# questions

tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2014 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">15</span> </div>
source_db: MarksBatch2_P1.db
title:
in-the-expansion-of-x-3-x-2-1-n-where-n-is-a-positive-integer-the-sum-of-the-coefficients-of-x-5-and-x-10-is-0-what-is-n-equal-to

slug:
in-the-expansion-of-x-3-x-2-1-n-where-n-is-a-positive-integer-the-sum-of-the-coefficients-of-x-5-and-x-10-is-0-what-is-n-equal-to-23011

question:
<div class="question">In the expansion of $\left(x^{3}-\frac{1}{x^{2}}\right)^{n}$ where n is a positive integer, the sum of the coefficients of $\mathrm{x}^{5}$ and $\mathrm{x}^{10}$ is $0 .$<br/>What is $n$ equal to ?</div>

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

answer:
<div class="solution">$\left(x^{3}-\frac{1}{x^{2}}\right)^{n}$<br/>$\quad$ General term, $T_{r+1}={ }^{n} C_{r}\left(x^{3}\right)^{n-r} \cdot\left(-\frac{1}{x^{2}}\right)^{r}$<br/>$\quad={ }^{n} C_{r} \cdot x^{(3 n-3 r)} \cdot(-1)^{r} \cdot x^{-2 r}$<br/>$={ }^{n} C_{r} \cdot(-1)^{r} \cdot x^{(3 n-5 r)}$ ...(i)<br/>For the coefficient $\mathrm{x}^{5}$<br/>Put $3 n-5 r=5$<br/>$5 r=3 n-5$<br/>$\therefore \mathrm{r}=\frac{3 \mathrm{n}}{5}-1$<br/>$\therefore$ Coefficient of $x^{5}={ }^{n} C\left(\frac{3 n}{5}-1\right)^{(-1)}\left(\frac{3 n}{5}-1\right)$<br/>For the coefficient of $\mathrm{x}^{10}$<br/>Put $3 n-5 r=10$<br/>$5 r=3 n-10$<br/>$\therefore \mathrm{r}=\frac{3 \mathrm{n}}{5}-2$ <br/>$\therefore$ Coefficient of $x^{10}={ }^{n} C_{\left(\frac{3 n}{5}-2\right)^{(-1)}}\left(\frac{3 n}{5}-2\right)$<br/>The sum of the coefficient of $x^{5}$ and $x^{10}=0$<br/>$\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-1\right)^{(-1)}\left(\frac{3 \mathrm{n}}{5}-1\right)}+{ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-2\right)}(-1)^{\left(\frac{3 \mathrm{n}}{5}-2\right)}=0$<br/>$\Rightarrow$<br/>$\left.(-1)^{\frac{3 n}{5}}\left[{ }^{n} C_{\left(\frac{3 n}{5}-1\right)} \cdot(-1)^{-1}+{ }^{n} C_{\left(\frac{3 n}{5}-2\right.}\right) \cdot(-1)^{(-2)}\right]=0$<br/>$\Rightarrow-{ }^{n} C_{\left(\frac{3 n}{5}-1\right)}+{ }^{n} C_{\left(\frac{3 n}{5}-2\right)}=0$ ...(ii)<br/><br/>From equation (ii)<br/>${ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-2\right)}={ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-1\right)}$<br/>$\Rightarrow \mathrm{n}=\left(\frac{3 \mathrm{n}}{5}-2\right)+\left(\frac{3 \mathrm{n}}{5}-1\right)$<br/>$\left[\because{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{x}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{y}} \Rightarrow \mathrm{n}=\mathrm{x}+\mathrm{y}\right]$<br/>$\Rightarrow n=\frac{6 n}{5}-3 \Rightarrow \frac{6 n}{5}-n=3$<br/>$\Rightarrow \frac{\mathrm{n}}{5}=3 \quad \therefore \mathrm{n}=15$</div>


tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2014 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P1.db
title:
in-the-expansion-of-x-3-x-2-1-n-where-n-is-a-positive-integer-the-sum-of-the-coefficients-of-x-5-and-x-10-is-0-what-is-the-sum-of-the-coefficients-of-

slug:
in-the-expansion-of-x-3-x-2-1-n-where-n-is-a-positive-integer-the-sum-of-the-coefficients-of-x-5-and-x-10-is-0-what-is-the-sum-of-the-coefficients-of-91185

question:
<div class="question">In the expansion of $\left(x^{3}-\frac{1}{x^{2}}\right)^{n}$ where n is a positive integer, the sum of the coefficients of $\mathrm{x}^{5}$ and $\mathrm{x}^{10}$ is $0 .$<br/>What is the sum of the coefficients of the two middle terms?</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">None of these</span> </li> </ul>

answer:
<div class="solution">$\left(x^{3}-\frac{1}{x^{2}}\right)^{n}$<br/>$\quad$ General term, $T_{r+1}={ }^{n} C_{r}\left(x^{3}\right)^{n-r} \cdot\left(-\frac{1}{x^{2}}\right)^{r}$<br/>$\quad={ }^{n} C_{r} \cdot x^{(3 n-3 r)} \cdot(-1)^{r} \cdot x^{-2 r}$<br/>$={ }^{n} C_{r} \cdot(-1)^{r} \cdot x^{(3 n-5 r)}$ ...(i)<br/>For the coefficient $\mathrm{x}^{5}$<br/>Put $3 n-5 r=5$<br/>$5 r=3 n-5$<br/>$\therefore \mathrm{r}=\frac{3 \mathrm{n}}{5}-1$<br/>$\therefore$ Coefficient of $x^{5}={ }^{n} C\left(\frac{3 n}{5}-1\right)^{(-1)}\left(\frac{3 n}{5}-1\right)$<br/>For the coefficient of $\mathrm{x}^{10}$<br/>Put $3 n-5 r=10$<br/>$5 r=3 n-10$<br/>$\therefore \mathrm{r}=\frac{3 \mathrm{n}}{5}-2$ <br/>$\therefore$ Coefficient of $x^{10}={ }^{n} C_{\left(\frac{3 n}{5}-2\right)^{(-1)}}\left(\frac{3 n}{5}-2\right)$<br/>The sum of the coefficient of $x^{5}$ and $x^{10}=0$<br/>$\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-1\right)^{(-1)}\left(\frac{3 \mathrm{n}}{5}-1\right)}+{ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-2\right)}(-1)^{\left(\frac{3 \mathrm{n}}{5}-2\right)}=0$<br/>$\Rightarrow$<br/>$\left.(-1)^{\frac{3 n}{5}}\left[{ }^{n} C_{\left(\frac{3 n}{5}-1\right)} \cdot(-1)^{-1}+{ }^{n} C_{\left(\frac{3 n}{5}-2\right.}\right) \cdot(-1)^{(-2)}\right]=0$<br/>$\Rightarrow-{ }^{n} C_{\left(\frac{3 n}{5}-1\right)}+{ }^{n} C_{\left(\frac{3 n}{5}-2\right)}=0$ ...(ii)<br/><br/>$\mathrm{n}=15$<br/>Total term in the expansion of $\left(\mathrm{x}^{3}-\frac{1}{\mathrm{x}^{2}}\right)^{15}$ is 16 . $\therefore$ middle term $=8^{\text {th }}$ term and $9^{\text {th }}$ term $\mathrm{T}_{8}=\mathrm{T}_{(7+1)}={ }^{15} \mathrm{C}_{7} \cdot(-1)^{7} \cdot \mathrm{x}^{(3 \times 15-5 \times 7)}$<br/>$=-{ }^{15} \mathrm{C}_{7} \cdot \mathrm{x}^{10} \quad$ (from eq. (i))<br/>$\mathrm{T}_{9}=\mathrm{T}_{(8+1)}={ }^{15} \mathrm{C}_{8} \cdot(-1)^{8} \cdot \mathrm{x}^{(3 \times 15-5 \times 8)}$<br/>$=-{ }^{15} \mathrm{C}_{8} \cdot \mathrm{x}^{5} \quad$ (from eq. (ii))<br/>The sum of the coefficients of the two middle terms<br/>$=-{ }^{15} \mathrm{C}_{7}+{ }^{15} \mathrm{C}_{8}=-{ }^{15} \mathrm{C}_{7}+{ }^{15} \mathrm{C}_{7} \cdot\left[\because{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}-\mathrm{r}}\right]$<br/>$=0$</div>


tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-the-expansion-of-x-3-x-2-1-n-where-n-is-a-positive-integer-the-sum-of-the-coefficients-of-x-5-and-x-10-is-0-what-is-the-value-of-the-independent-te

slug:
in-the-expansion-of-x-3-x-2-1-n-where-n-is-a-positive-integer-the-sum-of-the-coefficients-of-x-5-and-x-10-is-0-what-is-the-value-of-the-independent-te-42518

question:
<div class="question">In the expansion of $\left(x^{3}-\frac{1}{x^{2}}\right)^{n}$ where n is a positive integer, the sum of the coefficients of $\mathrm{x}^{5}$ and $\mathrm{x}^{10}$ is $0 .$<br/>What is the value of the independent term?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5005</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">7200</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$-5005$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$-7200$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-5005$</span> </div>

answer:
<div class="solution">$\left(x^{3}-\frac{1}{x^{2}}\right)^{n}$<br/>$\quad$ General term, $T_{r+1}={ }^{n} C_{r}\left(x^{3}\right)^{n-r} \cdot\left(-\frac{1}{x^{2}}\right)^{r}$<br/>$\quad={ }^{n} C_{r} \cdot x^{(3 n-3 r)} \cdot(-1)^{r} \cdot x^{-2 r}$<br/>$={ }^{n} C_{r} \cdot(-1)^{r} \cdot x^{(3 n-5 r)}$ ...(i)<br/>For the coefficient $\mathrm{x}^{5}$<br/>Put $3 n-5 r=5$<br/>$5 r=3 n-5$<br/>$\therefore \mathrm{r}=\frac{3 \mathrm{n}}{5}-1$<br/>$\therefore$ Coefficient of $x^{5}={ }^{n} C\left(\frac{3 n}{5}-1\right)^{(-1)}\left(\frac{3 n}{5}-1\right)$<br/>For the coefficient of $\mathrm{x}^{10}$<br/>Put $3 n-5 r=10$<br/>$5 r=3 n-10$<br/>$\therefore \mathrm{r}=\frac{3 \mathrm{n}}{5}-2$ <br/>$\therefore$ Coefficient of $x^{10}={ }^{n} C_{\left(\frac{3 n}{5}-2\right)^{(-1)}}\left(\frac{3 n}{5}-2\right)$<br/>The sum of the coefficient of $x^{5}$ and $x^{10}=0$<br/>$\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-1\right)^{(-1)}\left(\frac{3 \mathrm{n}}{5}-1\right)}+{ }^{\mathrm{n}} \mathrm{C}_{\left(\frac{3 \mathrm{n}}{5}-2\right)}(-1)^{\left(\frac{3 \mathrm{n}}{5}-2\right)}=0$<br/>$\Rightarrow$<br/>$\left.(-1)^{\frac{3 n}{5}}\left[{ }^{n} C_{\left(\frac{3 n}{5}-1\right)} \cdot(-1)^{-1}+{ }^{n} C_{\left(\frac{3 n}{5}-2\right.}\right) \cdot(-1)^{(-2)}\right]=0$<br/>$\Rightarrow-{ }^{n} C_{\left(\frac{3 n}{5}-1\right)}+{ }^{n} C_{\left(\frac{3 n}{5}-2\right)}=0$ ...(ii)<br/><br/>For the independent term, put $3 \mathrm{n}-5 \mathrm{r}=0 \quad[$ <br/>from eq. $(\mathrm{i})]$<br/>$\Rightarrow 5 \mathrm{r}=3 \mathrm{n}=3 \times 15$<br/>$5 \mathrm{r}=3 \times 3 \times 5$<br/>$\mathrm{r}=9$<br/>Putting the value of r in eq. (i), we get $\mathrm{T}_{9+1}={ }^{15} \mathrm{C}_{9} \cdot(-1)^{9} \cdot \mathrm{x}^{(3 \times 15-5 \times 9)}$<br/>$\Rightarrow \mathrm{T}_{10}=-{ }^{15} \mathrm{C}_{9} \cdot \mathrm{x}^{0}=-{ }^{15} \mathrm{C}_{9}$<br/>$\Rightarrow \mathrm{T}_{10}=-{ }^{15} \mathrm{C}_{6} \quad\left[\because{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{n}-\mathrm{r}}\right]$<br/>$=\frac{-15 !}{6 ! 9 !}$<br/>$\left[\because{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=\frac{\mathrm{n} !}{\mathrm{r} !(\mathrm{n}-\mathrm{r}) !}\right]$<br/>$=-5005$</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-the-experiment-for-the-determination-of-the-speed-of-sound-in-air-using-the-resonance-column-the-resonates-in-the-fundamental-mode-with-a-tuning-fo

slug:
in-the-experiment-for-the-determination-of-the-speed-of-sound-in-air-using-the-resonance-column-the-resonates-in-the-fundamental-mode-with-a-tuning-fo-59379

question:
<div class="question">In the experiment for the determination of the speed of sound in air using the resonance column, the resonates in the fundamental mode, with a tuning fork is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. When this length is changed to<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mn>0</mn><mo>.</mo><mn>35</mn><mo> </mo><mi mathvariant="normal">m</mi></math>, the same tuning fork resonates with the first overtone. Calculate the end correction.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>012</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 115px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></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>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 115px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>05</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 103px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>024</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 72px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></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>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mi mathvariant="normal">m</mi></math><div id="gtx-trans" style="position: absolute; left: 115px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution">Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â</mo><mi>l</mi></math> be the end correction. Given that,<br/><br/>Fundamental tone for a length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>1</mn><mi>m</mi><mo>=</mo></math>first overtone for the length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>35</mn><mo> </mo><mi mathvariant="normal">m</mi></math><br/><br/><math><mo>â´</mo><mfrac><mrow><mi>v</mi></mrow><mrow><mn>4</mn><mfenced separators="|"><mrow><mn>0.1</mn><mo>+</mo><mo>â</mo><mi>l</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>v</mi></mrow><mrow><mn>4</mn><mfenced separators="|"><mrow><mn>0.35</mn><mo>+</mo><mo>â</mo><mi>l</mi></mrow></mfenced></mrow></mfrac></math><br/><br/>Solving this equations we get <math><mo>â</mo><mi>l</mi></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mi mathvariant="normal">m</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>5 </mn><mi>cm</mi></math></div>


tags: ['Physics', 'Current Electricity', 'JEE Main', 'JEE Main 2014 (12 Apr Online)']
source_db: MarksBatch2_P1.db
title:
in-the-experiment-of-calibration-of-voltmeter-a-standard-cell-of-emf-11-volt-is-balanced-against-440-cm-of-potential-wire-the-potential-difference-acr

slug:
in-the-experiment-of-calibration-of-voltmeter-a-standard-cell-of-emf-11-volt-is-balanced-against-440-cm-of-potential-wire-the-potential-difference-acr-22583

question:
<div class="question">In the experiment of calibration of voltmeter, a standard cell of e.m.f. $1.1$ volt is balanced against $440 \mathrm{~cm}$ of potential wire. The potential difference across the ends of resistance is found to balance against $220 \mathrm{~cm}$ of the wire. The corresponding reading of voltmeter is $0.5$ volt. The error in the reading of volmeter will be:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$-0.15$ volt<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$0.15$ volt<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$0.5$ volt<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$-0.05$ volt</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$-0.05$ volt</span> </div>

answer:
<div class="solution">In a voltmeter<br/>$$<br/>\begin{gathered}<br/>\mathrm{V} \propto l \\<br/>\mathrm{~V}=\mathrm{k} l<br/>\end{gathered}<br/>$$<br/>Now, it is given $\mathrm{E}=1.1$ volt for $l_1=440 \mathrm{~cm}$ and $\mathrm{V}=0.5$ volt for $l_2=220 \mathrm{~cm}$ Let the error in reading of voltmeter be $\Delta \mathrm{V}$ then,<br/>$$<br/>\begin{aligned}<br/>&amp;1.1=400 \mathrm{~K} \text { and }(0.5-\Delta \mathrm{V})=220 \mathrm{~K} . \\<br/>&amp;\Rightarrow \frac{1.1}{440}=\frac{0.5-\Delta \mathrm{V}}{220} \\<br/>&amp;\therefore \Delta \mathrm{V}=-0.05 \text { volt }<br/>\end{aligned}<br/>$$</div>


title: in-the-following-compound-designated-as-a-b-c-will-be-numbered-as
slug: in-the-following-compound-designated-as-a-b-c-will-be-numbered-as-51824
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the following compound, designated as <math> <mrow> <mtext>A, B, C</mtext></mrow> </math> will be numbered as<br/> <br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/321385.PNG" style="max-width:100%; object-fit:contain"/></div>

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

answer:
<div class="solution">According to the hierarchy of functional groups, OH will be given top priority, followed by the secondary amine. Hence, the numbering will be<br/><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/321385_1.PNG" style="max-width:100%; object-fit:contain"/></div>


title: in-the-following-diagram-identify-the-structural-and-regulatory-proteins-of-muscles
slug: in-the-following-diagram-identify-the-structural-and-regulatory-proteins-of-muscles-66088
tags: ['Biology', 'Locomotion and Movement', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the following diagram identify the structural and regulatory proteins of muscles?<br/> <br/> <img alt="" src="data:image/png;base64,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"/></div>

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

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

answer:
<div class="solution">Actin : Protein that makes up most of the thin myofilaments in a sarcomere muscle fiber.<br/><br/>Troponin : Regulatory protein that binds to actin, tropomyosin, and calcium.<br/><br/>Tropomyosin : Regulatory protein that covers myosin-binding sites to prevent actin from binding to myosin.</div>


title: in-the-following-logic-circuit-the-values-of-y-1-y-2-and-y-3-are-respectively
slug: in-the-following-logic-circuit-the-values-of-y-1-y-2-and-y-3-are-respectively-65292
tags: ['Physics', 'Semiconductors', 'AP EAMCET', 'AP EAMCET 2017 (25 Apr Shift 2)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P1.db
question:
<div class="question">In the following logic circuit, the values of $\mathrm{Y}_1, \mathrm{Y}_2$ and $\mathrm{Y}_3$ are respectively<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/RGmVgAbId0GfMqm7vNaOHEYopqNDARxNKvKIdyGRSxk.original.fullsize.png"/><br/></div>

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

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


title: in-the-following-pair-of-halogen-compounds-which-would-undergo-s-n-2-reaction-faster
slug: in-the-following-pair-of-halogen-compounds-which-would-undergo-s-n-2-reaction-faster-59445
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>The Primary halide</div>
source_db: MarksBatch2_P1.db
question:
<div class="question">In the following pair of halogen compounds, which would undergo S<sub>N</sub>2 reaction faster?  <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/vXAgBo7DRdEVeiHfhXTcCvnFX92cvlWkAr9KfblxgrydcBh0zU..png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The Primary halide</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The Secondary halide</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both of them undergo S<sub>N</sub>2 reaction at the same rate</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither of them undergo S<sub>N</sub>2 reaction</span> </li> </ul>

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


title: in-the-following-sequence-of-reactions-the-final-product-d-is
slug: in-the-following-sequence-of-reactions-the-final-product-d-is-11426
tags: ['Chemistry', 'Aldehydes and Ketones', 'JEE Main', 'JEE Main 2021 (27 Aug Shift 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question"><p>In the following sequence of reactions, the final product <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">D</mi></math> is:</p><p><img height="99" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/3cd34091-7f11-4a3b-90fc-fb4307bad438-image.png" width="685"/></p></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><p><img height="81" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/aeb42c6f-90a2-43c9-8b32-04bcee45bfb4-image.png" style="float: left;" width="401"/></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/172113ca-8147-47fd-bb78-5e868d722f70-image.png" style="width: 459px; height: 42px;"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/63584e97-d944-49a5-98d4-3550069a93b1-image.png" style="width: 472px; height: 46px;"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/8d2aa016-04a6-430b-a976-d431643629cb-image.png" style="width: 388px; height: 86px;"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><img height="81" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/aeb42c6f-90a2-43c9-8b32-04bcee45bfb4-image.png" style="float: left;" width="401"/></p></span> </div>

answer:
<div class="solution"><blockquote><p><img height="251" src="https://cdn-question-pool.getmarks.app/pyq/jee_main/2f52430d-6a56-4184-b3c2-e86f4bdcdbe2-image.png" width="798"/></p><p>Terminal alkyne reacts sodamide to produce sodium salt of alkyne by elimination of ammonia molecule. Sodium salt of alkyne reacts with alkyl halide by nucleophilic substitution reaction mechanism. Secondary alcohol is oxidised by <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CrO</mi><mn>3</mn></msub></math> to produce ketone.</p></blockquote></div>


title: in-the-forest-ecosystem-yeasts-molds-and-mushrooms-are-grouped-as
slug: in-the-forest-ecosystem-yeasts-molds-and-mushrooms-are-grouped-as-84594
question: <div class="question">In the forest ecosystem, yeasts, molds, and mushrooms are grouped as</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Producer</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Consumer</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Secondary consumer</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Decomposer</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Decomposer</span> </div>

answer:
<div class="solution">The decomposers are those living organisms that decompose the dead body of producers, consumers and are known as reducers or transformers or osmotrophs. These are heterotrophic organisms that break up the dead bodies of plants and their waste products. They include fungi like yeasts, molds, and mushrooms and certain bacteria like <em>Bacillus subtilis</em> and <em>Pseudomonas fluorescens etc</em>. The enzymes secreted by these organisms digest the dead organisms and the debris into smaller bits or molecules. These molecules are absorbed by the reducers. After taking energy, the reducers release molecules to the environment as a chemical to be used again by the producers.<br/><br/> </div>


tags: ['Physics', 'Ray Optics', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-the-formation-of-primary-rainbow-the-sunlight-rays-emerge-at-minimum-deviation-from-raindrop-after

slug:
in-the-formation-of-primary-rainbow-the-sunlight-rays-emerge-at-minimum-deviation-from-raindrop-after-20682

question:
<div class="question">In the formation of primary rainbow, the sunlight rays emerge at minimum deviation from rain-drop after</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">One internal reflection and two refractions</span> </div>

answer:
<div class="solution">Both the primary and secondary rainbows are phenomena that formed by the reflection and refraction of sunlight in tiny water droplets. Different colors of sunlight have different refractive index so they will be reflected in slightly different directions inside a water droplet and dispersed to form rainbow. The sunlight rays after being refracted twice and reflected once by the water droplet form a primary rainbow and emerge at minimum deviation.</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">25</span> </div>
source_db: MarksBatch2_P1.db
title:
in-the-fundamental-mode-time-taken-by-the-wave-to-reach-the-closed-end-of-the-air-filled-pipe-is-001-s-the-fundamental-frequency-is

slug:
in-the-fundamental-mode-time-taken-by-the-wave-to-reach-the-closed-end-of-the-air-filled-pipe-is-001-s-the-fundamental-frequency-is-63676

question:
<div class="question">In the fundamental mode, time taken by the wave to reach the closed end of the air filled pipe is $0.01 \mathrm{~s}$. The fundamental frequency is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">25</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$12.5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">20</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">15</span> </li> </ul>

answer:
<div class="solution">In the fundamental mode,<br/>Frequency, $n=\frac{v}{\lambda}$<br/>$$<br/>\begin{array}{l}<br/>n=\frac{v}{4 l} \\<br/>n=\frac{l}{t \times 4 l} \quad\left[\because v=\frac{l}{t}\right] \\<br/>n=\frac{1}{0.01 \times 4} \\<br/>n=25<br/>\end{array}<br/>$$</div>


title: in-the-gaseous-phase-what-is-the-order-of-basicity-among-amines-including-nh-3
slug: in-the-gaseous-phase-what-is-the-order-of-basicity-among-amines-including-nh-3-64837
tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the gaseous phase, what is the order of basicity among amines, including NH<sub>3</sub>?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Tertiary amine &gt; Secondary amine &gt; Primary amine &gt; NH<sub>3</sub></span> </div>

answer:
<div class="solution">In the gaseous phase, the basicity of amines follows the order mentioned.</div>


title: in-the-give-diagram-typical-chordate-plan-is-given-identify-a-and-b
slug: in-the-give-diagram-typical-chordate-plan-is-given-identify-a-and-b-32793
tags: ['Biology', 'Animal Kingdom', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the give diagram, typical chordate plan is given. Identify A and B.<br/> <br/> <img alt="" object-fit:contain="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/29_bio_Qeuds.JPG" style="max-width:"/></div>

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

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

answer:
<div class="solution">Members possess 3 fundamental chordate characters at any stage of life :<br/><br/> <math><mn>1</mn><mo>.</mo></math>       Notochord -  Solid, mesodermal and later on develop into vertebral column.<br/><br/> <math><mn>2</mn><mo>.</mo></math>      Dorsal hollow nerve cord (or dorsal tubular nerve cord or neural tube) - Hollow, ectodermal and later on develop into CNS (central nervous system).<br/><br/> <math><mn>3</mn><mo>.</mo></math>      Pharyngeal gill slits.<br/><br/>        -       Bilaterally symmetrical, organ system level, triploblastic and eucoelomate.</div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P1.db
title:
in-the-given-compound-here-if-x-and-y-are-the-number-of-secondary-and-tertiary-catoms-respectively-find-the-value-of-sum-of-x-y-here

slug:
in-the-given-compound-here-if-x-and-y-are-the-number-of-secondary-and-tertiary-catoms-respectively-find-the-value-of-sum-of-x-y-here-27541

question:
<div class="question">In the given compound here<br/> <br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/24_qued_chdm.JPG" style="width: 200px; height: 78px;"/><br/> <br/>
If X and Y are the number of secondary and tertiary C-atoms respectively. Find the value of sum of X + Y here.</div>

answer:
<div class="solution"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/jee_main/images/24_solu_chdm.JPG" style="width: 200px; height: 99px;"/><br/><br/>Number of <math> <mrow> <msup> <mtext>s</mtext> <mtext>o</mtext> </msup> </mrow> </math> C-atoms (X) = 4<br/><br/>Number of <math> <mrow> <msup> <mtext>t</mtext> <mtext>o</mtext> </msup> </mrow> </math> C-atoms (Y) = 4<br/><br/>Sum of <math> <mrow> <mtext>X</mtext><mo>+</mo><mtext>Y</mtext><mo>=</mo><mn>4</mn><mo>+</mo><mn>4</mn><mo>=</mo><mn>8</mn></mrow></math>.</div>


tags: ['Physics', 'Waves and Sound']
options: None
correct_option: None
source_db: MarksBatch2_P1.db
title:
in-the-given-progressive-wave-y-5-sin-100-t-04-x-where-y-and-x-are-in-metre-t-is-in-second-what-is-the-a-amplitude-b-wavelength-c-frequency-d-wave-vel

slug:
in-the-given-progressive-wave-y-5-sin-100-t-04-x-where-y-and-x-are-in-metre-t-is-in-second-what-is-the-a-amplitude-b-wavelength-c-frequency-d-wave-vel-81855

question:
<div class="question">In the given progressive wave $y=5 \sin (100 \pi t-0.4 \pi x)$ where $y$ and $x$ are in metre, $t$ is in second. What is the<br/>(a) amplitude?<br/>(b) wavelength?<br/>(c) frequency?<br/>(d) wave velocity?<br/>(e) particle velocity amplitude?</div>

answer:
<div class="solution">Standard equation of a progressive wave is travelling along positive $x$-direction.<br/>$$<br/>y=a \sin (\omega t-k x+\phi)<br/>$$<br/>As given equation is<br/>$$<br/>y=5 \sin (100 \pi t-0.4 \pi x)<br/>$$<br/>Comparing equation (i) with the standard equation<br/>(a) Amplitude $(a)=5 \mathrm{~m}$<br/>(b) wavelength $(\lambda)$<br/>$$<br/>k=\frac{2 \pi}{\lambda}=0.4 \pi<br/>$$<br/>$\therefore$ Wavelength, $\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{0.4 \pi}=\frac{20}{4}=5 \mathrm{~m}$<br/>(c) $\omega=100 \pi$, from eq. (i), $v=\frac{\omega}{2 \pi}$<br/>$$<br/>\therefore \text { Frequency } v=\frac{100 \pi}{2 \pi}=50 \mathrm{~Hz}<br/>$$<br/>(d) Wave velocity<br/>$$<br/>v=v \lambda=50 \times 5=250 \mathrm{~m} / \mathrm{sec}(\because \lambda=5 \mathrm{~m})<br/>$$<br/>(e) Particle (medium) velocity in the direction of amplitude at a distance $x$ from source.<br/>$$<br/>y=5 \sin (100 \pi t-0.4 \pi x)<br/>$$<br/>So, differentiation equation w.r.t. ( $t$ )<br/>Particle velocity<br/>$$<br/>\frac{d y}{d t}=5(100 \pi) \cos [100 \pi t-0.4 \pi x]<br/>$$<br/>For maximum velocity of particle is at its mean position.<br/>So, particle velocity amplitude $\left(\frac{d y}{d t}\right)_{\max }$.<br/>then $\cos [100 \pi t-0.4 \pi x]_{\max }=1$<br/>$\therefore$ Particle velocity amplitude<br/>$$<br/>\begin{aligned}<br/>&amp;=\left(\frac{d y}{d t}\right)_{\max .}=5(100 \pi) \times 1=500 \pi \mathrm{m} / \mathrm{s} \\<br/>&amp;v_{\text {max. }} \text { of medium particle }=500 \pi \mathrm{m} / \mathrm{s} .<br/>\end{aligned}<br/>$$</div>


title: in-the-given-reaction-2
slug: in-the-given-reaction-2-53902
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the given reaction<br/> <img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/6f3e0e53-1d92-4987-8271-3ad7858ce586.png" style="max-width:100%; object-fit:contain"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mi mathvariant="normal">P</mi><mi mathvariant="normal">t</mi><mo>/</mo><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math><mi mathvariant="normal">P</mi><mi mathvariant="normal">d</mi><mo>/</mo><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></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><msub><mrow><mi mathvariant="normal">X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>/</mo><mi mathvariant="normal">N</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Jones reagent</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mi mathvariant="normal">P</mi><mi mathvariant="normal">d</mi><mo>/</mo><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/9c13e94b-615f-4086-a52d-9aedf1403c9f.png" style="max-width:100%; object-fit:contain"/><br/><math><mi mathvariant="normal">P</mi><mi mathvariant="normal">t</mi><mo>/</mo><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math> oxidised <math><mo>-</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi></math> into <math><mo>-</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi></math> and it has no effect on secondary hydroxyl group.</div>


title: in-the-given-reaction-r-i-nacn-dmf-r-c-n-r-i-may-not-be
slug: in-the-given-reaction-r-i-nacn-dmf-r-c-n-r-i-may-not-be-76791
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the given reaction<br/> <math> <mrow> <mtext>R</mtext><mo>−</mo><mtext>I</mtext><mtext> </mtext><mtext>+</mtext><mtext> </mtext><mtext>NaCN</mtext><mover> <mo>→</mo> <mrow> <mtext>DMF</mtext></mrow> </mover> <mtext>R</mtext><mo>−</mo><mtext>C</mtext><mo>≡</mo><mtext>N</mtext></mrow> </math> <br/> <math><mi mathvariant="normal">R</mi><mo>-</mo><mi mathvariant="normal">I</mi></math> may not be</div>

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

answer:
<div class="solution"><math> <mrow> <mtext>R</mtext><mo>−</mo><mtext>I</mtext><mtext> </mtext><mtext>+</mtext><mtext> </mtext><mtext>NaCN</mtext><mover> <mo>→</mo> <mrow> <mtext>DMF</mtext></mrow> </mover> <mtext>R</mtext><mo>−</mo><mtext>C</mtext><mo>≡</mo><mtext>N</mtext></mrow></math><br/>Here <math><mi mathvariant="normal">R</mi><mo>-</mo><mi mathvariant="normal">I</mi></math> cannot be tertiary halide as it is <math><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi mathvariant="normal">N</mi></mrow></msub><mn>2</mn></math> reaction.<br/></div>


title: in-the-given-reaction-rcn-i-i-h-2-o-h-i-r-m-g-x-x-x-will-be
slug: in-the-given-reaction-rcn-i-i-h-2-o-h-i-r-m-g-x-x-x-will-be-93971
tags: ['Chemistry', 'Amines', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Ketone</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">In the given reaction<br/> <math> <mrow> <mtext>RCN</mtext><munderover> <mo>â</mo> <mrow> <mo stretchy="false">(</mo><mtext>i</mtext><mtext>i</mtext><mo stretchy="false">)</mo><mtext>â</mtext><msub> <mtext>H</mtext> <mn>2</mn> </msub> <mtext>O</mtext><mo>/</mo><msup> <mtext>H</mtext> <mo>+</mo> </msup> </mrow> <mrow> <mo stretchy="false">(</mo><mtext>i</mtext><mo stretchy="false">)</mo><mtext>â</mtext><mtext>R</mtext><mtext>M</mtext><mtext>g</mtext><mtext>X</mtext></mrow> </munderover> <mo stretchy="false">(</mo><mtext>X</mtext><mo stretchy="false">)</mo></mrow> </math>, (X) will be</div>

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

answer:
<div class="solution">A Cyanide on reaction with Grignard reagent gives Ketone (except HCN)<br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/7a77a611-761a-4c63-9931-06f5df0803bc.png" style="max-width:100%; object-fit:contain"/><br/> </div>


title: in-the-given-reaction-the-reactivity-order-of-different-alcohols-is-r-o-h-h-x-r-x-h-2-o
slug: in-the-given-reaction-the-reactivity-order-of-different-alcohols-is-r-o-h-h-x-r-x-h-2-o-86120
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the given reaction, the reactivity order of different alcohols is <br/><math><mi mathvariant="normal">R</mi><mo>-</mo><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi><mo>+</mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">X</mi><mo>â</mo><mi mathvariant="normal">R</mi><mo>-</mo><mi mathvariant="normal">X</mi><mo>+</mo><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi></math></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary &gt; Secondary &gt; Tertiary</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Tertiary &gt; Secondary &gt; 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">C</span> <span class="option-data">Secondary &gt; Tertiary &gt; Primary</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Secondary &gt; Primary &gt; Tertiary</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Tertiary &gt; Secondary &gt; Primary</span> </div>

answer:
<div class="solution"><math><mi mathvariant="normal">R</mi><mo>-</mo><mi mathvariant="normal">O</mi><mi mathvariant="normal">X</mi><mo>+</mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">X</mi><mo>â</mo><mi mathvariant="normal">R</mi><mo>-</mo><mi mathvariant="normal">X</mi><mo>+</mo><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi></math> , the reaction occurs by <math><msub><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi mathvariant="normal">N</mi></mrow></msub><mn>1</mn></math> mechanism through carbocation intermediates. Reactivity order of alcohols for this reaction is <math><msup><mrow><mn>3</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup><mo>&gt;</mo><msup><mrow><mn>2</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup><mo>&gt;</mo><msup><mrow><mn>1</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></math></div>


title: in-the-given-reaction-x-will-be-2
slug: in-the-given-reaction-x-will-be-2-43429
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the given reaction<br/> <br/> <img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/07d1da4f-9927-497b-b59a-9356da7283ab.png" style="max-width:100%; object-fit:contain"/><br/> <br/>
(X) will be</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>2</mn><mo>Â°</mo></math> -Alcohol</span> </div>

answer:
<div class="solution">Here a secondary alcohol (butan-2-ol) is formed as follows<br/><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/674292_1.PNG" style="max-width:100%; object-fit:contain"/><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/674292_2.PNG" style="max-width:100%; object-fit:contain"/></div>


title: in-the-given-set-of-reactions-the-iupac-name-of-product-y-is
slug: in-the-given-set-of-reactions-the-iupac-name-of-product-y-is-70329
tags: ['Chemistry', 'Hydrogen', 'KCET', 'KCET 2015']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the given set of reactions.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/jHXFrt8zeYYUGl-WO1skrvuIHBUAOo9H8nf3v1KhgM8.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/jHXFrt8zeYYUGl-WO1skrvuIHBUAOo9H8nf3v1KhgM8.original.fullsize.png"/><br/>the IUPAC name of product ' \( Y \) ' is</div>

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

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

answer:
<div class="solution">AgCN is a covalent compound, therefore, attacking side ofthe \( \mathrm{CN}^{-} \)is \( \mathrm{N} \), hence, the product thus formed is a secondary<br/>amine. The reaction involved is,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/kcet/sol_145.png"/></div>


tags: ['Physics', 'Semiconductors', 'AIIMS', 'AIIMS 2007']
source_db: MarksBatch2_P1.db
title:
in-the-half-wave-rectifier-circuit-operating-from-50-mathrmhz-mains-frequency-the-fundamental-frequency-in-the-ripple-would-be

slug:
in-the-half-wave-rectifier-circuit-operating-from-50-mathrmhz-mains-frequency-the-fundamental-frequency-in-the-ripple-would-be-58498

question:
<div class="question">In the half wave rectifier circuit operating from \(50 \mathrm{~Hz}\) mains frequency, the fundamental frequency in the ripple would be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(25 \mathrm{~Hz}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(50 \mathrm{~Hz}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(70.7 \mathrm{~Hz}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(100 \mathrm{~Hz}\)</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/aiims/qMJHz6CmyRciqlgi5W-sJPQHfVbbT-pdLiWLPcPLQj0.original.fullsize.png"/><br/><br/>In full wave a.c. or half wave rectifier, the time interval between two peaks are the same. But in half wave rectification, the negative wave part is cut off. But as for frequency or the period, they will be the same as seen from the figures. Therefore, this also will be 50 cycles/second.</div>


tags: ['Physics', 'Semiconductors', 'VITEEE', 'VITEEE 2015']
source_db: MarksBatch2_P1.db
title:
in-the-half-wave-rectifier-circuit-operating-with-50-hz-mains-frequency-the-fundamental-frequency-in-the-ripple-will-be

slug:
in-the-half-wave-rectifier-circuit-operating-with-50-hz-mains-frequency-the-fundamental-frequency-in-the-ripple-will-be-28894

question:
<div class="question">In the half wave rectifier circuit operating with $50 \mathrm{~Hz}$ mains frequency. The fundamental frequency in the ripple will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$100 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$20 \mathrm{~Hz}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$50 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$25 \mathrm{~Hz}$</span> </li> </ul>

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

answer:
<div class="solution">The output is obtained for half cycle only in half wave rectifier. Therefore, frequency of the ripple is same as that of the input i.e. $50 \mathrm{~Hz}$.</div>


tags: ['Biology', 'Biological Classification', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-the-light-of-recent-classification-of-living-organisms-into-three-domains-of-life-bacteria-archaea-and-eukarya-which-one-of-the-following-statement

slug:
in-the-light-of-recent-classification-of-living-organisms-into-three-domains-of-life-bacteria-archaea-and-eukarya-which-one-of-the-following-statement-71793

question:
<div class="question">In the light of recent classification of living organisms into three domains of life (bacteria, archaea, and eukarya), which one of the following statements is true about archaea?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Archaea have some novel features that are absent in other prokaryotes and eukaryotes</span> </div>

answer:
<div class="solution">A domain of prokaryotic organisms containing the archaebacteria includes the methanogens which produce methane, the thermoacidophilic bacteria which live in an extremely hot and acidic environment and the halophilic bacteria which can only function at high salt concentrations and are abundant in the oceans.</div>


title: in-the-manufacture-of-sulphuric-acid-by-contact-process-tyndall-box-is-used-to
slug: in-the-manufacture-of-sulphuric-acid-by-contact-process-tyndall-box-is-used-to-44789
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'COMEDK', 'COMEDK 2013']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the manufacture of sulphuric acid by contact process, Tyndall box is used to</div>

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

answer:
<div class="solution">In the manufacture of sulphuric acid by contact process, Tyndall box is used to test the presence of dust particles.</div>


tags: ['Biology', 'Organisms and Populations', 'NEET', 'NEET 2007']
source_db: MarksBatch2_P1.db
title:
in-the-mean-and-the-median-pertaining-to-a-certain-character-of-a-population-arc-of-the-same-value-the-following-is-most-likely-to-occur

slug:
in-the-mean-and-the-median-pertaining-to-a-certain-character-of-a-population-arc-of-the-same-value-the-following-is-most-likely-to-occur-67020

question:
<div class="question">In the mean and the median pertaining to a certain character of a population arc of the same value, the following is most likely to occur:</div>

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

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

answer:
<div class="solution">The normal distribution is a symmetrical, bell-shaped distribution in which the mean, median and mode are all equal. It is a central component of inferential statistics. The standard normal distribution is a normal distribution represented in z scores. It always has a mean of zero and a standard deviation of one.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/NBwvxxnvyZx8GVpz7Un7BtqcPLXCZ9SywrvyKD2rCOo.original.fullsize.png"/><br/><br/>Related Theory<br/>If one tail is longer than another, the distribution is skewed. These distributions are sometimes called asymmetric or asymmetrical distributions as they don't show any kind of symmetry. Symmetry means that one half of the distribution is a mirror image of the other half.</div>


title: in-the-mechanism-of-action-of-a-protein-hormone-one-of-the-secondary-messengers-is
slug: in-the-mechanism-of-action-of-a-protein-hormone-one-of-the-secondary-messengers-is-92014
tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the mechanism of action of a protein hormone, one of the secondary messengers is</div>

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

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

answer:
<div class="solution">Hormonal action depends on whether the hormone is Lipid or water soluble. Lipid soluble hormones can cross the target cell membrane easily, get attached to the mobile receptors within the cytoplasm and reach the nucleus to perform their functions. However water soluble hormones like insulin, cannot cross the cell membrane easily. These get attached to the static receptors on the cell membrane. This attachment triggers the formation of secondary messengers that help these hormones to act on cells. These also cause amplification of hormonal action so that many targets are affected by a single hormone. This is the main difference between how a lipid-soluble or water soluble hormone act. Secondary messengers commonly seen in cells are cyclic AMP. Other examples are inositol triphosphate (IP3), calcium and cyclic GMP.</div>


tags: ['Biology', 'Ecosystem']
options: None
correct_option: None
source_db: MarksBatch2_P1.db
title:
in-the-north-east-region-of-india-during-the-process-of-jhum-cultivation-forests-are-cleared-by-burning-and-left-for-regrowth-after-a-year-of-cultivat

slug:
in-the-north-east-region-of-india-during-the-process-of-jhum-cultivation-forests-are-cleared-by-burning-and-left-for-regrowth-after-a-year-of-cultivat-63317

question:
<div class="question">In the North East region of India, during the process of jhum cultivation, forests are cleared by burning and left for regrowth after a year of cultivation. How would you explain the regrowth of forest in ecological term?</div>

answer:
<div class="solution">Forests that are cleared during jhum cultivation will show secondary succession. Since, soil is already present, the buried seeds open to germinate. New seeds will be brought into the area and new species will colonise the forest again due to wind dispersal and some other natural forces.</div>


title: in-the-order-of-ease-of-dehydration-which-type-of-alcohol-is-the-easiest-to-dehydrate
slug: in-the-order-of-ease-of-dehydration-which-type-of-alcohol-is-the-easiest-to-dehydrate-63194
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the order of ease of dehydration, which type of alcohol is the easiest to dehydrate?</div>

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

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

answer:
<div class="solution">Tertiary alcohols are the easiest to dehydrate among primary, secondary, and tertiary alcohols.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-the-order-of-increasing-acid-strength-which-of-the-following-correctly-represents-the-acidity-of-alcohols

slug:
in-the-order-of-increasing-acid-strength-which-of-the-following-correctly-represents-the-acidity-of-alcohols-78825

question:
<div class="question">In the order of increasing acid strength, which of the following correctly represents the acidity of alcohols?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primary &lt; Secondary &lt; Tertiary alcohols</span> </div>

answer:
<div class="solution">Primary alcohols are generally more acidic than secondary alcohols, and secondary alcohols are more acidic than tertiary alcohols.</div>


tags: ['Chemistry', 'Hydrocarbons', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-the-peroxide-effect-why-is-1bromopropane-formed-as-the-major-product-when-hbr-is-added-to-propene

slug:
in-the-peroxide-effect-why-is-1bromopropane-formed-as-the-major-product-when-hbr-is-added-to-propene-57512

question:
<div class="question">In the peroxide effect, why is 1-bromopropane formed as the major product when HBr is added to propene?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Formation of a secondary free radical</span> </div>

answer:
<div class="solution">In the peroxide effect, 1-bromopropane is formed as the major product because the secondary free radical formed in the mechanism is more stable than a primary free radical.</div>


title: in-the-reaction-sequence-c-6-h-5-c-h-o-n-a-c-n-h-c-l-x-h-2-o-h-product-product-will-be
slug: in-the-reaction-sequence-c-6-h-5-c-h-o-n-a-c-n-h-c-l-x-h-2-o-h-product-product-will-be-49364
tags: ['Chemistry', 'Aldehydes and Ketones', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the reaction sequence<br/> <math><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>5</mn></mrow></msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">O</mi><mover accent="false"><mo>â</mo><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">N</mi><mo>/</mo><mi mathvariant="normal">H</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">l</mi></mrow></mover><mo>(</mo><mi mathvariant="normal">X</mi><mo>)</mo><mover accent="false"><mo>â</mo><mrow><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mo>/</mo><msup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mo>â</mo></mrow></msup></mrow></mover></math> Product, Product will be</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Racemic mixture of two optically active <math><mi mathvariant="normal">Î±</mi></math> -hydroxy acids</span> </div>

answer:
<div class="solution">In the reaction sequence racemic mixture of two optically active <math><mi mathvariant="normal">Î±</mi></math> -hydroxy acids<br/><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/3641139c-9a5b-4989-9288-126636f401cb.png" style="max-width:100%; object-fit:contain"/></div>


title: in-the-reaction-sequence-c-6-h-5-c-h-o-n-a-c-n-hcl-x-h-2-o-h-product-product-will-be
slug: in-the-reaction-sequence-c-6-h-5-c-h-o-n-a-c-n-hcl-x-h-2-o-h-product-product-will-be-86973
tags: ['Chemistry', 'Aldehydes and Ketones', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the reaction sequence<br/> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub><msub><mi mathvariant="normal">H</mi><mn>5</mn></msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">O</mi><mover><mo>→</mo><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal">N</mi><mo>/</mo><mi>HCl</mi></mrow></mover><mo>[</mo><mi mathvariant="normal">X</mi><mo>]</mo><mover><mo>→</mo><mrow><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi><mo>/</mo><msup><mi mathvariant="normal">H</mi><mo>+</mo></msup><mo>/</mo><mi mathvariant="normal">Δ</mi></mrow></mover></math> Product<br/>
Product will be –</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Racemic mixture of two optically active <math><mi mathvariant="normal">Î±</mi><mo>-</mo></math> hydroxy acids</span> </div>

answer:
<div class="solution"><img alt="" object-fit:contain="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/631682s.JPG" style="max-width:"/><br/><br/>It is optically active compound but form raceme mixture.</div>


title: in-the-reaction-which-of-the-following-compounds-will-be-formed-1
slug: in-the-reaction-which-of-the-following-compounds-will-be-formed-1-51612
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET', 'NEET 2007']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the reaction:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/ZAhTuLS4XzHgaEUEANdj_1g7eWHrlczDpCLKC9oUzvE.original.fullsize.png"/><br/><br/>Which of the following compounds will be formed?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/uwzMofUzSw2W_EL8U5rPM382rx0GAfg0bo5Eqef9-EQ.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/Cy5p8tUCLLohZLstSY3yZ1JNE5AnUkh_ZOaZ4DBpjto.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/ueuDyOKKHaiwH9wXCJsy52wAmxQlo7J5zK1ELKxkMNY.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/jMTu-1GsAu3bh9HH247uKI90Pn7UWvsaFD-8jW8Wuqw.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/neet/ueuDyOKKHaiwH9wXCJsy52wAmxQlo7J5zK1ELKxkMNY.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">In the cleavage of mixed ethers with two different alkyl groups, the alcohol and alkyl iodide that form depend on the nature of alkyl group.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/zq3jT0BdxiY-s3MMb5FTxdmDPb9FIrFCJv5HOm5B8Ic.original.fullsize_2.png"/><br/><br/>A Caution<br/>$\Rightarrow$ When primary or secondary alkyl groups are present, it is the lower alkyl group that forms alkyl iodide.</div>


tags: ['Chemistry', 'Amines', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-the-reduction-of-nitriles-to-primary-amines-what-is-the-impact-of-increasing-the-number-of-carbon-atoms-in-the-starting-nitrile-compound

slug:
in-the-reduction-of-nitriles-to-primary-amines-what-is-the-impact-of-increasing-the-number-of-carbon-atoms-in-the-starting-nitrile-compound-27053

question:
<div class="question">In the reduction of nitriles to primary amines, what is the impact of increasing the number of carbon atoms in the starting nitrile compound?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Increased yield of primary amine</span> </div>

answer:
<div class="solution">Increasing the number of carbon atoms in the starting nitrile compound results in the ascent of the amine series, leading to the formation of primary amines with one more carbon atom.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-the-synthesis-of-ethers-via-the-williamson-ether-synthesis-which-type-of-alkyl-halide-leads-to-the-exclusive-formation-of-an-alkene-instead-of-an-e

slug:
in-the-synthesis-of-ethers-via-the-williamson-ether-synthesis-which-type-of-alkyl-halide-leads-to-the-exclusive-formation-of-an-alkene-instead-of-an-e-64228

question:
<div class="question">In the synthesis of ethers via the Williamson ether synthesis, which type of alkyl halide leads to the exclusive formation of an alkene instead of an ether?</div>

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

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

answer:
<div class="solution">Tertiary alkyl halides, when used in the Williamson ether synthesis, lead to the exclusive formation of an alkene through elimination reactions.</div>


title: in-the-system-of-classification-which-one-of-the-following-is-not-a-family-or-order
slug: in-the-system-of-classification-which-one-of-the-following-is-not-a-family-or-order-98191
tags: ['Biology', 'The Living World', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the system of classification, which one of the following is NOT a family or order?</div>

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

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

answer:
<div class="solution">There are 7 major categories, namely, the kingdom, phylum, class, order, family, genus and species. Angiospermae is not a category. Angiospermae is a division under kingdom Plantae. <br/> </div>


title: in-the-treatment-of-waste-water-discharge-which-treatment-stage-involves-biological-treatment
slug: in-the-treatment-of-waste-water-discharge-which-treatment-stage-involves-biological-treatment-24479
tags: ['Biology', 'Microbes in Human Welfare', 'JIPMER', 'JIPMER 2009']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the treatment of waste water discharge, which treatment stage involves biological treatment?</div>

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

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

answer:
<div class="solution">During waste water treatment :<br/>(a) Primary treatment involves physical process of removing the suspended matters.<br/>(b) Secondary treatment involves biological treatment.<br/>(c) Tertiary treatment involves the removal of phosphate, nitrate and sulphate.</div>


title: in-the-wave-equation-y-0-5-sin-2-400-t-x-m-the-velocity-of-the-wave-will-be
slug: in-the-wave-equation-y-0-5-sin-2-400-t-x-m-the-velocity-of-the-wave-will-be-93765
tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2022 (28 Jul Shift 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In the wave equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>sin</mi><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac><mfenced><mrow><mn>400</mn><mi>t</mi><mo>-</mo><mi>x</mi></mrow></mfenced><mi>m</mi></math> the velocity of the wave will be :</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>200</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></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><msqrt><mn>2</mn></msqrt><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</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></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><msqrt><mn>2</mn></msqrt><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></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>400</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></span> </div>

answer:
<div class="solution"><blockquote><p>Given equation of the wave is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>sin</mi><mfenced><mrow><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac><mn>400</mn><mi mathvariant="normal">t</mi><mo>-</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac><mi mathvariant="normal">x</mi></mrow></mfenced></math></p><p>Comparing it with the standard equation of motion <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>A</mi><mi>sin</mi><mfenced><mrow><mi>ω</mi><mi>t</mi><mo>-</mo><mi>k</mi><mi>x</mi></mrow></mfenced></math> we get,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac><mn>400</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac></math></p><p>Now the velocity of the wave will be,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mi>ω</mi><mi>k</mi></mfrac><mo> </mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>v</mi><mo>=</mo><mn>400</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></p></blockquote></div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-thermodynamics-why-is-it-important-to-have-a-boundary-that-separates-the-system-from-the-surroundings

slug:
in-thermodynamics-why-is-it-important-to-have-a-boundary-that-separates-the-system-from-the-surroundings-38392

question:
<div class="question">In thermodynamics, why is it important to have a boundary that separates the system from the surroundings?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">To control all movements of matter and energy</span> </div>

answer:
<div class="solution">The boundary is designed to enable control and monitoring of all movements of matter and energy between the system and surroundings.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-throwing-a-six-faced-die-let-a-be-the-event-that-an-even-number-occurs-b-be-the-event-that-an-odd-number-occurs-and-c-be-the-event-that-a-number-gr

slug:
in-throwing-a-six-faced-die-let-a-be-the-event-that-an-even-number-occurs-b-be-the-event-that-an-odd-number-occurs-and-c-be-the-event-that-a-number-gr-76321

question:
<div class="question">In throwing a six faced die, let $A$ be the event that an even number occurs, B be the event that an odd number occurs and $\mathrm{C}$ be the event that a number greater than 3 occurs. Which one of the following is correct?</div>

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

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

answer:
<div class="solution">$A=\{2,4,6\}, B=\{1,3,5\}, C=\{4,5,6\}$<br/>Hence, $A$ and $B$ are mutually exclusive.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">25</span> </div>
source_db: MarksBatch2_P1.db
title:
in-throwing-of-two-dice-the-number-of-exhaustive-events-that-5-will-never-appear-on-any-one-of-the-dice-is

slug:
in-throwing-of-two-dice-the-number-of-exhaustive-events-that-5-will-never-appear-on-any-one-of-the-dice-is-59955

question:
<div class="question">In throwing of two dice, the number of exhaustive events that ' 5 ' will never appear on any one of the dice is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">18</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">25</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">36</span> </li> </ul>

answer:
<div class="solution">$\mathrm{n}(\mathrm{S})=6 \times 6=36$<br/>$$<br/>\begin{array}{|rrrr|r|r}<br/>1,1 &amp; 1,2 &amp; 1,3 &amp; 1,4 &amp; 1,5 &amp; 1,6 \\<br/>2,1 &amp; 2,2 &amp; 2,3 &amp; 2,4 &amp; 2,5 &amp; 2,6 \\<br/>3,1 &amp; 3,2 &amp; 3,3 &amp; 3,4 &amp; 3,5 &amp; 3,6 \\<br/>4,1 &amp; 4,2 &amp; 4,3 &amp; 4,4 &amp; 4,5 &amp; 4,6 \\<br/>\hline 5,1 &amp; 5,2 &amp; 5,3 &amp; 5,4 &amp; 5,5 &amp; 5,6 \\<br/>\hline 6,1 &amp; 6,2 &amp; 6,3 &amp; 6,4 &amp; 6,5 &amp; 6,6<br/>\end{array}<br/>$$<br/>$\therefore \quad$ Required number of exhausistance events $=(6-1) \times(6-1)=5 \times 5=25$<br/>$\therefore \quad$ Option (c) is correct.</div>


title: in-throwing-of-two-dice-what-is-the-number-of-exhaustive-events
slug: in-throwing-of-two-dice-what-is-the-number-of-exhaustive-events-54029
question: <div class="question">In throwing of two dice, what is the number of exhaustive events ?</div>
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2006 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">36</span> </div>
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">6</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">36</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">18</span> </li> </ul>

answer:
<div class="solution">A dice has six faces. So, in throwing of two dice, the number of exhaustive events is $6 \times 6=36$.</div>


title: in-tossing-three-coins-at-a-time-what-is-the-probability-of-getting-at-most-one-head
slug: in-tossing-three-coins-at-a-time-what-is-the-probability-of-getting-at-most-one-head-73990
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In tossing three coins at a time, what is the probability of getting at most one head?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3}{8}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{7}{8}$</span> </li><li class="correct"> <span class="option-label">C</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">D</span> <span class="option-data">$\frac{1}{8}$</span> </li> </ul>

answer:
<div class="solution">Possible samples are as follows $\{$ HHH, HTH, HHT, THH, TTH, THT, HTT, TTT\}<br/>Let $A$ be the event of getting one head. Let $\mathrm{B}$ be the event of getting no head. Favourable outcome for<br/>$A=\{T T H, T H T, H T T\}$<br/>Favourable outcome for<br/>$$<br/>B=\{T T T\}<br/>$$<br/>Total no. of outcomes $=8$<br/>$$<br/>\therefore \quad P(A)=\frac{3}{8}, P(B)=\frac{1}{8}<br/>$$<br/>$\therefore$ Required probability $=$ Probability of getting one head<br/>+ Probability of getting no head<br/>$$<br/>=P(A)+P(B)=\frac{3}{8}+\frac{1}{8}=\frac{4}{8}=\frac{1}{2}<br/>$$</div>


tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-triangle-abc-if-c-o-s-2-a-c-o-s-2-b-c-o-s-2-c-s-i-n-2-a-s-i-n-2-b-s-i-n-2-c-2-then-the-triangle-is

slug:
in-triangle-abc-if-c-o-s-2-a-c-o-s-2-b-c-o-s-2-c-s-i-n-2-a-s-i-n-2-b-s-i-n-2-c-2-then-the-triangle-is-92293

question:
<div class="question">In triangle $\mathrm{ABC}$, if $\frac{\sin ^{2} \mathrm{~A}+\sin ^{2} \mathrm{~B}+\sin ^{2} \mathrm{C}}{\cos ^{2} \mathrm{~A}+\cos ^{2} \mathrm{~B}+\cos ^{2} \mathrm{C}}=2$ then the<br/>triangle is</div>

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

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

answer:
<div class="solution">Given, $\frac{\sin ^{2} A+\sin ^{2} B+\sin ^{2} C}{\cos ^{2} A+\cos ^{2} B+\cos ^{2} C}=2$.<br/>Let us take $\mathrm{A}=30^{\circ}, \mathrm{B}=60^{\circ}, \mathrm{C}=90^{\circ}$<br/>$\frac{\sin ^{2} 30^{\circ}+\sin ^{2} 60^{\circ}+\sin ^{2} 90^{\circ}}{\cos ^{2} 30^{\circ}+\cos ^{2} 60^{\circ}+\cos ^{2} 90^{\circ}}$<br/>$=\frac{\frac{1}{4}+\frac{3}{4}+1}{\frac{3}{4}+\frac{1}{4}+0}=\frac{1+1}{1}=\frac{2}{1}=2$<br/>So, the given triangle is right-angled triangle.</div>


title: in-vertebrates-the-notochord-is-modified-into
slug: in-vertebrates-the-notochord-is-modified-into-97426
question: <div class="question">In vertebrates, the notochord is modified into</div>
tags: ['Biology', 'Animal Kingdom', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Vertebral column</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Centrum of vertebrae</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Body of vertebrae</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Transverse process of vertebrae</span> </li> </ul>

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

answer:
<div class="solution">The members of subphylum vertebrata possess notochord during the embryonic period. The notochord is replaced by a cartilaginous or bony vertebral column in the adult. Besides the basic chordate characters, vertebrates have a ventral muscular heart with two, three or four chambers, kidneys for excretion and osmoregulation and paired appendages which may be fins or limbs.</div>


title: in-werners-theory-what-is-the-typical-nature-of-the-secondary-valences
slug: in-werners-theory-what-is-the-typical-nature-of-the-secondary-valences-33856
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In Werner's theory, what is the typical nature of the secondary valences?</div>

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

answer:
<div class="solution">Secondary valences in Werner's theory are non-ionizable and are typically satisfied by neutral molecules.</div>


title: in-what-ratio-does-the-line-y-x-2-0-cut-the-line-joining-3-1-and-8-9
slug: in-what-ratio-does-the-line-y-x-2-0-cut-the-line-joining-3-1-and-8-9-31304
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2007 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$2: 3$</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">In what ratio does the line $\mathrm{y}-\mathrm{x}+2=0$ cut the line joining $(3,-1)$ and $(8,9) ?$</div>

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

answer:
<div class="solution">Let the point of intersection divide the line segment joining points, $(3,-1)$ and $(8,9)$ in $\mathrm{k}: 1$ ratio then:<br/>The point is $\left(\frac{8 \mathrm{k}+3}{\mathrm{k}+1}, \frac{9 \mathrm{k}-1}{\mathrm{k}+1}\right)$<br/>Since this point lies on the line $\mathrm{y}-\mathrm{x}+2=0$<br/>We have, $\frac{9 \mathrm{k}-1}{\mathrm{k}+1}-\frac{8 \mathrm{k}+3}{\mathrm{k}+1}+2=0$<br/>$=\frac{9 \mathrm{k}-1-8 \mathrm{k}-3}{\mathrm{k}+1}+2=0=\frac{\mathrm{k}-4}{\mathrm{k}+1}+2=0$<br/>$=\mathrm{k}-4+2 \mathrm{k}+2=0=3 \mathrm{k}-2=0$<br/>$\mathrm{k}=\frac{2}{3}: 1$ i.e. $2: 3$</div>


title: in-which-disease-does-mosquitotransmitted-pathogen-cause-chronic-inflammation-of-lymphatic-vessels
tags: ['Biology', 'Human Health and Diseases', 'NEET', 'NEET 2018']
source_db: MarksBatch2_P1.db
slug:
in-which-disease-does-mosquitotransmitted-pathogen-cause-chronic-inflammation-of-lymphatic-vessels-48255

question:
<div class="question">In which disease does mosquito-transmitted pathogen cause chronic inflammation of lymphatic vessels?</div>

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

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

answer:
<div class="solution"><p dir="ltr">Elephantiasis, also known as lymphatic filariasis, is a very rare condition that’s spread by mosquitoes (<em>Culex</em>).<br/>The most common symptom of elephantiasis is swelling of body parts. The swelling tends to happen in the: legs, genitals, breasts, arms.<br/>The legs are the most commonly affected area. The swelling and enlargement of body parts can lead to pain and mobility issues. The skin is also affected and may be: dry, thick, ulcerated, darker than normal and pitted.<br/>Some people experience additional symptoms, such as fever and chills. Elephantiasis affects the immune system. People with this condition are also at increased risk for a secondary infection.</p><p dir="ltr">Ascariasis is caused by the helminth <em>Ascaris</em>, commonly called a roundworm. Amoebiasis is caused by the pathogen <em>Entamoeba histolytica</em>. It causes a form of dysentery (also called amoebic dysentery). Both of these diseases are transmitted through contaminated food and water. Ringworm diseases are caused by fungi belonging to the genus <em>Microsporum</em>, <em>Trichophyton</em>, <em>Epidermaphyton. </em>They are transmitted through soil or personal items of infected people.</p></div>


tags: ['Chemistry', 'Biomolecules', 'AP EAMCET', 'AP EAMCET 2023 (18 May Shift 2)']
source_db: MarksBatch2_P1.db
title:
in-which-of-the-following-amino-acids-oh-group-is-present-beginarraycccc-lysine-serine-tyrosine-valine-a-b-c-d-endarray

slug:
in-which-of-the-following-amino-acids-oh-group-is-present-beginarraycccc-lysine-serine-tyrosine-valine-a-b-c-d-endarray-76439

question:
<div class="question">In which of the following amino acids - $\mathrm{OH}$ group is present?<br/>\begin{array}{cccc} <br/>Lysine &amp; Serine &amp; Tyrosine &amp; Valine \\<br/>A &amp; B &amp; C &amp; D<br/>\end{array}</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/rSTqGvHa1RoiCHqwkaL4yKUMJf-Rh4C_JcZNFOWWmUQ.original.fullsize.png"/><br/></div>


title: in-which-of-the-following-aspect-pcr-is-not-leading-over-gene-cloning
slug: in-which-of-the-following-aspect-pcr-is-not-leading-over-gene-cloning-62338
question: <div class="question">In which of the following aspect PCR is not leading over gene cloning ?</div>
tags: ['Biology', 'Biotechnology - Principles and Processes', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Efficiency</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Less user's skill</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Error probability</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Less expensive</span> </li> </ul>

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

answer:
<div class="solution">In Error probability aspect PCR is not leading over gene cloning. If standard PCR conditions do not yield the desired amplicon, PCR optimization is necessary to attain better results. The stringency of a reaction may be modulated such that the specificity is adjusted by altering variables (e.g., reagent concentrations, cycling conditions) that affect the outcome of the amplicon profile. For example, if the reaction is not stringent enough, many spurious amplicons will be generated with variable lengths. If the reaction is too stringent, no product will be produced. Troubleshooting PCR reactions may be a frustrating endeavor at times. However, careful analysis and a good understanding of the reagents used in a PCR experiment can reduce the amount of time and trials needed to obtain the desired results. Of all the considerations that impact PCR stringency, titration of Mg2+ and/or manipulating annealing temperatures likely will solve most problems. However, before changing anything, be sure that an erroneous result was not due to human error. Start by confirming all reagents were added to a given reaction and that the reagents were not contaminated.</div>


title: in-which-of-the-following-cartilaginous-ring-support-will-not-be-observed
slug: in-which-of-the-following-cartilaginous-ring-support-will-not-be-observed-67783
tags: ['Biology', 'Breathing and Exchange of Gases', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In which of the following cartilaginous ring support will not be observed?</div>

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

answer:
<div class="solution">Cartilaginous ring structures are found the tubes of the respiratory system to prevent its collapse. It is present in the trachea, two initial branches of bronchi along with the secondary and tertiary bronchi. The initial bronchioles also have it. The terminal bronchioles are not having any rings and they give rise to number of thing vascularized structures called alveoli. The terminal bronchi is also called as the respiratory bronchioles.</div>


title: in-which-of-the-following-cases-a-chemical-reaction-is-possible
slug: in-which-of-the-following-cases-a-chemical-reaction-is-possible-35023
question: <div class="question">In which of the following cases a chemical reaction is possible?</div>
tags: ['Chemistry', 'Electrochemistry', 'KCET', 'KCET 2020']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{ZnSO}_{4}(a q)$ is placed in a copper vessel</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{AgNO}_{3}$ solution is stirred with a copper spoon</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Conc. $\mathrm{HNO}_{3}$ is stored in a platinum vessel</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">gold ornaments are washed with dil. $\mathrm{HCl}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{AgNO}_{3}$ solution is stirred with a copper spoon</span> </div>

answer:
<div class="solution">A chemical reaction is possible when $\mathrm{AgNO}_{3}$ solution is stirred with copper spoon as copper has lesser positive value of standard electrode reduction potential as compared to Ag.<br/>The reaction will be,<br/>$2 \mathrm{AgNO}_{3}+\mathrm{Cu} \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}+2 \mathrm{Ag}$</div>


tags: ['Biology', 'Principles of Inheritance and Variation', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-which-of-the-following-chromosomal-disorders-do-we-observe-the-features-like-a-long-furrowed-tongue-and-short-stature

slug:
in-which-of-the-following-chromosomal-disorders-do-we-observe-the-features-like-a-long-furrowed-tongue-and-short-stature-82981

question:
<div class="question">In which of the following chromosomal disorders do we observe the features like a long furrowed tongue and short stature?</div>

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

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

answer:
<div class="solution"><table border="1"><tr><td> Syndrome</td><td> Chromosomal set up</td><td> Features</td></tr><tr><td> <math><mn>1</mn><mo>.</mo></math> Downâs Syndrome (first described by Langdon Down In 1866)</td><td> Trisomy of Chromosome number 21</td><td> - Short statured with small round head. - Long and furrowed tongue. - Partially open mouth. - Physical, mental and psychomotor development retarded.</td></tr><tr><td> <math><mn>2</mn><mo>.</mo></math> Klinefelterâs syndrome</td><td> Trisomy of sex chromosome (44 + XXY)</td><td> - Such males have some feminine features like gynaecomastia (development of breast), etc. - Sterile.</td></tr><tr><td> <math><mn>3</mn><mo>.</mo></math> Turnerâs  syndrome</td><td> Monosomy of sex chromosome (44 + XO)</td><td> - Such females have rudimentary ovaries and lack other secondary sexual characters. - Sterile.</td></tr></table></div>


title: in-which-of-the-following-locations-are-sacred-groves-found
slug: in-which-of-the-following-locations-are-sacred-groves-found-17462
question: <div class="question">In which of the following locations are sacred groves found?</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Khasi and Jaintia Hills in Meghalaya</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Aravalli Hills of Rajasthan</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Sarguja, Chanda and Bastar areas of Madhya Pradesh</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">In many cultures, tracts of forest were set aside, and all the trees and wildlife within were venerated and given total protection. Such sacred groves are found in Khasi and Jaintia hills in Meghalaya; Aravalli hills in Rajasthan; Western Ghat regions of Karnataka and Maharashtra and the Sarguja, Chanda and Bastar areas of Madhya Pradesh. In Meghalaya, the sacred groves are the last refuges for a large number of rare and threatened plants. </div>


tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-which-of-the-following-method-of-biodiversity-conservation-tracts-of-forest-are-set-aside-and-all-the-trees-and-wildlife-within-are-venerated-and-g

slug:
in-which-of-the-following-method-of-biodiversity-conservation-tracts-of-forest-are-set-aside-and-all-the-trees-and-wildlife-within-are-venerated-and-g-73481

question:
<div class="question">In which of the following method of biodiversity conservation, tracts of forest are set aside, and all the trees and wildlife within are venerated and given total protection?</div>

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

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

answer:
<div class="solution">India has also a history of religious and cultural traditions that emphasize the protection of nature. In many cultures, tracts of forest were set aside, and all the trees and wildlife within were venerated and given total protection. Such sacred groves are found in Khasi and Jaintia hills in Meghalaya, Aravalli hills of Rajasthan, Western Ghat regions of Karnataka and Maharashtra and the Sarguja, Chanda and Bastar areas of Madhya Pradesh. In Meghalaya, the sacred groves are the last refuges for a large number of rare and threatened plants.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-which-of-the-following-reactions-standard-entropy-change-s-is-positive-and-standard-gibbs-energy-change-g-decreases-sharply-with-increasing-tempera-1

slug:
in-which-of-the-following-reactions-standard-entropy-change-s-is-positive-and-standard-gibbs-energy-change-g-decreases-sharply-with-increasing-tempera-1-36349

question:
<div class="question">In which of the following reactions, standard entropy change $\left(\Delta \mathrm{S}^{\circ}\right)$ is positive and standard Gibb's energy change $\left(\Delta \mathrm{G}^{\circ}\right)$ decreases sharply with increasing temperature?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g})$</span> </div>

answer:
<div class="solution">Since, in the first reaction gaseous products are forming from solid carbon hence entropy will increase i.e. $\Delta \mathrm{S}=+\mathrm{ve}$.
<br/>$\mathrm{C}(\mathrm{gr} .)+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g}) ; \Delta \mathrm{S}^{\circ}=+\mathrm{ve}$
<br/>Since, $\Delta \overrightarrow{\mathrm{G}^{\circ}}=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}$ hence the value of
<br/>$\Delta$ G decrease on increasing temperature.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P1.db
title:
in-which-of-the-following-reactions-standard-entropy-change-s-is-positive-and-standard-gibbs-energy-change-g-decreases-sharply-with-increasing-tempera

slug:
in-which-of-the-following-reactions-standard-entropy-change-s-is-positive-and-standard-gibbs-energy-change-g-decreases-sharply-with-increasing-tempera-42406

question:
<div class="question">In which of the following reactions, standard entropy change $\left(\Delta \mathrm{S}^{\circ}\right)$ is positive and standard Gibb's energy change $\left(\Delta \mathrm{G}^{\circ}\right)$ decreases sharply with increasing temperature?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g})$</span> </div>

answer:
<div class="solution">Since, in the first reaction gaseous products are forming from solid carbon hence entropy will increase i.e. $\Delta \mathrm{S}=+\mathrm{ve}$.
<br/>$\mathrm{C}(\mathrm{gr} .)+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g}) ; \Delta \mathrm{S}^{\circ}=+\mathrm{ve}$
<br/>Since, $\Delta \overrightarrow{\mathrm{G}^{\circ}}=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}$ hence the value of
<br/>$\Delta$ G decrease on increasing temperature.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET', 'NEET 2012 (Screening)']
source_db: MarksBatch2_P1.db
title:
in-which-of-the-following-reactions-standard-reaction-entropy-changes-s-is-positive-and-standard-gibbs-energy-change-g-decreases-sharply-with-increasi

slug:
in-which-of-the-following-reactions-standard-reaction-entropy-changes-s-is-positive-and-standard-gibbs-energy-change-g-decreases-sharply-with-increasi-63957

question:
<div class="question">In which of the following reactions, standard reaction entropy changes $\left(\Delta S^{\circ}\right)$ is positive and standard Gibb's energy change $\left(\Delta G^{\circ}\right)$ decreases sharply with increasing temperature?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}(g)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Mg}(s)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{MgO}(s)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2} \mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \frac{1}{2} \mathrm{CO}_2(g)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}(g)$</span> </div>

answer:
<div class="solution">Among the given reactions only in the case of
<br/>$\mathrm{C} \text { (graphite) }+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g})$
<br/>entropy increases because randomness (disorder) increases. Thus, standard entropy change $\left(\Delta S^{\circ}\right)$ is positive.
<br/>Moreover, it is a combustion reaction and all the combustion reactions are generally exothermic, i.e., $\Delta H^{\circ}=-$ ve
<br/>We know that
<br/>$\begin{aligned}
<br/>&amp; \Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ} \\
<br/>&amp; \Delta G^{\circ}=-v \mathrm{v}-T(+\mathrm{ve})
<br/>\end{aligned}$
<br/>Thus, as the temperature increases, the value of $\Delta G^{\circ}$ decreases.</div>


title: in-which-of-the-following-sporophylls-may-form-distinct-compact-structures-called-strobili-is-found
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P1.db
slug:
in-which-of-the-following-sporophylls-may-form-distinct-compact-structures-called-strobili-is-found-84051

question:
<div class="question">In which of the following, sporophylls may form distinct compact structures called strobili is found</div>

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

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

answer:
<div class="solution">The sporophytes bear sporangia that are subtended by leaf-like appendages called sporophylls. In some cases, sporophylls may form distinct compact structures called strobili or cones (<em>Selaginella, Equisetum</em>).</div>


title: in-which-of-the-following-this-kind-of-vascular-bundle-can-be-seen
slug: in-which-of-the-following-this-kind-of-vascular-bundle-can-be-seen-65058
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/Conjoint.png" style="width: 275px; height: 206px;"/><br/> <br/>
In which of the following, this kind of vascular bundle can be seen?</div>

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

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

answer:
<div class="solution">A large number of vascular bundles are arranged in a ring; the âringâ arrangement of vascular bundles is a characteristic of dicot stem. Each vascular bundle is conjoint, open, and with endarch protoxylem.</div>


title: in-which-of-the-following-tyndall-effect-is-not-observed
slug: in-which-of-the-following-tyndall-effect-is-not-observed-27784
question: <div class="question">In which of the following, Tyndall effect is not observed?</div>
tags: ['Chemistry', 'Surface Chemistry', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Smoke</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Emulsion</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Sugar solution</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Gold sol</span> </li> </ul>

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

answer:
<div class="solution">Tyndall effect is not observed in sugar solution because it is a true homogeneous solution. Colloidal solutions show Tyndall effect.</div>


title: in-which-of-the-following-will-be-observed-the-webbed-neck-condition
slug: in-which-of-the-following-will-be-observed-the-webbed-neck-condition-25229
question: <div class="question">In which of the following will be observed the webbed neck condition?</div>
tags: ['Biology', 'Principles of Inheritance and Variation', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">XO</span> </div>
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">XXY</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">XY</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">XO</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">XXX</span> </li> </ul>

answer:
<div class="solution">The chromosomal disorder occurs when there is an addition or deletion of the chromosome in the individual. In case of trisomy of the <math><msup><mrow><mn>21</mn></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi></mrow></msup></math> chromosome, Down's syndrome will be observed. Turner's syndrome is a type of chromosomal disorder occurring due to the loss of one X chromosome resulting in the genotype as <math><mn>44</mn><mo>+</mo><mi mathvariant="normal">X</mi><mi mathvariant="normal"> </mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal"> </mi><mn>44</mn><mo>+</mo><mi mathvariant="normal">X</mi><mi mathvariant="normal">O</mi></math>.<br/><br/>Such females are characterized by stunted height and webbed-neck. They are sterile as ovaries are rudimentary and lack secondary sexual characteristics.<br/><br/>XXY condition is called Klinefelter's syndrome where an individual has an extra copy of X chromosome.</div>


title: in-which-one-of-the-following-cases-would-you-except-to-get-a-negative-correlation
slug: in-which-one-of-the-following-cases-would-you-except-to-get-a-negative-correlation-75092
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2018 (Phase 2)']
answer: <div class="solution">By definition.</div>
source_db: MarksBatch2_P1.db
question:
<div class="question">In which one of the following cases would you except to get a negative correlation?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Insurance companies profits and the number of claims they have to pay</span> </div>


title: in-which-one-of-the-following-intervals-is-the-function-f-x-x-2-5-x-6-decreasing
slug: in-which-one-of-the-following-intervals-is-the-function-f-x-x-2-5-x-6-decreasing-54867
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In which one of the following intervals is the function $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-5 \mathrm{x}+6$ decreasing?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$(-\infty, 2]$</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">$[3, \infty]$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(-\infty, \infty)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(2,3)$</span> </li> </ul>

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

answer:
<div class="solution">$\Rightarrow f^{\prime}(x)=x^{2}-5 x+6$<br/>$\Rightarrow \quad f^{\prime}(x)   &lt; 0$<br/>$\Rightarrow \quad 2 x-5 &lt; 0$<br/>$\Rightarrow \quad x &lt; \frac{5}{2}$<img src="https://cdn-question-pool.getmarks.app/pyq/nda/CGQK9pxn-vCcq5zcbKblCHesK9qUOKUyGzezYt4CR0w.original.fullsize.png"/><br/><br/>Hence, $f(x)$ is decreasing in $(-\infty, 2.5]$</div>


tags: ['Biology', 'Structural Organisation in Animals', 'NEET', 'NEET 2007']
source_db: MarksBatch2_P1.db
title:
in-which-one-of-the-following-preparations-are-you-likely-to-come-across-cell-junctions-most-frequently

slug:
in-which-one-of-the-following-preparations-are-you-likely-to-come-across-cell-junctions-most-frequently-14473

question:
<div class="question">In which one of the following preparations are you likely to come across cell junctions most frequently?</div>

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

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

answer:
<div class="solution">Cell junctions are especially abundant in epithelial tissues. They consist of protein complexes and provide contact between neighbouring cells, between a cell and the extracellular matrix, or they built up the paracellular barrier of epithelia and control the paracellular transport. The other three (thrombocytes, tendon and hyaline cartilage) belongs to connective tissue. Thrombocytes or platelets aid the formation of blood clots by releasing various protein substances. Tendon attaches a muscle to a bone and hyaline cartilage gives flexibility and support at the joints.<br/>Related Theory<br/>Ciliated epithelium is a region of epithelium consisting of columnar or cuboidal cells bearing hairlike appendages that are capable of beating rapidly. Ciliated epithelium performs the function of moving particles or fluid over the epithelial surface in such structures as the trachea, bronchial tubes, and nasal cavities. It ofien occurs in the vicinity of mucus-secreting goblet cells.</div>


tags: ['Biology', 'Biological Classification', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-which-one-of-the-following-the-genus-name-its-two-characters-and-its-phylum-are-incorrectly-matched

slug:
in-which-one-of-the-following-the-genus-name-its-two-characters-and-its-phylum-are-incorrectly-matched-51392

question:
<div class="question">In which one of the following the genus name, its two characters and its phylum are incorrectly matched?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 100%;"> <thead> <tr> <th scope="col"> </th> <th scope="col">Genus name</th> <th scope="col">Two characters</th> <th scope="col"> </th> </tr> </thead> <tbody> <tr> <td>a)</td> <td> <em>Pila</em></td> <td> <math><mrow><mfrac><mrow><mtext>   </mtext> <mtext>Body Segmented</mtext> </mrow> <mrow> <mtext>        Mouth with radula</mtext> </mrow> </mfrac> </mrow> </math></td> <td> Mollusca</td> </tr> </tbody></table></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 100%;"> <thead> <tr> <th scope="col"> </th> <th scope="col">Genus name</th> <th scope="col">Two characters</th> <th scope="col"> </th> </tr> </thead> <tbody> <tr> <td>b)</td> <td> <em>Asterias</em></td> <td> <math> <mrow><mfrac><mrow><mtext>   </mtext> <mtext>Spiny Skinned</mtext> </mrow> <mrow> <mtext>           Water vascular system</mtext> </mrow> </mfrac> </mrow> </math></td> <td> Echinoermata</td> </tr> </tbody></table></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 100%;"> <thead> <tr> <th scope="col"> </th> <th scope="col">Genus name</th> <th scope="col">Two characters</th> <th scope="col"> </th> </tr> </thead> <tbody> <tr> <td>c)</td> <td> <em>Sycon</em></td> <td> <math> <mrow><mfrac><mrow><mtext>   </mtext> <mtext>Pore bearing</mtext> </mrow> <mrow> <mtext>      Canal system</mtext> </mrow> </mfrac> </mrow> </math></td> <td> Porifera</td> </tr> </tbody></table></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 100%;"> <thead> <tr> <th scope="col"> </th> <th scope="col">Genus name</th> <th scope="col">Two characters</th> <th scope="col"> </th> </tr> </thead> <tbody> <tr> <td>d)</td> <td> <em>Periplaneta</em></td> <td> <math> <mrow><mfrac><mrow><mtext>   </mtext> <mtext>Jointed appendages</mtext> </mrow> <mrow> <mtext>      Chitinous exoskeleton</mtext> </mrow> </mfrac> </mrow> </math></td> <td> Arthropoda</td> </tr> </tbody></table></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><table align="center" border="1" cellpadding="1" cellspacing="1" style="width: 100%;"> <thead> <tr> <th scope="col"> </th> <th scope="col">Genus name</th> <th scope="col">Two characters</th> <th scope="col"> </th> </tr> </thead> <tbody> <tr> <td>a)</td> <td> <em>Pila</em></td> <td> <math><mrow><mfrac><mrow><mtext>   </mtext> <mtext>Body Segmented</mtext> </mrow> <mrow> <mtext>        Mouth with radula</mtext> </mrow> </mfrac> </mrow> </math></td> <td> Mollusca</td> </tr> </tbody></table></span> </div>

answer:
<div class="solution">Molluscs are soft-bodied animals, bilaterally symmetric, triploblastic and coelomate. Their soft body is covered by a calcareous shell and is unsegmented with a distinct head, muscular foot and visceral hump.<br/>e.g. Pila (apple snail), sepia (cuttle fish), pinctada (pearl oyster), etc. </div>


title: in-which-part-of-the-plant-is-potassium-required-in-more-abundant-quantities
slug: in-which-part-of-the-plant-is-potassium-required-in-more-abundant-quantities-69180
tags: ['Biology', 'Mineral Nutrition', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In which part of the plant is Potassium required in more abundant quantities?</div>

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

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

answer:
<div class="solution">In plants, Potassium is required in more abundant quantities in the meristematic tissues, buds, leaves and root tips</div>


title: in-which-region-of-pbr322-5-gaattc-3-sequence-will-be-present
slug: in-which-region-of-pbr322-5-gaattc-3-sequence-will-be-present-82389
question: <div class="question">In which region of pBR322, 5' GAATTC 3' sequence will be present?</div>
tags: ['Biology', 'Biotechnology - Principles and Processes', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">rop</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><msup><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow><mrow><mi mathvariant="normal">R</mi></mrow></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><msup><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">R</mi></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">none 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">none of these</span> </div>

answer:
<div class="solution">Bolivar and Rodriguez inserted genes for antibiotic resistance in a plasmid from E.coli to form a new plasmid called pBR 322. pBR322 is one of the standard cloning vectors widely used in gene cloning experiments. pBR322 has the following regions ori: Region for origin for replication. rop: This region codes for the proteins involved in the replication of plasmid. This region also has recognition sequence for restriction endonuclease Pvu II (<em>Proteus vulgaris</em>). tetR - This region provides resistance against the antibiotic tetracycline. This region also has recognition sequence for restriction endonucleases: Bam H I from <em>Bacillus amyloliquefaciens</em> and Sal I from <em>Streptomyces albus.</em> ampR - This region provides resistance against the antibiotic ampicillin. This region also has recognition sequence for restriction endonucleases: Pvu I from <em>Proteus vulgaris</em> and Pst I from <em>Providencia stuarti.</em> Apart from these, pBR 322 also shows recognition sequence for restriction endonucleases: EcoR I (its recognition site is 5' GAATTC 3') from <em>Escherichia coli</em>, Hind III from <em>Haemophilus influenza</em> and Cla I from <em>Caryophanon latum.<br/><br/><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/pBR322-Pic.jpg" style="max-width:100%; object-fit:contain"/></em></div>


title: in-x-1-d-x-in-x-2-d-x-is-equal-to
slug: in-x-1-d-x-in-x-2-d-x-is-equal-to-37506
tags: ['Mathematics', 'Indefinite Integration', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">$\int(\operatorname{In} x)^{-1} \mathrm{~d} x-\int(\operatorname{In} x)^{-2} \mathrm{~d} x$ is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$x(\operatorname{In} x)^{-1}+c$</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">B</span> <span class="option-data">$x(\operatorname{In} x)^{-2}+c$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$x(\operatorname{In} x)+c$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$x(\ln x)^{2}+c$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x(\operatorname{In} x)^{-1}+c$</span> </div>

answer:
<div class="solution">$\int(\ln x)^{-1} \mathrm{dx}-\int(\ln x)^{-2} \mathrm{dx}$<br/>$=\int\left[\frac{1}{\ell^{n} x}-\frac{1}{(\ell n x)^{2}}\right] \cdot d x$<br/>Put $\ell \mathrm{n} \mathrm{x}=\mathrm{t} \Rightarrow \mathrm{x}=\mathrm{e}^{\mathrm{t}}$<br/>$\mathrm{dx}=\mathrm{e}^{\mathrm{l}} \cdot \mathrm{dt}$<br/>$\therefore \int\left[\frac{1}{\ln x}-\frac{1}{(\ell n x)^{2}}\right] \mathrm{dx}=\int\left(\frac{1}{t}-\frac{1}{t^{2}}\right) \cdot \mathrm{e}^{\mathrm{t}} \cdot \mathrm{dt}$<br/>$=\int \mathrm{e}^{\mathrm{t}} \cdot\left(\frac{1}{\mathrm{t}}-\frac{1}{\mathrm{t}^{2}}\right) \mathrm{dt}$<br/>$=\frac{\mathrm{e}^{\mathrm{t}}}{\mathrm{t}}+\mathrm{c}=\frac{\mathrm{x}}{\ln \mathrm{x}}+\mathrm{c}$<br/>$=x(\ln x)^{-1}+c$</div>


title: incorrect-statement-for-tyndall-effect-is
slug: incorrect-statement-for-tyndall-effect-is-28235
question: <div class="question">Incorrect statement for Tyndall effect is</div>
tags: ['Chemistry', 'Surface Chemistry', 'JEE Main', 'JEE Main 2022 (25 Jun Shift 1)']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The diameter of the dispersed particles is much smaller than the wavelength of the light used.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">It is used to distinguish a true solution from a colloidal solution.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">During projection of movies in the cinemas hall, Tyndall effect is noticed.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The diameter of the dispersed particles is much smaller than the wavelength of the light used.</span> </div>

answer:
<div class="solution"><p>Tyndall effect is observed only when the following two conditions are satisfied.</p><p>(i) The diameter of the dispersed particles is not much smaller than the wavelength of the light used; and</p><p>(ii) The refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude.</p><p>This is a characteristic property of the colloid solutions.</p></div>


title: industrial-melanism-is-an-example-of-2
slug: industrial-melanism-is-an-example-of-2-74785
question: <div class="question">Industrial melanism is an example of:</div>
tags: ['Biology', 'Evolution', 'NEET', 'NEET 2015 (Phase 2)']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Natural selection</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Mutation</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Neo Lamarckism</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neo Darwinism</span> </li> </ul>

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

answer:
<div class="solution">One of the most striking examples, which demonstrates the action of natural selection, is the industrial melanism in England. The peppered moth <em>Biston betularia</em>, with a dull grey colour, was abundant in England before the industrial revolution. A black coloured form of the same moth (melanic, a dominant mutant differing in a single gene), <em>Biston carbonaria</em>, was very rare. After industrial revolution, the proportion of <em>Biston carbonaria</em>, increased to almost 90 percent.</div>


title: initiation-of-lateral-roots-and-vascular-cambium-during-secondary-growth-takes-place-in-cells-of
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2022 (Phase 2)']
source_db: MarksBatch2_P1.db
slug:
initiation-of-lateral-roots-and-vascular-cambium-during-secondary-growth-takes-place-in-cells-of-18322

question:
<div class="question">Initiation of lateral roots and vascular cambium during secondary growth takes place in cells of :</div>

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

answer:
<div class="solution">In Dicot root, the vascular bundles are radial, in which vascular cambium is purely secondary and arise from pericycle with lateral roots as well. Lateral roots thus have endogenous origin.</div>


title: inner-lining-of-blood-vessels-is-formed-by
slug: inner-lining-of-blood-vessels-is-formed-by-14011
question: <div class="question">Inner lining of blood vessels is formed by</div>
tags: ['Biology', 'Structural Organisation in Animals', 'JIPMER', 'JIPMER 2005']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">ciliated epithelium</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">squamous epithelium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">cubical epithelium</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">columnar epithelium</span> </li> </ul>

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

answer:
<div class="solution">Inner lining of blood vessels is formed by squamous epithelium. Spuamous epithelium consists of a layer of thin, flat, scale-like cells with prominent nuclei. The cell have irregular boundaries that fit closely into those of neighbouring cells.</div>


title: insulin-cannot-be-orally-administered-to-a-diabetic-patient-because
slug: insulin-cannot-be-orally-administered-to-a-diabetic-patient-because-94216
question: <div class="question">Insulin cannot be orally administered to a diabetic patient because</div>
tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">It is bitter in taste</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">It is a glycoprotein</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">It is proteinaceous</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 very expensive to get oral form of insulin</span> </li> </ul>

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

answer:
<div class="solution">Insulin is a hormone secreted by beta cells of Islets of Langerhans of Pancreas. Its main function is to transport glucose from blood to the cells. In some individuals the gland is not able to secrete sufficient amounts of Insulin as a result of which the cellular uptake of glucose is affected. This is known as Insulin dependant Diabetes mellitus. In such individuals artificial Insulin is given so that the cells do not starve of glucose. This cannot be given orally as Insulin is proteinaceous in nature.  Being a protein it is easily digestible in stomach due to enzyme Pepsin and in small intestine due to Trypsin and Dipeptidases. Thus insulin breaks before entering the bloodstream and this makes it ineffective.</div>


title: interfascicular-cambium-and-cork-cambium-are-formed-due-to
slug: interfascicular-cambium-and-cork-cambium-are-formed-due-to-80540
question: <div class="question">Interfascicular cambium and cork cambium are formed due to</div>
tags: ['Biology', 'Anatomy of Flowering Plants']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>cell division<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>cell differentiation<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>cell dedifferentiation <br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>redifferentiation</span> </li> </ul>

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

answer:
<div class="solution">Dedifferentiation is the phenomenon of regeneration of permanent tissue to become meristematic. Cork cambium, wound cambium and interfascicular vascular cambium are the examples of secondary meristems which are always produced through dedifferentiation.</div>


title: interfascicular-cambium-is-present-between
slug: interfascicular-cambium-is-present-between-43928
question: <div class="question">Interfascicular cambium is present between :</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2022 (Phase 2)']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary xylem and primary phloem</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Pericycle and endodermis</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Two vascular bundles</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 xylem and secondary phloem</span> </li> </ul>

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

answer:
<div class="solution">Inter fascicular cambium is present between two vascular bundles and formed from de differentiation of permanent tissues in medullary rays. Interfascicular cambium is present in between primary xylem and primary phloem.</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main', 'JEE Main 2024 (01 Feb Shift 1)']
source_db: MarksBatch2_P1.db
title:
ionic-reactions-with-organic-compounds-proceed-through-a-homolytic-bond-cleavage-b-heterolytic-bond-cleavage-c-free-radical-formation-d-primary-free-r

slug:
ionic-reactions-with-organic-compounds-proceed-through-a-homolytic-bond-cleavage-b-heterolytic-bond-cleavage-c-free-radical-formation-d-primary-free-r-43678

question:
<div class="question"><p>Ionic reactions with organic compounds proceed through:</p><p>(A) Homolytic bond cleavage  (B) Heterolytic bond cleavage  (C) Free radical formation</p><p>(D) Primary free radical  (E) Secondary free radical</p><p>Choose the correct answer from the options given below:</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">(A) only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">(C) only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">(B) 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">(D) andÂ (E) only</span> </li> </ul>

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

answer:
<div class="solution"><p>Heterolytic fission, also known as heterolysis, is a type of bond fission in which a covalent bond between two chemical species is broken in an unequal manner, resulting in the bond pair of electrons being retained by one of the chemical species (while the other species does not retain any of the electrons from the bond pair). When a neutrally charged molecule undergoes heterolytic fission, one of the products will have a positive charge whereas the other product will have a negative charge.<br/>Polar reactions occur when two bonded atoms come apart, one taking more of the shared electrons than the other. They involve heterolytic cleavage. The result is two charged speciesâone cation and one anion.<br/>Hence,Â organic reactions which proceed through heterolytic bond cleavage are called polar reactions.</p><p>InÂ homolytic reactions, free radicals are formed and these reaction takes place in gaseous phase.</p></div>


title: iron-displaces-copper-from-its-salt-solution-because
slug: iron-displaces-copper-from-its-salt-solution-because-19276
question: <div class="question">Iron displaces copper from its salt solution, because</div>
tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Atomic number of iron is less than that of copper</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The standard reduction potential of iron is less than that of copper</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 standard reduction potential of iron is more than that of copper</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The iron salt is more soluble in water than the copper salt</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The standard reduction potential of iron is less than that of copper</span> </div>

answer:
<div class="solution">The answer to the question is (2) The standard reduction potential of iron is less than that of copper.<br/>Here's why this is the correct answer:<br/>- The standard reduction potential is a measure of a metal's tendency to gain electrons and be reduced from a cation to a metal atom in an electrochemical reaction. Metals with more negative reduction potentials are better reducing agents (more reactive) than metals with less negative or positive reduction potentials.<br/>- In the reaction between iron and copper sulfate, iron ( $\mathrm{Fe}$ ) is displacing copper $(\mathrm{Cu})$ from its salt solution $\left(\mathrm{CuSO}_4\right)$. This means iron is more reactive than copper.<br/>- Iron has a more negative standard reduction potential than copper, which means it is easier for iron to be reduced (gain electrons) than copper. This greater ease of reduction allows iron to take electrons away from the copper ions in copper sulfate, reducing the copper ions to copper metal and oxidizing itself to ferrous iron $\left(\mathrm{Fe}^{2+}\right)$.</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P1.db
title:
is-a-couple-of-layers-thick-made-of-narrow-thin-walled-and-nearly-rectangular-cells-it-cuts-off-cells-on-both-sides-the-outer-cells-differentiate-into

slug:
is-a-couple-of-layers-thick-made-of-narrow-thin-walled-and-nearly-rectangular-cells-it-cuts-off-cells-on-both-sides-the-outer-cells-differentiate-into-41779

question:
<div class="question">______ is a couple of layers thick, made of narrow, thin walled and nearly rectangular cells. It cuts off cells on both sides. The outer cells differentiate into __________ or __________ while the inner differentiate into _________ or ____________. The three together is called ____________.<br/> <br/>
Select the right sequence of words to complete the above.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Phellogen, cork, phellem, secondary cortex, phelloderm, periderm</span> </div>

answer:
<div class="solution">Phellogen is thick with a couple of layers. It is made of narrow, thin-welled and nearly rectangular cells. Phellogen cuts off cells on both sides. The outer cells differentiate into cork or phellem, whereas the inner cells differentiate into secondary cortex or phelloderm. The cork is impervious to water due to suberin deposition in the cell wall. The cells of the secondary cortex are parenchymatous. Phellogen, phellem and phelloderm are collectively known as periderm.</div>


tags: ['Physics', 'Atomic Physics', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Photon</span> </div>
source_db: MarksBatch2_P1.db
title:
is-a-discrete-packet-of-energy-related-to-electromagnetic-radiation-light-in-which-energy-is-e-which-is-proportional-to-frequency-of-radiation-v

slug:
is-a-discrete-packet-of-energy-related-to-electromagnetic-radiation-light-in-which-energy-is-e-which-is-proportional-to-frequency-of-radiation-v-11118

question:
<div class="question">____is a discrete packet of energy related to electromagnetic radiation (light), in which energy is E which is proportional to frequency of radiation $v$.</div>

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

answer:
<div class="solution">- Definition: A photon is a fundamental particle of light and other forms of electromagnetic radiation. It behaves both as a particle and as a wave, displaying characteristics of both.
<br/>- Energy and Frequency Relationship: The energy of a photon (E) is directly proportional to the frequency of the radiation \((v)\). This relationship is described by the equation \(\mathrm{E}=\) hv, where h is Planck's constant.
<br/>- Quantization of Energy: The concept of a photon arises from the quantization of energy in electromagnetic radiation. Energy is not continuous but exists in discrete packets called photons.
<br/>- Particle-like Behavior: Photons exhibit particle-like behavior, carrying a fixed amount of energy. They can interact with matter, transferring their energy and momentum in discrete units.</div>


title: is-a-taxonomic-category-and-identified-on-the-basis-of-aggregates-of-characters
slug: is-a-taxonomic-category-and-identified-on-the-basis-of-aggregates-of-characters-62886
tags: ['Biology', 'The Living World', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Order</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">_________ is a taxonomic category and identified on the basis of aggregates of characters.</div>

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


title: is-adding-a-scalar-to-a-vector-of-the-same-dimensions-a-meaningful-algebraic-operation
slug: is-adding-a-scalar-to-a-vector-of-the-same-dimensions-a-meaningful-algebraic-operation-38206
tags: ['Chemistry', 'Motion In Two Dimensions', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">Is adding a scalar to a vector of the same dimensions a meaningful algebraic operation?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Yes, because it results in a new vector with the same dimensions.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Yes, because it results in a scalar quantity.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">No, because scalar and vector quantities cannot be combined algebraically.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">No, because the dimensions of scalar and vector quantities are fundamentally different.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">No, because scalar and vector quantities cannot be combined algebraically.</span> </div>

answer:
<div class="solution">Correct Option is : (C)<br/>No, because scalar and vector quantities cannot be combined algebraically.</div>


title: is-competition-always-based-on-limiting-resources
slug: is-competition-always-based-on-limiting-resources-33161
question: <div class="question">Is competition always based on limiting resources?</div>
tags: ['Biology', 'Organisms and Populations', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">No</span> </div>
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">No</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Yes</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Sometimes</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Only in laboratory experiments</span> </li> </ul>

answer:
<div class="solution">Competition need not be based on limiting resources as in interference competition, the feeding efficiency of one species might be reduced due to the interfering and inhibitory presence of the other species, even if resources (food and space) are abundant.</div>


title: is-defined-as-an-ecological-state-of-a-species-being-unique-to-a-specific-geographic-location
slug: is-defined-as-an-ecological-state-of-a-species-being-unique-to-a-specific-geographic-location-51400
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">_________ is defined as an ecological state of a species being unique to a specific geographic location.</div>

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

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

answer:
<div class="solution">A species which is located to a specific geographic area or location is called as endemic species. Species which is brought form other geographical is called as endemic species.</div>


tags: ['Biology', 'Biodiversity and its Conservation']
options: None
correct_option: None
source_db: MarksBatch2_P1.db
title:
is-it-possible-that-productivity-and-diversity-of-a-natural-community-remains-constant-over-a-time-period-of-say-one-hundred-years

slug:
is-it-possible-that-productivity-and-diversity-of-a-natural-community-remains-constant-over-a-time-period-of-say-one-hundred-years-48724

question:
<div class="question">Is it possible that productivity and diversity of a natural community remains constant over a time period of, say one hundred years?</div>

answer:
<div class="solution">Productivity and diversity of a natural community cannot remain constant over a certain time period.<br/>This is due to the following reasons<br/>(i) In real, the natural habitat is never maintained.<br/>(ii) Resources available are never abundant, they are always in short supply or just enough.<br/>(iii) Environmental conditions for survival and reproduction are changing continuously.</div>


title: is-rubber-a-primary-metabolite-or-a-secondary-metabolite-write-four-sentences-about-rubber
slug: is-rubber-a-primary-metabolite-or-a-secondary-metabolite-write-four-sentences-about-rubber-68885
tags: ['Biology', 'Biomolecules']
options: None
correct_option: None
source_db: MarksBatch2_P1.db
question:
<div class="question">Is rubber a primary metabolite or a secondary metabolite? Write four sentences about rubber.</div>

answer:
<div class="solution">Secondary metabolites are chemicals produced by plants which do not play any [role] in growth, photosynthesis reproduction or other primary functions of the plant. Rubber (cis 1, 4-polyisopyrene) is a secondary metabolite.<br/>(i) Rubber is extracted from Hevea brasiliensis (rubber tree)<br/>(ii) It is a byproduct of the lactiferous tissue of the vessels that are in the form of latex.<br/>(iii) It contains over 400 isoprene units and thus is the largest of the terpenoids.<br/>(iv) It is elastic, water proof and a good conductor of electricity.</div>


title: isopropyl-amine-is-a
slug: isopropyl-amine-is-a-20363
question: <div class="question">Iso-propyl amine is a</div>
tags: ['Chemistry', 'General Organic Chemistry', 'MHT CET', 'MHT CET 2009']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">primary amine</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">secondary amine</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">tertiary amine</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">quaternary amine</span> </li> </ul>

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

answer:
<div class="solution">The structure of iso-propyl amine is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/GsJ8mOqpIk2f86vZzKZULdB-KGQ4SsfBV3vouwIe1UU.original.fullsize.png"/><br/><br/>It is a primary amine.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
it-has-been-found-that-if-a-and-b-play-a-game-12-times-a-wins-6-times-b-wins-4-times-and-they-draw-twice-a-and-b-take-part-in-a-series-of-3-games-the-

slug:
it-has-been-found-that-if-a-and-b-play-a-game-12-times-a-wins-6-times-b-wins-4-times-and-they-draw-twice-a-and-b-take-part-in-a-series-of-3-games-the-20346

question:
<div class="question">It has been found that if $A$ and $B$ play a game 12 times, $A$ wins 6 times, $B$ wins 4 times and they draw twice. $A$ and $B$ take part in a series of 3 games. The probability that they win alternately, is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 / 12$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$5 / 36$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$19 / 27$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5 / 27$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 / 36$</span> </div>

answer:
<div class="solution">$\mathrm{P}(\mathrm{A})=\frac{6}{12}=\frac{1}{2}, \mathrm{P}(\mathrm{B})=\frac{4}{12}=\frac{1}{3}$<br/>Req. probability $=\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2}+\frac{1}{3} \cdot \frac{1}{2} \cdot \frac{1}{3}=\frac{1}{12}+\frac{1}{18}=\frac{5}{36}$</div>


tags: ['Biology', 'Environmental Issues']
options: None
correct_option: None
source_db: MarksBatch2_P1.db
title:
it-is-a-common-practice-to-plant-trees-and-shurbs-near-the-boundary-walls-of-buildings-what-purpose-do-they-serve

slug:
it-is-a-common-practice-to-plant-trees-and-shurbs-near-the-boundary-walls-of-buildings-what-purpose-do-they-serve-63431

question:
<div class="question">It is a common practice to plant trees and shurbs near the boundary walls of buildings. What purpose do they serve?</div>

answer:
<div class="solution">There is a common practice of growing and maintaining trees and shrubs near the boundary walls of residential, and official buildings to act as a barrier for sound and keep noise pollution under control. This green belt of trees and shrub also act as an effective measure to check primary air pollutants like dust, flyash, etc.</div>


tags: ['Physics', 'Units and Dimensions']
options: None
correct_option: None
source_db: MarksBatch2_P1.db
title:
it-is-claimed-that-two-cesium-clocks-if-allowed-to-run-for-100-years-free-from-any-disturbance-may-differ-by-only-about-0025-s-what-does-this-imply-fo

slug:
it-is-claimed-that-two-cesium-clocks-if-allowed-to-run-for-100-years-free-from-any-disturbance-may-differ-by-only-about-0025-s-what-does-this-imply-fo-51975

question:
<div class="question">It is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about $0.025 \mathrm{~s}$. What does this imply for the accuracy of the standard cesium clock in measuring a time interval of $1 \mathbf{s}$ ?</div>

answer:
<div class="solution">Error in 100 years $=0.02 \mathrm{~s}$<br/>$\therefore \quad$ Error in $1 \mathrm{sec}$<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{\Delta t}{t}=\frac{0.02}{100 \times 365 \times 2.5 \times 24 \times 60 \times 60}=\frac{0.02}{3.5576 \times 10^9} \\<br/>=&amp; 0.0063 \times 10^{-9}=0.63 \times 10^{-11}<br/>\end{aligned}<br/>$$<br/>So, there is an accuracy of $1 \mathrm{~s}$ is $10^{-11} \mathrm{~s}$.</div>


title: it-is-given-that-cos-u-a-cos-b-what-is-cos-equal-to
slug: it-is-given-that-cos-u-a-cos-b-what-is-cos-equal-to-82862
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">It is given that $\cos (\theta-u)-a, \cos (\theta-\beta)-\mathrm{b}$<br/>What is $\cos (\alpha-\beta)$ equal to ?</div>

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

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

answer:
<div class="solution">Given, $\cos (\theta-\alpha)=\mathrm{a} \Rightarrow \sin (\theta-\alpha)=\sqrt{1-a^{2}}$<br/>$$<br/>\begin{array}{l}<br/>\cos (\theta-\beta)=\mathrm{b} \Rightarrow \sin (\theta-\beta)=\sqrt{1-b^{2}} \\<br/>\therefore \cos (\alpha-\beta)=\cos (\theta-\beta-(\theta-\alpha)) \\<br/>=\cos (\theta-\beta) \cos (\theta-\alpha)+\sin (\theta-\beta) \sin (\theta-\alpha) \\<br/>=(b)(a)+\sqrt{1-b^{2}} \sqrt{1-a^{2}} \\<br/>=a b+\sqrt{1-a^{2}} \sqrt{1-b^{2}}<br/>\end{array}<br/>$$</div>


title: it-is-given-that-cos-u-a-cos-b-what-is-sin-2-2-ab-cos-equal-to
slug: it-is-given-that-cos-u-a-cos-b-what-is-sin-2-2-ab-cos-equal-to-34299
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">It is given that $\cos (\theta-u)-a, \cos (\theta-\beta)-\mathrm{b}$<br/>What is $\sin ^{2}(\alpha-\beta)+2 a b \cos (\alpha-\beta)$ equal to ?</div>

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

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

answer:
<div class="solution">$\begin{aligned} &amp; \sin ^{2}(\alpha-\beta)+2 a b \cos (\alpha-\beta)=1-\cos ^{2}(\alpha-\beta)+2 a b \cos \\ &amp;(\alpha-\beta)=1-\cos (\alpha-\beta)[\cos (\alpha-\beta)-2 a b] \\ &amp;=1-\left(a b+\sqrt{1-a^{2}} \sqrt{1-b^{2}}\right) \\ &amp; \quad\left[a b+\sqrt{1-a^{2}} \sqrt{1-b^{2}}-2 a b\right] \\ &amp;=1-\left(\sqrt{1-a^{2}} \sqrt{1-b^{2}}+a b\right)\left(\sqrt{1-a^{2}} \sqrt{1-b^{2}}-a b\right) \\ &amp;=1-\left[\left(\sqrt{1-a^{2}} \sqrt{1-b^{2}}\right)^{2}-(a b)^{2}\right] \\ &amp;=1-\left[\left(1-a^{2}\right)\left(1-b^{2}\right)-a^{2} b^{2}\right) \\ &amp;=1-\left(1-b^{2}-a^{2}+a^{2} b^{2}-a^{2} b^{2}\right) \\ &amp;=1-1+b^{2}+a^{2}=a^{2}+b^{2}</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
it-is-given-that-the-roots-of-the-equation-x-2-4-x-lo-g-3-p-are-real-for-this-the-minimum-value-of-p-is

slug:
it-is-given-that-the-roots-of-the-equation-x-2-4-x-lo-g-3-p-are-real-for-this-the-minimum-value-of-p-is-84806

question:
<div class="question">It is given that the roots of the equation $x^{2}-4 x-\log _{3} P=$ are real. For this, the minimum value of $\mathrm{P}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{27}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{64}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{81}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{81}$</span> </div>

answer:
<div class="solution">$x^{2}-4 x-\log _{3} P=0$<br/>We know, roots are real if discriminant is greater than or equal to 0 . i.e., $b^{2}-4 a c \geq 0 \Rightarrow b^{2} \geq 4 a c$<br/>In the given equation, $\mathrm{a}=1, \mathrm{~b}=-4, \mathrm{c}=-\log _{3} \mathrm{P}$.<br/>$\therefore b^{2} \geq 4 a c \Rightarrow(-4)^{2} \geq 4(1)\left(-\log _{3} P\right)$<br/>$\Rightarrow 16 \geq-4 \log _{3} \mathrm{P}$<br/>$\Rightarrow 4 \geq-\log _{3} P$<br/>$\Rightarrow 4 \geq \log _{3}\left(\frac{1}{\mathrm{P}}\right) \quad\left(\because \sin \theta-\log a=\log \frac{1}{\mathrm{a}}\right)$<br/>$\Rightarrow 3^{4} \geq \frac{1}{\mathrm{P}}$<br/>$\Rightarrow 81 \geq \frac{1}{\mathrm{P}} \Rightarrow \mathrm{P} \geq \frac{1}{81}$<br/>$\therefore$ The minimum value of $\mathrm{P}$ is $\frac{1}{81}$</div>


title: it-is-given-that-x-10-y-90-x-3-y-12-and-i-xy-08-the-regression-equation-of-x-on-y-is
slug: it-is-given-that-x-10-y-90-x-3-y-12-and-i-xy-08-the-regression-equation-of-x-on-y-is-36691
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">It is given that $\overline{\mathrm{X}}=10, \overline{\mathrm{Y}}=90, \sigma_{\mathrm{X}}=3, \sigma_{\mathrm{Y}}=12$ and<br/>$\mathrm{I}_{\mathrm{XY}}=0.8$. The regression equation of $\mathrm{X}$ on $\mathrm{Y}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad Y=3.2 X+58$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{X}=3.2 \mathrm{Y}+58$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\quad X=-8+0.2 Y$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$Y=-8+0.2 X$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad X=-8+0.2 Y$</span> </div>

answer:
<div class="solution">$\overline{\mathrm{X}}=10, \overline{\mathrm{Y}}=90, \sigma_{\mathrm{x}}=3, \sigma_{\mathrm{y}}=12, \mathrm{r}_{\mathrm{xy}}=0.8$<br/>Regression equation $\mathrm{x}$ on $\mathrm{y}$ is<br/>$\mathrm{x}-10=\mathrm{r} \cdot \frac{\sigma_{\mathrm{x}}}{\sigma_{\mathrm{y}}}(\mathrm{y}-90)$<br/>$\Rightarrow x-10=0.8 \times \frac{3}{12}(y-90)$<br/>$\Rightarrow x-10=\frac{2.4}{12}(y-90)$<br/>$10=0.2(\mathrm{y}-90)$<br/>$\Rightarrow x-10=0.2 y-18$<br/>$\Rightarrow x=0.2 y-8$</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1: 2$</span> </div>
source_db: MarksBatch2_P1.db
title:
it-the-sum-of-first-10-terms-of-an-arithmetic-progression-with-first-term-p-and-common-difference-q-is-4-times-the-sum-of-the-first-5-terms-then-what-

slug:
it-the-sum-of-first-10-terms-of-an-arithmetic-progression-with-first-term-p-and-common-difference-q-is-4-times-the-sum-of-the-first-5-terms-then-what-23003

question:
<div class="question">It the sum of first 10 terms of an arithmetic progression with first term $p$ and common difference $q$, is 4 times the sum of the first 5 terms, then what is the ratio $p: q$ ?</div>

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

answer:
<div class="solution">Since first term $=\mathrm{p}$ and common difference $=\mathrm{q}$. Sum of first 10 terms $=\frac{10}{2}[2 \mathrm{p}+(10-1) \mathrm{q}]$ and<br/>Sum of first 5 terms $=\frac{5}{2}[2 \mathrm{p}+(5-1) \mathrm{q}]$ According to question, $\frac{10}{2}[2 p+9 q]=4 \times \frac{5}{2}[2 p+4 q]$<br/>$\Rightarrow 2 \mathrm{p}+9 \mathrm{q}=4 \mathrm{p}+8 \mathrm{q}$<br/>$\Rightarrow 2 \mathrm{p}=\mathrm{q}$<br/>$\Rightarrow \mathrm{p}: \mathrm{q}=1: 2$</div>


title: jute-fibres-are-obtained-from-the
slug: jute-fibres-are-obtained-from-the-47877
question: <div class="question">Jute fibres are obtained from the:</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Secondary phloem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Pith</span> </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">Endodermis</span> </li> </ul>

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

answer:
<div class="solution">Jute fibers are bast fibers or phloem fibers. Secondary phloem forms the fibre which are long and are commercially important. Other fibers like flax and hemp are also phloem fibers.</div>


title: jute-is-a
slug: jute-is-a-84398
question: <div class="question">Jute is a</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'JIPMER', 'JIPMER 2015']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">bast fibre from secondary xylem</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">bast fibre from primary xylem</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">bast fibre from secondary phloem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">bast fibre from primary phloem</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">bast fibre from secondary phloem</span> </div>

answer:
<div class="solution">Fibres are elongated cells with usually lignified walls. Bast fibres from phloem is called jute. There are secondary phloem cells.</div>


title: ketones-where-r-r-alkyl-group-can-be-obtained-in-one-step-by
slug: ketones-where-r-r-alkyl-group-can-be-obtained-in-one-step-by-96249
tags: ['Chemistry', 'Aldehydes and Ketones', 'VITEEE', 'VITEEE 2013']
source_db: MarksBatch2_P1.db
question:
<div class="question">Ketones <img src="https://cdn-question-pool.getmarks.app/pyq/viteee/uDpdqP3rgjELRCAlaAQok4tW4XBPFUUmG1W26-lyD3o.original.fullsize.png"/><br/> where, $R=R^{\prime}=$ alkyl group can be obtained in one step by</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Oxidation of secondary alcohols</span> </div>

answer:
<div class="solution">Oxidation of Ketones, yield secondary alcohol<br/><img src="https://cdn-question-pool.getmarks.app/pyq/viteee/NgWN5uUpzd-hdbPD2Z7XJKMxy9UxJm4N_0i-irv3TJw.original.fullsize.png"/></div>


tags: ['Chemistry', 'Chemical Equilibrium', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">229.8</span> </div>
source_db: MarksBatch2_P1.db
title:
kp-for-the-conversion-of-oxygen-to-ozone-at-400-mathrmk-is-10-times-1030-its-standard-gibbs-energy-change-in-mathrmkj-mathrmmol1-is-approximately-1

slug:
kp-for-the-conversion-of-oxygen-to-ozone-at-400-mathrmk-is-10-times-1030-its-standard-gibbs-energy-change-in-mathrmkj-mathrmmol1-is-approximately-1-42785

question:
<div class="question">\(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\), its standard Gibbs energy change in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is approximately</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">229.8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">114.9</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">-229.8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">-114.9</span> </li> </ul>

answer:
<div class="solution">Given, \(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\).<br/>\(\left(\Delta G^{\circ}\right)\) standard Gibbs energy change \(=\) ?<br/>\(\Delta G^{\circ}=-R T \ln K_p=2.303 R T \log _{10} K_p\)<br/>Here,<br/>\(R=8.314 \mathrm{~J} / \mathrm{mol}\)<br/>\(\begin{aligned}<br/>T &amp; =400 \mathrm{~K} \\<br/>\Delta G^{\circ} &amp; =-R T \log K_p \\<br/>&amp; =-8.314 \times 400 \times 2.303 \times \log 10^{-30} \\<br/>&amp; =22976570 \mathrm{~J} \mathrm{~mol}^{-1} \\<br/>&amp; =229.765 \mathrm{~kJ} \mathrm{~mol}^{-1}<br/>\end{aligned}\)</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'AP EAMCET', 'AP EAMCET 2019 (22 Apr Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">229.8</span> </div>
source_db: MarksBatch2_P1.db
title:
kp-for-the-conversion-of-oxygen-to-ozone-at-400-mathrmk-is-10-times-1030-its-standard-gibbs-energy-change-in-mathrmkj-mathrmmol1-is-approximately

slug:
kp-for-the-conversion-of-oxygen-to-ozone-at-400-mathrmk-is-10-times-1030-its-standard-gibbs-energy-change-in-mathrmkj-mathrmmol1-is-approximately-55036

question:
<div class="question">\(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\), its standard Gibbs energy change in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is approximately</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">229.8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">114.9</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">-229.8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">-114.9</span> </li> </ul>

answer:
<div class="solution">Given, \(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\).<br/>\(\left(\Delta G^{\circ}\right)\) standard Gibbs energy change \(=\) ?<br/>\(\Delta G^{\circ}=-R T \ln K_p=2.303 R T \log _{10} K_p\)<br/>Here,<br/>\(R=8.314 \mathrm{~J} / \mathrm{mol}\)<br/>\(\begin{aligned}<br/>T &amp; =400 \mathrm{~K} \\<br/>\Delta G^{\circ} &amp; =-R T \log K_p \\<br/>&amp; =-8.314 \times 400 \times 2.303 \times \log 10^{-30} \\<br/>&amp; =22976570 \mathrm{~J} \mathrm{~mol}^{-1} \\<br/>&amp; =229.765 \mathrm{~kJ} \mathrm{~mol}^{-1}<br/>\end{aligned}\)</div>


title: lab-stands-for
slug: lab-stands-for-53087
question: <div class="question">LAB stands for</div>
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Lactic acid bacteria</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><em>Lactobacillus basophilus</em> bacteria</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Lactose acetaldehyde bacteria</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Laboratory</span> </li> </ul>

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

answer:
<div class="solution">Although many genera of bacteria produce lactic acid as a primary or secondary end-product of fermentation, the term Lactic acid bacteria is conventionally reserved for genera in the order Lactobacillales, which includes <em>Lactobacillus, Leuconostoc, Pediococcus</em>, etc. Lactic acid bacteria (LAB) are responsible for a great diversification in the flavor and texture of food products due to their fermentation of food raw materials. However, in some circumstances, they can be responsible for food spoilage.</div>


title: lateral-roots-and-vascular-cambium-originates-due-to-the-activity-of-which-tissue-in-dicot-root
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P1.db
slug:
lateral-roots-and-vascular-cambium-originates-due-to-the-activity-of-which-tissue-in-dicot-root-11807

question:
<div class="question">Lateral roots and vascular cambium originates due to the activity of which tissue in dicot root?</div>

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

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

answer:
<div class="solution">In dicot root, lateral root originates endogenously due to the activity of cells of pericycle, which undergoes dedifferentiation and becomes meristematic. During secondary growth cells of pericycle and the parenchyma cells of conjuctive tissue becomes meristematic and forms vascular cambium.</div>


title: leftbeginarraylllab-bc-ca-bc-ca-ab-ca-ab-bcendarrayright
slug: leftbeginarraylllab-bc-ca-bc-ca-ab-ca-ab-bcendarrayright-77571
tags: ['Mathematics', 'Determinants', 'WBJEE', 'WBJEE 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">\(\left|\begin{array}{lll}a-b &amp; b-c &amp; c-a \\ b-c &amp; c-a &amp; a-b \\ c-a &amp; a-b &amp; b-c\end{array}\right|=\)</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">2</span> </li> </ul>

answer:
<div class="solution">Hints : \(\mathrm{c}_1 \rightarrow \mathrm{c}_1+\mathrm{c}_2+\mathrm{c}_3\)</div>


title: let-0-4-5-which-one-of-the-following-is-correct
slug: let-0-4-5-which-one-of-the-following-is-correct-49085
tags: ['Mathematics', 'Trigonometric Equations', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">Let $0^{\circ}   &lt; \theta &lt; 45^{\circ}$. Which one of the following is correct?</div>

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

answer:
<div class="solution">(a) In such a problem, we have to check option, oneby-one $\begin{aligned} &amp; \sin ^{2} \theta+\cos ^{6} \theta=\sin ^{6} \theta+\cos ^{2} \theta \\ \Rightarrow &amp; \sin ^{6} \theta-\cos ^{6} \theta=\sin ^{2} \theta-\cos ^{2} \theta \end{aligned}$<br/>Taking L.H.S, $\sin ^{6} \theta-\cos ^{6} \theta=\left(\sin ^{2} \theta\right)^{3}-\left(\cos ^{2} \theta\right)^{3}$<br/>Which is not equal to $\mathrm{R}$.H.S., $\sin ^{2} \theta-\cos ^{2} \theta$<br/>Option (a) is not correct.<br/>(b) $\because \operatorname{cosec}^{6} \theta-\cot ^{6} \theta$<br/>$\left(\operatorname{cosec}^{2} \theta-\cot ^{2} \theta\right)\left[\left(\operatorname{cosec}^{2} \theta-\cot ^{2} \theta\right)^{2}+(\operatorname{cosec} \theta \cot \theta)\right]$<br/>Which is not equal to $\operatorname{cosec}^{2} \theta-\cot ^{2} \theta$.<br/>$\therefore$ Option (b) is also not correct.<br/>(c) $\sin ^{4} \theta+\cos ^{4} \theta=\left(\sin ^{2} \theta+\cos ^{2} \theta\right)^{2}-2 \sin ^{2} \theta \cos ^{2} \theta$<br/>$=1-2 \sin ^{2} \theta \cos ^{2} \theta .$<br/>Which is not equal to $\sin ^{2} \theta-\cos ^{2} \theta$.<br/>Hence, option (c) is also not correct. (d) $\begin{aligned} &amp;\left(\operatorname{cosec}^{2} \theta+\cot ^{4} \theta\right) \\=&amp; \operatorname{cosec}^{2} \theta+\left(\operatorname{cosec}^{2} \theta-1\right)^{2} \\ &amp;=\operatorname{cosec}^{2} \theta+\operatorname{cosec}^{4} \theta+1-2 \operatorname{cosec}^{2} \theta \\ &amp;=\operatorname{cosec}^{4} \theta+1-\operatorname{cosec}^{2} \theta \\ &amp;=\operatorname{cosec}^{4} \theta+\cot ^{2} \theta \end{aligned}$<br/>Thus option (d) is correct.</div>


tags: ['Mathematics', 'Statistics', 'TS EAMCET', 'TS EAMCET 2018 (07 May Shift 1)']
source_db: MarksBatch2_P1.db
title:
let-1-2-be-the-standard-deviations-of-two-distributions-d-1-and-d-2-respectively-and-d-1-be-more-consistent-than-d-2-if-the-means-of-d-1-and-d-2-are-s

slug:
let-1-2-be-the-standard-deviations-of-two-distributions-d-1-and-d-2-respectively-and-d-1-be-more-consistent-than-d-2-if-the-means-of-d-1-and-d-2-are-s-31070

question:
<div class="question">Let $\sigma_1, \sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are same, then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sigma_1-\sigma_2}{\sigma_2} \times 100$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sigma_1-\sigma_2}{\sigma_1} \times 100$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\sigma_2-\sigma_1}{\sigma_2} \times 100$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{\sigma_2-\sigma_1}{\sigma_1} \times 100$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\frac{\sigma_2-\sigma_1}{\sigma_1} \times 100$</span> </div>

answer:
<div class="solution">Since mean of both the distribution are same, therefore<br/>Percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/rsDM12BaUG0BczJRG_G2cTQlml1bf83WSFsPUrgMh1Q.original.fullsize.png"/><br/><br/>$$<br/>=\frac{\sigma_2-\sigma_1}{\sigma_1} \times 100<br/>$$</div>


title: let-1-x-1-if-cos-sin-1-x-2-1-then-how-many-value-does-tan-cos-1-x-assume
slug: let-1-x-1-if-cos-sin-1-x-2-1-then-how-many-value-does-tan-cos-1-x-assume-82789
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2008 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Two</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">Let $-1 \leq x \leq 1$. If $\cos \left(\sin ^{-1} x\right)=\frac{1}{2}$, then how many value does $\tan \left(\cos ^{-1} \mathrm{x}\right)$ assume?</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">Four</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Infinite</span> </li> </ul>

answer:
<div class="solution">As given :<br/>$\cos \left(\sin ^{-1} \mathrm{x}\right)=\frac{1}{2}$<br/>$\Rightarrow \sin ^{-1} x=\cos ^{-1}\left(\frac{1}{2}\right)$<br/>$\Rightarrow \sin ^{-1} x=\frac{\pi}{3} \Rightarrow x=\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}$<br/>$\therefore \tan \left(\cos ^{-1} x\right)=\tan \left(\cos ^{-1} \frac{\sqrt{3}}{2}\right)$<br/>$=\tan \left(\pm \frac{\pi}{6}\right)=\pm \frac{1}{\sqrt{3}}$<br/>Hence, $\tan \left(\cos ^{-1} \mathrm{x}\right)$ have two values.</div>


title: let-4-5-9-0-if-tan-cot-tan-i-cot-j-for-some-i-2-then-what-is-the-value-of-sin-cos
slug: let-4-5-9-0-if-tan-cot-tan-i-cot-j-for-some-i-2-then-what-is-the-value-of-sin-cos-90358
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">Let $45^{\circ} \leq \theta   &lt; 90^{\circ}$. If $\tan \theta+\cot \theta=(\tan \theta)^{\mathrm{i}}+(\cot \theta)^{\mathrm{j}}$ for some<br/>$\mathrm{i} \geq 2$, then what is the value of $\sin \theta+\cos \theta$ ?</div>

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

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

answer:
<div class="solution">As given, $\tan \theta+\cot \theta=(\tan \theta)^{\mathrm{i}}+(\cot \theta)^{\mathrm{i}}$<br/>Also, $45^{\circ} \leq \theta   &lt; 90^{\circ}$ and $\mathrm{i} \geq 2$<br/>which is possible only when $\theta=45^{\circ}$ Since, $\tan 45^{\circ}+\cot 45^{\circ}=1+1=2$<br/>and $\left(\tan 45^{\circ}\right)^{\mathrm{i}}+\left(\cot 45^{\circ}\right)^{\mathrm{i}}=1+1=2$<br/>Thus, $\sin \theta+\cos \theta=\sin 45^{\circ}+\cos 45^{\circ}$<br/>$=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=\frac{1+1}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}$</div>


title: let-16-x-2-3-y-2-32-x-12-y-44-represents-a-hyperbola-then
slug: let-16-x-2-3-y-2-32-x-12-y-44-represents-a-hyperbola-then-17815
question: <div class="question">Let $16 x^{2}-3 y^{2}-32 x-12 y=44$ represents a hyperbola. Then,</div>
tags: ['Mathematics', 'Hyperbola', 'WBJEE', 'WBJEE 2015']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">length of the transverse axis is $2 \sqrt{3}$</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="correct"> <span class="option-label">B</span> <span class="option-data">length of each latusrecturn is $32 / \sqrt{3}$</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="correct"> <span class="option-label">C</span> <span class="option-data">eccentricity is $\sqrt{19 / 3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">equation of a directrix is $x=\frac{\sqrt{19}}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">length of the transverse axis is $2 \sqrt{3}$, length of each latusrecturn is $32 / \sqrt{3}$, eccentricity is $\sqrt{19 / 3}$</span> </div>

answer:
<div class="solution">Given equation of hyperbola is $16 x^{2}-3 y^{2}-32 x-12 y=44$
<br/>$\Rightarrow 16 x^{2}+16-32 x-3 y^{2}-12-12 y$
<br/>$=44+4$
<br/>$\Rightarrow 16(x-1)^{2}-3(y+2)^{2}=48$
<br/>$\Rightarrow \quad \frac{(x-1)^{2}}{3}-\frac{(y+2)^{2}}{16}=1$
<br/>On comparing the equation with standard equation of hyperbola, we get $a=\sqrt{3}, b=4$
<br/>Now, length of transverse axis $=2 a=2 \sqrt{3}$
<br/>and length of latusrectum $=\frac{2 b^{2}}{a}=\frac{2 \times 16}{\sqrt{3}}=\frac{32}{\sqrt{3}}$
<br/>$\therefore$ Eccentricity $(e)=\sqrt{1+\frac{b^{2}}{a^{2}}}$
<br/>$=\sqrt{1+\frac{16}{3}}=\sqrt{\frac{19}{3}}$
<br/>Equation of directrix is $x=\pm \frac{a}{e}$ $\Rightarrow x-1=\pm \frac{\sqrt{3} \times \sqrt{3}}{\sqrt{19}}$
<br/>$\Rightarrow \quad x=1 \pm \frac{3}{\sqrt{19}}$</div>


title: let-a-0-b-0-a-b-a-b-a-2-b-2-holds-if-and-only-if
slug: let-a-0-b-0-a-b-a-b-a-2-b-2-holds-if-and-only-if-48298
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">Let $|\overrightarrow{\mathrm{a}}| \neq 0,|\overrightarrow{\mathrm{b}}| \neq 0$<br/>$(\vec{a}+\vec{b}) \cdot(\vec{a}+\vec{b})=|\vec{a}|^{2}+|\vec{b}|^{2}$ holds if and only if</div>

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

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

answer:
<div class="solution">$(\vec{a}+\vec{b}) \cdot(\vec{a}+\vec{b})=a^{2}+2 \vec{a} \cdot \vec{b}+b^{2}=a^{2}+b^{2}$<br/>$\Rightarrow \quad \vec{a} \cdot \vec{b}=0 \Rightarrow \vec{a} \perp \vec{b}$</div>


title: let-a-1-0-0-1-and-b-1-0-x-1-if-ab-ba-then-what-is-the-value-of-x
slug: let-a-1-0-0-1-and-b-1-0-x-1-if-ab-ba-then-what-is-the-value-of-x-94303
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">Let $\mathrm{A}=\left[\begin{array}{cc}1 &amp; 0 \\ 0 &amp; -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}1 &amp; \mathrm{x} \\ 0 &amp; 1\end{array}\right]$<br/>If $\mathrm{AB}=\mathrm{BA}$, then what is the value of $\mathrm{x}$?</div>

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

answer:
<div class="solution">As given $\mathrm{A}=\left[\begin{array}{cc}1 &amp; 0 \\ 0 &amp; -1\end{array}\right]$ and $\mathrm{B}=\left|\begin{array}{ll}1 &amp; \mathrm{x} \\ 0 &amp; 1\end{array}\right|$<br/>$\mathrm{AB}=\left[\begin{array}{cc}1 &amp; 0 \\ 0 &amp; -1\end{array}\right]\left[\begin{array}{ll}1 &amp; \mathrm{x} \\ 0 &amp; 1\end{array}\right]=\left[\begin{array}{cc}1 &amp; \mathrm{x} \\ 0 &amp; -1\end{array}\right]$<br/>and $\mathrm{BA}=\left[\begin{array}{ll}1 &amp; \mathrm{x} \\ 0 &amp; 1\end{array}\right]\left[\begin{array}{cc}1 &amp; 0 \\ 0 &amp; -1\end{array}\right]=\left[\begin{array}{cc}1 &amp; -\mathrm{x} \\ 0 &amp; -1\end{array}\right]$<br/>Given that $\mathrm{AB}=\mathrm{BA}$<br/>We have, $\left[\begin{array}{cc}1 &amp; \mathrm{x} \\ 0 &amp; -1\end{array}\right]=\left[\begin{array}{cc}1 &amp; -\mathrm{x} \\ 0 &amp; -1\end{array}\right]$<br/>$\Rightarrow \mathrm{x}=-\mathrm{x} \Rightarrow 2 \mathrm{x}=0 \Rightarrow \mathrm{x}=0$</div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
let-a-1-1-1-1-1-1-1-1-1-be-a-square-matrix-of-order-3-then-for-any-positive-integer-n-what-is-a-n-equal-to

slug:
let-a-1-1-1-1-1-1-1-1-1-be-a-square-matrix-of-order-3-then-for-any-positive-integer-n-what-is-a-n-equal-to-15105

question:
<div class="question">Let $\mathrm{A}=\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]$ be a square matrix of order 3 . Then for any positive integer $\mathrm{n}$, what is $\mathrm{A}^{\mathrm{n}}$ equal to?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(3^{n-1}\right) \mathrm{A}$</span> </div>

answer:
<div class="solution">Given matrix is $\mathrm{A}=\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]$<br/>So, $\mathrm{A}^{2}=\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]$<br/>$=\left[\begin{array}{lll}3 &amp; 3 &amp; 3 \\ 3 &amp; 3 &amp; 3 \\ 3 &amp; 3 &amp; 3\end{array}\right]=3\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]$<br/>and $\mathrm{A}^{3}=3\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]$<br/>$=3\left[\begin{array}{lll}3 &amp; 3 &amp; 3 \\ 3 &amp; 3 &amp; 3 \\ 3 &amp; 3 &amp; 3\end{array}\right]=9\left[\begin{array}{lll}1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1 \\ 1 &amp; 1 &amp; 1\end{array}\right]$<br/>$=3^{2} \mathrm{~A}$<br/>Similarly $\mathrm{A}^{4}=3^{3} \mathrm{~A} .$ Hence, $A^{\mathrm{n}}=3^{\mathrm{n}-1} \mathrm{~A}$</div>


title: let-a-1-2-3-4-5-6-7-8-9-10-then-the-number-of-subsets-of-a-containing-exactly-two-elements-is
slug: let-a-1-2-3-4-5-6-7-8-9-10-then-the-number-of-subsets-of-a-containing-exactly-two-elements-is-65120
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">45</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">Let $\mathrm{A}=\{1,2,3,4,5,6,7,8,9,10\}$. Then the number of subsets of A containing exactly two elements is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">20</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">40</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">45</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">90</span> </li> </ul>

answer:
<div class="solution">$\mathrm{A}=\{1,2,3,4,5,6,7,8,9,10\}$<br/>Number of subsets of A containing two elements $=9+8+7+6+5+4+3+2+1$<br/>$\frac{9(9+1)}{2}=\frac{90}{2}=45$<br/>$\therefore$ Option $(\mathrm{c})$ is correct Alternate Method The number of subsets of A containing exactly two elements is:<br/>${ }^{10} \mathrm{C}_{2}=\frac{10 \times 9}{2 \times 1}=45$</div>


title: let-a-1-2-3-4-5-6-7-8-9-10-then-the-number-of-subsets-of-a-containing-two-or-three-elements-is
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">165</span> </div>
source_db: MarksBatch2_P1.db
slug:
let-a-1-2-3-4-5-6-7-8-9-10-then-the-number-of-subsets-of-a-containing-two-or-three-elements-is-91716

question:
<div class="question">Let $\mathrm{A}=\{1,2,3,4,5,6,7,8,9,10\}$. Then the number of subsets of A containing two or three elements is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">45</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">120</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">165</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">32</span> </li> </ul>

answer:
<div class="solution">Given, A $\{1,2,3,4,5,6,7,8,9,10\}$ Set $\mathrm{A}$ has 10 elements. Number of sub sets Containing 2 and 3 elements is<br/>${ }^{10} \mathrm{c}_{\mathrm{c}}+10_{\mathrm{c}_{3}}$<br/>$10_{\mathrm{c}_{2}}+10_{\mathrm{c}_{3}}=\frac{10 \times 9}{2}+\frac{10 \times 9 \times 8}{3 \times 2}$<br/>$=45+120=165$</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
let-a-1-2-3-and-b-3-1-2-be-two-vectors-and-c-be-a-vector-of-length-l-and-parallel-to-a-b-what-is-c-equal-to

slug:
let-a-1-2-3-and-b-3-1-2-be-two-vectors-and-c-be-a-vector-of-length-l-and-parallel-to-a-b-what-is-c-equal-to-11813

question:
<div class="question">Let $\vec{a}=(1,-2,3)$ and $\vec{b}=(3,1,2)$ be two vectors and $\vec{c}$ be a<br/>vector of length $l$ and parallel to $(\vec{a}+\vec{b})$. What is $\vec{c}$ equal<br/>to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{\sqrt{4}}(-2,-3,1)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{\sqrt{2}}(1,0,1)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{\sqrt{42}}(-5,-4,-1)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None 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>

answer:
<div class="solution">Given $\overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$<br/>and $\overrightarrow{\mathbf{b}}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$<br/>$\therefore \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}=4 \hat{\mathbf{i}}-\mathbf{j}+5 \hat{\mathbf{k}}$<br/>Then, $\overrightarrow{\mathbf{c}}=\lambda(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}})$<br/>$=\lambda(4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}})$<br/>$\Rightarrow l=\sqrt{16 \lambda^{2}+\lambda^{2}+25 \lambda^{2}}$<br/>$\Rightarrow l=\sqrt{42} \lambda$<br/>$\lambda=\frac{l}{\sqrt{42}}$<br/>$\therefore \quad \overrightarrow{\mathbf{c}}=\frac{l}{\sqrt{42}}(4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}})=\frac{1}{\sqrt{42}}(4,-1,5)$</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">3</span> </div>
source_db: MarksBatch2_P1.db
title:
let-a-1-2-5-8-b-0-1-3-6-7-and-r-be-the-relation-is-one-less-than-from-a-to-b-then-how-many-elements-will-r-contain

slug:
let-a-1-2-5-8-b-0-1-3-6-7-and-r-be-the-relation-is-one-less-than-from-a-to-b-then-how-many-elements-will-r-contain-26254

question:
<div class="question">Let $A=\{-1,2,5,8\}, B=\{0,1,3,6,7\}$ and $R$ be the relation 'is<br/>one less than' from $A$ to $B$, then how many elements will $R$ contain?</div>

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

answer:
<div class="solution">Given, $\mathrm{A}=\{-1,2,5,8\}$ and $\mathrm{B}=\{0,1,3,6,7\}$<br/>Since, $\mathrm{R}$ be the relation 'is one less than' from $\mathrm{A}$ to $\mathrm{B}$ $\mathrm{R}=\{(-1,0),(2,3),(5,6)\}$<br/>Hence, R contains 3 elements.</div>


title: let-a-1-3-2-4-a-ij-where-i-j-1-2-if-its-inverse-matrix-is-b-ij-what-is-b-22
slug: let-a-1-3-2-4-a-ij-where-i-j-1-2-if-its-inverse-matrix-is-b-ij-what-is-b-22-11673
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">Let $A=\left[\begin{array}{ll}1 &amp; 2 \\ 3 &amp; 4\end{array}\right]=\left[a_{i j}\right]$, where $i, j=1,2$, If its inverse matrix is $\left[b_{i j}\right]$, what is $b_{22} ?$</div>

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

answer:
<div class="solution">Let $A=\left[\begin{array}{ll}1 &amp; 2 \\ 3 &amp; 4\end{array}\right]$<br/>$|A|=4 \times 1-2 \times 3=4-6=-2$<br/>$\therefore \quad A^{-1}=-\frac{1}{2}\left[\begin{array}{rr}4 &amp; -2 \\ -3 &amp; 1\end{array}\right]$<br/>$\Rightarrow\left[b_{i j}\right]=-\frac{1}{2}\left[\begin{array}{rr}4 &amp; -2 \\ -3 &amp; 1\end{array}\right]=\left[\begin{array}{lc}-2 &amp; 1 \\ \frac{3}{2} &amp; -\frac{1}{2}\end{array}\right]$<br/>$\Rightarrow b_{22}=\frac{1}{2}$</div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
let-a-1-3-2-4-and-b-a-0-0-b-where-a-b-are-natural-numbers-then-which-one-of-the-following-is-correct

slug:
let-a-1-3-2-4-and-b-a-0-0-b-where-a-b-are-natural-numbers-then-which-one-of-the-following-is-correct-48828

question:
<div class="question">Let $A=\left[\begin{array}{ll}1 &amp; 2 \\ 3 &amp; 4\end{array}\right]$ and $B=\left[\begin{array}{ll}a &amp; 0 \\ 0 &amp; b\end{array}\right]$ where $a, b$ are natural numbers, 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">There exist more than one but finite number of $B$ 's such that $A B=B A$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">There exists exactly one $\mathrm{B}$ such that $A B=B A$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">There exist infinitely many $B$ 's such that $A B=B A$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">There cannot exist any $B$ such that $A B=B A$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">There exist infinitely many $B$ 's such that $A B=B A$</span> </div>

answer:
<div class="solution">$A B=\left[\begin{array}{ll}1 &amp; 2 \\ 3 &amp; 4\end{array}\right]\left[\begin{array}{ll}a &amp; 0 \\ 0 &amp; b\end{array}\right]=\left[\begin{array}{cc}a &amp; 2 b \\ 3 a &amp; 4 b\end{array}\right]$<br/>and $B A=\left[\begin{array}{ll}a &amp; 0 \\ 0 &amp; b\end{array}\right]\left[\begin{array}{ll}1 &amp; 2 \\ 3 &amp; 4\end{array}\right]=\left[\begin{array}{cc}a &amp; 2 a \\ 3 b &amp; 4 b\end{array}\right]$<br/>If $A B=B A$<br/>$\Rightarrow\left[\begin{array}{cc}a &amp; 2 b \\ 3 a &amp; 4 b\end{array}\right]=\left[\begin{array}{cc}a &amp; 2 a \\ 3 b &amp; 4 b\end{array}\right] \Rightarrow a=b$<br/>From the above it is clear that there exist infinitely many B's such that $\mathrm{AB}=\mathrm{BA}$.</div>


