan ^{-1}\left(\frac{1}{70}\right)$ and $z=\tan ^{-1}\left(\frac{1}{99}\right)$. <br/>What is $x$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\tan ^{-1}\left(\frac{60}{119}\right)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\tan ^{-1}\left(\frac{120}{119}\right)$</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">$\tan ^{-1}\left(\frac{90}{169}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\tan ^{-1}\left(\frac{170}{169}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\tan ^{-1}\left(\frac{120}{119}\right)$</span> </div>

answer:
<div class="solution">$\mathrm{x}=4 \tan ^{-1}\left(\frac{1}{5}\right)$<br/>$=2\left[2 \tan ^{-1} \frac{1}{5}\right]=2\left[\tan ^{-1} \frac{\frac{2}{5}}{1-\left(\frac{1}{5}\right)^{2}}\right]$<br/>$=2 \tan ^{-1}\left(\frac{\frac{2}{5} \times 25}{24}\right)=2 \tan ^{-1} \frac{10}{24}=2 \tan ^{-1} \frac{5}{12}$<br/>$=\tan ^{-1}\left(\frac{2 \times \frac{5}{12}}{1-\frac{25}{144}}\right)=\tan ^{-1} \frac{120}{119} .$</div>


title: consider-x-4-tan-1-5-1-y-tan-1-70-1-and-z-tan-1-99-1-what-is-x-y-equal-to
slug: consider-x-4-tan-1-5-1-y-tan-1-70-1-and-z-tan-1-99-1-what-is-x-y-equal-to-87854
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider $x=4 \tan ^{-1}\left(\frac{1}{5}\right), y=\tan ^{-1}\left(\frac{1}{70}\right)$ and $z=\tan ^{-1}\left(\frac{1}{99}\right)$.<br/>What is $x-y$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\tan ^{-1}\left(\frac{828}{845}\right)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\tan ^{-1}\left(\frac{8287}{8450}\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\tan ^{-1}\left(\frac{8281}{8450}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\tan ^{-1}\left(\frac{8287}{8471}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\tan ^{-1}\left(\frac{8281}{8450}\right)$</span> </div>

answer:
<div class="solution">$x-\mathrm{y}=\tan ^{-1}\left(\frac{120}{119}\right)-\tan ^{-1} \frac{1}{70}$<br/>$=\tan ^{-1} \mid \frac{\frac{120}{119}-\frac{1}{70}}{1+\left(\frac{120}{119} \times \frac{1}{70}\right) \mid}$<br/>$$<br/>=\tan ^{-1}\left|\frac{\frac{8400-119}{8330}}{1+\frac{120}{8330}}\right|<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/-pAl1yq4t8YbbBdh1eXiQNntSUdgcP1jlqIwZqp4RB8.original.fullsize.png"/><br/><br/>$\therefore \quad$ Option (c) is correct.</div>


title: consider-x-4-tan-1-5-1-y-tan-1-70-1-and-z-tan-1-99-1-what-is-x-y-z-equal-to
slug: consider-x-4-tan-1-5-1-y-tan-1-70-1-and-z-tan-1-99-1-what-is-x-y-z-equal-to-13944
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Consider $x=4 \tan ^{-1}\left(\frac{1}{5}\right), y=\tan ^{-1}\left(\frac{1}{70}\right)$ and $z=\tan ^{-1}\left(\frac{1}{99}\right)$.<br/>What is $x-y+z$ equal to?</div>

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

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

answer:
<div class="solution">$x-y=\tan ^{-1} \frac{8281}{8450} \Rightarrow \tan ^{-1}\left|\frac{8281}{8450}\right|+\tan ^{-1}\left(\frac{1}{99}\right)$<br/>$=\tan ^{-1}\left|\frac{\frac{8281}{8450}+\frac{1}{99}}{1-\frac{8281}{8450} \times \frac{1}{99}}\right|=\tan ^{-1} \mid \frac{\frac{828269}{836550}}{\frac{828269}{836550} \mid=1}$<br/>$\tan ^{-1}=(1)=\frac{\pi}{4}$<br/>$\therefore \quad$ Option (d) is correct.</div>


tags: ['Mathematics', 'Indefinite Integration', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-x-tan-1-x-d-x-a-x-2-1-tan-1-x-b-x-c-where-c-is-the-constant-of-integration-what-is-the-value-of-a

slug:
consider-x-tan-1-x-d-x-a-x-2-1-tan-1-x-b-x-c-where-c-is-the-constant-of-integration-what-is-the-value-of-a-63266

question:
<div class="question">Consider $\int x \tan ^{-1} x d x=A\left(x^{2}+1\right) \tan ^{-1} x+B x+C$,<br/>where $\mathrm{C}$ is the constant of integration.<br/>What is the value of $A$?</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">$1 / 2$</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">$-1 / 2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 4$</span> </li> </ul>

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

answer:
<div class="solution">Given, $\int x \tan ^{-1} x d x=A\left(x^{2}+1\right) \tan ^{-1} x+B x+C$<br/>where, $\mathrm{C}$ is the constant of integration<br/>Consider, $\int_{I I}{x \tan ^{-1} x d x}$<br/>$\quad=\tan ^{-1} x \cdot \frac{x^{2}}{2}-\int \frac{d}{d x}\left(\tan ^{-1} x\right) \cdot \frac{x^{2}}{2} d x$<br/>(using integration by parts)<br/>$=\frac{x^{2} \cdot \tan ^{-1} x}{2}-\frac{1}{2} \int \frac{x^{2}}{1+x^{2}} d x$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{1}{2}\left(\int\left(\frac{1+x^{2}-1}{1+x^{2}}\right) d x\right)$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{1}{2}\left(\int d x-\int \frac{d x}{1+x^{2}}\right)$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{1}{2}\left(x-\tan ^{-1} x\right)+C$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{x}{2}+\frac{\tan ^{-1} x}{2}+C$<br/>$=\frac{1}{2}\left(x^{2}+1\right) \tan ^{-1} x-\frac{x}{2}+C$<br/>$\mathrm{A}=\frac{1}{2}$, hence option (b) is correct.</div>


tags: ['Mathematics', 'Indefinite Integration', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
consider-x-tan-1-x-d-x-a-x-2-1-tan-1-x-b-x-c-where-c-is-the-constant-of-integration-what-is-the-value-of-b

slug:
consider-x-tan-1-x-d-x-a-x-2-1-tan-1-x-b-x-c-where-c-is-the-constant-of-integration-what-is-the-value-of-b-73830

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

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

answer:
<div class="solution">Given, $\int x \tan ^{-1} x d x=A\left(x^{2}+1\right) \tan ^{-1} x+B x+C$<br/>where, $\mathrm{C}$ is the constant of integration<br/>Consider, $\int_{I I}{x \tan ^{-1} x d x}$<br/>$\quad=\tan ^{-1} x \cdot \frac{x^{2}}{2}-\int \frac{d}{d x}\left(\tan ^{-1} x\right) \cdot \frac{x^{2}}{2} d x$<br/>(using integration by parts)<br/>$=\frac{x^{2} \cdot \tan ^{-1} x}{2}-\frac{1}{2} \int \frac{x^{2}}{1+x^{2}} d x$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{1}{2}\left(\int\left(\frac{1+x^{2}-1}{1+x^{2}}\right) d x\right)$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{1}{2}\left(\int d x-\int \frac{d x}{1+x^{2}}\right)$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{1}{2}\left(x-\tan ^{-1} x\right)+C$<br/>$=\frac{x^{2} \tan ^{-1} x}{2}-\frac{x}{2}+\frac{\tan ^{-1} x}{2}+C$<br/>$=\frac{1}{2}\left(x^{2}+1\right) \tan ^{-1} x-\frac{x}{2}+C$<br/>$\mathrm{B}=-\frac{1}{2}$, hence option (c) is correct.</div>


tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
title:
considering-the-longitudinal-section-of-a-root-starting-from-the-tip-identify-the-correct-order-for-the-arrangement-of-the-four-different-zones

slug:
considering-the-longitudinal-section-of-a-root-starting-from-the-tip-identify-the-correct-order-for-the-arrangement-of-the-four-different-zones-77880

question:
<div class="question">Considering the longitudinal section of a root, starting from the tip, identify the correct order for the arrangement of the four different zones?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Root cap zone, region of cell division, region of cell enlargement, region of cell maturation.</span> </div>

answer:
<div class="solution">The root system of a plant develops from the hypocotyl of the embryo. The root shows the following four regions which usually merge into one another, without distinct boundaries between them. The four zones, successively from the apex to the base are:<br/><strong>Root cap zone</strong>: The apex of each root is covered by a cushion of thin-walled cells known as root cap.<br/><strong>Region of cell division</strong>: It lies just behind the root cap. It is the main growing region of the root where active cell divisions take place.<br/><strong>Region of elongation</strong>: The region of elongation is responsible for growth in length of the root.<br/><strong>Region of maturation</strong>: Epidermal cells of this region give out small, thin, cylindrical unicellular outgrowth, known as root hairs. These are the main absorbing organs of the root.</div>


tags: ['Chemistry', 'Electrochemistry']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
consult-the-table-of-standard-electrode-potentials-and-suggest-three-substances-that-can-oxidise-ferrous-ions-under-suitable-conditions

slug:
consult-the-table-of-standard-electrode-potentials-and-suggest-three-substances-that-can-oxidise-ferrous-ions-under-suitable-conditions-99887

question:
<div class="question">Consult the table of standard electrode potentials and suggest three substances that can oxidise ferrous ions under suitable conditions.</div>

answer:
<div class="solution">Oxidation of \(\mathrm{Fe}^{2+}\) converts it to \(\mathrm{Fe}^{3+}\), i.e.,<br/>\(\mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{3+}+\mathrm{e}^{-} ; \mathrm{E}_{\mathrm{ox}}^{\mathrm{o}}=-0.77 \mathrm{~V}\)<br/>Only those substances can oxidise \(\mathrm{Fe}^{2+}\) to \(\mathrm{Fe}^{3+}\) which are stronger oxidizing agents and have positive reduction potentials greater than \(0.77 \mathrm{~V}\), so that EMF of the cell reaction is positive. This is so for elements lying below \(\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}\) in the series ex: \(\mathrm{BO}_2, \mathrm{Cl}_2\) and \(\mathrm{F}_2\).</div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
answer: <div class="solution">Correct Option is : (C)<br/>Copper, Mercury, and Lead</div>
source_db: MarksBatch1_P2.db
title:
consult-the-table-of-standard-electrode-potentials-and-suggest-three-substances-that-can-oxidize-ferrous-ions-under-suitable-conditions

slug:
consult-the-table-of-standard-electrode-potentials-and-suggest-three-substances-that-can-oxidize-ferrous-ions-under-suitable-conditions-81432

question:
<div class="question">Consult the table of standard electrode potentials and suggest three substances that can oxidize ferrous ions under suitable conditions.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Copper, Mercury, and Lead</span> </div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2018 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3,1</span> </div>
answer: <div class="solution">Go through the option (c)</div>
source_db: MarksBatch1_P2.db
title:
coordinates-of-the-points-o-p-q-and-r-are-respectively-0-0-0-4-6-2-m-2-0-2-n-and-2-4-6-let-l-m-n-and-k-be-points-on-the-sides-or-op-pq-and-qr-respecti

slug:
coordinates-of-the-points-o-p-q-and-r-are-respectively-0-0-0-4-6-2-m-2-0-2-n-and-2-4-6-let-l-m-n-and-k-be-points-on-the-sides-or-op-pq-and-qr-respecti-81393

question:
<div class="question">Coordinates of the points $\mathrm{O}, \mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are respectively $(0,0,0),(4,6,2 \mathrm{~m}),(2,0,2 \mathrm{n})$ and $(2,4,6)$. Let $\mathrm{L}, \mathrm{M}, \mathrm{N}$ and $\mathrm{K}$ be<br/>points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides<br/>side L.K are each of length $\sqrt{2}$. What are the values of $\mathrm{m}$ and<br/>n respectively?</div>

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


title: coordination-number-of-nickel-in-ni-c-2-o-4-3-4-is
slug: coordination-number-of-nickel-in-ni-c-2-o-4-3-4-is-53429
tags: ['Chemistry', 'Coordination Compounds', 'COMEDK', 'COMEDK 2012']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Coordination number of nickel in $\left[\mathrm{Ni}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{4-}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">12</span> </li><li class="correct"> <span class="option-label">C</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">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution">Oxalate $\left(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\right)$ is an example of bidendate ligand. Three oxalate ligands form six coordinate bond around $\mathrm{Ni}^{2+}$ ion. Hence, coordination number is 6 .<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/comedk/wWAkJ3VW-8dWufLAOO2AzXR6rTYJSZ9hFFA4g2l-KSY.original.fullsize.png"/><br/></div>


title: cork-cambium-forms-tissues-that-form-the-cork-do-you-agree-with-this-statement-explain
slug: cork-cambium-forms-tissues-that-form-the-cork-do-you-agree-with-this-statement-explain-30694
tags: ['Biology', 'Anatomy of Flowering Plants']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Cork cambium forms tissues that form the cork. Do you agree with this statement? Explain.</div>

answer:
<div class="solution">Cork cambium : As the stem continues to increase in girth due to the activity of vascular cambium, the outer cortical and epidermal layers get broken and need to be replaced to provide new protective cell layers. Hence, sooner or later, another meristematic tissue called cork cambium or phellogen develops, usually in the cortex region. Phellogen is a couple of layers thick. It is made of narrow, thin-walled and nearly rectangular cells. Phellogen cuts off cells on both sides. The outer cells differentiate into cork or phellem while the inner cells differentiate into secondary cortex or phelloderm. This is clear how cork cambium forms tissues that form the cork.</div>


title: cork-cambium-is-developed-from
slug: cork-cambium-is-developed-from-85748
question: <div class="question">Cork cambium is developed from</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Apical meristem</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Intercalary meristem</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Primitive meristem</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Lateral meristem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Lateral meristem</span> </div>

answer:
<div class="solution">Cork cambium (phellogen) is an outermost lateral meristem in woody plants, that develops from permanent tissues in the region of epidermis hypodermis, cortex, and even in outer layers of phloem. It is also known as a phellogen that forms a layer of cells that produces a secondary protective layer of the stem called the periderm.</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2004']
source_db: MarksBatch1_P2.db
title:
cork-cambium-results-in-the-formation-of-cork-which-becomes-impermeable-to-water-due-to-the-accumulation-of-1

slug:
cork-cambium-results-in-the-formation-of-cork-which-becomes-impermeable-to-water-due-to-the-accumulation-of-1-26828

question:
<div class="question">Cork cambium results in the formation of cork which becomes impermeable to water due to the accumulation of</div>

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

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

answer:
<div class="solution">Cork cambium is a secondary lateral meristem that may arise from permanent living cells of hypodermis or outer cortex. It is composed of a single layer of meristematic cells. Its cells divide tangentially and periclinally towards the outer face and produce cork cells. These cells are compactly arranged and have thin cellulose walls in the beginning. As they mature there is a gradual loss of living matter and cells get elongated radially, vertically or tangentially. The cell walls become thick because of development of fatty substance called suberin, which is impervious to water.</div>


title: cork-is-commonly-used-for-sealing-bottles-it-is-produced-by
slug: cork-is-commonly-used-for-sealing-bottles-it-is-produced-by-95793
question: <div class="question">Cork is commonly used for sealing bottles. It is produced by</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">dermatogen</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">phellogen</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">xylem</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">vascular cambium</span> </li> </ul>

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

answer:
<div class="solution">Cork cambium or phellogen is a type of cambium arising within the outer layer of the stems of woody plants, usually as a complete ring surrounding the inner tissues. The cells of the cork cambium divide to produce an outer corky tissue (cork or phellem) and an innerly secondary cortex (phelloderm). The common bottle cork produced from <em>Quercus suber </em>is a product of phellogen.</div>


title: correct-diagram-for-the-determination-of-internal-resistance-of-a-primary-cell-by-potentiometer-is
tags: ['Physics', 'Current Electricity', 'NEET']
source_db: MarksBatch1_P2.db
slug:
correct-diagram-for-the-determination-of-internal-resistance-of-a-primary-cell-by-potentiometer-is-72104

question:
<div class="question">Correct diagram for the determination of internal resistance of a primary cell by potentiometer is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/0644718_1.JPG" style="width: 180px; height: 142px;"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/0644718_2.JPG" style="width: 180px; height: 143px;"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/fvnanxurbsyqcutucozgjlagpgkgyzdegkocoieqymsqkxgznt.jpeg"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/0644718_4.JPG" style="width: 180px; height: 138px;"/></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/nta_abhyas/neet/images/fvnanxurbsyqcutucozgjlagpgkgyzdegkocoieqymsqkxgznt.jpeg"/></span> </div>

answer:
<div class="solution">The polarity of primary cell and secondary cell should be in same sense. Also, a key is kept in series with resistance box to measure emf when the key is open.</div>


title: correlation-between-two-variable-is-said-to-be-perfect-if
slug: correlation-between-two-variable-is-said-to-be-perfect-if-14197
question: <div class="question">Correlation between two variable is said to be perfect if</div>
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">one variable increases, the other also increases</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">one variable increases, the other decreases</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">one variable increases, the other also increases proportionally</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">one variable increases, the other decreases proportionally</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">one variable increases, the other also increases proportionally</span> </div>

answer:
<div class="solution">Correlation between two variables is said to be perfect if one variable increases, the other also increase:<br/>proportionally.</div>


title: cos-a-cos-2-a-cos-4-a-cos-2-n-1-a-equals-1
slug: cos-a-cos-2-a-cos-4-a-cos-2-n-1-a-equals-1-86286
question: <div class="question">$\cos A \cos 2 A \cos 4 A \ldots \cos 2^{n-1} A$ equals</div>
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'AP EAMCET', 'AP EAMCET 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\sin 2^n A}{2^n \sin A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2^n \sin 2^n A}{\sin A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2^n \sin A}{\sin 2^n A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\sin A}{2^n \sin 2^n A}$</span> </li> </ul>

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

answer:
<div class="solution">It is a standard result.<br/>$\begin{gathered}<br/>\cos A \cos 2 A \cos 2^2 A \ldots \cos 2^{n-1} A \\<br/>=\frac{\sin 2^n A}{2^n \sin A}<br/>\end{gathered}$</div>


title: cryopreservation-seed-bank-gene-bank-and-wild-safari-parks-are-the-methods-of
slug: cryopreservation-seed-bank-gene-bank-and-wild-safari-parks-are-the-methods-of-42694
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Cryopreservation, seed bank, gene bank and wild safari parks are the methods of</div>

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

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

answer:
<div class="solution"><em>Ex-situ </em>conservation literally means 'off-site conservation'. It is the process of protecting an endangered species, variety or breed of plant or animal outside its natural habitat. Threatened plant or animal is taken out from its natural habitat and placed in special setting, where they can be protected and given special care.</div>


tags: ['Biology', 'Strategies for Enhancement in Food Production', 'NEET']
source_db: MarksBatch1_P2.db
title:
culturing-of-shoot-apex-as-explant-on-nutrient-medium-in-tissue-culture-gives-to-diseasefree-plants-because

slug:
culturing-of-shoot-apex-as-explant-on-nutrient-medium-in-tissue-culture-gives-to-diseasefree-plants-because-77537

question:
<div class="question">Culturing of shoot apex as explant on nutrient medium in tissue culture gives to disease-free plants because:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Such explant is pathogen free</span> </div>

answer:
<div class="solution">Culturing of shoot apex as an explant on nutrient medium in tissue gives rise to disease-free plants because the shoot tips regenerated are free of infections or pathogen such as bacteria, fungi, virus, etc. The infection cannot invade into the shoot tip because the shoot tip cells show a high rate of cell division.</div>


title: curve-of-intersection-of-two-spheres-is
slug: curve-of-intersection-of-two-spheres-is-68132
question: <div class="question">Curve of intersection of two spheres is</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2008 (Phase 2)']
answer: <div class="solution">a circle (obviously)</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">an ellipse</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">a circle</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">a parabola</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">a circle</span> </div>


tags: ['Chemistry', 'Aldehydes and Ketones', 'JEE Main', 'JEE Main 2023 (31 Jan Shift 2)']
source_db: MarksBatch1_P2.db
title:
cyclohexylamine-when-treated-with-nitrous-acid-yields-p-on-treating-p-with-pcc-results-in-q-when-q-is-heated-with-dil-naoh-we-get-r-the-final-product-

slug:
cyclohexylamine-when-treated-with-nitrous-acid-yields-p-on-treating-p-with-pcc-results-in-q-when-q-is-heated-with-dil-naoh-we-get-r-the-final-product-52281

question:
<div class="question">Cyclohexylamine when treated with nitrous acid yields (P). On treating (P) with PCC results in (Q). When (Q) is heated with dil. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>NaOH</mi></math> we get (R) The final product (R) is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img alt="" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/9476dad8-747d-4da5-b5d1-929d6fb88a78-9896610.PNG" style="width: 178px; height: 150px;"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img alt="" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/c7f0ce89-0fd4-4f25-aa77-576cd76372a2-9896610_1.PNG" style="width: 169px; height: 150px;"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img alt="" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/590e4ec4-c998-4773-9a4c-1c901a31899b-9896610_2.PNG" style="width: 183px; height: 150px;"/> </span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img alt="" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/fa2d0c77-ec0f-4f29-a8b4-820119c873dd-9896610_3.PNG" style="width: 189px; height: 150px;"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img alt="" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/c7f0ce89-0fd4-4f25-aa77-576cd76372a2-9896610_1.PNG" style="width: 169px; height: 150px;"/></span> </div>

answer:
<div class="solution"><p>Cyclohexylamine when treated with nitrous acid yields cyclohexanol.On treating cyclohexanol with PCC which is a mild oxidising agent and oxidises the alcohols into aldehyde (in case of primary alcohol) or ketones (in case of secondary alcohol) in the presence of dichloromethane results cyclohexanone. When cyclohexanone is heated with dilute <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>NaOH</mi></math> dehydration of aldol takes place by the removal of water molecules we get the final product.</p><p><img alt="" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/b66380fe-0a65-4185-b44c-e963ad6052b6-13835c82-f123-4d20-9f4f-0bc5eaaf7924-9896610_4.PNG" style="width: 577px; height: 112px;"/></p></div>


title: d-b-is-a-standard-abbreviation-used-for-the-quantitative-expression-of
slug: d-b-is-a-standard-abbreviation-used-for-the-quantitative-expression-of-47776
tags: ['Biology', 'Environmental Issues', 'NEET', 'NEET 2010 (Screening)']
source_db: MarksBatch1_P2.db
question:
<div class="question">$d B$ is a standard abbreviation used for the quantitative expression of</div>

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

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

answer:
<div class="solution">Noise pollution is a physical form of pollution that affects the receiver directly. $\mathrm{dB}$ (decibel) is a standard abbreviation used for the quantitative expression of noise. Noise or pollutant sound has a value of $80 \mathrm{~dB}$ and above, it harms hearing system. The WHO has fixed $45 \mathrm{~dB}$ as the safe noise level for a city.</div>


title: d-glucopyranose-is
slug: d-glucopyranose-is-41484
question: <div class="question">$\beta-\mathrm{D}-(+)-$ Glucopyranose is</div>
tags: ['Chemistry', 'Biomolecules', 'AP EAMCET', 'AP EAMCET 2017 (24 Apr Shift 1)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/kAtdKOohKxZiQzmWl3-C3W9rVSE0i_GFw1D6Tf0jVds.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">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/6BxClR-AgjVLW3yiVwKKCL2jcot63VRjNDA3JgotShE.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/PwQsN2-RFrGBzTpSm-lKDmHxa1UTp7wdjm9X8AolOxU.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/MOaEuVRBlZ01-Xg6YPhwn1Nwg2Z7yDAeiBrnvdPhDno.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/ap_eamcet/kAtdKOohKxZiQzmWl3-C3W9rVSE0i_GFw1D6Tf0jVds.original.fullsize.png"/><br/></span> </div>


title: d-x-d-sin-1-3-x-4-x-3-2-1-x-1-is
slug: d-x-d-sin-1-3-x-4-x-3-2-1-x-1-is-71462
tags: ['Mathematics', 'Differentiation', 'MHT CET', 'MHT CET 2022 (05 Aug Shift 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\frac{d}{d x}\left(\sin ^{-1}\left(3 x-4 x^3\right)\right), \frac{1}{2}<x is=""> <div class="tags" data-pagefind-ignore=""> <span class="tag">Mathematics</span><span class="tag">Differentiation</span><span class="tag">MHT CET</span><span class="tag">MHT CET 2022 (05 Aug Shift 1)</span> </div> <span class="label">Options:</span>
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{3 \sqrt{1-x^2}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{-3}{\sqrt{1-x^2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{-1}{3 \sqrt{1-x^2}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{3}{\sqrt{1-x^2}}$</span> </li> </ul> <!-- /Question --> <!-- Solution --> <section class="solution-container" id="accepted-answer"> <div class="solution-header"> <span class="label">Solution:</span> <div class="badges-container" data-pagefind-ignore=""> <span class="badge upvotes-count"> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.625 5.0075C14.4842 4.84795 14.3111 4.72019 14.1171 4.63269C13.9231 4.54519 13.7128 4.49996 13.5 4.5H10V3.5C10 2.83696 9.73661 2.20107 9.26777 1.73223C8.79893 1.26339 8.16304 1 7.5 1C7.40711 0.999934 7.31604 1.02574 7.237 1.07454C7.15795 1.12333 7.09407 1.19318 7.0525 1.27625L4.69125 6H2C1.73478 6 1.48043 6.10536 1.29289 6.29289C1.10536 6.48043 1 6.73478 1 7V12.5C1 12.7652 1.10536 13.0196 1.29289 13.2071C1.48043 13.3946 1.73478 13.5 2 13.5H12.75C13.1154 13.5001 13.4684 13.3668 13.7425 13.1252C14.0166 12.8835 14.1931 12.5501 14.2388 12.1875L14.9888 6.1875C15.0153 5.97626 14.9966 5.76179 14.9339 5.55833C14.8712 5.35488 14.7659 5.16711 14.625 5.0075ZM2 7H4.5V12.5H2V7Z" fill="#014A82"></path> </svg> 2930 Upvotes
</span> <span class="badge expert-verification-badge" data-pagefind-ignore=""> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.1163 6.42625C13.8806 6.18 13.6369 5.92625 13.545 5.70312C13.46 5.49875 13.455 5.16 13.45 4.83187C13.4406 4.22187 13.4306 3.53062 12.95 3.05C12.4694 2.56937 11.7781 2.55937 11.1681 2.55C10.84 2.545 10.5012 2.54 10.2969 2.455C10.0744 2.36312 9.82 2.11937 9.57375 1.88375C9.1425 1.46937 8.6525 1 8 1C7.3475 1 6.85812 1.46937 6.42625 1.88375C6.18 2.11937 5.92625 2.36312 5.70312 2.455C5.5 2.54 5.16 2.545 4.83187 2.55C4.22187 2.55937 3.53062 2.56937 3.05 3.05C2.56937 3.53062 2.5625 4.22187 2.55 4.83187C2.545 5.16 2.54 5.49875 2.455 5.70312C2.36312 5.92562 2.11937 6.18 1.88375 6.42625C1.46937 6.8575 1 7.3475 1 8C1 8.6525 1.46937 9.14187 1.88375 9.57375C2.11937 9.82 2.36312 10.0738 2.455 10.2969C2.54 10.5012 2.545 10.84 2.55 11.1681C2.55937 11.7781 2.56937 12.4694 3.05 12.95C3.53062 13.4306 4.22187 13.4406 4.83187 13.45C5.16 13.455 5.49875 13.46 5.70312 13.545C5.92562 13.6369 6.18 13.8806 6.42625 14.1163C6.8575 14.5306 7.3475 15 8 15C8.6525 15 9.14187 14.5306 9.57375 14.1163C9.82 13.8806 10.0738 13.6369 10.2969 13.545C10.5012 13.46 10.84 13.455 11.1681 13.45C11.7781 13.4406 12.4694 13.4306 12.95 12.95C13.4306 12.4694 13.4406 11.7781 13.45 11.1681C13.455 10.84 13.46 10.5012 13.545 10.2969C13.6369 10.0744 13.8806 9.82 14.1163 9.57375C14.5306 9.1425 15 8.6525 15 8C15 7.3475 14.5306 6.85812 14.1163 6.42625ZM10.8538 6.85375L7.35375 10.3538C7.30731 10.4002 7.25217 10.4371 7.19147 10.4623C7.13077 10.4874 7.06571 10.5004 7 10.5004C6.93429 10.5004 6.86923 10.4874 6.80853 10.4623C6.74783 10.4371 6.69269 10.4002 6.64625 10.3538L5.14625 8.85375C5.05243 8.75993 4.99972 8.63268 4.99972 8.5C4.99972 8.36732 5.05243 8.24007 5.14625 8.14625C5.24007 8.05243 5.36732 7.99972 5.5 7.99972C5.63268 7.99972 5.75993 8.05243 5.85375 8.14625L7 9.29313L10.1462 6.14625C10.1927 6.09979 10.2479 6.06294 10.3086 6.0378C10.3692 6.01266 10.4343 5.99972 10.5 5.99972C10.5657 5.99972 10.6308 6.01266 10.6914 6.0378C10.7521 6.06294 10.8073 6.09979 10.8538 6.14625C10.9002 6.1927 10.9371 6.24786 10.9622 6.30855C10.9873 6.36925 11.0003 6.4343 11.0003 6.5C11.0003 6.5657 10.9873 6.63075 10.9622 6.69145C10.9371 6.75214 10.9002 6.8073 10.8538 6.85375Z" fill="#00672E"></path> </svg>
Verified Answer
</span> </div> </div> <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{-3}{\sqrt{1-x^2}}$</span> </div> <div class="solution">$\begin{aligned} &amp; \frac{\mathrm{d}\left(\sin ^{-1}\left(3 \mathrm{x}-4 \mathrm{x}^3\right)\right)}{\mathrm{dx}} \\ &amp; =\frac{\mathrm{d}\left(\pi-3 \sin ^{-1} \mathrm{x}\right)}{\mathrm{dx}}\left[\text { as } \frac{1}{2}&lt;\mathrm{x}&lt;1\right]=\frac{-3}{\sqrt{1-\mathrm{x}^2}}\end{aligned}$</div> </section> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{3 \sqrt{1-x^2}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{-3}{\sqrt{1-x^2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{-1}{3 \sqrt{1-x^2}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{3}{\sqrt{1-x^2}}$</span> </li> </ul>

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

answer:
<div class="solution">$\begin{aligned} &amp; \frac{\mathrm{d}\left(\sin ^{-1}\left(3 \mathrm{x}-4 \mathrm{x}^3\right)\right)}{\mathrm{dx}} \\ &amp; =\frac{\mathrm{d}\left(\pi-3 \sin ^{-1} \mathrm{x}\right)}{\mathrm{dx}}\left[\text { as } \frac{1}{2}&lt;\mathrm{x}&lt;1\right]=\frac{-3}{\sqrt{1-\mathrm{x}^2}}\end{aligned}$</div>


tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch1_P2.db
title:
danny-ate-spinach-salad-and-mutton-curry-for-lunch-at-which-of-the-following-trophic-levels-did-danny-function-in-this-food-chain-i-producer-ii-primar

slug:
danny-ate-spinach-salad-and-mutton-curry-for-lunch-at-which-of-the-following-trophic-levels-did-danny-function-in-this-food-chain-i-producer-ii-primar-53150

question:
<div class="question">Danny ate spinach, salad and mutton curry for lunch. At which of the following trophic levels did Danny function in this food chain?<br/> <br/>
(i) Producer<br/> <br/>
(ii) Primary Consumer<br/> <br/>
(iii) Secondary Consumer<br/> <br/>
(iv) Tertiary Consumer</div>

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

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

answer:
<div class="solution">Plants are the producers in the food chain. The organism consuming plants is the Primary consumer. The organism consuming animals which in turn derive energy from plants is a Secondary consumer. Thus in the above example Danny is consuming plants is a primary consumer as well as he had mutton which comes from goats which are dependent on plants for their food and acts as the secondary consumer also.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2017 (Phase 1)']
answer: <div class="solution">Data can be represented in all three forms</div>
source_db: MarksBatch1_P2.db
title:
data-can-be-represented-in-which-of-the-following-forms-textual-form-tabular-form-3-graphical-form-select-the-correct-answer-using-the-code-given-belo

slug:
data-can-be-represented-in-which-of-the-following-forms-textual-form-tabular-form-3-graphical-form-select-the-correct-answer-using-the-code-given-belo-29106

question:
<div class="question">Data can be represented in which of the following forms? Textual form Tabular form 3 . Graphical form Select the correct answer using the code given below</div>

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

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


title: db-is-a-standard-abbreviation-used-for-the-quantitative-expression-of
slug: db-is-a-standard-abbreviation-used-for-the-quantitative-expression-of-69754
question: <div class="question">'dB' is a standard abbreviation used for the quantitative expression of</div>
tags: ['Biology', 'Environmental Issues', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The density of bacteria in medium</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">A particular pollutant</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The dominant <em>Bacillus</em> in a culture</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">A certain pesticide</span> </li> </ul>

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

answer:
<div class="solution">dB is a standard abbreviation for the quantitative expression of noise. Unwanted sound is called noise. Generally, sound above 80 dB is considered as noise.</div>


tags: ['Mathematics', 'Limits', 'AP EAMCET', 'AP EAMCET 2019 (22 Apr Shift 1)']
source_db: MarksBatch1_P2.db
title:
define-fxleftbeginarraycc-fracsqrt1p-xsqrt1p-xx-text-if-1-leq-x-0-frac2-x1x2-text-if-0-leq-x-leq-1-endarrayright-if-lim-x-rightarrow-0-fx-exists-then-

slug:
define-fxleftbeginarraycc-fracsqrt1p-xsqrt1p-xx-text-if-1-leq-x-0-frac2-x1x2-text-if-0-leq-x-leq-1-endarrayright-if-lim-x-rightarrow-0-fx-exists-then-60462

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

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

answer:
<div class="solution">Given, \(f(x)=\left\{\begin{array}{cl}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, &amp; \text { if }-1 \leq x  &lt; 0 \\ \frac{2 x+1}{x-2}, &amp; \text { if } 0 \leq x \leq 1\end{array}\right.\)<br/>Now, RHL \(=\) LHL (at \(x=0\))<br/>\(\Rightarrow \quad \lim _{x \rightarrow 0^{+}} \frac{2 x+1}{x-2}=\lim _{x \rightarrow 0^{-}} \frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}\)<br/>Apply L'Hospital rule in LHL<br/>\(\Rightarrow \quad-\frac{1}{2}=\lim _{x \rightarrow 0^{-}} \frac{\frac{p}{2 \sqrt{1+p x}}+\frac{p}{2 \sqrt{1-p x}}}{1}\)<br/>\(\Rightarrow \quad-\frac{1}{2}=\frac{p}{2}+\frac{p}{2} \Rightarrow-\frac{1}{2}=p \Rightarrow p=-\frac{1}{2}\)</div>


title: define-uniport-symport-and-antiport-do-they-require-energy
slug: define-uniport-symport-and-antiport-do-they-require-energy-42310
question: <div class="question">Define uniport, symport and antiport. Do they require energy?</div>
tags: ['Biology', 'Transport in Plants']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">For movement of substances the biological membranes have many mechanism. Some are active and some are passive. Specific membrane proteins are also involved for special types of transport mechanisms. These mechanisms include: Uniport is a membranetransport system by an integral membrane protein that is involved in facilitated diffusion. These channels open in response to a stimulus for free flow of specific molecules in a specific direction. These channels transport molecule with a solute gradient without energy expenditure.<br/>Symport involves the movement of two or more different molecules or ions, across the membrane in the same direction, with no expenditure of energy.<br/>Antiport is called exchanger. This integral membrane protein is involved in secondary active transport of two or more different molecules or ions across the membrane in opposite directions, without affecting the transport of other molecules.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/z8BN0crc-l60CbLEh4CwIwIf1I68JTi5iq85-PF7N0w.original.fullsize.png"/><br/></div>


title: define-zero-population-growth-rate-draw-an-age-pyramid-for-the-same
slug: define-zero-population-growth-rate-draw-an-age-pyramid-for-the-same-97036
question: <div class="question">Define 'zero population growth rate'. Draw an age pyramid for the same.</div>
tags: ['Biology', 'Organisms and Populations']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">Zero population growth rate is when the pre-reproductive age group individuals are comparatively less and both reproductive and post-reproductive stages are almost in equal stage or at same level.<br/>An inverted bell shaped age pyramid is obtained for zero population growth rate.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/VucTBxfLBzBX_LnNBulgTJnlczV3Cz8NDAfjhDY2Zv8.original.fullsize.png"/><br/></div>


title: degeneration-of-a-genetic-code-is-attributed-to-the
slug: degeneration-of-a-genetic-code-is-attributed-to-the-51304
question: <div class="question">Degeneration of a genetic code is attributed to the:</div>
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET', 'NEET 2003']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">first member of a codon</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">second member of codon</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">entire codon</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">third member of a codon</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">third member of a codon</span> </div>

answer:
<div class="solution">Each codon is specific for only one amino acid (or one stop signal), yet the genetic code is described as degenerate, or redundant, because a single amino acid may be coded for by more than one codon. The codons that code for one amino acid can differ in any of their places; nevertheless, the second or third codon is more frequent.</div>


tags: ['Chemistry', 'Amines']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
describe-a-method-for-the-identification-of-primary-secondary-and-tertiary-amines-also-write-chemical-equations-of-the-reactions-involved

slug:
describe-a-method-for-the-identification-of-primary-secondary-and-tertiary-amines-also-write-chemical-equations-of-the-reactions-involved-55818

question:
<div class="question">Describe a method for the identification of primary, secondary and tertiary amines. Also write chemical equations of the reactions involved.</div>

answer:
<div class="solution">The three type of amines can be distinguished by Hinsberg test. In this test, the amine is shaken with benzenesulphonyl chloride \(\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{SO}_2 \mathrm{Cl}\right)\) in the presence of excess of aqueous \(\mathrm{NaOH}\) or \(\mathrm{KOH}\). A primary amine reacts to give a clear solution, which on acidification yields an insoluble compound.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/YqP117PYTBW70PSOvXOIYF5hHcjXLQQDP_o_gTMOotA.original.fullsize.png"/><br/><br/>A secondary amine forms an insoluble compound, which remains insoluble even on acidification.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/ZSM-nVb4oG2Vgg2jVmw0TQ8hsrVJ8pBAAJNpceney3w.original.fullsize.png"/><br/><br/>A tertiary amine does not react with the reagent, but dissolves is acid.</div>


title: describe-the-components-of-an-ecosystem
slug: describe-the-components-of-an-ecosystem-91668
question: <div class="question">Describe the components of an ecosystem.</div>
tags: ['Biology', 'Ecosystem']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">The components of an ecosystem can be divided into two categories : biotic and abiotic.<br/>(1) Biotic components :<br/>(i) Producers - Green plants which can synthesize their own food.<br/>(ii) Consumers - They donot synthesize their food. They may be<br/>- Primary consumer/herbivores - consuming plants as food.<br/>- Secondary and tertiary consumers or carnivores - They feed on either herbivores or carnivores.<br/>(iii) Decomposers - These organisms breakdown the dead bodies or waste products of plants and animals into simpler inorganic compounds.<br/>(2) Abiotic components :<br/>(i) Climatic components<br/>- Light<br/>- Temperature<br/>- Wind<br/>- Atmospheric gases<br/>- Rain<br/>- Atmospheric humidity<br/>(ii) Soil factors<br/>- Organic materials<br/>- Minerals<br/>- Soil, water<br/>- Soilair<br/>(iii) Topographic factors<br/>- Altitude<br/>- Direction and steepness slope</div>


title: describe-the-importance-of-the-following-i-limestone-ii-cement-iii-plaster-of-paris
slug: describe-the-importance-of-the-following-i-limestone-ii-cement-iii-plaster-of-paris-52615
tags: ['Chemistry', 's Block Elements']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Describe the importance of the following:<br/>(i) limestone<br/>(ii) cement<br/>(iii) Plaster of Paris.</div>

answer:
<div class="solution">(i) Limestone. Specially precipitated \(\mathrm{CaCO}_3\) is extensively used in the manufacture of high quality paper. It is also used as an antacid, mild abrasive in toothpaste, a constituent of chewing gum and as a filler in cosmetics.<br/>(ii) Cement. Uses of cement:<br/>- Bridge construction<br/>- Plastering<br/>- Most important ingredient in concrete<br/>(iii) Plaster of Paris. Uses of Plaster of Paris:<br/>- Used to make casts and moulds<br/>- Used to make surgical bandages</div>


title: describe-various-types-of-epithelial-tissues-with-the-help-of-labelled-diagrams
slug: describe-various-types-of-epithelial-tissues-with-the-help-of-labelled-diagrams-42708
tags: ['Biology', 'Structural Organisation in Animals']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Describe various types of epithelial tissues with the help of labelled diagrams.</div>

answer:
<div class="solution">Epithelial tissues<br/>Epithelial tissues provide covering to the inner and outer lining of various organs. The cells of epithelial tissues are compactly packed with little intercellular matrix.<br/>There are two types of epithelial tissues :<br/>(i) Simple epithelium<br/>(ii) Compound epithelium<br/>(i) Simple epithelium :<br/>Composed of single layer of cells and functions as a lining for body cavities ducts and tubes. It is further divided into three types on the basis of structure modifications-<br/>(a) Squamous epithelium - It is made of a single layer of flattened cells with irregular boundaries.<br/>It is found as a lining for body cavities, ducts and tubes such as in the walls of blood vessels and air sacs of lungs.<br/>Functions - It helps in forming a diffusion boundaries.<br/>(b) Cuboidal epithelium - It is made of single layer of cube-like cells.<br/>It is commonly found in ducts of glands and tubular parts of nephrons in kidneys. Specialized cuboidal cells are capable of producing gametes found in gonads called germinal epithellium.<br/>Functions - It helps in secretion and absorption and also in moving particles or mucus in a specific direction over the epithellium.<br/>(c) Columnar epithelium - It is composed of a single layer of tall and slender cells.<br/>Nuclei are located at base.<br/>Its free surface may have microvilli.<br/>It is found in lining of stomach and intestine.<br/>Functions - It helps in secretion and absorption.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/lb63q-awQNdsdLR7E_8Zir3lc-JnmE-SFysmKPyfmzw.original.fullsize.png"/><br/><br/>(ii) Compound epithelium :<br/>It is made of more than one layer (multi-layered) of cells and thus it has very limited role in secretion and absorption.<br/>It is located at dry surfaces of the skin, moist surface of buccal cavity, pharynx inner lining of ducts of salivary glands and of pancreatic ducts.<br/>Functions - To provide protection against chemical and mechanical stresses.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/v4fDonImfy5_yllb9iMa8-hfX4o4c4NNOmvGLYWrzrY.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
determine-mean-and-standard-deviation-of-first-n-terms-of-an-ap-whose-first-term-is-a-and-common-difference-is-d

slug:
determine-mean-and-standard-deviation-of-first-n-terms-of-an-ap-whose-first-term-is-a-and-common-difference-is-d-72141

question:
<div class="question">Determine mean and standard deviation of first $n$ terms of an A.P. whose first term is a and common difference is $\mathrm{d}$.</div>

answer:
<div class="solution">$$<br/>\begin{array}{|c|c|c|}<br/>\hline x &amp; d=x-a &amp; d^2 \\<br/>\hline a &amp; 0 &amp; 0 \\<br/>a+d &amp; d &amp; d^2 \\<br/>a+2 d &amp; 2 d &amp; 4 d^2 \\<br/>\ldots \ldots \ldots &amp; \ldots \ldots \ldots &amp; \ldots \ldots \ldots \\<br/>\ldots \ldots \ldots &amp; \ldots \ldots \ldots &amp; \ldots \ldots \ldots \\<br/>\ldots \ldots \ldots &amp; \ldots \ldots \ldots &amp; \ldots \ldots \ldots \\<br/>\hline a+(n-1) d &amp; (n-1) d &amp; (n-1)^2 d^2 \\<br/>\hline<br/>\end{array}<br/>$$<br/><br/><br/>where $\mathrm{a}=$ Assumed Mean<br/>$$<br/>\begin{aligned}<br/>\Sigma \mathrm{d} &amp;=0+\mathrm{d}+2 \mathrm{~d}+3 \mathrm{~d}+\ldots+(\mathrm{n}-1) \mathrm{d} \\<br/>&amp;=\mathrm{d}\{1+2+3+\ldots+(\mathrm{n}-1)\} \\<br/>&amp;=\frac{\mathrm{d}(\mathrm{n}-1) \mathrm{n}}{2} \\<br/>\Rightarrow \quad \Sigma \mathrm{d}^2 &amp;=\mathrm{d}^2\left[1^2+2^2+3^2+\ldots .+(n-1)^2\right] \\<br/>&amp;=\frac{\mathrm{n}(\mathrm{n}-1)(2 \mathrm{n}-1) \mathrm{d}^2}{6} \\<br/>\therefore \quad \overline{\mathrm{x}} &amp;=\mathrm{a}+\frac{\Sigma \mathrm{d}}{\mathrm{n}}=\mathrm{a}+\frac{(\mathrm{n}-1) \mathrm{d}}{2}<br/>\end{aligned}<br/>$$<br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp;\text { S.D. } \sqrt{\frac{\Sigma d^2}{n}-\left(\frac{\Sigma d}{n}\right)^2}\\<br/>&amp;=\sqrt{\frac{(n-1)(2 n-1) d^2}{6}-\left(\frac{n-1}{2}\right)^2 d^2}\\<br/>&amp;=(d) \sqrt{\left(\frac{\mathrm{n}-1}{2}\right)\left[\frac{2 \mathrm{n}-1}{3}-\frac{\mathrm{n}-1}{2}\right]}\\<br/>&amp;d \cdot \sqrt{\frac{(n-1)(n+1)}{12}}\\<br/>&amp;\Rightarrow \mathrm{SD}=\mathrm{d} \cdot \sqrt{\frac{\mathrm{n}^2-1}{12}}<br/>\end{aligned}<br/>$$</div>


tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
title:
determine-the-incorrect-statements-regarding-the-process-of-female-gamete-production-i-the-oogonia-keep-on-adding-in-the-ovary-till-menopause-ii-the-p

slug:
determine-the-incorrect-statements-regarding-the-process-of-female-gamete-production-i-the-oogonia-keep-on-adding-in-the-ovary-till-menopause-ii-the-p-84135

question:
<div class="question">Determine the incorrect statements regarding the process of female gamete production.<br/> <br/>
I. The oogonia keep on adding in the ovary till menopause.<br/>
II. The primary oocytes are halted at prophase-I of meiotic division.<br/>
III. The fluid-filled cavity present in the secondary follicle is called the atrium.<br/>
IV. The secondary oocyte forms a membrane called zona glomerulosa around it.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">I, III and IV</span> </div>

answer:
<div class="solution">I. No more oogonia are added to the ovary after birth.III. The fluid filled cavity present in the tertiary follicle is called antrum.IV. The secondary oocyte forms a membrane called zona pellucida around it.</div>


tags: ['Biology', 'Body Fluids and Circulation', 'NEET']
source_db: MarksBatch1_P2.db
title:
determine-the-wrong-statements-with-respect-to-the-nucleated-blood-cells-i-the-most-abundant-leucocyte-is-a-granulocyte-while-the-least-abundant-leuco

slug:
determine-the-wrong-statements-with-respect-to-the-nucleated-blood-cells-i-the-most-abundant-leucocyte-is-a-granulocyte-while-the-least-abundant-leuco-72389

question:
<div class="question">Determine the wrong statement/s with respect to the nucleated blood cells.<br/> <br/>
I. The most abundant leucocyte is a granulocyte while the least abundant leucocyte is an agranulocyte.<br/>
II. The largest leucocyte is a granulocyte while the smallest leucocyte is an agranulocyte.<br/>
III. Phagocytic leucocytes may be agranulocyte or granulocyte.<br/>
IV. Polymorphonuclear leucocytes are the largest granulocyte while the largest agranulocyte has a kidney-shaped nucleus.</div>

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

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

answer:
<div class="solution">The most abundant leucocyte (neutrophil) is a granulocyte while the least abundant leucocyte (basophil) is also a granulocyte. The largest leucocyte (monocyte) is an agranulocyte while the smallest leucocyte (lymphocyte) is also an agranulocyte. Phagocytic leucocytes are neutrophils (granulocyte) and monocyte (agranulocyte). Polymorphonuclear leucocytes (neutrophils) are the largest granulocyte while the largest agranulocyte (monocyte) has a kidney shaped nucleus.</div>


title: dicot-stem-has-open-vascular-bundles-they-are-called-open-because-they
slug: dicot-stem-has-open-vascular-bundles-they-are-called-open-because-they-95870
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Dicot stem has open vascular bundles. They are called 'open' because they</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Are surrounded by pericycle but no endodermis</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Are capable of producing secondary xylem and 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><li class=""> <span class="option-label">C</span> <span class="option-data">Possess conjunctive tissue between xylem and phloem</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Are not surrounded by pericycle</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Are capable of producing secondary xylem and phloem</span> </div>

answer:
<div class="solution">In the vascular bundles of dicotyledonous stems, cambium is present between phloem and xylem. This cambium has the ability to form secondary xylem and phloem tissues. This the vascular bundles can grow continuously. Hence they are called open vascular bundles.</div>


tags: ['Chemistry', 'General Organic Chemistry', 'NEET']
source_db: MarksBatch1_P2.db
title:
differentiate-between-the-principle-of-estimation-of-nitrogen-in-an-organic-compound-by-i-dumas-method-and-ii-kjeldahls-method

slug:
differentiate-between-the-principle-of-estimation-of-nitrogen-in-an-organic-compound-by-i-dumas-method-and-ii-kjeldahls-method-48301

question:
<div class="question">Differentiate between the principle of estimation of nitrogen in an organic compound by (i) Dumas method and (ii) Kjeldahlâs method.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Dumas method and Kjeldahls method are not applicable for estimation of nitrogen in organic compounds</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">In the Dumas method, the organic compound is heated in a combustion tube with copper oxide (CuO) to convert all nitrogen to nitrogen gas (N<sub>2</sub>), which is collected and measured. In Kjeldahl's method, the organic compound is digested with concentrated sulphuric acid (H<sub>2</sub>SO<sub>4</sub>), converting the nitrogen to ammonium sulphate (NH<sub>4</sub>)<sub>2</sub>SO<sub>4</sub>.The liberated ammonia (NH<sub>3</sub>) is then titrated with a standardized acid.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both the Dumas and Kjeldahl's methods involve heating the organic compound to convert nitrogen into nitrogen oxides and then titrating the resulting solution with a standardized acid. However, the specific reagents and procedures used differ.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The Dumas method relies on the decomposition of the organic compound in the presence of a catalyst to release nitrogen gas, which is measured. In Kjeldahl's method, the organic compound is digested with sulphuric acid to convert the nitrogen to ammonia, which is subsequently distilled and titrated.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">In the Dumas method, the organic compound is heated in a combustion tube with copper oxide (CuO) to convert all nitrogen to nitrogen gas (N<sub>2</sub>), which is collected and measured. In Kjeldahl's method, the organic compound is digested with concentrated sulphuric acid (H<sub>2</sub>SO<sub>4</sub>), converting the nitrogen to ammonium sulphate (NH<sub>4</sub>)<sub>2</sub>SO<sub>4</sub>.The liberated ammonia (NH<sub>3</sub>) is then titrated with a standardized acid.</span> </div>

answer:
<div class="solution">Correct Option is : (B)<br/>In the Dumas method, the organic compound is heated in a combustion tube with copper oxide (CuO) to convert all nitrogen to nitrogen gas (N<sub>2</sub>), which is collected and measured. In Kjeldahl's method, the organic compound is digested with concentrated sulphuric acid (H<sub>2</sub>SO<sub>4</sub>), converting the nitrogen to ammonium sulphate (NH<sub>4</sub>)<sub>2</sub>SO<sub>4</sub>.The liberated ammonia (NH<sub>3</sub>) is then titrated with a standardized acid.</div>


tags: ['Chemistry', 'General Organic Chemistry']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
differentiate-between-the-principle-of-estimation-of-nitrogen-in-an-organic-compound-by-i-dumas-method-ii-kjeldahls-method

slug:
differentiate-between-the-principle-of-estimation-of-nitrogen-in-an-organic-compound-by-i-dumas-method-ii-kjeldahls-method-58586

question:
<div class="question">Differentiate between the principle of estimation of nitrogen in an organic compound by<br/>(i) Duma's method<br/>(ii) Kjeldahl's method.</div>

answer:
<div class="solution">(i) Duma's method: The nitrogen containing organic compounds, when heated with copper oxide in an atmosphere of carbon dioxide, yields free nitrogen in addition to carbon dioxide and water. \% nitrogen is measured as follows :<br/>\(\mathrm{C}_{\mathrm{x}} \mathrm{H}_{\mathrm{y}} \mathrm{N}_2+\left(\frac{2 \mathrm{x}+\mathrm{y}}{2}\right) \mathrm{CuO} \rightarrow \mathrm{xCO}_2+\frac{\mathrm{y}}{2} \mathrm{H}_2 \mathrm{O}(\mathrm{~N}_2+\left(\frac{2 \mathrm{x}+\mathrm{y}}{2}\right) \mathrm{Cu}\)<br/>\(\%\) of Nitrogen \(=\frac{28 \times \mathrm{z} \times 100}{2} \)\<br/>\(2400 \times \mathrm{m}\)<br/>(ii) Kjeldahl method: Nitrogen containing compound is treated with conc. \(\mathrm{H}_2 \mathrm{SO}_4\) to get ammonium sulphate which liberates ammonia on treating with \(\mathrm{NaOH}\); ammonia is absorbed in known volume of standard acid with the help of this \(\%\) nitrogen is calculated.<br/>- Organic compound \(+\mathrm{H}_2 \mathrm{SO}_4 \longrightarrow\left(\mathrm{NH}_4\right)_2 \mathrm{SO}_4 \stackrel{2 \mathrm{NaOH}}{\longrightarrow} \mathrm{Na}_2 \mathrm{SO}_4+2 \mathrm{NH}_3+2 \mathrm{H}_2 \mathrm{O}\)<br/>\(\begin{aligned}<br/>&amp;2 \mathrm{NH}_3+\mathrm{H}_2 \mathrm{SO}_4 \longrightarrow\left(\mathrm{NH}_4\right)_2 \mathrm{SO}_4 \\<br/>&amp;\% \text { of nitrogen }=\frac{1.4 \times \mathrm{M} \times 2\left(\mathrm{~V}-\mathrm{V}_1 / 2\right)}{\mathrm{m}}<br/>\end{aligned}\)<br/>\(-\mathrm{V}\) and \(\mathrm{V}_1\) are volume \((\mathrm{mL})\) of \(\mathrm{H}_2 \mathrm{SO}_4\) and volume \((\mathrm{mL})\) of \(\mathrm{NaOH}\) respectively.</div>


title: differentiation-of-organs-and-tissues-in-a-developing-organism-is-associated-with
slug: differentiation-of-organs-and-tissues-in-a-developing-organism-is-associated-with-12524
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET', 'NEET 2007']
source_db: MarksBatch1_P2.db
question:
<div class="question">Differentiation of organs and tissues in a developing organism, is associated with:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">differential expression of genes</span> </div>

answer:
<div class="solution">Differential expression of different genes at different stages of development leads to organ and tissues differentiation, for example, size and pattern of puffs of polytene chromosomes, which are site of transcription, varies at different developmental stages, indicating differential gene activity. Transcription factor is the molecular basis of organ differentiation.<br/>Related Theory<br/>The fate of a cell describes what it will become in the course of normal development. The fate of a particular cell can be discovered by labelling that cell and observing what structures it becomes a part of. The developmental potential, or potency, of a cell describes the range of different cell types it can become. The zygote and its very early descendants are totipotent - these cells have the potential to develop into a complete organism. The determination of different cell types (cell fates) involves progressive restrictions in their developmental potentials. Differentiation follows determination, as the cell elaborates a cell-specific developmental program. Differentiation results in the presence of cell types that have clear-cut identities, such as muscle cells, nerve cells, and skin cells.</div>


title: dikaryon-formation-is-characteristics-of
slug: dikaryon-formation-is-characteristics-of-15282
question: <div class="question">Dikaryon formation is characteristics of</div>
tags: ['Biology', 'Biological Classification', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Ascomycetes and Basidiomycetes</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Phycomycetes and Ascomycetes</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Basidiomycetes and Zygomycetes</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Phycomycetes and Deuteromycetes.</span> </li> </ul>

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

answer:
<div class="solution">The formation of secondary mycelium is the feature of Ascomycetes and Basidiomycetes. A secondary mycelium forms upon conjugation of two sexually compatible hyphae. The secondary mycelium is dikaryotic, in that it has two haploid nuclei, one from each parent. As the dikaryotic mycelium grows, the cells divide and more septa are formed between the new cells.</div>


tags: ['Biology', 'Environmental Issues']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
discuss-briefly-the-following-a-radioactive-wastes-b-defunct-ships-and-ewastes-c-municipal-solid-wastes

slug:
discuss-briefly-the-following-a-radioactive-wastes-b-defunct-ships-and-ewastes-c-municipal-solid-wastes-97207

question:
<div class="question">Discuss briefly the following:<br/>(a) Radioactive wastes<br/>(b) Defunct ships and e-wastes<br/>(c) Municipal solid wastes</div>

answer:
<div class="solution">(a) Radioactive waste : Radioactive waste include materials that are radioactive \&amp; for which there is no further practical use. These are generated by nuclear reactor, nuclear fallout, man made (refining and mining of platinum and thorium), natural radioactive waste and release of radiation in radiation therapy.<br/>Increased risk of cancer, birth defects \&amp; infertility are few harmful effects caused by nuclear waste. So, nuclear waste is an extremely potent pollutant.<br/>(b) Defunct ships \&amp; e-wastes - The dismantling of defunct ship is a technically complex process, which is potentially harmful to the environment \&amp; human health. Defunct ships contain toxicants like asbestos, mercury, etc. The workers breaking the ships are not suitably protected and are exposed to toxic chemicals. The coastal areas in the vicinity of the ship-breaking yard also becomes polluted. At the international level, it is accepted that there is uncertainty about the relevant controls for the dismantling of such vessels $\&amp;$ there is an urgent need to establish a specific enforceable control framework.<br/>Electronic waste comprised of irrepairable computer and other electronic goods, generated by developed countries.<br/>It is valuable source of secondary raw materials, if treated properly, however if not treated properly it is the major source of toxins. Eventually recycling is the only solution for the treatment of e-wastes provided it is carried out in an environment friendly manner.<br/>(c) Municipal solid wastes : These are commonly known as trash or garbage. It consists of everyday items such as product packaging, furniture, clothing, bottles, food scraps, newspapers.<br/>Appliances, paints, batteries etc. Source reduction, recycling and compositing are several municipal social waste management practices. Source reduction involves altering the design, manufacture or use of products \&amp; materials to reduce the amount and toxicity of what gets thrown away. Recycling diverts items such as paper, glass, plastic \&amp; metals into a new products. Composting decomposes organic waste such as food scraps \&amp; yard trimmings with micro-organisms, producing a humus-like substance.</div>


title: distinction-between-primary-secondary-and-tertiary-alcohol-is-done-by
slug: distinction-between-primary-secondary-and-tertiary-alcohol-is-done-by-43649
question: <div class="question">Distinction between primary, secondary and tertiary alcohol is done by</div>
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Oxidation method</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Lucas test</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Victor Meyer method</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution"><p>Distinction between primary, secondary and tertiary alcohol is done by all three methods : oxidation, Victormeyer and Lucas test.</p><p>Victor Meyer's method : The given alcohol is converted into an iodide by concentrated HI or red phosphorous and iodine.If a blood red colour is obtained, the original alcohol is primary. If a blue colour is obtained, the alcohol is secondary. If no colour is produced, the alcohol is tertiary.</p><p>Oxidation Test :  Primary alcohol gets easily oxidized to an aldehyde and can further be oxidized to carboxylic acids too. Secondary alcohol gets easily oxidized to ketone but further oxidation is not possible. Tertiary alcohol doesn't get oxidized in the presence of sodium dichromate.</p><p>Lucas test : Primary  alchol give white turbidity immediatly.</p><p>secondary alcohol gives white turbidity in 5-10 min.</p><p>Tertiary alcohol given white turbidity in 30 min.</p></div>


tags: ['Biology', 'Ecosystem']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
distinguish-between-a-grazing-food-chain-and-detritus-food-chain-b-production-and-decomposition-c-upright-and-inverted-pyramid-d-food-chain-and-food-w

slug:
distinguish-between-a-grazing-food-chain-and-detritus-food-chain-b-production-and-decomposition-c-upright-and-inverted-pyramid-d-food-chain-and-food-w-21819

question:
<div class="question">Distinguish between<br/>(a) Grazing food chain and detritus food chain<br/>(b) Production and decomposition<br/>(c) Upright and inverted pyramid<br/>(d) Food chain and food web<br/>(e) Litter and detritus<br/>(f) Primary and secondary productivity</div>

answer:
<div class="solution">(a) Grazing Food Chain (GFC) begins with primary producers or plants and ends in carnivores (tertiary or top carnivores) whereas Detritus Food Chain (DFC) begins with detritus or dead organic matter and it ends in carnivores. In GFC, energy for the food chain comes from sun whereas in DFC, energy for the food chain comes from organic remains or detritus.<br/>(b) Production is the phenomenon in which the energy is produced by the process of synthesis of organic compound from inorganic substances(such as $\mathrm{CO}_2, \mathrm{H}_2 \mathrm{O}$ \&amp; minerals) utilizing generally the sunlight. It traps energy. Decomposition refers to the breakdown of complex organic matter into simpler ones. It releases energy.<br/>(c) In upright pyramid (e.g., grassland \&amp; cropland ecosystem), biomass or number of organisms or amount of energy decreases on moving to upper trophic levels while in an inverted pyramid (eg. tree ecosystem) these quantities tend to increase on going to successive trophic levels.<br/>(d) A food chain is a sequence of different types of organisms by which the flow of energy occurs from one trophic level to another whereas food web is the network of various food chains inter-connected to each other. Food webs increase adaptability and competitiveness of the organisms.<br/>(e) Litter is the dead organic material fallen on the surface of the soil like leaves, remains of animals and excreta. Detritus is the dead organic matter found below the soil surface which is eaten up by the detritivores or broken down by decomposers.<br/>(f) Primary productivity is the rate of synthesis of biomass or energy fixation by the plants. It is comparatively quite high.<br/>Secondary productivity is the rate of synthesis of biomass by consumers (herbivores and carnivores). It is small and decreases with rise of trophic level.</div>


title: diversification-in-plant-life-appeared
slug: diversification-in-plant-life-appeared-72398
question: <div class="question">Diversification in plant life appeared:</div>
tags: ['Biology', 'Evolution', 'NEET', 'NEET 2004']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">due to long periods of evolutionary changes</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">due to abrupt mutations</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">suddenly on earth</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">by seed dispersal.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">due to long periods of evolutionary changes</span> </div>

answer:
<div class="solution">Diversification in plant life appeared due to long periods of evolutionary changes. Earlier, the plants were thalloid and there were no differentiation among root, stem and leaves. Vascular tissues were absent as in alglae and bryophytes. In pteridophytes, seed habit was observed for the first time. Gymnosperm consists of vascular tissue and naked seed habitat. Angiosperms showed secondary growth, along with fruit formation.</div>


title: do-secondary-metabolites-have-any-ecological-importance
slug: do-secondary-metabolites-have-any-ecological-importance-49934
question: <div class="question">Do secondary metabolites have any ecological importance?</div>
tags: ['Biology', 'Biomolecules (B)', 'NEET']
answer: <div class="solution">some secondary metabolites have ecological importance.</div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">No, they do not have any ecological importance.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Yes, they have some ecological importance.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The ecological importance of secondary metabolites is not yet known.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Secondary metabolites only have ecological importance in plant and fungal cells.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Yes, they have some ecological importance.</span> </div>


tags: ['Biology', 'Reproduction in Organisms', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Yes</span> </div>
source_db: MarksBatch1_P2.db
title:
do-sexually-reproducing-organisms-exhibit-events-and-processes-that-have-remarkable-fundamental-similarity

slug:
do-sexually-reproducing-organisms-exhibit-events-and-processes-that-have-remarkable-fundamental-similarity-62039

question:
<div class="question">Do sexually reproducing organisms exhibit events and processes that have remarkable fundamental similarity?</div>

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

answer:
<div class="solution">After attainment of maturity, all sexually reproducing organisms exhibit events and processes that have remarkable fundamental similarity.</div>


title: double-fertilization-means
slug: double-fertilization-means-18848
question: <div class="question">Double fertilization means</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'JIPMER', 'JIPMER 2004']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">fusion of nucleus of male gamete with the egg nucleus</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">fusion of two polar nuclei</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">fusion of sperm nucleus with secondary nucleus</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">fusion of one sperm nucleus with nucleus and fusion of other sperm nucleus with secondary nucleus</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">fusion of one sperm nucleus with nucleus and fusion of other sperm nucleus with secondary nucleus</span> </div>

answer:
<div class="solution">Double fertilization is the process the one sperm fuses with the egg while the other sperm fuses with the two polar nuclei. mien pollen tube enters ovule, it strikes one of the synergids and burst open to release the two male gametes which fuses with two different structures in the same female gametophyte. The fusion two polar nuclei forms endosperm. So, the correct answer is option D.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jipmer/fst343ftrfr7657645tfsgcfgfdghfghf.png"/></div>


title: double-fertilization-occurs-in
slug: double-fertilization-occurs-in-29425
question: <div class="question">Double fertilization occurs in</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'JIPMER', 'JIPMER 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Nostoc</span> </div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Riccia</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Pteridium</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Cycas</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Nostoc</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Double fertilization is the characteristic feature of angiosperms, e.g., Capsella. It includes fusion of one male gamete with egg and second male gamete with secondary nucleus (this forms endosperm).</div>


title: draw-a-standard-ecg-and-explain-the-different-segments-in-it
slug: draw-a-standard-ecg-and-explain-the-different-segments-in-it-80916
question: <div class="question">Draw a standard ECG and explain the different segments in it.</div>
tags: ['Biology', 'Body Fluids and Circulation']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">The recording of electrical potential generated by the spread of cardiac impulse, is called electrocardiogram (ECG). ECG is the graphic record of electronic current produced by the excitation of cardiac muscles. A normal electrocardiogram is composed of $\mathrm{P}$ wave, $\mathrm{QRS}$ complex and $\mathrm{T}$ wave, $\mathrm{P}$ wave indicate the depolarisation of the atria. QRS complex expresses the ventricular depolarisation. T wave indicate an repolarisation of ventricles.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/59DwTezLkSiSgJyZA5mO6mHWeJeT-J6QyOTeg3GTas4.original.fullsize.png"/><br/></div>


tags: ['Biology', 'Human Health and Diseases']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
drugs-like-lsd-barbiturates-amphetamines-etc-are-used-as-medicines-to-help-patients-with-mental-illness-however-excessive-doses-and-abusive-usage-are-

slug:
drugs-like-lsd-barbiturates-amphetamines-etc-are-used-as-medicines-to-help-patients-with-mental-illness-however-excessive-doses-and-abusive-usage-are-97016

question:
<div class="question">Drugs like LSD, barbiturates, amphetamines, etc., are used as medicines to help patients with mental illness. However, excessive doses and abusive usage are harmful. Enumerate the major adverse effects of such drugs in humans.</div>

answer:
<div class="solution">Drugs like LSD, barbiturates have several harmful effects. They include<br/>(i) Reckless behaviour, vandalism and violence.<br/>(ii) Withdrawal, isolation, depression, fatigue, aggressive behaviour.<br/>(iii) Problems in social adjustment.<br/>(iv) Lack of interest in personal hygiene, fluctuations in weight and appetite.<br/>(v) Withdrawal symptoms can be severeand life threatening.<br/>(vi) Anxiety, shakiness, nausea and sweating, loss of mind control.<br/>(vii) Excessive doses of drugs may lead to coma and death may occur due to respiratory faliure, heart faliure or cerebral haemorrhage.</div>


title: due-to-overexploitation-one-of-the-endangered-species-of-indian-medicinal-plants-is
slug: due-to-overexploitation-one-of-the-endangered-species-of-indian-medicinal-plants-is-99776
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Due to overexploitation, one of the endangered species of Indian medicinal plants is</div>

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

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

answer:
<div class="solution"><em>Podophyllum hexandrum</em> is a Himalayan medicinal plant belonging to the family Berberidaceae. It is one of the endangering species. The overexploitation of this plant takes place for the treatment of many cancers. The plant produces an important compound etoposide, a podophyllotoxin derivative, which is anti-cancerous in nature.</div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
due-to-which-of-the-following-reasons-can-potassium-permanganate-not-be-prepared-as-a-primary-standard

slug:
due-to-which-of-the-following-reasons-can-potassium-permanganate-not-be-prepared-as-a-primary-standard-28480

question:
<div class="question">Due to which of the following reasons can potassium permanganate not be prepared as a primary standard?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Its solutions are volatile.</span> </div>

answer:
<div class="solution">Potassium permanganate has the chemical formula $\mathrm{KMnO}_4$.<br/>It is a flexible and potent oxidant that may be used to classify a variety of substances by direct or indirect titration.<br/>It is not used as a major standard since obtaining the pure form of $\mathrm{KMnO}_4$ is challenging because it is not free of $\mathrm{MnO}_2$.<br/>Furthermore, the color of Potassium permanganate is so vibrant that it serves as its own indicator.<br/>Hence, $\mathrm{KMnO}_4$ is not used as a primary standard, because it is difficult to obtain the pure state of $\mathrm{KMnO} 4$ as it is not free from $\mathrm{MnO} 2$. Also, the colour is so intense that it acts as its own indicator.</div>


title: duramen-is-present-in
slug: duramen-is-present-in-17391
question: <div class="question">Duramen is present in</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'JIPMER', 'JIPMER 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">inner region of secondary wood</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">part of sap wood</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">outer region of secondary wood</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">region of pericycle</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">inner region of secondary wood</span> </div>

answer:
<div class="solution">After certain years of growth, the xylem elements of the stems of a number of trees develop dark brown colouration, especially in the central or innermost layers. This region comprises dead element with highly lignified walls and is called heart wood or duramen. It is present in inner region of secondary wood.</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2009 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">133</span> </div>
source_db: MarksBatch1_P2.db
title:
during-a-certain-plane-period-a-state-out-of-a-total-budget-of-rs-1400-crores-had-spent-28-of-the-total-amount-on-agriculture-35-on-industry-12-on-ene

slug:
during-a-certain-plane-period-a-state-out-of-a-total-budget-of-rs-1400-crores-had-spent-28-of-the-total-amount-on-agriculture-35-on-industry-12-on-ene-89917

question:
<div class="question">During a certain plane period a state out of a total budget of Rs 1400 crores had spent $28 \%$ of the total amount on Agriculture, $35 \%$ on Industry, $12 \%$ on Energy and $8 \%$ on Social Welfare, 105 crores on Education and the balance amount on Transport. What is the amount spent on Transport in crores of rupees?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">123</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">145</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">165</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">133</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Total Budget $=1400$ crores Total expenditure $=28 \%+35 \%+12 \%+8 \%+105 \mathrm{cr}$.<br/>$=83 \%+105$ crores<br/>Thus, total expenditure $=\left(1400 \times \frac{83}{100}+105\right) \mathrm{cr}$.<br/>$=(1162+105) \mathrm{cr}$<br/>$=1267 \mathrm{cr}$<br/>Now, Balance amount $=(1400-1267) \mathrm{cr} .=133 \mathrm{cr}$. Hence, Amount spent an Transport in crores ofrupees is 1</div>


title: during-a-cloudy-day-a-primary-and-a-secondary-rainbow-may-be-created-then-the
slug: during-a-cloudy-day-a-primary-and-a-secondary-rainbow-may-be-created-then-the-40374
tags: ['Physics', 'Ray Optics', 'NEET', 'NEET 2022 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">During a cloudy day, a primary and a secondary rainbow may be created, then the:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">secondary rainbow is due to double internal reflection and is formed above the primary one.</span> </div>

answer:
<div class="solution">Secondary rainbow is formed due to double internal reflection and is formed above the primary rainbow. The secondary rainbow is brighter than the primary rainbow.</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'JEE Main', 'JEE Main 2003']
source_db: MarksBatch1_P2.db
title:
during-an-adiabatic-process-the-pressure-of-a-gas-is-found-to-be-proportional-to-the-cube-of-its-absolute-temperature-the-ratio-c-p-c-v-for-the-gas-is-2

slug:
during-an-adiabatic-process-the-pressure-of-a-gas-is-found-to-be-proportional-to-the-cube-of-its-absolute-temperature-the-ratio-c-p-c-v-for-the-gas-is-2-53224

question:
<div class="question">During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}}$ for the gas is</div>

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

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

answer:
<div class="solution">$\mathrm{P} \propto \mathrm{T}^3 \quad\left(\frac{\mathrm{P}_1}{\mathrm{P}_2}\right)=\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^3$<br/>Comparing it with standard eq. $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma=\frac{3}{2}$</div>


tags: ['Physics', 'Current Electricity', 'NEET']
source_db: MarksBatch1_P2.db
title:
during-an-experiment-with-a-metre-bridge-the-galvanometer-shows-a-null-point-when-the-jockey-is-pressed-at-40-0-cm-using-a-standard-resistance-of-90-a

slug:
during-an-experiment-with-a-metre-bridge-the-galvanometer-shows-a-null-point-when-the-jockey-is-pressed-at-40-0-cm-using-a-standard-resistance-of-90-a-50859

question:
<div class="question">During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>cm </mi></math>using a standard resistance of <math><mn>90</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Î©</mi></math> ,as shown in the figure. The least count of the scale used in the metre bridge is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mi>mm</mi></math>. The unknown resistance is<br/> <br/> <br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/ci/image9-b3319f15-d980-4e53-940f-9365525b918d.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>60</mn><mo>Â±</mo><mn>0.15</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>135</mn><mo>Â±</mo><mn>0.56</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mn>60</mn><mo>Â±</mo><mn>0.25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Î©</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><mn>135</mn><mo>Â±</mo><mn>0.23</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>60</mn><mo>Â±</mo><mn>0.25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Î©</mi></math></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfrac><mi>x</mi><mrow><mn>100</mn><mo>-</mo><mi>x</mi></mrow></mfrac><mn>90</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi>R</mi><mo>=</mo><mn>60</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Ω</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">d</mi><mi>R</mi></mrow><mi>R</mi></mfrac><mo>=</mo><mfrac><mn>100</mn><mrow><mfenced separators="|"><mi>x</mi></mfenced><mfenced separators="|"><mrow><mn>100</mn><mo>-</mo><mi>x</mi></mrow></mfenced></mrow></mfrac><mi mathvariant="normal">d</mi><mi>x</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal">d</mi><mi>R</mi><mo>=</mo><mfrac><mn>100</mn><mrow><mfenced separators="|"><mn>40</mn></mfenced><mfenced separators="|"><mn>60</mn></mfenced></mrow></mfrac><mn>0.1</mn><mo>×</mo><mn>60</mn></math><br/><br/><math><mo>=</mo><mn>0.25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Ω</mi></math><br/><br/>Alternatively<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">d</mi><mi>R</mi></mrow><mi>R</mi></mfrac><mo>=</mo><mfrac><mn>0.1</mn><mn>40</mn></mfrac><mo>+</mo><mfrac><mn>0.1</mn><mn>60</mn></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal">d</mi><mi>R</mi><mo>=</mo><mn>0.25</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Ω</mi></math></div>


tags: ['Biology', 'Respiration in Plants', 'NEET', 'NEET 2003']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">lignin</span> </div>
source_db: MarksBatch1_P2.db
title:
during-anaerobic-digestion-of-organic-waste-such-as-in-producing-biogas-which-one-of-the-following-is-left-undegraded

slug:
during-anaerobic-digestion-of-organic-waste-such-as-in-producing-biogas-which-one-of-the-following-is-left-undegraded-86943

question:
<div class="question">During anaerobic digestion of organic waste, such as in producing biogas, which one of the following is left undegraded ?</div>

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

answer:
<div class="solution">During bio-gas formation, digestion of cellulose is slow (ratc-limiting) and most of the lignin Is not decomposed. Lignin is a complex polymeric molecule, made up of phenyl propanoid units. This complexity has thus far proven as resistant to microbial degradation. After cellulose lignin is the most abundant plant polymer. It forms 20 to $30 \%$ of the wood of the tree. Cellulose is a large chained polymer of glucose molecules which are linked with each other by glycosidic bonds. Hemicellulose are branched polymers of glucose, xylose, galactose, mannose and arabinose.</div>


title: during-biological-nitrogen-fixation-nitrogen-is-converted-to
slug: during-biological-nitrogen-fixation-nitrogen-is-converted-to-75347
question: <div class="question">During biological nitrogen fixation, nitrogen is converted to</div>
tags: ['Biology', 'Mineral Nutrition', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">ammonia</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">nitrate</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">nitrite</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">amino acid</span> </li> </ul>

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

answer:
<div class="solution">Very few living organisms can utilise the nitrogen in the form N<sub>2</sub>, available abundantly in the air. Only certain prokaryotic species are capable of fixing nitrogen. Reduction of nitrogen to ammonia by living organisms is called biological nitrogen fixation. The enzyme, nitrogenase which is capable of nitrogen reduction, is present exclusively in prokaryotes. Such microbes are called N<sub>2</sub>- fixers.</div>


title: during-spermatogenesis-second-meiotic-division-occurs-during
slug: during-spermatogenesis-second-meiotic-division-occurs-during-80947
question: <div class="question">During spermatogenesis, second meiotic division occurs during</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Spermatogonia A  <math><mo>â</mo></math>  Spermatogonia B</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Primary spermatocyte  <math><mo>â</mo></math>  Secondary spermatocyte</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Spermatogonia B  <math><mo>â</mo></math>  Primary spermatocyte</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Secondary spermatocyte <math><mo>â</mo></math> Spermatid</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Secondary spermatocyte <math><mo>â</mo></math> Spermatid</span> </div>

answer:
<div class="solution">During spermatogenesis, some spermatogonia (termed as primary spermatocytes) periodically undergo meiosis. A primary spermatocyte completes meiosis-I (reduction division) and gives rise to 2 equal-sized cells called secondary spermatocytes (n = 23). Both secondary spermatocytes undergo meiosis-II (equational division) to produce 2 equal spermatids (n) each.</div>


title: during-spermatogenesis-secondary-spermatocytes-are-result-of
slug: during-spermatogenesis-secondary-spermatocytes-are-result-of-38690
question: <div class="question">During spermatogenesis, secondary spermatocytes are result of</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Mitosis</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Meiosis-I</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Meiosis -II</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Growth</span> </li> </ul>

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

answer:
<div class="solution">Having completed the first meiotic division, these cells give rise to daughter cells called secondary spermatocytes, which divide to complete meiosis to form round spermatids.<br/><br/>The round spermatids do not divide but undergo a complex metamorphosis, called spermiogenesis, to become spermatozoa that are released into the lumen of the seminiferous tubule by a process called spermiation.</div>


title: during-the-denaturation-of-proteins-which-of-these-structures-will-remain-intact
slug: during-the-denaturation-of-proteins-which-of-these-structures-will-remain-intact-31316
tags: ['Chemistry', 'Biomolecules', 'JEE Main', 'JEE Main 2022 (25 Jul Shift 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">During the denaturation of proteins, which of these structures will remain intact ?</div>

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

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

answer:
<div class="solution"><blockquote><p>Protein structures are made by condensation of amino acids forming peptide bonds. The sequence of amino acids in a protein is called its primary structure. The secondary structure is determined by the dihedral angles of the peptide bonds, the tertiary structure by the folding of protein chains in space.</p><p>Denaturation involves the breaking of many of the weak linkages, or bonds (e.g., hydrogen bonds), within a protein molecule that are responsible for the highly ordered structure of the protein in its natural (native) state. </p><p>During denaturation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>°</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>°</mo></math> structures are destroyed but <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>°</mo></math> structure remains intact</p></blockquote></div>


