# questions

tags: ['Physics', 'Electromagnetic Waves', 'NEET', 'NEET 2009 (Screening)']
source_db: MarksBatch2_P2.db
title:
the-electric-field-part-of-an-electromagnetic-wave-in-a-medium-is-represented-by-beginaligned-ex0-ey25-mathrmnc1-cos-leftleft2-pi-times-106-mathrmrad-

slug:
the-electric-field-part-of-an-electromagnetic-wave-in-a-medium-is-represented-by-beginaligned-ex0-ey25-mathrmnc1-cos-leftleft2-pi-times-106-mathrmrad-24537

question:
<div class="question">The electric field part of an electromagnetic wave in a medium is represented by<br/>\(\begin{aligned} &amp; E_x=0 \\ &amp; E_y=2.5 \mathrm{NC}^{-1} \cos \left[\left(2 \pi \times 10^6 \mathrm{rad} \mathrm{s}^{-1}\right) \mathrm{t}-\left(\pi \times 10^{-2} \mathrm{rad} \mathrm{m}^{-1}\right) \mathrm{x}\right] \\ &amp; E_z=0\end{aligned}\)
<br/>The wave is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">moving along $y$ direction with frequency $2 \pi \times 10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">moving along $x$ direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $100 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">moving along $x$ direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">moving along $-x$ direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">moving along $y$ direction with frequency $2 \pi \times 10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$.</span> </div>

answer:
<div class="solution">Comparing the given equation<br/>$$<br/>\begin{aligned}<br/>&amp; \mathrm{E}_{\mathrm{y}}=2.5 \frac{\mathrm{N}}{\mathrm{C}} \cos \left[\left(2 \pi \times 10^6 \frac{\mathrm{rad}}{\mathrm{m}}\right) \mathrm{t}\right. \\<br/>&amp;\left.-\left(\pi \times 10^{-2} \frac{\mathrm{rad}}{\mathrm{sec}}\right) \mathrm{x}\right]<br/>\end{aligned}<br/>$$<br/>With the standard equation<br/>$$<br/>\mathrm{E}_{\mathrm{y}}=\mathrm{E}_0 \cos (\omega \mathrm{t}-\mathrm{kx})<br/>$$<br/>we get<br/>$$<br/>\begin{array}{ll} <br/>&amp; \omega=2 \pi \mathrm{f}=2 \pi \times 10^6 \\<br/>\therefore &amp; \mathrm{f}=10^6 \mathrm{~Hz}<br/>\end{array}<br/>$$<br/>Moreover, we know that<br/>$$<br/>\Rightarrow \quad \begin{aligned}<br/>\frac{2 \pi}{\lambda} &amp; =\mathrm{k}=\pi \times 10^{-2} \mathrm{~m}^{-1} \\<br/>\Rightarrow \quad \lambda &amp; =200 \mathrm{~m}<br/>\end{aligned}<br/>$$<br/>Hence, the wave is moving along positive $x$-direction with frequency $10^6 \mathrm{~Hz}$ and wavelength $200 \mathrm{~m}$.</div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-electrode-potential-e-for-the-reduction-of-m-n-o-4-to-m-n-2-in-acidic-medium-is-151-v-which-of-the-following-metals-will-be-oxidised-the-reduction

slug:
the-electrode-potential-e-for-the-reduction-of-m-n-o-4-to-m-n-2-in-acidic-medium-is-151-v-which-of-the-following-metals-will-be-oxidised-the-reduction-41040

question:
<div class="question">The electrode potential, <math><mi mathvariant="normal">E</mi><mo>Â°</mo></math> , for the reduction of <math><mi mathvariant="normal">M</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>4</mn></mrow><mrow><mo>-</mo></mrow></msubsup></math> to <math><mi mathvariant="normal">M</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></math> in acidic medium is +1.51 V. Which of the following metal(s) will be oxidised? The reduction reactions and standard electrode potentials for <math><mi mathvariant="normal">Z</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>,</mo><mi mathvariant="normal">A</mi><msup><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mo>+</mo></mrow></msup></math> and <math><mi mathvariant="normal">A</mi><msup><mrow><mi mathvariant="normal">u</mi></mrow><mrow><mo>+</mo></mrow></msup></math> are given as<br/> <br/> <math><mi mathvariant="normal">Z</mi><msubsup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi></mrow></mfenced></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msubsup><mo>+</mo><mn>2</mn><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>â</mo><mi mathvariant="normal">Z</mi><msub><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">s</mi></mrow></mfenced></mrow></msub><mo>,</mo><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>=</mo><mo>-</mo><mn>0.762</mn><mi mathvariant="normal">V</mi></math><br/> <br/> <math><mi mathvariant="normal">A</mi><msubsup><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi></mrow></mfenced></mrow><mrow><mo>+</mo></mrow></msubsup><mo>+</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>â</mo><mi mathvariant="normal">A</mi><msub><mrow><mi mathvariant="normal">g</mi></mrow><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">x</mi></mrow></mfenced></mrow></msub><mo>,</mo><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>=</mo><mo>+</mo><mn>0.80</mn><mi mathvariant="normal">V</mi></math><br/> <br/> <math><mi mathvariant="normal">A</mi><msubsup><mrow><mi mathvariant="normal">u</mi></mrow><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi></mrow></mfenced></mrow><mrow><mo>+</mo></mrow></msubsup><mo>+</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>â</mo><mi mathvariant="normal">A</mi><msub><mrow><mi mathvariant="normal">u</mi></mrow><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">s</mi></mrow></mfenced></mrow></msub><mo>,</mo><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>=</mo><mo>+</mo><mn>1.69</mn><mi mathvariant="normal">V</mi></math></div>

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

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

answer:
<div class="solution">More +ve the value of reduction potential more will be the tendency to undergo reduction.<br/><br/>The <math> <mrow> <msubsup> <mtext>E</mtext> <mrow> <mtext>red</mtext></mrow> <mtext>o</mtext> </msubsup> <mfenced> <mrow> <msubsup> <mrow> <mtext>MnO</mtext></mrow> <mn>4</mn> <mo>−</mo> </msubsup> <mo>|</mo><msup> <mrow> <mtext>Mn</mtext></mrow> <mrow> <mn>2</mn><mo>+</mo></mrow> </msup> </mrow> </mfenced><mo>=</mo><mo>+</mo><mn>1.51</mn><mtext> </mtext><mtext>V</mtext></mrow></math> value is greater than <math> <mrow> <msubsup> <mtext>E</mtext> <mrow> <mtext>red</mtext></mrow> <mtext>o</mtext> </msubsup> <mfenced> <mrow> <msup> <mrow> <mtext>Zn</mtext></mrow> <mrow> <mn>2</mn><mo>+</mo></mrow> </msup> <mo>|</mo><mtext>Zn</mtext></mrow> </mfenced><mo>=</mo><mo>−</mo><mn>0.762</mn><mtext> </mtext><mtext>V</mtext></mrow></math> and <math> <mrow> <msubsup> <mtext>E</mtext> <mrow> <mtext>red</mtext></mrow> <mtext>o</mtext> </msubsup> <mfenced> <mrow> <msup> <mrow> <mtext>Ag</mtext></mrow> <mo>+</mo> </msup> <mo>|</mo><mtext>Ag</mtext></mrow> </mfenced><mo>=</mo><mo>+</mo><mn>0.80</mn><mtext> </mtext><mtext>V</mtext></mrow></math>. Thus, only Zn and Ag will be oxidised.</div>


tags: ['Chemistry', 'Electrochemistry', 'AP EAMCET', 'AP EAMCET 2019 (21 Apr Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-electrode-potential-for-m-2-a-q-e-m-a-q-m-a-q-e-m-s-a-re-015-mathrmv-an-d-050-mathrmv-res-p-ec-t-i-v-e-l-y-t-h-e-v-a-l-u-eo-f-ecirc-m2-m-will-be

slug:
the-electrode-potential-for-m-2-a-q-e-m-a-q-m-a-q-e-m-s-a-re-015-mathrmv-an-d-050-mathrmv-res-p-ec-t-i-v-e-l-y-t-h-e-v-a-l-u-eo-f-ecirc-m2-m-will-be-10063

question:
<div class="question">The electrode potential for<br/>$$<br/>\begin{aligned}<br/>&amp; M^{2+}(a q)+e^{-} \longrightarrow M^{+}(a q) \\<br/>&amp; M^{+}(a q)+e^{-} \longrightarrow M(s)<br/>\end{aligned}<br/>$$<br/>are $+0.15 \mathrm{~V}$ and $+0.50 \mathrm{~V}$ respectively. The value of $E^{\circ}{ }_{M^{2+} / M}$ will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.150 V</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.300 V</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">0.325 V</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.650 V</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">0.325 V</span> </div>

answer:
<div class="solution">Given,<br/>$$<br/>\begin{aligned}<br/>&amp; M^{2+}(a q)+e^{-} \longrightarrow M^{+}(a q), E_1^{\circ}=+0.15 \mathrm{~V} \\<br/>&amp; M^{+}(a q)+e^{-} \longrightarrow M(s), E_2^{\circ}=0.5 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/>$\because$ Free energy, i.e. $\left[\Delta G^{\circ}\right]=-n F E^{\circ}$<br/>where, $n=$ number of electron involved<br/>$$<br/>E^{\circ}=\text { standard electrode potential. }<br/>$$<br/>$F=$ Faraday's constant<br/>To find $E_3^{\circ}$ for $E_{\left(M^{2+} / M\right)}^{\circ}$<br/>Thus,<br/>$$<br/>\begin{array}{lr}<br/>-\Delta G_1^{\circ}=n E_1^{\circ}=E_1^{\circ} &amp; (\because n=1) \\<br/>-\Delta G_2^{\circ}=n E_2^{\circ}=E_{{ }_2}{ }_2 &amp; (\because n=1) \\<br/>-\Delta G_3^{\circ}=n E_3=2 E_3^{\circ} &amp; (\because n=2) \\<br/>\text { [For reaction : } M^{2+}(a q)+2 e^{-} &amp; \longrightarrow M(s) \text { ] }<br/>\end{array}<br/>$$<br/><br/>Therefore,<br/>$$<br/>\begin{aligned}<br/>-\Delta G_3^{\circ} &amp; =(-) \Delta G_1^{\circ}+(-) \Delta G_2^{\circ} \\<br/>-2 E_3^{\circ} &amp; =-\left(n E_1^{\circ}+n E_2^{\circ}\right) \\<br/>2 E_3^{\circ} &amp; =E_1^{\circ}+E_2^{\circ} \\<br/>2 E_3^{\circ} &amp; =0.15+0.5 \\<br/>2 E_3^{\circ} &amp; =0.65 \mathrm{~V} \\<br/>E_3^{\circ} &amp; =\frac{0.65}{2}=0.325 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/><br/>Hence, option (c) is the correct answer.</div>


tags: ['Physics', 'Electrostatic Potential and Capacitance']
source_db: MarksBatch2_P2.db
title:
the-electrostatic-potential-on-the-surface-of-a-charged-conducting-sphere-is-100-v-two-statements-are-made-in-this-regard-s-1-at-any-point-inside-the-

slug:
the-electrostatic-potential-on-the-surface-of-a-charged-conducting-sphere-is-100-v-two-statements-are-made-in-this-regard-s-1-at-any-point-inside-the-76385

question:
<div class="question">The electrostatic potential on the surface of a charged conducting sphere is $100 \mathrm{~V}$. Two statements are made in this regard $S_1$ at any point inside the sphere, electric intensity is zero. $\mathrm{S}_2$ at any point inside the sphere, the electrostatic potential is $100 \mathrm{~V}$. Which of the following is a correct statement?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{S}_1$ is true, $\mathrm{S}_2$ is also true and $\mathrm{S}_1$ is the cause of $\mathrm{S}_2$<br/></span> </div>

answer:
<div class="solution">As we know that the relation between electric field intensity $E$ and electric potential $V$ is<br/>$$<br/>\mathrm{E}=-\frac{\mathrm{dV}}{\mathrm{dr}}<br/>$$<br/>Electric field intensity $E=0$ then $\frac{\mathrm{dV}}{\mathrm{dr}}=0$<br/>This imply that $\mathrm{V}=$ constant<br/>Thus, $\mathrm{E}=0$ inside the charged conducting sphere then the constant electrostatic potential $100 \mathrm{~V}$ at every where inside the sphere and it verifies the shielding effect also.</div>


title: the-element-which-is-the-most-abundant-in-the-earth-crust-is
slug: the-element-which-is-the-most-abundant-in-the-earth-crust-is-27634
question: <div class="question">The element which is the most abundant in the earth crust is</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'AIIMS', 'AIIMS 2007']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\mathrm{O}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">\(\mathrm{S}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\mathrm{Al}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\mathrm{H}\).</span> </li> </ul>

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

answer:
<div class="solution">Oxygen is the most abundant element in the earth's crust. (above \(45.5 \mathrm{wt}~ \%\))</div>


tags: ['Chemistry', 'Electrochemistry', 'TS EAMCET', 'TS EAMCET 2021 (06 Aug Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Cu</span> </div>
source_db: MarksBatch2_P2.db
title:
the-element-with-highest-standard-reduction-potential-in-volt-m-2-m-among-the-first-row-of-transition-elements-is

slug:
the-element-with-highest-standard-reduction-potential-in-volt-m-2-m-among-the-first-row-of-transition-elements-is-54394

question:
<div class="question">The element with highest standard reduction potential (in volt) $\left[\mathrm{M}^{2+} \rightarrow M\right]$ among the first row of transition elements is</div>

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

answer:
<div class="solution">In the electrochemical series, $\mathrm{Cu}$ is below hydrogen. Hence, it has positive value of standard reduction potential $\left(E_{M^{2+} / M}\right)$.<br/>The standard reduction potentials are<br/>$$<br/>\begin{gathered}<br/>\mathrm{Ni}(Z=28) \Rightarrow-0.257 \mathrm{~V} \\<br/>\mathrm{Cu}(Z=29) \Rightarrow+0.337 \mathrm{~V} \\<br/>\operatorname{Cr}(Z=24) \Rightarrow-0.90 \mathrm{~V} \\<br/>\operatorname{Ti}(Z=21) \Rightarrow-1.63 \mathrm{~V}<br/>\end{gathered}<br/>$$<br/>Highest reduction potential is of $\mathrm{Cu}$ as, it has positive value of reduction potential, while $\mathrm{Ni}, \mathrm{Cr}$ and Ti have negative reduction potential value.</div>


tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-ellipse-169-x-2-25-y-2-1-has-the-same-eccentricity-as-the-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-ratio-of-a-to-b

slug:
the-ellipse-169-x-2-25-y-2-1-has-the-same-eccentricity-as-the-ellipse-a-2-x-2-b-2-y-2-1-what-is-the-ratio-of-a-to-b-70224

question:
<div class="question">The ellipse $\frac{x^{2}}{169}+\frac{y^{2}}{25}=1$ has the same eccentricity as the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. What is the ratio of $a$ to $b$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 / 13$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$13 / 5$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7 / 8$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">87</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$13 / 5$</span> </div>

answer:
<div class="solution">Given ellipse is $\frac{x^{2}}{169}+\frac{y^{2}}{25}=1$<br/>$e=\sqrt{1-\frac{25}{169}}=\frac{12}{13}$<br/>Also, standard equation of ellipse is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$<br/>nd eccentricity, $e=\sqrt{1-\frac{b^{2}}{a^{2}}}$<br/>$\frac{12}{13}=\sqrt{1-\frac{b^{2}}{a^{2}}} \Rightarrow \frac{b^{2}}{a^{2}}=1-\frac{144}{169}=\frac{25}{169}$<br/>$\Rightarrow \frac{b}{a}=\frac{5}{13} \Rightarrow \frac{a}{b}=\frac{13}{5}$</div>


title: the-embryo-sac-of-an-angiosperm-is-made-up-of
slug: the-embryo-sac-of-an-angiosperm-is-made-up-of-88841
question: <div class="question">The embryo sac of an angiosperm is made up of</div>
tags: ['Biology', 'Plant Kingdom']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>8 cells<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>7 cells and 8 nuclei<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>8 nuclei<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>7 cells and 7 nuclei</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>7 cells and 8 nuclei<br/></span> </div>

answer:
<div class="solution">Embryo sac in angiosperm contains 2 synergids, 1 egg cell, 3 antipodal cells and one secondary nucleus.</div>


tags: ['Physics', 'Electromagnetic Induction', 'AP EAMCET', 'AP EAMCET 2020 (07 Oct Special)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P2.db
title:
the-emf-induced-in-the-secondary-coil-due-to-unit-rate-of-change-of-current-in-the-primary-is-called

slug:
the-emf-induced-in-the-secondary-coil-due-to-unit-rate-of-change-of-current-in-the-primary-is-called-55849

question:
<div class="question">The emf induced in the secondary coil due to unit rate of change of current in the primary is called</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Mutual induction of two coils</span> </div>


title: the-emf-of-a-galvanic-cell-constituted-with-the-electrodes-zn-2-zn-076-v-and-fe-2-fe-041-v-is
slug: the-emf-of-a-galvanic-cell-constituted-with-the-electrodes-zn-2-zn-076-v-and-fe-2-fe-041-v-is-38037
tags: ['Chemistry', 'Electrochemistry', 'KCET', 'KCET 2013']
source_db: MarksBatch2_P2.db
question:
<div class="question">The emf of a galvanic cell constituted with the electrodes $\mathrm{Zn}^{2+} \mid \mathrm{Zn}(-0.76 \mathrm{~V})$ and $\mathrm{Fe}^{2+} \mid \mathrm{Fe}(-0.41 \mathrm{~V})$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-0.35 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$+1.17 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$+0.35 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-1.17 \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$+0.35 \mathrm{~V}$</span> </div>

answer:
<div class="solution">The cell reaction may be split into two half reactions as<br/>$\begin{aligned}<br/>&amp;\mathrm{Zn}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn} ; \quad E_{\mathrm{red}}^{\circ}=-0.76 \mathrm{~V} \\<br/>&amp;\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe} ; \quad E_{\mathrm{red}}^{\circ}=-0.44 \mathrm{~V}<br/>\end{aligned}$<br/>As $\mathrm{Zn}^{2+}$ ion has lower reduction potential than $\mathrm{Fe}^{2+}$ ion. Thus, oxidation takes place on zinc electrode standard EMF of the cell<br/>$=\left[\begin{array}{l}\text { Standard reduction potential of the } \\ \text { the reduction half reaction }\end{array}\right]-$<br/>$\left[\begin{array}{l}\text { Standard reduction potential of } \\ \text { the oxidation half reaction }\end{array}\right]$<br/>$=-0.44-(-0.76)$<br/>$=+0.35 \mathrm{~V}$</div>


title: the-end-product-in-hofmanns-exhaustive-of-amines-is
slug: the-end-product-in-hofmanns-exhaustive-of-amines-is-99453
question: <div class="question">The end product in Hofmann's exhaustive of amines is</div>
tags: ['Chemistry', 'Amines', 'MHT CET', 'MHT CET 2022 (07 Aug Shift 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary amine</span> </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="correct"> <span class="option-label">D</span> <span class="option-data">Quaternary ammonium 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> </ul>

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

answer:
<div class="solution">$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{NH}_2+\underset{\text { Excess }}{\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{I}} \underset{-\mathrm{HI}}{\longrightarrow}\left(\mathrm{CH}_3 \mathrm{CH}_2\right)_4 \mathrm{~N}^{+} \mathrm{I}^{-}$</div>


title: the-energy-available-to-the-organism-at-the-third-trophic-level-is-called
slug: the-energy-available-to-the-organism-at-the-third-trophic-level-is-called-41080
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The energy available to the organism at the third trophic level is called</div>

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

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

answer:
<div class="solution">Carnivores are organisms which obtain nutrient by killing and eating other animals. These form the secondary consumers present in the third trophic level and are preceded by the herbivore in the food chain. The rate of assimilation of food energy by consumers is called secondary productivity and this energy is available to carnivores as they are the consumers.<br/><br/>Total production of organic matter is called gross primary productivity and the energy left after utilization of producers is termed net primary productivity. Community productivity is the difference between GPP and the community respiration.</div>


tags: ['Physics', 'Units and Dimensions', 'AP EAMCET', 'AP EAMCET 2008']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Zero</span> </div>
source_db: MarksBatch2_P2.db
title:
the-energy-e-angular-momentum-l-and-universal-gravitational-constant-g-are-chosen-as-fundamental-quantities-the-dimensions-of-universal-gravitational--1

slug:
the-energy-e-angular-momentum-l-and-universal-gravitational-constant-g-are-chosen-as-fundamental-quantities-the-dimensions-of-universal-gravitational-1-11732

question:
<div class="question">The energy $(E)$, angular momentum $(L)$ and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is</div>

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

answer:
<div class="solution">$\begin{aligned}<br/>&amp; h \propto G^x L^y E^z \\<br/>&amp; {\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right] \propto\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]^x\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right]^y\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]^z} \\<br/>&amp; {\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right]=k\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]^x\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right]^y}<br/>\end{aligned}$<br/>$\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]^z$<br/>Comparing the powers, we get<br/>$\begin{aligned}<br/>1 &amp; =-x+y+z \\<br/>2 &amp; =3 x+2 y+2 z \\<br/>-1 &amp; =-2 x-y-2 z<br/>\end{aligned}$<br/>On solving Eq. (i), (ii) and (iii), we get $x=0$</div>


tags: ['Physics', 'Units and Dimensions', 'TS EAMCET', 'TS EAMCET 2008']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Zero</span> </div>
source_db: MarksBatch2_P2.db
title:
the-energy-e-angular-momentum-l-and-universal-gravitational-constant-g-are-chosen-as-fundamental-quantities-the-dimensions-of-universal-gravitational-

slug:
the-energy-e-angular-momentum-l-and-universal-gravitational-constant-g-are-chosen-as-fundamental-quantities-the-dimensions-of-universal-gravitational-40746

question:
<div class="question">The energy $(E)$, angular momentum $(L)$ and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is</div>

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

answer:
<div class="solution">$\begin{aligned}<br/>&amp; h \propto G^x L^y E^z \\<br/>&amp; {\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right] \propto\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]^x\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right]^y\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]^z} \\<br/>&amp; {\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right]=k\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]^x\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-1}\right]^y}<br/>\end{aligned}$<br/>$\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]^z$<br/>Comparing the powers, we get<br/>$\begin{aligned}<br/>1 &amp; =-x+y+z \\<br/>2 &amp; =3 x+2 y+2 z \\<br/>-1 &amp; =-2 x-y-2 z<br/>\end{aligned}$<br/>On solving Eq. (i), (ii) and (iii), we get $x=0$</div>


tags: ['Chemistry', 'Thermodynamics (C)']
options: None
correct_option: None
answer: <div class="solution">(ii) zero</div>
source_db: MarksBatch2_P2.db
title:
the-enthalpies-of-all-elements-in-their-standard-states-are-i-unity-ii-zero-iii-0-iv-different-for-each-element

slug:
the-enthalpies-of-all-elements-in-their-standard-states-are-i-unity-ii-zero-iii-0-iv-different-for-each-element-79398

question:
<div class="question">The enthalpies of all elements in their standard states are :<br/>(i) unity<br/>(ii) zero<br/>(iii) \( &lt; 0\)<br/>(iv) different for each element</div>


title: the-enthalpies-of-all-elements-in-their-standard-states-are
slug: the-enthalpies-of-all-elements-in-their-standard-states-are-20736
question: <div class="question">The enthalpies of all elements in their standard states are</div>
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'JIPMER', 'JIPMER 2004']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
answer: <div class="solution">The enthalphy of elements are zero in their standard state.</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\gt0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$ \lt 0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">unity</span> </li> </ul>


tags: ['Chemistry', 'Thermodynamics (C)', 'TS EAMCET', 'TS EAMCET 2023 (12 May Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">+98 kJ</span> </div>
source_db: MarksBatch2_P2.db
title:
the-enthalpies-of-formation-of-gaseous-n-2-o-and-no-at-298-k-are-820-and-900-kj-mol-1-respectively-the-enthalpy-change-of-the-reaction-n-2-o-g-2-1-o-2

slug:
the-enthalpies-of-formation-of-gaseous-n-2-o-and-no-at-298-k-are-820-and-900-kj-mol-1-respectively-the-enthalpy-change-of-the-reaction-n-2-o-g-2-1-o-2-18049

question:
<div class="question">The enthalpies of formation of gaseous $\mathrm{N}_2 \mathrm{O}$ and $\mathrm{NO}$ at $298 \mathrm{~K}$ are 82.0 and $90.0 \mathrm{KJ} \mathrm{mol}^{-1}$ respectively. The enthalpy change of the reaction $\mathrm{N}_2 \mathrm{O}(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow$ $2 \mathrm{NO}(\mathrm{g})$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-74 \mathrm{~kJ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">+98 kJ</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">+89 kJ</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">-47 kJ</span> </li> </ul>

answer:
<div class="solution">$$<br/>\Delta \mathrm{H}_{\mathrm{r}}^{\circ}=\left[2 \Delta \mathrm{H}_{\mathrm{f}}^{\circ}(\mathrm{NO})\right]-\left[\Delta \mathrm{H}_{\mathrm{f}}^{\circ}\left(\mathrm{N}_2 \mathrm{O}\right)+\frac{1}{2} \Delta \mathrm{H}_{\mathrm{f}}^{\circ}\left(\mathrm{O}_2\right)\right]<br/>$$<br/>$\Delta \mathrm{H}_{\mathrm{f}}^{\circ}\left(\mathrm{O}_2\right)=0$ (standard state of an element)<br/>$$<br/>\begin{gathered}<br/>\Rightarrow \Delta \mathrm{H}_{\mathrm{r}}{ }^{\circ}=[2 \times 90.0]-[82.0+0.0] \\<br/>\quad=180.0-82.0=+98.0 \mathrm{~kJ} .<br/>\end{gathered}<br/>$$</div>


title: the-enthalpies-of-the-elements-in-their-standard-states-are-assumed-to-be
slug: the-enthalpies-of-the-elements-in-their-standard-states-are-assumed-to-be-59775
tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The enthalpies of the elements in their standard states are assumed to be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Zero at 298 K</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Unit at 298 K</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Zero at all temperature</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Zero at 273 K</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Zero at 298 K</span> </div>

answer:
<div class="solution">The enthalpies of the elements in their standard states are assumed to be zero at 298 K</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Main', 'JEE Main 2006']
source_db: MarksBatch2_P2.db
title:
the-enthalpy-changes-for-the-following-processes-are-listed-below-cl-2-g-2-cl-g-i-2-g-2-i-g-icl-g-i-g-cl-g-i-2-s-i-2-g-2423-kj-mol-1-1510-kj-mol-1-211

slug:
the-enthalpy-changes-for-the-following-processes-are-listed-below-cl-2-g-2-cl-g-i-2-g-2-i-g-icl-g-i-g-cl-g-i-2-s-i-2-g-2423-kj-mol-1-1510-kj-mol-1-211-99387

question:
<div class="question">The enthalpy changes for the following processes are listed below:<br/>$\begin{array}{ll}\mathrm{Cl}_2(\mathrm{~g})=2 \mathrm{Cl}(\mathrm{g}), &amp; 242.3 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ \mathrm{I}_2(\mathrm{~g})=2 \mathrm{I}(\mathrm{g}), &amp; 151.0 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ \mathrm{ICl}(\mathrm{g})=\mathrm{I}(\mathrm{g})+\mathrm{Cl}(\mathrm{g}), &amp; 211.3 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ \mathrm{I}_2(\mathrm{~s})=\mathrm{I}_2(\mathrm{~g}), &amp; 62.76 \mathrm{~kJ} \mathrm{~mol}^{-1}\end{array}$<br/>Given that the standard states for iodine and chlorine are $\mathrm{I}_2(\mathrm{~s})$ and $\mathrm{Cl}_2(\mathrm{~g})$, the standard enthalpy of formation for $\mathrm{ICl}(\mathrm{g})$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$-14.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$-16.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$+16.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$<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/>$+244.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$+16.8 \mathrm{~kJ} \mathrm{~mol}^{-1}$<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \frac{1}{2} \mathrm{I}_2(\mathrm{~s})+\frac{1}{2} \mathrm{Cl}_2 \longrightarrow \mathrm{ICl}(\mathrm{g}) \\<br/>&amp; \Delta \mathrm{H}=\left[\frac{1}{2} \Delta \mathrm{H}_{\mathrm{b}_2(s) \rightarrow k_2(g)}+\frac{1}{2} \mu_{1-1}+\frac{1}{2} \mu_{\mathrm{cl}-\mathrm{cl}}\right]-\left[\mu_{1-a}\right] \\<br/>&amp; =\left(\frac{1}{2} \times 62.76+\frac{1}{2} \times 151.0+\frac{1}{2} \times 242.3\right)-(211.3) \\<br/>&amp; =228.03-211.3 \\<br/>&amp; \Delta \mathrm{H}=16.73 \\<br/>&amp;<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-enthalpy-of-reaction-for-the-reaction-2h-2-g-o-2-g-2h-2-ol-is-r-h-572-kj-mol-1-what-will-be-standard-enthalpy-of-formation-of-h-2-ol

slug:
the-enthalpy-of-reaction-for-the-reaction-2h-2-g-o-2-g-2h-2-ol-is-r-h-572-kj-mol-1-what-will-be-standard-enthalpy-of-formation-of-h-2-ol-74190

question:
<div class="question">The enthalpy of reaction for the reaction : 2H<sub>2</sub>(g) + O<sub>2</sub>(g) â 2H<sub>2</sub>O(l)  is â<sub>r</sub>H<sup>â</sup>= â 572 kJ mol<sup>â1</sup>. What will be standard enthalpy of formation of H<sub>2</sub>O(l)?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">â<sub>f</sub>H<sup>â</sup>(H<sub>2</sub>O(l)) = +286 kJ / mol</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">â<sub>f</sub>H<sup>â</sup>(H<sub>2</sub>O(l)) = -214 kJ / mol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">â<sub>f</sub>H<sup>â</sup>(H<sub>2</sub>O(l)) = -365 kJ / mol</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">â<sub>f</sub>H<sup>â</sup>(H<sub>2</sub>O(l)) = -286 kJ / mol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">â<sub>f</sub>H<sup>â</sup>(H<sub>2</sub>O(l)) = -286 kJ / mol</span> </div>

answer:
<div class="solution">Correct Option is : (D)<br/>â<sub>f</sub>H<sup>â</sup>(H<sub>2</sub>O(l)) = -286 kJ / mol</div>


title: the-equation-1-x-x-2-5-has
slug: the-equation-1-x-x-2-5-has-95365
question: <div class="question">The equation $|1-x|+x^{2}=5$ has</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">a rational root and an irrational root</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">two rational roots</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">two irrational roots</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">no real roots</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">a rational root and an irrational root</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp;|1-x|+z^{2}=5 \\ &amp; \Rightarrow|x-1|+x^{2}=5 \\ &amp; \text { First case: If } x   &lt; 1,|x-1| \text { is negative. } \end{aligned}$<br/>$\begin{aligned} &amp; \therefore-(x-1)+x^{2}=5 \\ &amp; \Rightarrow-x+1+x^{2}=5 \\ \Rightarrow &amp; x^{2}-x+1=5 \\ \Rightarrow &amp; x^{2}-x-4=0 \end{aligned}$<br/>Roots are $\frac{-(-1) \pm \sqrt{(-1)^{2}-4(1)(-4)}}{2(1)}$<br/>$=\frac{1 \pm \sqrt{1+16}}{2}=\frac{1 \pm \sqrt{17}}{2}$<br/>Since, $x &lt; 1$, root cannot be $\frac{1+\sqrt{17}}{2} .$ So, the root is<br/>$\frac{1-\sqrt{17}}{2}$, which is irrational.<br/>Second case: If $x&gt;1,|x-1|=x-1$ $\mathrm{x}-1 \mid+2^{2}=5$<br/>$\Rightarrow \quad x-1+x^{2}=5$<br/>$\Rightarrow \quad x^{2}+x-6=0$<br/>$\Rightarrow \quad x^{2}+3 x-2 x-6=0$<br/>$\Rightarrow \quad x(x-3)-2(x+3)=0$<br/>$\Rightarrow \quad x=2,-3$<br/>Since $x&gt;1$, root cannot be $-3 .$ So, root is 2 which is rational.<br/>$\therefore$ Given expression has one irrational root and One rational root</div>


title: the-equation-2-x-2-3-y-2-6-0-represents
slug: the-equation-2-x-2-3-y-2-6-0-represents-85970
question: <div class="question">The equation $2 \mathrm{x}^{2}-3 \mathrm{y}^{2}-6=0$ represents</div>
tags: ['Mathematics', 'Hyperbola', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a circle</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">a parabola</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">an ellipse</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">a hyperbola</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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 hyperbola</span> </div>

answer:
<div class="solution">Given equation, $2 x^{2}-3 y^{2}-6=0$ $\Rightarrow 2 x^{2}-3 y^{2}=6$<br/>$\Rightarrow \frac{x^{2}}{3}-\frac{y^{2}}{2}=1$<br/>This equation represents hyperbola.</div>


tags: ['Mathematics', 'Pair of Lines', 'MHT CET', 'MHT CET 2008']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$-12$</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equation-12-x-2-7-x-y-a-y-2-13-x-y-3-0-represents-a-pair-of-perpendicular-lines-then-the-value-of-a-is

slug:
the-equation-12-x-2-7-x-y-a-y-2-13-x-y-3-0-represents-a-pair-of-perpendicular-lines-then-the-value-of-a-is-51907

question:
<div class="question">The equation $12 x^{2}+7 x y+a y^{2}+13 x-y+3=0$<br/>represents a pair of perpendicular lines. Then the value of ' $a$ ' is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{7}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-19$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$-12$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">12</span> </li> </ul>

answer:
<div class="solution">Comparing the given equation with standard equation, we get $a=12$ and $b=a$, for perpendicular lines coefficient of $x^{2}+$ coefficient of $y^{2}=0$ $\therefore \quad 12+a=0$<br/>$\Rightarrow \quad a=-12$</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-a-2-b-2-x-2-2-b-a-c-x-b-2-c-2-0-has-equal-roots-which-one-of-the-following-is-correct-about-a-b-and-c

slug:
the-equation-a-2-b-2-x-2-2-b-a-c-x-b-2-c-2-0-has-equal-roots-which-one-of-the-following-is-correct-about-a-b-and-c-51474

question:
<div class="question">The equation $\left(a^{2}+b^{2}\right) x^{2}-2 b(a+c) x+\left(b^{2}+c^{2}\right)=0$ has equal roots. Which one of the following is correct about $\mathrm{a}, \mathrm{b}$, and $\mathrm{c}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">They are in AP</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Theyare in GP</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">They are in $\mathrm{HP}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">They are neither in AP, nor in GP, nor in HP</span> </li> </ul>

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

answer:
<div class="solution">The given equation $\left(a^{2}+b^{2}\right) x^{2}-2 b(a+c) x+\left(b^{2}+c^{2}\right)=0$<br/>has equal roots, so, discriminant $=0$ Hence, $\{2 \mathrm{~b}(\mathrm{a}+\mathrm{c})\}^{2}-4\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)\left(\mathrm{b}^{2}+\mathrm{c}^{2}\right)=0$<br/>$\Rightarrow 4 b^{2}\left(a^{2}+c^{2}+2 c a\right)-4\left(a^{2} b^{2}+a^{2} c^{2}+b^{4}+b^{2} c^{2}\right)$<br/>$=0$<br/>$\Rightarrow b^{2} a^{2}+b^{2} c^{2}+2 b^{2} c a-a^{2} b^{2}-a^{2} c^{2}-b^{4}-b^{2} c^{2}=0$<br/>$\Rightarrow 2 b^{2} c a=b^{4}+a^{2} c^{2}$<br/>$\Rightarrow b^{4}-2 b^{2} c a+a^{2} c^{2}=0$<br/>$\Rightarrow\left(b^{2}\right)^{2}-2\left(b^{2}\right)(a c)+(a c)^{2}=0$<br/>$\Rightarrow\left(b^{2}-a c\right)^{2}=0$<br/>$\Rightarrow \mathrm{b}^{2}=\mathrm{ac}$<br/>$\Rightarrow \mathrm{a}, \mathrm{b}, \mathrm{c}$ are in GP.</div>


title: the-equation-b-y-cz-d-0-represents-a-plane-parallel-to-which-one-of-the-following
slug: the-equation-b-y-cz-d-0-represents-a-plane-parallel-to-which-one-of-the-following-53518
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation $b y+c z+d=0$ represents a plane parallel to which one of the following?</div>

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

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

answer:
<div class="solution">Direction cosines of the normal to the given plane $b y+c z+d=0$ are $0, b, c$<br/>Direction cosines of the $\mathrm{x}$ -axis are $1,0,0$<br/>Since, $0 \times 1+b \times 0+c \times 0=0$<br/>Hence $x$ -axis is perpendicular to normal to the given plane. Therefore $x$ -axis is parallel to the given plane</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2012 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3 :1</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equation-formed-by-multiplying-each-root-of-a-x-2-b-x-c-0-by-2-is-x-2-36-x-24-0-what-is-bc-equal-to

slug:
the-equation-formed-by-multiplying-each-root-of-a-x-2-b-x-c-0-by-2-is-x-2-36-x-24-0-what-is-bc-equal-to-47613

question:
<div class="question">The equation formed by multiplying each root of $a x^{2}+b x+c=0$ by 2 is $x^{2}+36 x+24=0$<br/>What is b:c equal to?</div>

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

answer:
<div class="solution">Let $\alpha, \beta$ be roots of equation $a x^{2}+b x+c$ $\alpha+\beta=-\mathrm{b} / \mathrm{a}, \alpha \beta=\mathrm{c} / \mathrm{a}$<br/>are roots of equation $x^{2}+36 x+24$ Now, $2 \alpha+2 \beta=-36$<br/>$\Rightarrow \alpha+\beta=-18 \Rightarrow-\frac{\mathrm{b}}{\mathrm{a}}=-18 \Rightarrow \mathrm{b}=18 \mathrm{a}$<br/>and $(2 \alpha)(2 \beta)=24$<br/>$\Rightarrow \alpha \beta=6 \Rightarrow \frac{\mathrm{c}}{\mathrm{a}}=6 \Rightarrow \mathrm{c}=6 \mathrm{a}$<br/>$\mathrm{c}=3: 1$</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-formed-by-multiplying-each-root-of-a-x-2-b-x-c-0-by-2-is-x-2-36-x-24-0-which-one-of-the-following-is-correct

slug:
the-equation-formed-by-multiplying-each-root-of-a-x-2-b-x-c-0-by-2-is-x-2-36-x-24-0-which-one-of-the-following-is-correct-53345

question:
<div class="question">The equation formed by multiplying each root of $a x^{2}+b x+c=0$ by 2 is $x^{2}+36 x+24=0$<br/>Which one of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$b c=a^{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$b c=36 a^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$b c=72 a^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$b c=108 a^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$b c=108 a^{2}$</span> </div>

answer:
<div class="solution">$\therefore \mathrm{bc}=(18 \mathrm{a})(6 \mathrm{a})=108 \mathrm{a}^{2}$</div>


title: the-equation-of-a-circle-whose-end-points-of-a-diameter-are-x-1-y-1-and-x-2-y-2-is
slug: the-equation-of-a-circle-whose-end-points-of-a-diameter-are-x-1-y-1-and-x-2-y-2-is-41567
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation of a circle whose end points of a diameter are $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$ and $\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(x-x_{1}\right)\left(x-x_{2}\right)+\left(y-y_{1}\right)\left(y-y_{2}\right)=0$</span> </div>

answer:
<div class="solution">Equation of circle is<br/>$\left(x-x_{1}\right)\left(x-x_{2}\right)+\left(y-y_{1}\right)\left(y-y_{2}\right)=0$</div>


tags: ['Physics', 'Waves and Sound', 'COMEDK', 'COMEDK 2020']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-progressive-wave-can-be-given-by-y-15-sin-660-t-002-x-cm-the-frequency-of-the-wave-is-2

slug:
the-equation-of-a-progressive-wave-can-be-given-by-y-15-sin-660-t-002-x-cm-the-frequency-of-the-wave-is-2-23595

question:
<div class="question">The equation of a progressive wave can be given by $y=15 \sin (660 \pi t-0.02 \pi x) \mathrm{cm}$. The frequency of the wave is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$330 \mathrm{~Hz}$</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">B</span> <span class="option-data">$342 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$365 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$660 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$330 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">Given, equation of progressive wave,<br/>$$<br/>y=15 \sin (660 \pi t-0.02 \pi x)<br/>$$<br/>Comparing this equation with standard equation of progressive wave as $y=A \sin \left(\frac{2 \pi}{T}, t-\frac{2 \pi}{\lambda}, x\right)$<br/>We get,<br/>$\begin{aligned} \frac{2 \pi}{T} &amp;=660 \pi \\ \Rightarrow \quad T &amp;=\frac{2 \pi}{660 \pi} \\ \Rightarrow \quad T &amp;=\frac{1}{330} \\ \therefore \text { Frequency of the wave, } \\ v &amp;=\frac{1}{T} \\ &amp;=\frac{1}{1 / 330}=330 \mathrm{~Hz} \end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-progressive-wave-can-be-given-by-y-15-sin-660-t-002-x-cm-the-frequency-of-the-wave-is-3

slug:
the-equation-of-a-progressive-wave-can-be-given-by-y-15-sin-660-t-002-x-cm-the-frequency-of-the-wave-is-3-12858

question:
<div class="question">The equation of a progressive wave can be given by $y=15 \sin (660 \pi t-0.02 \pi x) \mathrm{cm}$. The frequency of the wave is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$330 \mathrm{~Hz}$</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">B</span> <span class="option-data">$342 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$365 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$660 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$330 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">Given, equation of progressive wave,<br/>$$<br/>y=15 \sin (660 \pi t-0.02 \pi x)<br/>$$<br/>Comparing this equation with standard equation of progressive wave as $y=A \sin \left(\frac{2 \pi}{T}, t-\frac{2 \pi}{\lambda}, x\right)$<br/>We get,<br/>$\begin{aligned} \frac{2 \pi}{T} &amp;=660 \pi \\ \Rightarrow \quad T &amp;=\frac{2 \pi}{660 \pi} \\ \Rightarrow \quad T &amp;=\frac{1}{330} \\ \therefore \text { Frequency of the wave, } \\ v &amp;=\frac{1}{T} \\ &amp;=\frac{1}{1 / 330}=330 \mathrm{~Hz} \end{aligned}$</div>


tags: ['Physics', 'Waves and Sound', 'AIIMS', 'AIIMS 2015']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-progressive-wave-is-given-by-y-5-sin-100-t-04-x-where-y-and-x-are-in-m-and-t-is-in-s-1-the-amplitude-of-the-wave-is-5-m-2-the-wavele

slug:
the-equation-of-a-progressive-wave-is-given-by-y-5-sin-100-t-04-x-where-y-and-x-are-in-m-and-t-is-in-s-1-the-amplitude-of-the-wave-is-5-m-2-the-wavele-88006

question:
<div class="question">The equation of a progressive wave is given by $y=5 \sin (100 \pi t-0.4 \pi x)$ where $y$ and $x$ are in $\mathrm{m}$ and $t$ is in $\mathrm{s}$.<br/>(1) The amplitude of the wave is $5 \mathrm{~m}$.<br/>(2) The wavelength of the wave is $5 \mathrm{~m}$.<br/>(3) The frequency of the wave is $50 \mathrm{~Hz}$.<br/>(4) The velocity of the wave is $250 \mathrm{~m} \mathrm{~s}^{-1}$.<br/>Which of the following statements are correct?</div>

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

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

answer:
<div class="solution">The equation of a given progressive wave is<br/>$$<br/>y=5 \sin (100 \pi t-0.4 \pi x)<br/>$$<br/>The standard equation of a progressive wave is<br/>$$<br/>y=a \sin (\omega t-k x)<br/>$$<br/>Comparing (i) and (ii), we get<br/>$$<br/>a=5 \mathrm{~m}, \omega=100 \pi \mathrm{rad} \mathrm{s}^{-1}, k=0.4 \pi \mathrm{m}^{-1}<br/>$$<br/><br/><br/><br/>(1) Amplitude of the wave, $a=5 \mathrm{~m}$<br/>(2) Wavelength of the wave,<br/>$$<br/>\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{0.4 \pi}=5 \mathrm{~m}<br/>$$<br/>(3) Frequency of the wave,<br/>$$<br/>v=\frac{\omega}{2 \pi}=\frac{100 \pi}{2 \pi}=50 \mathrm{~Hz}<br/>$$<br/>(4) Velocity of the wave,<br/>$$<br/>v=v \lambda=\left(50 \mathrm{~s}^{-1}\right)(5 \mathrm{~m})=250 \mathrm{~m} \mathrm{~s}^{-1}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-simple-harmonic-wave-is-given-by-y-6-sin-2-2-t-0-l-x-where-x-and-y-are-in-mm-and-t-is-in-seconds-the-phase-difference-between-two-pa-1

slug:
the-equation-of-a-simple-harmonic-wave-is-given-by-y-6-sin-2-2-t-0-l-x-where-x-and-y-are-in-mm-and-t-is-in-seconds-the-phase-difference-between-two-pa-1-60702

question:
<div class="question">The equation of a simple harmonic wave is given by $y=6 \sin 2 \pi(2 t-0 . l x)$, where $x$ and $y$ are in $\mathrm{mm}$ and $t$ is in seconds. The phase difference between two particles $2 \mathrm{~mm}$ apart at any instant is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$18^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$36^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$54^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$72^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">Equalion of simple harmonic wave is given as<br/>$$<br/>y=6 \sin 2 \pi(2 t-0.1 x)<br/>$$<br/>Path difference, $\Delta x=2 \mathrm{~mm}$<br/>Comparing with standard equation of wave,<br/>$$<br/>\begin{aligned}<br/>y &amp;=A \sin (\omega t-k x) \\<br/>&amp;=A \sin 2 \pi\left(v t-\frac{k}{2 \pi} \cdot x\right) \\<br/>\frac{k}{2 \pi} &amp;=0.1 \\<br/>k &amp;=0.2 \pi<br/>\end{aligned}<br/>$$<br/>Wavelength, $\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{0.2 \pi}=10 \mathrm{~mm}$<br/>$\therefore$ We know that, phase difference,<br/>$$<br/>\begin{aligned}<br/>\phi &amp;=\frac{2 \pi}{\lambda} \times \text { path difference }(\Delta x) \\<br/>&amp;=\frac{2 \pi}{10} \times 2=\frac{2 \pi}{5}=\frac{2 \times 180}{5}=72^{\circ}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'COMEDK', 'COMEDK 2018']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-simple-harmonic-wave-is-given-by-y-6-sin-2-2-t-0-l-x-where-x-and-y-are-in-mm-and-t-is-in-seconds-the-phase-difference-between-two-pa

slug:
the-equation-of-a-simple-harmonic-wave-is-given-by-y-6-sin-2-2-t-0-l-x-where-x-and-y-are-in-mm-and-t-is-in-seconds-the-phase-difference-between-two-pa-24200

question:
<div class="question">The equation of a simple harmonic wave is given by $y=6 \sin 2 \pi(2 t-0 . l x)$, where $x$ and $y$ are in $\mathrm{mm}$ and $t$ is in seconds. The phase difference between two particles $2 \mathrm{~mm}$ apart at any instant is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$18^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$36^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$54^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$72^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">Equalion of simple harmonic wave is given as<br/>$$<br/>y=6 \sin 2 \pi(2 t-0.1 x)<br/>$$<br/>Path difference, $\Delta x=2 \mathrm{~mm}$<br/>Comparing with standard equation of wave,<br/>$$<br/>\begin{aligned}<br/>y &amp;=A \sin (\omega t-k x) \\<br/>&amp;=A \sin 2 \pi\left(v t-\frac{k}{2 \pi} \cdot x\right) \\<br/>\frac{k}{2 \pi} &amp;=0.1 \\<br/>k &amp;=0.2 \pi<br/>\end{aligned}<br/>$$<br/>Wavelength, $\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{0.2 \pi}=10 \mathrm{~mm}$<br/>$\therefore$ We know that, phase difference,<br/>$$<br/>\begin{aligned}<br/>\phi &amp;=\frac{2 \pi}{\lambda} \times \text { path difference }(\Delta x) \\<br/>&amp;=\frac{2 \pi}{10} \times 2=\frac{2 \pi}{5}=\frac{2 \times 180}{5}=72^{\circ}<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-sphere-is-x-2-y-2-z-2-10-z-0-if-one-end-point-of-a-diameter-of-the-sphere-is-3-4-5-what-is-the-other-end-point

slug:
the-equation-of-a-sphere-is-x-2-y-2-z-2-10-z-0-if-one-end-point-of-a-diameter-of-the-sphere-is-3-4-5-what-is-the-other-end-point-30978

question:
<div class="question">The equation of a sphere is $x^{2}+y^{2}+z^{2}-10 z=0$. If one end point of a diameter of the sphere is $(-3,-4,5)$, what is the other end point?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(3,4,5)$</span> </div>

answer:
<div class="solution">The equation of the given sphere is $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}-10 \mathrm{z}=0$<br/>Its centre is $(0,0,5)$. Coordinates of one end point of a diameter of the sphere is given as $(-3,-4,5)$ Let Coordinates of another end point of this diameter $\left(\mathrm{x}_{1}, \mathrm{y}_{1}, \mathrm{z}_{1}\right)$<br/>$\frac{-3+\mathrm{x}_{1}}{2}=0 \quad \Rightarrow \mathrm{x}_{1}=3$<br/>$\frac{-4+y_{1}}{2}=0 \quad \Rightarrow y_{1}=4$<br/>and $\frac{5+z_{1}}{2}=5 \Rightarrow z_{1}=5$<br/>$\therefore \quad$ Required coordinates are $(3,4,5)$.</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">20 cm</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-stationary-wave-is-y-08-cos-20-x-sin-200-t-where-x-is-in-cm-and-t-is-in-sec-the-separation-between-consecutive-nodes-will-be

slug:
the-equation-of-a-stationary-wave-is-y-08-cos-20-x-sin-200-t-where-x-is-in-cm-and-t-is-in-sec-the-separation-between-consecutive-nodes-will-be-74037

question:
<div class="question">The equation of a stationary wave is<br/>$y=0.8 \cos \left(\frac{\pi x}{20}\right) \sin 200 \pi t$ , where $x$ is in $\mathrm{cm}$ and $t$ is in sec.<br/>The separation between consecutive nodes will be</div>

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

answer:
<div class="solution">On comparing the given equation with standard equation $y=2 a \sin \frac{2 \pi x}{\lambda} \cos \frac{2 \pi v t}{\lambda}$<br/>We get $\frac{2 \pi}{\lambda}=\frac{\pi}{20} \Rightarrow \lambda=40$<br/>Separation between two consecutive nodes $=\frac{\lambda}{2}=\frac{40}{2}=20 \mathrm{~cm}$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-straight-line-which-cuts-off-an-intercept-of-5-units-on-negative-direction-of-yaxis-and-makes-an-angle-12-0-with-positive-direction-

slug:
the-equation-of-a-straight-line-which-cuts-off-an-intercept-of-5-units-on-negative-direction-of-yaxis-and-makes-an-angle-12-0-with-positive-direction-50949

question:
<div class="question">The equation of a straight line which cuts off an intercept of 5 units on negative direction of y-axis and makes an angle $120^{\circ}$ with positive direction of $\mathrm{x}$ -axis is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{y}+\sqrt{3} \mathrm{x}+5=0$</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">$y-\sqrt{3} x+5=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$y+\sqrt{3} x-5=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$y-\sqrt{3} x-5=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{y}+\sqrt{3} \mathrm{x}+5=0$</span> </div>

answer:
<div class="solution">Slope of the required line, $\mathrm{m}=\tan 120^{\circ}=-\sqrt{3}$ (since it is making angle with positive direction of $\mathrm{x}$ -axis). Given, line cuts off an intercept of 5 units on negative direction of y-axis. This means line is intersecting $\mathrm{y}$ axis at $(0,-5)$<br/>$\mathrm{P}=(0,-5)$ and $\mathrm{m}=-\sqrt{3}$.<br/>Equation of line is $\mathrm{y}-(-5)=-\sqrt{3}(\mathrm{x}-0)$<br/>$\Rightarrow \mathrm{y}+5=-\sqrt{3} \mathrm{x}$<br/>$\Rightarrow \mathrm{y}+\sqrt{3} \mathrm{x}+5=0$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-straight-line-which-makes-an-angle-4-5-with-the-x-axis-with-yintercept-101-units-is

slug:
the-equation-of-a-straight-line-which-makes-an-angle-4-5-with-the-x-axis-with-yintercept-101-units-is-58621

question:
<div class="question">The equation of a straight line which makes an angle $45^{\circ}$ with the $\mathrm{x}$ -axis with y-intercept 101 units is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{x}+101 \mathrm{y}=1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$101 \mathrm{x}+\mathrm{y}=1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$x+y-101=0$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$x-y+101=0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x-y+101=0$</span> </div>

answer:
<div class="solution">The equation of the required line is, $\mathrm{y}=\mathrm{mx}+\mathrm{c}$$\ldots \ldots$ (i)<br/>where $m=\tan 45^{\circ}=1$<br/>and $\mathrm{c}=\mathrm{y}-$ intercept $=101$ units<br/>from (i) $\mathrm{y}=\mathrm{x}+101 \Rightarrow \mathrm{x}-\mathrm{y}+101=0$</div>


tags: ['Physics', 'Waves and Sound', 'KCET', 'KCET 2013']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-transverse-wave-is-given-by-y-005-sin-2-t-002-x-where-x-y-are-in-metre-and-t-is-in-second-the-minimum-distance-of-separation-between

slug:
the-equation-of-a-transverse-wave-is-given-by-y-005-sin-2-t-002-x-where-x-y-are-in-metre-and-t-is-in-second-the-minimum-distance-of-separation-between-84701

question:
<div class="question">The equation of a transverse wave is given by $y=0.05 \sin \pi(2 t-0.02 x)$, where $x, y$ are in metre and $t$ is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$50 \mathrm{~m}, 50 \mathrm{~ms}^{-1}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$100 \mathrm{~m}, 100 \mathrm{~ms}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$50 \mathrm{~m}, 100 \mathrm{~ms}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$100 \mathrm{~m}, 50 \mathrm{~ms}^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$100 \mathrm{~m}, 100 \mathrm{~ms}^{-1}$</span> </div>

answer:
<div class="solution">Given, $y=0.05 \sin \pi(2 t-0.02 x)$<br/>or $\quad y=0.05 \sin (2 \pi t-0.02 \pi x)$<br/>On comparing this equation with standard equation<br/>$y=a \sin (\omega t-k x)$<br/>where $\omega=\frac{2 \pi}{T}$ and $K=\frac{2 \pi}{\lambda}$, we have<br/>$\frac{2 \pi}{\lambda}=0.02 \pi \Rightarrow \lambda=100 \mathrm{~m}$<br/>Also, $\quad \omega=\frac{2 \pi}{T}=2 \pi$<br/>or $\quad \frac{1}{T}=1 \Rightarrow v=1$<br/>So, $v=r \lambda=1 \times 100=100 \mathrm{~m} / \mathrm{s}$</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-transverse-wave-is-given-by-y-10-s-i-n-001-x-2-t-where-x-and-y-are-in-cm-and-t-is-in-seconds-its-frequency-is

slug:
the-equation-of-a-transverse-wave-is-given-by-y-10-s-i-n-001-x-2-t-where-x-and-y-are-in-cm-and-t-is-in-seconds-its-frequency-is-10394

question:
<div class="question">The equation of a transverse wave is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>10</mn><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>nÏ</mi><mfenced separators="|"><mrow><mn>0.01</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>t</mi></mrow></mfenced></math> where <math><mi>x</mi></math> and <math><mi>y</mi></math> are in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cm</mi></math> and <math><mi>t</mi></math> is in seconds. Its frequency is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mi mathvariant="normal"> </mi><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>2</mn><mi mathvariant="normal"> </mi><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>1</mn><mi mathvariant="normal"> </mi><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>0.01</mn><mi mathvariant="normal"> </mi><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>1</mn><mi mathvariant="normal"> </mi><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </div>

answer:
<div class="solution"><p>Comparing with the standard equation, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>Asin</mi><mfenced separators="|"><mrow><mi mathvariant="normal">k</mi><mi>x</mi><mo>-</mo><mi mathvariant="normal">ω</mi><mi>t</mi></mrow></mfenced></math>, we have<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo> </mo><mi mathvariant="normal">r</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi><mo>/</mo><mi mathvariant="normal">s</mi></math></p><p>Frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mi>ω</mi><mrow><mn>2</mn><mi>π</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac><mo>=</mo><mn>1</mn><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>n</mi><mo>=</mo><mn>1</mn><mi mathvariant="normal"> </mi><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-wave-is-y-2-sin-05-x-200-t-where-x-and-y-are-expressed-in-cm-and-t-in-sec-the-wave-velocity-is

slug:
the-equation-of-a-wave-is-y-2-sin-05-x-200-t-where-x-and-y-are-expressed-in-cm-and-t-in-sec-the-wave-velocity-is-24750

question:
<div class="question">The equation of a wave is $y=2 \sin \pi(0.5 x-200 t)$, where $x$ and $y$ are expressed in $\mathrm{cm}$ and $t$ in sec.<br/>The wave velocity is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$100 \mathrm{~cm} / \mathrm{sec}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$200 \mathrm{~cm} / \mathrm{sec}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$300 \mathrm{~cm} / \mathrm{sec}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$400 \mathrm{~cm} / \mathrm{sec}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$400 \mathrm{~cm} / \mathrm{sec}$</span> </div>

answer:
<div class="solution">Cemparing given equation with standard equation of progressive wave. The velocity of wave<br/>$v=\frac{\omega(\text { Co }- \text { efficientof } t)}{k(\text { Co }- \text { efficientof } x)}=\frac{200 \pi}{0.5 \pi}=400 \mathrm{~cm} / \mathrm{s}$</div>


tags: ['Physics', 'Waves and Sound', 'JIPMER', 'JIPMER 2010']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-wave-is-y-5-sin-004-t-4-x-where-x-is-in-cm-and-t-is-in-second-the-maximum-velocity-of-the-wave-will-be

slug:
the-equation-of-a-wave-is-y-5-sin-004-t-4-x-where-x-is-in-cm-and-t-is-in-second-the-maximum-velocity-of-the-wave-will-be-32476

question:
<div class="question">The equation of a wave is $y=5 \sin \left(\frac{t}{0.04}-\frac{x}{4}\right)$; where, $x$ is in cm and $t$ is in second. The maximum velocity of the wave will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \mathrm{~ms}^{-1}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~ms}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.5 \mathrm{~ms}^{-1}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1.25 \mathrm{~ms}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.25 \mathrm{~ms}^{-1}$</span> </div>

answer:
<div class="solution">Equation of wave<br/>$y=5 \sin \left(\frac{t}{0.04}-\frac{x}{4}\right)$<br/>The standard equation of a wave in the given form is<br/>$y=a \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right)$<br/>Comparing the given equation with the standard equation, we get<br/>$a=5 \text { and } \omega=\frac{1}{0.04}=25$<br/>Therefore, maximum velocity of particles of the medium,<br/>$v_{\max }=a \omega=5 \times 25=125 \mathrm{cms}^{-1}=1.25 \mathrm{~ms}^{-1}$</div>


tags: ['Mathematics', 'Ellipse', 'AP EAMCET', 'AP EAMCET 2021 (25 Aug Shift 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-an-ellipse-in-its-standard-form-given-the-distance-between-its-foci-is-2-units-and-the-length-of-its-latusrectum-is-2-15-units-is

slug:
the-equation-of-an-ellipse-in-its-standard-form-given-the-distance-between-its-foci-is-2-units-and-the-length-of-its-latusrectum-is-2-15-units-is-96744

question:
<div class="question">The equation of an ellipse in its standard form, given the distance between its foci is 2 units and the length of its latusrectum is $\frac{15}{2}$ units, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15 x^2+4 y^2=15$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 x^2+15 y^2=60$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$15 x^2+16 y^2=240$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$16 x^2+15 y^2=40$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$15 x^2+16 y^2=240$</span> </div>

answer:
<div class="solution">Standard form of ellipse, $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$<br/>a &gt; b<br/>$\because$ Distance between foci $=2 a e$<br/>2 = 2ae<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/ERvmD90Yc6ikhDqJxpHan5GPlV40Ux51Cp1AlnYZskA.original.fullsize.png"/><br/><br/>$\Rightarrow \quad a e=1$...(ii)<br/>$\begin{aligned} &amp; \text { and length of latusrectum }=\frac{2 b^2}{a} \\ &amp; \qquad \begin{aligned} \frac{15}{2} &amp; =\frac{2 b^2}{a} \Rightarrow b^2=\frac{15 a}{4} \\ \because \quad b^2 &amp; =a^2\left(-e^2+1\right)=-a^2 e^2+a^2 \\ \frac{15 a}{4} &amp; =-1+a^2\end{aligned}\end{aligned}$<br/>$\begin{aligned} &amp; \Rightarrow \quad 4 a^2-15 a-4=0 \\ &amp; 4 a^2-16 a+a-4=0 \\ &amp; 4 a(a-4)+(a-4)=0 \\ &amp;(4 a+1)(a-4)=0 \\ &amp; \Rightarrow \quad a=-1 / 4 \text { and } 4\end{aligned}$<br/>When, a = + 4<br/>$$<br/>\Rightarrow \quad b^2=\frac{15 a}{4}=\frac{15 \times 4}{4} \Rightarrow b=\sqrt{15}<br/>$$<br/>$\therefore$ Equation of ellipse, $\frac{x^2}{16}+\frac{y^2}{15}=1$<br/>$$<br/>\Rightarrow \quad 15 x^2+16 y^2=240<br/>$$</div>


tags: ['Physics', 'Oscillations', 'MHT CET', 'MHT CET 2022 (06 Aug Shift 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-motion-of-a-particle-performing-linear-shm-is-x-5-sin-4-t-6-where-x-is-its-displacement-in-cm-the-velocity-of-the-particle-when-its-di

slug:
the-equation-of-motion-of-a-particle-performing-linear-shm-is-x-5-sin-4-t-6-where-x-is-its-displacement-in-cm-the-velocity-of-the-particle-when-its-di-86768

question:
<div class="question">The equation of motion of a particle performing linear S.H.M is $x=5 \sin \left[4 t-\frac{\pi}{6}\right]$, where $x$ is its displacement in $\mathrm{cm}$. The velocity of the particle when its displacement is $3 \mathrm{~cm}$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$8 \mathrm{~cm} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6 \mathrm{~cm} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$16 \mathrm{~cm} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{~cm} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$16 \mathrm{~cm} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Comparing with standard equation:<br/>$x=a \sin [\omega t+\phi]$<br/>The amplitude of the wave is $a=5$ and the angular velocity of the wave is $\omega=4$ The velocity of the wave can be obtained by taking derivative as:<br/>$\begin{aligned} &amp; \frac{d x}{d t}=\omega a \cos [\omega t+\phi]=\omega \sqrt{a^2-x^2} \\ &amp; \therefore v=\omega \sqrt{a^2-y^2}=4 \sqrt{(5)^2-(3)^2}=16 \mathrm{~cm} / \mathrm{s}\end{aligned}$</div>


tags: ['Physics', 'Oscillations', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-equation-of-simple-harmonic-motion-of-a-particle-is-a-4-2-x-0-where-a-is-the-instantaneous-linear-acceleration-at-displacement-x-the-frequency-of-

slug:
the-equation-of-simple-harmonic-motion-of-a-particle-is-a-4-2-x-0-where-a-is-the-instantaneous-linear-acceleration-at-displacement-x-the-frequency-of-36538

question:
<div class="question">The equation of simple harmonic motion of a particle is <math><mi>a</mi><mo>+</mo><mn>4</mn><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>x</mi><mo>=</mo><mn>0</mn></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> is the instantaneous linear acceleration at displacement <math><mi>x</mi></math> . The frequency of motion is</div>

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

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

answer:
<div class="solution">Comparing <math><mi>a</mi><mo>+</mo><mn>4</mn><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>x</mi><mo>=</mo><mn>0</mn></math> with standard equation of simple harmonic motion <math><mi>a</mi><mo>+</mo><msup><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>x</mi><mo>=</mo><mn>0</mn></math><br/><br/><math><msup><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>4</mn><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>ω</mi><mo>=</mo><mn>2</mn><mi>π</mi></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>π</mi><mi>n</mi><mo>=</mo><mn>2</mn><mi>π</mi><mo>,</mo><mi>n</mi><mo>=</mo><mn>1</mn><mo> </mo><mi>Hz</mi></math></div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2021 (21 Sep Shift 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-simple-harmonic-wave-produced-in-the-string-under-tension-04-n-is-given-by-y-4-sin-3-x-60-t-m-the-mass-per-unit-length-of-the-string-i

slug:
the-equation-of-simple-harmonic-wave-produced-in-the-string-under-tension-04-n-is-given-by-y-4-sin-3-x-60-t-m-the-mass-per-unit-length-of-the-string-i-88889

question:
<div class="question">The equation of simple harmonic wave produced in the string under tension $0.4 \mathrm{~N}$ is given by $\mathrm{y}=4 \sin (3 \mathrm{x}+60 \mathrm{t}) \mathrm{m}$. The mass per unit length of the string is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10^{-5} \mathrm{~kg} \mathrm{~m}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10^{-3} \mathrm{~g} \mathrm{~cm}^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10^{-5} \mathrm{~g} \mathrm{~cm}^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$</span> </div>

answer:
<div class="solution">The standard equation of a wave can be written as<br/>$$<br/>\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t})<br/>$$<br/>Speed of wave $\mathrm{V}=\frac{\omega}{\mathrm{k}}=\frac{60}{3}=20 \mathrm{~m} / \mathrm{s}$<br/>Also, $V=\sqrt{\frac{T}{m}}$<br/>$$<br/>\therefore \mathrm{m}=\frac{\mathrm{T}}{\mathrm{V}^2}=\frac{0.4}{400}=10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}<br/>$$</div>


title: the-equation-of-sound-wave-is-y-0-0015-sin-62-4-x-316-t-the-wavelength-of-this-wave-is
slug: the-equation-of-sound-wave-is-y-0-0015-sin-62-4-x-316-t-the-wavelength-of-this-wave-is-38589
tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation of sound wave is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>0015</mn><mo> </mo><mi>sin</mi><mo>(</mo><mn>62</mn><mo>.</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>316</mn><mi>t</mi><mo> </mo><mo>)</mo></math>. The wavelength of this wave is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mi>unit</mi></math></span> </div>

answer:
<div class="solution">Sound wave equation is,<br/><br/>              <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>0015</mn><mo> </mo><mi>sin</mi><mo>(</mo><mn>62</mn><mo>.</mo><mn>4</mn><mi>x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>316</mn><mi>t</mi><mo>)</mo></math><br/><br/>Standard equation of wave motion is,<br/><br/>                <math> <mrow> <mtext>y</mtext> <mo>=</mo> <mtext>A sin </mtext> <mn>2</mn> <mi>π</mi> <mfenced close="]" open="[" separators=","> <mrow> <mfrac> <mrow> <mtext>x</mtext> </mrow> <mrow> <mi>λ</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mtext>t</mtext> </mrow> <mrow> <mtext>T</mtext> </mrow> </mfrac> </mrow> </mfenced> </mrow> </math><br/><br/>Comparing the given equation with the standard equation, we get<br/><br/>                <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mi>λ</mi></mfrac><mo>=</mo><mn>62</mn><mo>.</mo><mn>4</mn></math><br/><br/>or, the wavelength of the wave, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>62</mn><mo>.</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mi>unit</mi></math></div>


tags: ['Physics', 'Waves and Sound', 'JIPMER', 'JIPMER 2006']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3 cm</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equation-of-stationary-wave-along-a-stretched-string-is-given-by-y-5-sin-3-x-cos-40-t-where-x-and-y-are-in-cm-and-t-in-second-the-separation-betwe

slug:
the-equation-of-stationary-wave-along-a-stretched-string-is-given-by-y-5-sin-3-x-cos-40-t-where-x-and-y-are-in-cm-and-t-in-second-the-separation-betwe-16756

question:
<div class="question">The equation of stationary wave along a stretched string is given by $y=5 \sin \frac{\pi x}{3} \cos 40 \pi t$, where, $x$ and $y$ are in cm and $t$ in second. The separation between two adjacent nodes is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.5 cm</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">3 cm</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6 cm</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4 cm</span> </li> </ul>

answer:
<div class="solution">Given, equation<br/>$y=5 \sin \frac{\pi x}{3} \cos 40 \pi t$<br/>Comparing with standard equation $y=A \sin k x \cos \omega t$<br/>$\begin{array}{rlrl}\therefore &amp; k &amp; =\frac{\pi}{3} \\ \Rightarrow &amp; \frac{2 \pi}{\lambda} &amp; =\frac{\pi}{3} \\ \lambda &amp; =6 \mathrm{~cm}\end{array}$<br/>Separation between two consecutive nodes $=\frac{\lambda}{2}=\frac{6}{2}=3 \mathrm{~cm}$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (10 Aug Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-stationary-wave-on-a-string-clamped-at-both-ends-and-vibrating-in-third-harmonic-is-y-05-sin-0314-x-cos-600-t-where-x-and-y-are-in-cm-

slug:
the-equation-of-stationary-wave-on-a-string-clamped-at-both-ends-and-vibrating-in-third-harmonic-is-y-05-sin-0314-x-cos-600-t-where-x-and-y-are-in-cm-35537

question:
<div class="question">The equation of stationary wave on a string clamped at both ends and vibrating in third harmonic is $Y=0.5 \sin (0.314 x) \cos (600 \pi t)$ where $x$ and $y$ are in $\mathrm{cm}, t$ in second. The length of the vibrating string is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$30 \mathrm{~cm}$</span> </div>

answer:
<div class="solution">The standard equation of a standing wave is<br/>$y=2 A \sin (k x) \cos (\omega t)$<br/>On comparing with standard equation,<br/>$\omega=600 \pi \mathrm{s}^{-1}$ and $k=\frac{\pi}{10}$<br/>The wavelength of the wave can be obtained by using the wave number: $k=\frac{2 \pi}{\lambda}=\frac{\pi}{10}$<br/>The wavelength is $\lambda=20 \mathrm{~cm}$<br/>Frequency of the third harmonics is three times the fundamental.<br/>Therefore, length of the string is: $L=3\left(\frac{\lambda}{2}\right)=3(10)=30 \mathrm{~cm}$</div>


tags: ['Mathematics', 'Circle', 'AP EAMCET', 'AP EAMCET 2019 (22 Apr Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-circle-which-cuts-the-circles-beginaligned-s1-equiv-x2y240-s2-equiv-x2y26-x8-y100-s3-equiv-x2y22-x4-y20-endaligned-at-the-extremit

slug:
the-equation-of-the-circle-which-cuts-the-circles-beginaligned-s1-equiv-x2y240-s2-equiv-x2y26-x8-y100-s3-equiv-x2y22-x4-y20-endaligned-at-the-extremit-92034

question:
<div class="question">The equation of the circle which cuts the circles<br/>\(\begin{aligned}<br/>&amp; S_1 \equiv x^2+y^2-4=0 \\<br/>&amp; S_2 \equiv x^2+y^2-6 x-8 y+10=0 \\<br/>&amp; S_3 \equiv x^2+y^2+2 x-4 y-2=0<br/>\end{aligned}\)<br/>at the extremities of diameters of these circles is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(x^2+y^2-4 x-6 y-4=0\)</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">\(x^2+y^2+4 x-4=0\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(x^2+y^2=25\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(x^2+y^2+x+y+1=0\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(x^2+y^2-4 x-6 y-4=0\)</span> </div>

answer:
<div class="solution">Let the equation of required circle is<br/>\(S \equiv x^2+y^2+2 g x+2 f y+c=0\)<br/>and equation of given circles<br/>\(\begin{aligned}<br/>&amp; S_1 \equiv x^2+y^2-4=0 \\<br/>&amp; S_2 \equiv x^2+y^2-6 x-8 y+10=0 \\<br/>&amp; S_3=x^2+y^2+2 x-4 y-2=0<br/>\end{aligned}\)<br/>\(\because\) Circle \(S=0\) cuts the circles \(S_1=0, S_2=0\) and \(S_3=0\) at the extermities of the diameters, so common chord of \(S=0\) and \(S_1=0\) passes through the centre of the circle \(S_1=0\), so \(c=-4\)<br/>Similarly \((2 g+6) x+(2 f+8) y-14=0\) passes through \((3,4)\), so \(6 g+8 f+36=0\)<br/>\(\Rightarrow \quad 3 g+4 f+18=0\)...(i)<br/>and \((2 g-2) x+(2 f+4) y-2=0\), passes through \((-1,2)\), so<br/>\(-2 g+4 f+8=0\)...(ii)<br/>From Eqs. (i) and (ii), we get<br/>\((g, f)=(-2,-3)\)<br/>So equation of required circle is<br/>\(x^2+y^2-4 x-6 y-4=0\)</div>


title: the-equation-of-the-circle-which-passes-through-the-points-1-0-0-6-and-3-4-is
slug: the-equation-of-the-circle-which-passes-through-the-points-1-0-0-6-and-3-4-is-79866
tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation of the circle which passes through the points $(1,0),(0,-6)$ and $(3,4)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 x^{2}+4 y^{2}+142 x+47 y+140=0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 x^{2}+4 y^{2}-142 x-47 y+138=0$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$4 x^{2}+4 y^{2}-142 x+47 y+138=0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 x^{2}+4 y^{2}+150 x-49 y+138=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 x^{2}+4 y^{2}-142 x+47 y+138=0$</span> </div>

answer:
<div class="solution">Let $\mathrm{A}=(1,0), \mathrm{B}=(0,-6), \mathrm{C}=(3,4)$<br/>Equation of $\mathrm{AB}$ is $\mathrm{L}: \frac{\mathrm{y}-0}{-6-0}=\frac{\mathrm{x}-1}{0-1}$<br/>$\Rightarrow \frac{y}{-6}=\frac{x-1}{-1} \Rightarrow y=6 x-6$<br/>$\Rightarrow 6 x-y-6=0 .$<br/>Equation of circle (c) with $\mathrm{AB}$ as diameter is $(\mathrm{x}-1)(\mathrm{x}-$ $0)+(y-0)(y+6)=0$<br/>$\Rightarrow x^{2}-x+y^{2}+6 y=0 .$<br/>The system of circle passing through the intersection of the circle $\mathrm{C}$ and the line $\mathrm{L}$ is given by $\mathrm{C}+\mathrm{kL}=0$ $\Rightarrow x^{2}-x+y^{2}+6 y+k(6 x-y-6)=0$<br/>This circle is passing through $(3,4)$. $\therefore(3)^{2}-3+(4)^{2}+6(4)+\mathrm{k}[6(3)-4-6]=0$<br/>$\Rightarrow 9-3+16+24+\mathrm{k}(18-10)=0$<br/>$\Rightarrow 46+8 \mathrm{k}=0 \Rightarrow 8 \mathrm{k}=-46 \Rightarrow \mathrm{k}=\frac{-46}{8}=\frac{-23}{4}$<br/>$\therefore$ Equation of circle is<br/>$x^{2}-x+y^{2}+6 y+\left(\frac{-23}{4}\right)(6 x-y-6)=0$<br/>$\Rightarrow 4 x^{2}-4 x+4 y^{2}+24 y-138 x+23 y+138=0$<br/>$\Rightarrow 4 x^{2}+4 y^{2}-142 x+47 y+138=0 .$</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2008 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-circle-which-touches-the-axes-at-a-distance-5-from-the-origin-is-y-2-x-2-2-x-2-y-2-0-what-is-the-value-of-u

slug:
the-equation-of-the-circle-which-touches-the-axes-at-a-distance-5-from-the-origin-is-y-2-x-2-2-x-2-y-2-0-what-is-the-value-of-u-77824

question:
<div class="question">The equation of the circle which touches the axes at a distance 5 from the origin is $y^{2}+x^{2}-2 \alpha x-2 \alpha y+\alpha^{2}=0$. What is the value of $u ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">7</span> </li> </ul>

answer:
<div class="solution">Coordinates of the centre of given circle $=(\alpha, \alpha)$ and<br/>radius $=\sqrt{(\alpha)^{2}+(\alpha)^{2}-\alpha^{2}}=\sqrt{\alpha^{2}}=\alpha$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/dnL_L-gF3Z5CHP0mqJnPEFd6RrcPZORg7J2Ji59ZEKM.original.fullsize.png"/><br/><br/>$\therefore(\alpha-5)^{2}+(\alpha)^{2}=(\alpha)^{2}$<br/>$\Rightarrow \alpha^{2}+25-10 \alpha=0$<br/>$\Rightarrow(\alpha-5)^{2}=0$<br/>$\Rightarrow \alpha=5$<br/>Then, other root will always real.</div>


title: the-equation-of-the-curve-passing-through-the-point-1-2-which-satisfies-dx-dy-x-2-x-3-1-is
slug: the-equation-of-the-curve-passing-through-the-point-1-2-which-satisfies-dx-dy-x-2-x-3-1-is-72395
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation of the curve passing through the point<br/>$(-1,-2)$ which satisfies $\frac{\mathrm{dy}}{\mathrm{dx}}=-\mathrm{x}^{2}-\frac{1}{\mathrm{x}^{3}}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$17 x^{2} y-6 x^{2}+3 x^{5}-2=0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$6 x^{2} y+17 x^{2}+2 x^{5}-3=0$</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">$6 x y-2 x^{2}+17 x^{5}+3=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$17 x^{2} y+6 x y-3 x^{5}+5=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6 x^{2} y+17 x^{2}+2 x^{5}-3=0$</span> </div>

answer:
<div class="solution">$\frac{d y}{d x}=-x^{2}-\frac{1}{x^{3}}$<br/>$\Rightarrow \quad \int d y=\int\left(-x^{2}-\frac{1}{x^{3}}\right) d x$<br/>$\Rightarrow \quad y=-\frac{x^{3}}{3}+\frac{1}{2 x^{2}}+c$<br/>Putting $(-1,-2)$, we get $-2=\frac{1}{3}+\frac{1}{2}+c \Rightarrow \mathrm{C}=-\frac{17}{6}$<br/>$\therefore \quad y=-\frac{x^{3}}{3}+\frac{1}{2 x^{2}}-\frac{17}{6}$<br/>$\Rightarrow \quad 6 x^{2} y=-2 x^{5}+3-17 x^{2}$<br/>$\Rightarrow 6 x^{2} y+17 x^{2}+2 x^{5}-3=0$</div>


tags: ['Mathematics', 'Ellipse', 'TS EAMCET', 'TS EAMCET 2020 (09 Sep Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-ellipse-in-the-standard-form-whose-length-of-the-latus-rectum-is-4-and-whose-distance-between-the-foci-is-4-2-is

slug:
the-equation-of-the-ellipse-in-the-standard-form-whose-length-of-the-latus-rectum-is-4-and-whose-distance-between-the-foci-is-4-2-is-66457

question:
<div class="question">The equation of the ellipse in the standard form whose length of the latus rectum is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> and whose distance between the foci is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msqrt><mn>2</mn></msqrt></math>, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>x</mi><mn>2</mn></msup><mn>2</mn></mfrac><mo>+</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mn>3</mn></mfrac><mo>=</mo><mn>1</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>8</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>16</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>25</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>16</mn></math></span> </div>

answer:
<div class="solution"><p>Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>a</mi><mi>e</mi><mo>=</mo><mn>4</mn><msqrt><mn>2</mn></msqrt><mo>,</mo><mo> </mo><mo> </mo><mfrac><mrow><mn>2</mn><msup><mi>b</mi><mn>2</mn></msup></mrow><mi>a</mi></mfrac><mo>=</mo><mn>4</mn></math></p><p>Now <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>2</mn><mi>a</mi><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>1</mn></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>e</mi><mo>=</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>a</mi><mn>2</mn></msup><msup><mi>e</mi><mn>2</mn></msup><mo>=</mo><mn>8</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>8</mn><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mo>∵</mo><msup><mi>e</mi><mn>2</mn></msup><mo>=</mo><mn>1</mn><mo>-</mo><mfrac><msup><mi>b</mi><mn>2</mn></msup><msup><mi>a</mi><mn>2</mn></msup></mfrac></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>a</mi><mo>-</mo><mn>8</mn><mo>=</mo><mn>0</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>a</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>2</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mn>2</mn></math> not possible <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>≠</mo><mo>-</mo><mn>4</mn></mrow></mfenced></math></p><p>So <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mn>2</mn></msup><mo>=</mo><mn>16</mn><mo>,</mo><mo> </mo><msup><mi>b</mi><mn>2</mn></msup><mo>=</mo><mn>8</mn></math></p><p>Required ellipse <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>x</mi><mn>2</mn></msup><mn>16</mn></mfrac><mo>+</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mn>8</mn></mfrac><mo>=</mo><mn>1</mn></math></p></div>


tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-ellipse-whose-centre-is-at-origin-major-axis-is-along-x-axis-with-eccentricity-4-3-and-latus-rectum-4-units-is

slug:
the-equation-of-the-ellipse-whose-centre-is-at-origin-major-axis-is-along-x-axis-with-eccentricity-4-3-and-latus-rectum-4-units-is-60593

question:
<div class="question">The equation of the ellipse whose centre is at origin, major<br/>axis is along $x$ -axis with eccentricity $\frac{3}{4}$ and latus rectum 4<br/>units is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{x^{2}}{1024}+\frac{7 y^{2}}{64}=1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{49 \mathrm{x}^{2}}{1024}+\frac{7 \mathrm{y}^{2}}{64}=1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{7 x^{2}}{1024}+\frac{49 y^{2}}{64}=1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{x^{2}}{1024}+\frac{y^{2}}{64}=1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{49 \mathrm{x}^{2}}{1024}+\frac{7 \mathrm{y}^{2}}{64}=1$</span> </div>

answer:
<div class="solution">Given, $b^{2}=2 a, c^{2}=\left(\frac{3}{4}\right)^{2} a^{2}=\frac{9}{16} a^{2}$<br/>We know, $a^{2}=b^{2}+c^{2}$<br/>So<br/>$\mathrm{a}^{2}=2 \mathrm{a}+\frac{9}{16} \mathrm{a}^{2} \Rightarrow 16 \mathrm{a}^{2}=32 \mathrm{a}+9 \mathrm{a}^{2} \Rightarrow 7 \mathrm{a}^{2}=32 \mathrm{a}$<br/>$\Rightarrow \mathrm{a}=\frac{32}{7}$<br/>$\therefore b^{2}=\frac{64}{7}$<br/>Equation of ellipse is<br/>$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \Rightarrow \frac{x^{2}}{\left(\frac{32}{7}\right)^{2}}+\frac{y^{2}}{\frac{64}{7}}=1 \Rightarrow \frac{49 x^{2}}{1024}+\frac{7 y^{2}}{64}=1$</div>


title: the-equation-of-the-ellipse-whose-vertices-are-5-0-and-foci-at-4-0-is
slug: the-equation-of-the-ellipse-whose-vertices-are-5-0-and-foci-at-4-0-is-29015
tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation of the ellipse whose vertices are $(\pm 5,0)$ and foci at $(\pm 4,0)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{x^{2}}{25}+\frac{y^{2}}{16}=1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$</span> </div>

answer:
<div class="solution">Since vertices of an ellipse are $(\pm a, 0)$ and foci are $(\pm \mathrm{ae}, 0)$<br/>$\therefore \quad a=5$ and $a e=4$<br/>$\Rightarrow e=\frac{4}{5}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/sKCd8BPT5Iwp8F5CFbsJzrSMf-m9pjOaIZKXqf0IWrk.original.fullsize.png"/><br/><br/>$\Rightarrow \frac{16}{25}=1-\frac{\mathrm{b}^{2}}{25}$<br/>$\Rightarrow \frac{\mathrm{b}^{2}}{25}=\frac{9}{25} \Rightarrow \mathrm{b}^{2}=9$<br/>Hence, Required equation is<br/>$\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-line-joining-the-origin-to-the-point-of-interesection-of-the-lines-a-x-b-y-1-and-b-x-a-y-1-is

slug:
the-equation-of-the-line-joining-the-origin-to-the-point-of-interesection-of-the-lines-a-x-b-y-1-and-b-x-a-y-1-is-41438

question:
<div class="question">The equation of the line joining the origin to the point of<br/>interesection of the lines $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{b}+\frac{y}{a}=1$ is</div>

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

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

answer:
<div class="solution">$\frac{x}{a}+\frac{y}{b}=1$ ...(i)<br/>and $\frac{x}{b}+\frac{y}{a}=1$ ...(ii)<br/>From solving equations (i) and (ii), we get the intersection point. $b x+a y=a x+b y$<br/>$\Rightarrow(b-a) x=(b-a) y$<br/>$\therefore \quad x=y$ ...(iii)<br/>$\Rightarrow \frac{x}{a}+\frac{x}{b}=1$<br/>$\therefore \quad x(a+b)=a b$<br/>$\therefore \quad \mathrm{x}=\frac{\mathrm{ab}}{\mathrm{a}+\mathrm{b}}$ and $\mathrm{y}=\frac{\mathrm{ab}}{\mathrm{a}+\mathrm{b}}$ from equation (iii)<br/>Now, equation of line joining $(0,0)$ and $\left(\frac{a b}{a+b}, \frac{a b}{a+b}\right)$<br/>Here, slope of line $=1$ <br/>$\therefore \quad y=x$<br/>$\therefore \quad x-y=0$<br/>$\therefore \quad$ Option (a) is correct.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-line-passing-through-the-point-2-3-and-the-point-of-intersection-of-lines-2-x-3-y-7-0-and-7-x-4-y-2-0-is

slug:
the-equation-of-the-line-passing-through-the-point-2-3-and-the-point-of-intersection-of-lines-2-x-3-y-7-0-and-7-x-4-y-2-0-is-16814

question:
<div class="question">The equation of the line passing through the point $(2,3)$ and the point of intersection of lines $2 \mathrm{x}-3 \mathrm{y}+7=0$ and $7 x+4 y+2=0$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$21 \mathrm{x}+46 \mathrm{y}-180=0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$21 x-46 y+96=0$</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">$46 \mathrm{x}+21 \mathrm{y}+155=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$46 \mathrm{x}-21 \mathrm{y}-29=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$21 x-46 y+96=0$</span> </div>

answer:
<div class="solution">Required line is $(2 x-3 y+7)+k(7 x+4 y+2)=0$. Given that this line passes through $(2,3)$ $\therefore(2(2)-3(3)+7)+\mathrm{k}(7(2)+4(3)+2)=0$<br/>$\Rightarrow 4-9+7+\mathrm{k}(14+12+2)=0$<br/>$\Rightarrow 2+\mathrm{k}(28)=0$<br/>$\Rightarrow 28 \mathrm{k}=-2 \Rightarrow \mathrm{k}=\frac{-1}{14}$<br/>Required line<br/>$\Rightarrow(2 x-3 y+7)+\left(\frac{-1}{14}\right)(7 x+4 y+2)=0$<br/>$\Rightarrow 28 x-42 y+98-7 x-4 y-2=0$<br/>$\Rightarrow 21 \mathrm{x}-46 \mathrm{y}+96=0 .$</div>


title: the-equation-of-the-line-the-reciprocals-of-whose-intercepts-on-the-axes-are-m-and-n-is-given-by
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2014 (Phase 1)']
source_db: MarksBatch2_P2.db
slug:
the-equation-of-the-line-the-reciprocals-of-whose-intercepts-on-the-axes-are-m-and-n-is-given-by-67178

question:
<div class="question">The equation of the line, the reciprocals of whose intercepts on the axes are $m$ and $n$, is given by</div>

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

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

answer:
<div class="solution">Let line be $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=1$<br/>given that $\frac{1}{\mathrm{a}}=\mathrm{m}$ and $\frac{1}{\mathrm{~b}}=\mathrm{n}$<br/>$\mathrm{a}=\frac{1}{\mathrm{~m}}, \mathrm{~b}=\frac{1}{\mathrm{n}}$<br/>equation of line, $m x+n y=1$</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-line-when-the-portion-of-it-intercepted-between-the-axes-is-divided-by-the-point-2-3-in-the-ratio-of-3-2-is

slug:
the-equation-of-the-line-when-the-portion-of-it-intercepted-between-the-axes-is-divided-by-the-point-2-3-in-the-ratio-of-3-2-is-49095

question:
<div class="question">The equation of the line, when the portion of it intercepted between the axes is divided by the point $(2,3)$ in the ratio of $3: 2$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Either $\mathrm{x}+\mathrm{y}=4$ or $9 \mathrm{x}+\mathrm{y}=12$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Either $\mathrm{x}+\mathrm{y}=5$ or $4 \mathrm{x}+9 \mathrm{y}=30$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Either $\mathrm{x}+\mathrm{y}=4$ or $\mathrm{x}+9 \mathrm{y}=12$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Either $\mathrm{x}+\mathrm{y}=5$ or $9 \mathrm{x}+4 \mathrm{y}=30$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Either $\mathrm{x}+\mathrm{y}=5$ or $9 \mathrm{x}+4 \mathrm{y}=30$</span> </div>

answer:
<div class="solution">Intercept form of line is $\frac{x}{a}+\frac{y}{b}=1$.<br/>We know, the point which divides a line joining two points $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$ and $\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ in the ratio $\mathrm{m}: \mathrm{n}$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/BIPp13fhigx5Z1nBC2-QQGfmcdmwu6M3RKLtQUywuU0.original.fullsize.png"/><br/><br/>$\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)$<br/>Case $1: \mathrm{m}: \mathrm{n}=2: 3$<br/>$\therefore(2,3)=\left(\frac{(2)(\mathrm{a})+3(0)}{2+3}, \frac{2(0)+3(\mathrm{~b})}{2+3}\right)$<br/>$\Rightarrow(2,3)=\left(\frac{2 \mathrm{a}}{5}, \frac{3 \mathrm{~b}}{5}\right)$<br/>$\Rightarrow \frac{2 \mathrm{a}}{5}=2 \quad ; \frac{3 \mathrm{~b}}{5}=3$<br/>$\Rightarrow \mathrm{a}=5 ; \mathrm{b}=5$<br/>Equation of line is $\frac{x}{5}+\frac{y}{5}=1 \Rightarrow x+y=5$<br/>Case $2: \mathrm{m}: \mathrm{n}=3: 2$<br/>$\therefore(2,3)=\left(\frac{3(a)+2(0)}{3+2} ; \frac{3(0)+2(b)}{3+2}\right)$<br/>$\Rightarrow(2,3)=\left(\frac{3 \mathrm{a}}{5}, \frac{2 \mathrm{~b}}{5}\right)$<br/>$\Rightarrow \frac{3 a}{5}=2 ; \frac{2 b}{5}=3$<br/>$\Rightarrow \mathrm{a}=\frac{10}{3}, \mathrm{~b}=\frac{15}{2}$<br/>Equation of line is $\frac{\frac{x}{10}}{3}+\frac{y}{\frac{15}{2}}=1$<br/>$\Rightarrow \frac{3 x}{10}+\frac{2 y}{15}=1$<br/>$\Rightarrow 9 \mathrm{x}+4 \mathrm{y}=30$</div>


title: the-equation-of-the-locus-of-a-point-which-is-equidistant-from-the-axes-is
slug: the-equation-of-the-locus-of-a-point-which-is-equidistant-from-the-axes-is-12699
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation of the locus of a point which is equidistant from the axes is</div>

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

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/dqEfI_9FdbG7LW-5fpvowDlbX3l0pFRi0Kwf3ZMhKhg.original.fullsize.png"/><br/><br/>$\sqrt{(x-0)^{2}+(y+y)^{2}}=\sqrt{(x-x)^{2}+(y-0)^{2}}$<br/>$\Rightarrow \sqrt{(\mathrm{x}-0)^{2}}=\sqrt{(\mathrm{y}-0)^{2}}$<br/>$\Rightarrow \sqrt{\mathrm{x}^{2}}=\sqrt{\mathrm{y}^{2}}$<br/>$\Rightarrow \mathrm{y}=\pm \mathrm{x}$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-plane-passing-through-the-intersection-of-the-planes-2-x-y-2-z-9-4-x-5-y-4-z-1-and-the-point-3-2-1-is

slug:
the-equation-of-the-plane-passing-through-the-intersection-of-the-planes-2-x-y-2-z-9-4-x-5-y-4-z-1-and-the-point-3-2-1-is-18439

question:
<div class="question">The equation of the plane passing through the intersection of the planes $2 \mathrm{x}+\mathrm{y}+2 z=9,4 \mathrm{x}-5 \mathrm{y}-4 \mathrm{z}=1$ and the point $(3,2,1)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$10 x-2 y+2 z=28$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 x+2 y+2 z=28$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 x+2 y-2 z=28$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 x-2 y-2 z=24$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 x-2 y+2 z=28$</span> </div>

answer:
<div class="solution">The equation of plane passing through the intersection of planes $2 x+y+2 z=9$ and $4 x-5 y-4 z=1$ is $(2 x+y+2 z-9)+\lambda(4 x-5 y-4 z-1)=0$<br/>Given that this plane passes through $(3,2,1)$ $\Rightarrow 2(3)+2+2(1)-9+\lambda[4(3)-5(2)-4(1)-1]=0$<br/>$\Rightarrow 1+\lambda(-3)=0$<br/>$\Rightarrow \lambda=\frac{1}{3}$<br/>$\therefore$ Equation is $(2 x+y+2 z-9)$<br/>$+\frac{1}{3}(4 x-5 y-4 z-1)=0$<br/>$\Rightarrow 6 x+3 y+6 z-27+4 x-5 y-4 z-1=0$<br/>$\Rightarrow 10 x-2 y+2 z-28=0$<br/>$\Rightarrow 10 x-2 y+2 z=28$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-the-plane-passing-through-the-line-of-intersection-of-the-planes-x-y-z-1-2-x-3-y-4-z-7-and-perpendicular-to-the-plane-x-5-y-3-z-5-is-g

slug:
the-equation-of-the-plane-passing-through-the-line-of-intersection-of-the-planes-x-y-z-1-2-x-3-y-4-z-7-and-perpendicular-to-the-plane-x-5-y-3-z-5-is-g-34020

question:
<div class="question">The equation of the plane passing through the line of intersection of the planes $x+y+z=1,2 x+3 y+4 z=7$, and perpendicular to the plane $x-5 y+3 z=5$ is given by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$x+2 y+3 z-6=0$</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">$x+2 y+3 z+6=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 x+4 y+5 z-8=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 x+4 y+5 z+8=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x+2 y+3 z-6=0$</span> </div>

answer:
<div class="solution">Given planes, $\mathrm{p}_{1}: \mathrm{x}+\mathrm{y}+\mathrm{z}=1$<br/>$\mathrm{p}_{2}: 2 \mathrm{x}+3 \mathrm{y}+4 \mathrm{z}=7$<br/>So, equation of plane passing through intersection of planes $\mathrm{p}_{1}$ and $\mathrm{p}_{2}$ is $x+y+z-1+k(2 x+3 y+4 z-7)=0$<br/>$\Rightarrow x+y+z-1+2 k x+3 k y+4 k z-7 k=0$<br/>$\Rightarrow x(1+2 k)+y(1+3 k)+z(1+4 k)-1-7 k=0 .$<br/>This is perpendicular to $x-5 y+3 z=5$. $\Rightarrow x-5 y+3 z-5=0$<br/>$\Rightarrow 1(1+2 k)-5(1+3 k)+3(1+4 k)=0$<br/>$\Rightarrow 1+2 k-5-15 k+3+12 k=0$<br/>$\Rightarrow-k-1=0 \Rightarrow k=-1$<br/>$\therefore$ Equation of plane is $x+y+z-1-1(2 x+3 y+4 z-7)=0$<br/>$\Rightarrow x+y+z-1-2 x-3 y-4 z+7=0$<br/>$\Rightarrow-x-2 y-3 z+6=0$<br/>$\Rightarrow x+2 y+3 z-6=0 .$</div>


tags: ['Physics', 'Motion In Two Dimensions', 'AP EAMCET', 'AP EAMCET 2005']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">18</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equation-of-trajectory-of-a-projectile-is-y-10-x-9-5-x-2-if-we-assume-g-10-ms-2-the-range-of-projectile-in-metre-is-1

slug:
the-equation-of-trajectory-of-a-projectile-is-y-10-x-9-5-x-2-if-we-assume-g-10-ms-2-the-range-of-projectile-in-metre-is-1-20212

question:
<div class="question">The equation of trajectory of a projectile is $y=10 x-\left(\frac{5}{9}\right) x^2$.<br/><br/>If we assume $g=10 \mathrm{~ms}^{-2}$, the range of projectile (in metre) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">36</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">24</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">18</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">9</span> </li> </ul>

answer:
<div class="solution">Equation of projectile is<br/>$y=10 x-\left(\frac{5}{9}\right) x^2$<br/>Standard equation is<br/>$y=x \tan \theta-\frac{g}{2 u^2 \cos ^2 \theta} \cdot x^2$<br/>On comparing,<br/>$\tan \theta=10$<br/>and<br/>$\begin{array}{rlrl} <br/>&amp; \frac{g}{2 u^2 \cos ^2 \theta} &amp; =\frac{9}{9} \\<br/>\Rightarrow &amp; 10 u^2 \cos ^2 \theta &amp; =9 \mathrm{~g} \\<br/>&amp; \ddots &amp; g &amp; =10 \mathrm{~m} / \mathrm{s}^2 \\<br/>&amp; \therefore &amp; u^2 \cos ^2 \theta &amp; =9<br/>\end{array}$<br/>(given)<br/>$\therefore$ Range of projectile $R=\frac{2 u^2 \sin \theta \cos \theta}{g}$<br/>$\begin{aligned}<br/>&amp; =\frac{2 u^2 \tan \theta \cdot \cos ^2 \theta}{g} \\<br/>&amp; =\frac{2\left(u^2 \cos ^2 \theta\right) \cdot \tan \theta}{g} \\<br/>&amp; =\frac{2 \times 9 \times 10}{10}=18 \mathrm{~m}<br/>\end{aligned}$</div>


tags: ['Physics', 'Motion In Two Dimensions', 'TS EAMCET', 'TS EAMCET 2005']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">18</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equation-of-trajectory-of-a-projectile-is-y-10-x-9-5-x-2-if-we-assume-g-10-ms-2-the-range-of-projectile-in-metre-is

slug:
the-equation-of-trajectory-of-a-projectile-is-y-10-x-9-5-x-2-if-we-assume-g-10-ms-2-the-range-of-projectile-in-metre-is-46194

question:
<div class="question">The equation of trajectory of a projectile is $y=10 x-\left(\frac{5}{9}\right) x^2$.<br/><br/>If we assume $g=10 \mathrm{~ms}^{-2}$, the range of projectile (in metre) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">36</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">24</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">18</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">9</span> </li> </ul>

answer:
<div class="solution">Equation of projectile is<br/>$y=10 x-\left(\frac{5}{9}\right) x^2$<br/>Standard equation is<br/>$y=x \tan \theta-\frac{g}{2 u^2 \cos ^2 \theta} \cdot x^2$<br/>On comparing,<br/>$\tan \theta=10$<br/>and<br/>$\begin{array}{rlrl} <br/>&amp; \frac{g}{2 u^2 \cos ^2 \theta} &amp; =\frac{9}{9} \\<br/>\Rightarrow &amp; 10 u^2 \cos ^2 \theta &amp; =9 \mathrm{~g} \\<br/>&amp; \ddots &amp; g &amp; =10 \mathrm{~m} / \mathrm{s}^2 \\<br/>&amp; \therefore &amp; u^2 \cos ^2 \theta &amp; =9<br/>\end{array}$<br/>(given)<br/>$\therefore$ Range of projectile $R=\frac{2 u^2 \sin \theta \cos \theta}{g}$<br/>$\begin{aligned}<br/>&amp; =\frac{2 u^2 \tan \theta \cdot \cos ^2 \theta}{g} \\<br/>&amp; =\frac{2\left(u^2 \cos ^2 \theta\right) \cdot \tan \theta}{g} \\<br/>&amp; =\frac{2 \times 9 \times 10}{10}=18 \mathrm{~m}<br/>\end{aligned}$</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-p-x-2-q-x-r-0-where-p-q-r-all-are-positive-has-distinct-real-roots-a-and-b-which-one-of-the-following-is-correct

slug:
the-equation-p-x-2-q-x-r-0-where-p-q-r-all-are-positive-has-distinct-real-roots-a-and-b-which-one-of-the-following-is-correct-55263

question:
<div class="question">The equation $p x^{2}+q x+r=0$ (where $p, q, r$, all are positive) has distinct real roots a and $\mathrm{b}$. Which one of the following is correct?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{a}   &lt; 0, \mathrm{~b} &lt; 0$</span> </div>

answer:
<div class="solution">$\mathrm{px}^{2}+\mathrm{qx}+\mathrm{r}=0,(\mathrm{p}, \mathrm{q}, \mathrm{r}$ arepositive)<br/>Whenever the coefficients and constant are positive in quadratic equation, its roots are always negative $\therefore \mathrm{a}   &lt; 0, \mathrm{~b} &lt; 0$</div>


tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-equation-sin-1-3-x-4-x-3-3-sin-1-x-is-true-for-all-values-of-x-lying-in-which-one-of-the-following-intervals

slug:
the-equation-sin-1-3-x-4-x-3-3-sin-1-x-is-true-for-all-values-of-x-lying-in-which-one-of-the-following-intervals-54506

question:
<div class="question">The equation $\sin ^{-1}\left(3 x-4 x^{3}\right)=3 \sin ^{-1}(x)$ is true for all<br/>values of $x$ lying in which one of the following intervals?</div>

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

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

answer:
<div class="solution">Let $\sin ^{-1} x=\theta \Rightarrow x=\sin \theta$<br/>$\sin ^{-1}\left(3 \sin \theta-4 \sin ^{3} \theta\right)=\sin ^{-1} \sin 3 \theta=3 \theta=3 \sin ^{-1} x$<br/>Equaion $\sin ^{-1}\left(3 x-4 x^{3}\right)=3 \sin ^{-1} x$ is true for all values<br/>of $\mathrm{x}$ lying in the interval $[-1,1]$.</div>


title: the-equation-tan-1-1-x-tan-1-1-x-2-is-satisfied-by
slug: the-equation-tan-1-1-x-tan-1-1-x-2-is-satisfied-by-63432
tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$x=0$</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation $\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}$ is satisfied by</div>

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

answer:
<div class="solution">$\tan ^{-1}(1+\mathrm{x})+\tan ^{-1}(1-\mathrm{x})=\frac{\pi}{2}$<br/>$\tan ^{-1}\left[\frac{(1+x)+(1-x)}{1-(1+x)(1-x)}\right]=\frac{\pi}{2}$<br/>$\Rightarrow \quad \frac{1+x+1-x}{1-(1+x)(1-x)}=\tan \frac{\pi}{2}$<br/>$\Rightarrow \quad \frac{2}{1-(1+\mathrm{x})(1-\mathrm{x})}=\frac{1}{0}$<br/>$\Rightarrow \quad 1-(1+\mathrm{x})(1-\mathrm{x})=0$<br/>$\Rightarrow(1+\mathrm{x})(1-\mathrm{x})=1$<br/>$1-\mathrm{x}^{2}=1$<br/>$\mathrm{x}^{2}=0$<br/>$\mathrm{x}=0$<br/>$\therefore$ Option (c) is correct.</div>


title: the-equation-tan-2-tan-6-tan-3-sec-2-is
slug: the-equation-tan-2-tan-6-tan-3-sec-2-is-99924
tags: ['Mathematics', 'Trigonometric Equations', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation $\tan ^{2} \phi+\tan ^{6} \phi=\tan ^{3} \phi \cdot \sec ^{2} \phi$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">not an identity</span> </div>

answer:
<div class="solution">Given equation is $\tan ^{2} \phi+\tan ^{6} \phi=\tan ^{3} \phi \cdot \sec ^{2} \phi$<br/>$\Rightarrow \tan ^{2} \phi\left(1+\tan ^{4} \phi\right)=\tan ^{3} \phi \cdot \sec ^{2} \phi$<br/>$\Rightarrow\left(1+\tan ^{4} \phi\right)=\tan \phi \cdot \sec ^{2} \phi$<br/>Now, $\sec ^{2} \phi=1+\tan ^{2} \phi$<br/>$\therefore\left(1+\tan ^{4} \phi\right)=\tan \phi\left(1+\tan ^{2} \phi\right)$<br/>$\Rightarrow 1+\tan ^{4} \phi=\tan \phi+\tan ^{3} \phi$<br/>It is not an identity</div>


title: the-equation-tan-4-x-2-sec-2-x-a-2-0-will-have-at-least-one-real-solution-if
slug: the-equation-tan-4-x-2-sec-2-x-a-2-0-will-have-at-least-one-real-solution-if-45523
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation $\tan ^{4} x-2 \sec ^{2} x+a^{2}=0$ will have at least one<br/>real solution if</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$|a| \leq 4$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$|a| \leq 2$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$|a| \leq \sqrt{3}$</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=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

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

answer:
<div class="solution">$\Rightarrow\left(\tan ^{2} x\right)^{2}-2 \tan ^{2} x+a^{2}-2=0$<br/>This is the quadratic equation in $\tan x$. So, roots of this will be real when discriminant $\geq 0$ a. $b^{2}-4 a c \geq 0$<br/>$\Rightarrow 12-4 a^{2} \geq 0 \Rightarrow 4\left(3-a^{2}\right) \geq 0$<br/>$\Rightarrow 3-a^{2} \geq 0 \quad(\because 4 \neq 0)$<br/>$\Rightarrow a^{2} \leq 3$<br/>$\Rightarrow a \leq \pm \sqrt{3} \Rightarrow|a| \leq \sqrt{3}$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-to-sphere-passing-through-origin-and-the-points-1-0-0-0-2-0-and-0-0-3-is-x-2-y-2-z-2-f-x-y-z-0-what-is-f-x-y-z-equal-to

slug:
the-equation-to-sphere-passing-through-origin-and-the-points-1-0-0-0-2-0-and-0-0-3-is-x-2-y-2-z-2-f-x-y-z-0-what-is-f-x-y-z-equal-to-33938

question:
<div class="question">The equation to sphere passing through origin and the points $(-1,0,0),(0,-2,0)$ and $(0,0,-3)$ is $\mathrm{x}^{2}+y^{2}+z^{2}+f(x,$,<br/>$y, z)=0$. What is $f(x, y, z)$ equal to? $\quad$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x+2 y+3 z$</span> </div>

answer:
<div class="solution">As we know, general equation of sphere is given as<br/>$x^{2}+y^{2}+z^{2}+2 u x+2 v y+2 w z+d=0$<br/>Given equation of sphere is $x^{2}+y^{2}+z^{2}+f(x, y, z)=0$<br/>On comparing both the equations $(1)$ and $(2)$, we get $f(x, y, z)=2 t x+2 v y+2 w z+d$<br/>Since, sphere passing through $(0,0,0),(-1,0,0)$, $(0,-2,0),(0,0,-3)$<br/>we have from (1),<br/>$d=0,1-2 u=0 \Rightarrow u=\frac{1}{2}$,<br/>$4-4 v=0 \Rightarrow v=1,9-6 w=0 \Rightarrow w=\frac{3}{2}$<br/>Hence,<br/>$f(x, y, z)=2 x\left(\frac{1}{2}\right)+2 y(1)+2 z\left(\frac{3}{2}\right)+0$<br/>$=x+2 y+3 z$</div>


title: the-equation-to-the-locus-of-a-point-which-is-always-equidistant-from-the-points-1-0-and-0-2-is
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
slug:
the-equation-to-the-locus-of-a-point-which-is-always-equidistant-from-the-points-1-0-and-0-2-is-44976

question:
<div class="question">The equation to the locus of a point which is always equidistant from the points $(1,0)$ and $(0,-2)$ is :</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\quad 2 x+4 y+3=0$</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">$\quad 4 x+2 y+3=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad 2 x+4 y-3=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 x+2 y-3=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad 2 x+4 y+3=0$</span> </div>

answer:
<div class="solution">Let $\mathrm{P}(\mathrm{x}, \mathrm{y})$ be the point. Let $\mathrm{A}=(1,0)$ and $\mathrm{B}=(0,-2)$ then $\mathrm{PA}=\mathrm{PB}$<br/>$\Rightarrow(\mathrm{PA})^{2}=(\mathrm{PB})^{2}$<br/>$\Rightarrow(\mathrm{x}-1)^{2}+\mathrm{y}^{2}=\mathrm{x}^{2}+(\mathrm{y}+2)^{2}$<br/>$\Rightarrow \quad 1-2 x=4 y+4$<br/>$\Rightarrow \quad 2 \mathrm{x}+4 \mathrm{y}+3=0$</div>


title: the-equation-x-2-4-x-29-0-hasone-root-2-5-i-what-is-the-other-root-i-1
slug: the-equation-x-2-4-x-29-0-hasone-root-2-5-i-what-is-the-other-root-i-1-12036
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2011 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$2-5$</span> </div>
answer: <div class="solution">Since, complex roots occur in pairs therefore other root is $2-5 i$</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The equation $x^{2}-4 x+29=0$ hasone root $2+5 i$. What is the  other root? <br/>$(i=\sqrt{-1})$</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">5</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2+5$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2-5$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>


title: the-equation-x-2-x-1-1-1-2-x-1-1-has
slug: the-equation-x-2-x-1-1-1-2-x-1-1-has-99818
question: <div class="question">The equation $x-2(x-1)^{-1}=1-2(x-1)^{-1}$ has</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">no roots</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">one root</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">two equal roots</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">infinite roots</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">no roots</span> </div>

answer:
<div class="solution">Given, $x-2(x-1)^{-1}=1-2(x-1)^{-1}$<br/>$x-\frac{2}{x-1}=1-\frac{2}{x-1}$<br/>$\Rightarrow \frac{x(x-1)-2}{x-1}=\frac{x-1-2}{x-1}$<br/>$\Rightarrow x^{2}-x-2=x-1-2$<br/>$\Rightarrow x^{2}-x-2-x+3=0$<br/>$\Rightarrow x^{2}-2 x+1=0$<br/>$\Rightarrow(x-1)^{2}=0$<br/>$\Rightarrow x=1$<br/>But $x=1$ is not sat isfied in the given equation.<br/>Hence, no roots exist.</div>


tags: ['Physics', 'Motion In Two Dimensions', 'AP EAMCET', 'AP EAMCET 2003']
source_db: MarksBatch2_P2.db
title:
the-equations-of-motion-of-a-projectile-are-given-by-x-36-t-metre-and-2-y-96-t-98-t-2-metre-the-angle-of-projection-is-1

slug:
the-equations-of-motion-of-a-projectile-are-given-by-x-36-t-metre-and-2-y-96-t-98-t-2-metre-the-angle-of-projection-is-1-99711

question:
<div class="question">The equations of motion of a projectile are given by $x=36 t$ metre and $2 y=96 t-9.8 t^2$ metre. The angle of projection is :</div>

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

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

answer:
<div class="solution">$x=36 t$ metre<br/>$2 y=\left(96 t-9.8 t^2\right)$ metre<br/>Standard equations are,<br/>$x=(u \cos \theta) t$<br/>$y=u \sin \theta t-\frac{1}{2} g t^2$<br/>$u \cos =36$<br/>$u \sin \theta=\frac{96}{2}=48$<br/>$\therefore \quad \tan \theta=\frac{u \sin \theta}{u \cos \theta}=\frac{48}{36}=\frac{4}{3}$<br/>$\theta=\tan ^{-1} \frac{4}{3}$<br/>or $\theta=\sin ^{-1} \frac{4}{5}$</div>


tags: ['Physics', 'Motion In Two Dimensions', 'TS EAMCET', 'TS EAMCET 2003']
source_db: MarksBatch2_P2.db
title:
the-equations-of-motion-of-a-projectile-are-given-by-x-36-t-metre-and-2-y-96-t-98-t-2-metre-the-angle-of-projection-is

slug:
the-equations-of-motion-of-a-projectile-are-given-by-x-36-t-metre-and-2-y-96-t-98-t-2-metre-the-angle-of-projection-is-93135

question:
<div class="question">The equations of motion of a projectile are given by $x=36 t$ metre and $2 y=96 t-9.8 t^2$ metre. The angle of projection is :</div>

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

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

answer:
<div class="solution">$x=36 t$ metre<br/>$2 y=\left(96 t-9.8 t^2\right)$ metre<br/>Standard equations are,<br/>$x=(u \cos \theta) t$<br/>$y=u \sin \theta t-\frac{1}{2} g t^2$<br/>$u \cos =36$<br/>$u \sin \theta=\frac{96}{2}=48$<br/>$\therefore \quad \tan \theta=\frac{u \sin \theta}{u \cos \theta}=\frac{48}{36}=\frac{4}{3}$<br/>$\theta=\tan ^{-1} \frac{4}{3}$<br/>or $\theta=\sin ^{-1} \frac{4}{5}$</div>


title: the-equations-x-2-y-3-z-1-2-x-y-3-z-2-5-x-5-y-9-z-4
slug: the-equations-x-2-y-3-z-1-2-x-y-3-z-2-5-x-5-y-9-z-4-10359
question: <div class="question">The equations <br/>$x+2 y+3 z=1$<br/>$2 x+y+3 z=2$<br/>$5 x+5 y+9 z=4$</div>
tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">have the unique solution</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">have infinitely many solutions</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">are inconsistent</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

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

answer:
<div class="solution">$\begin{aligned} &amp; x+2 y+3 z=1 \\ &amp; 2 x+y+3 z=2 \\ &amp; 5 x+5 y+9 z=4 \end{aligned}$<br/>Writing in matrix form, $\mathrm{Ax}=\mathrm{B}$<br/>$A=\left[\begin{array}{lll}1 &amp; 2 &amp; 3 \\ 2 &amp; 1 &amp; 3 \\ 5 &amp; 5 &amp; 9\end{array}\right]$<br/>$|\mathrm{A}|=1(9-15)-2(18-15)+3(10-5)$<br/>$=-6-2(3)+3(5)=-12+15=3 \neq 0$<br/>So, these equations have unique solution</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equilibrium-constant-for-a-reaction-is-10-what-will-be-the-magnitude-value-of-delta-mathrmgcirc-mathrmr831-mathrmjk1-mathrmmol1-mathrmt314-mathrmk

slug:
the-equilibrium-constant-for-a-reaction-is-10-what-will-be-the-magnitude-value-of-delta-mathrmgcirc-mathrmr831-mathrmjk1-mathrmmol1-mathrmt314-mathrmk-74193

question:
<div class="question">The equilibrium constant for a reaction is \( 10 \). What will be the magnitude value of \( \Delta \mathrm{G}^{\circ} \) ?<br/>\( \mathrm{R}=8.31 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}, \mathrm{~T}=314 \mathrm{~K} .\left(\right. \) Approximate integer value in \( \left.\mathrm{KJ} \mathrm{mol}^{-1}\right) \)</div>

answer:
<div class="solution"><blockquote><p>Given:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mi>eq</mi></msub><mo>=</mo><mn>10</mn><mspace linebreak="newline"></mspace><mi mathvariant="normal">R</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo> </mo><msup><mi>JK</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mspace linebreak="newline"></mspace><mi mathvariant="normal">T</mi><mo>=</mo><mn>314</mn><mo> </mo><mi mathvariant="normal">K</mi></math></p><p>As we know, the relation between the standard Gibbs free energy change and equilibrium constant is given by:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><msup><mi mathvariant="normal">G</mi><mn>0</mn></msup><mo>=</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>303</mn><mo> </mo><mi>RT</mi><mo> </mo><mi>log</mi><mo> </mo><msub><mi mathvariant="normal">K</mi><mi>eq</mi></msub><mspace linebreak="newline"></mspace><mo>∆</mo><msup><mi mathvariant="normal">G</mi><mn>0</mn></msup><mo>=</mo><mo>-</mo><mn>2</mn><mo>.</mo><mn>303</mn><mo> </mo><mfenced><mrow><mn>8</mn><mo>.</mo><mn>31</mn></mrow></mfenced><mfenced><mn>314</mn></mfenced><mo> </mo><mi>log</mi><mo> </mo><mn>10</mn><mspace linebreak="newline"></mspace><mo>∆</mo><msup><mi mathvariant="normal">G</mi><mn>0</mn></msup><mo>≃</mo><mo>-</mo><mn>6</mn></math></p><p>So, the magnitude will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math>.</p></blockquote></div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main', 'JEE Main 2023 (29 Jan Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">17</span> </div>
source_db: MarksBatch2_P2.db
title:
the-equilibrium-constant-for-the-reaction-zn-s-sn-2-aq-zn-2-aq-sn-s-is-1-10-20-at-298-k-the-magnitude-of-standard-electrode-potential-of-sn-sn-2-if-e-

slug:
the-equilibrium-constant-for-the-reaction-zn-s-sn-2-aq-zn-2-aq-sn-s-is-1-10-20-at-298-k-the-magnitude-of-standard-electrode-potential-of-sn-sn-2-if-e-47030

question:
<div class="question"><p>The equilibrium constant for the reaction <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Zn</mi><mfenced><mi mathvariant="normal">s</mi></mfenced><mo>+</mo><msup><mi>Sn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mi>aq</mi></mfenced><mo>⇌</mo><msup><mi>Zn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mi>aq</mi></mfenced><mo>+</mo><mi>Sn</mi><mfenced><mi mathvariant="normal">s</mi></mfenced></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>20</mn></msup></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>298</mn><mo> </mo><mi mathvariant="normal">K</mi></math>. The magnitude of standard electrode potential of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sn</mi><mo>/</mo><msup><mi>Sn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></math> if <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">E</mi><mrow><msup><mi>Zn</mi><mrow><mn>2</mn><mo>*</mo></mrow></msup><mo>/</mo><mi>Zn</mi></mrow><mn>0</mn></msubsup><mo>=</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>76</mn><mo> </mo><mi mathvariant="normal">V</mi></math> is _____ <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">V</mi></math>. (Nearest integer)</p><p>Given : <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>.</mo><mn>303</mn><mi>RT</mi></mrow><mi mathvariant="normal">F</mi></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>059</mn><mo> </mo><mi mathvariant="normal">V</mi></math></p></div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Zn</mi><mfenced><mi mathvariant="normal">s</mi></mfenced><mo>+</mo><msup><mi>Sn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mi>aq</mi></mfenced><mo>⇌</mo><msup><mi>Zn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mfenced><mi>aq</mi></mfenced><mo>+</mo><mi>Sn</mi><mfenced><mi mathvariant="normal">s</mi></mfenced></math></p><p>Given: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>.</mo><mn>303</mn><mi>RT</mi></mrow><mi mathvariant="normal">F</mi></mfrac><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>059</mn><mo> </mo><mi mathvariant="normal">V</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">E</mi><mi>cell</mi><mn>0</mn></msubsup><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>303</mn><mi>RT</mi></mrow><mrow><mn>2</mn><mi mathvariant="normal">F</mi></mrow></mfrac><mo> </mo><mi>log</mi><mo> </mo><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">c</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mi>cell</mi><mn>0</mn></msubsup><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>059</mn></mrow><mn>2</mn></mfrac><mo> </mo><mi>log</mi><mo> </mo><mo>(</mo><msup><mn>10</mn><mn>20</mn></msup><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mi>cell</mi><mn>0</mn></msubsup><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>059</mn></mrow><mn>2</mn></mfrac><mo> </mo><mo>×</mo><mo> </mo><mn>20</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mi>cell</mi><mn>0</mn></msubsup><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>59</mn><mo> </mo><mi mathvariant="normal">V</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi mathvariant="normal">E</mi><mi>cell</mi><mn>0</mn></msubsup><mo> </mo><mo>=</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mrow><msup><mi>Sn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>/</mo><mi>Sn</mi></mrow><mn>0</mn></msubsup><mo> </mo><mo>-</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mrow><msup><mi>Zn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>/</mo><mi>Zn</mi></mrow><mn>0</mn></msubsup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mi>cell</mi><mn>0</mn></msubsup><mo> </mo><mo>=</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mrow><msup><mi>Sn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>/</mo><mi>Sn</mi></mrow><mn>0</mn></msubsup><mo> </mo><mo>-</mo><mo> </mo><mo>(</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>76</mn><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mrow><msup><mi>Sn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>/</mo><mi>Sn</mi></mrow><mn>0</mn></msubsup><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>76</mn><mo> </mo><mo>+</mo><mo> </mo><mn>059</mn><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>17</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msubsup><mi mathvariant="normal">E</mi><mrow><mi>Sn</mi><mo>/</mo><msup><mi>Sn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></mrow><mn>0</mn></msubsup><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>17</mn><mo> </mo><mo>=</mo><mo> </mo><mn>17</mn><mo> </mo><mo>×</mo><mo> </mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p><p>So, answer is 17.</p></div>


tags: ['Chemistry', 'Chemical Equilibrium', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-equilibrium-constant-k-p-for-a-homogenous-gaseous-reaction-is-1-0-3-the-standard-gibbs-free-energy-change-g-for-the-reaction-at-27-c-using-r-2-cal

slug:
the-equilibrium-constant-k-p-for-a-homogenous-gaseous-reaction-is-1-0-3-the-standard-gibbs-free-energy-change-g-for-the-reaction-at-27-c-using-r-2-cal-63250

question:
<div class="question">The equilibrium constant <math><msub><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math> for a homogenous gaseous reaction is <math><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>-</mo><mn>3</mn></mrow></msup></math> . The standard Gibbs free energy change <math><mi mathvariant="normal">Î</mi><mi mathvariant="normal">G</mi><mo>Â°</mo></math> for the reaction at <math><mn>27</mn><mo>Â°</mo><mi mathvariant="normal">C</mi></math> (using R = 2 cal <math><msup><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> ) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">-1.8 kcal</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">-4.1454 kcal</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">+4.1454 kcal</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">+4.1454 kcal</span> </div>

answer:
<div class="solution"><math> <mrow> <mtext>ÎG</mtext><mtext>â</mtext><mtext>=</mtext><mtext>â</mtext><mo>â</mo><mtext>2</mtext><mtext>.303</mtext><mtext>â</mtext><mtext>RT</mtext><mtext>â</mtext><mtext>log</mtext><mtext>â</mtext><msub> <mtext>K</mtext> <mtext>p</mtext> </msub> </mrow> </math><br/><math> <mrow> <mo>=</mo><mo>â</mo><mn>2.303</mn><mo>Ã</mo><mn>2</mn><mo>Ã</mo><mn>300</mn><mtext>â</mtext><mtext>log</mtext><mtext>â</mtext><msup> <mrow> <mn>10</mn></mrow> <mrow> <mo>â</mo><mn>3</mn></mrow> </msup> </mrow> </math><br/><math> <mrow> <mtext>=</mtext><mo>â</mo><mtext>2</mtext><mtext>.303</mtext><mtext>â</mtext><mtext>Ã</mtext><mtext>â</mtext><mtext>2</mtext><mtext>â</mtext><mtext>Ã</mtext><mtext>â</mtext><mtext>300</mtext><mtext>â</mtext><mtext>Ã</mtext><mtext>â</mtext><mtext>(</mtext><mo>â</mo><mtext>3)</mtext></mrow> </math><br/><math> <mrow> <mtext>=</mtext><mtext> </mtext><mtext>1445</mtext><mtext>.4</mtext><mtext> </mtext><mtext>cal</mtext><mtext> </mtext><mtext>=</mtext><mtext> </mtext><mtext>4</mtext><mtext>.1454</mtext><mtext> </mtext><mtext>kcal</mtext></mrow></math></div>


tags: ['Chemistry', 'Electrochemistry', 'KCET', 'KCET 2012']
source_db: MarksBatch2_P2.db
title:
the-equilibrium-constant-of-a-reaction-is-0008-at-298-k-the-standard-free-energy-change-of-the-reaction-at-the-same-temperature-is

slug:
the-equilibrium-constant-of-a-reaction-is-0008-at-298-k-the-standard-free-energy-change-of-the-reaction-at-the-same-temperature-is-24131

question:
<div class="question">The equilibrium constant of a reaction is $0.008$ at $298 \mathrm{~K}$. The standard free energy change of the reaction at the same temperature is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-11.96 \mathrm{~kJ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-5.43 \mathrm{~kJ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-8.46 \mathrm{~kJ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">+ $11.96 \mathrm{~kJ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">+ $11.96 \mathrm{~kJ}$</span> </div>

answer:
<div class="solution">Standard free energy change,<br/>$\begin{aligned} \Delta \mathrm{G}^{\circ} &amp;=-2.303 \mathrm{RT} \log \mathrm{K} \\ &amp;=-2.303 \times 8.314 \times 298 \times \log 0.008 \\ &amp;=-2.303 \times 8.314 \times 298 \times(3 \log 2-3 \log 10) \\ &amp;=-2.303 \times 8.314 \times 298 \times(0.903-3.0) \\ &amp;=-2.303 \times 8.314 \times 298 \times(-2.097) \\ &amp;=+11965.16 \mathrm{~J}=+11.96 \mathrm{~kJ} \end{aligned}$</div>


tags: ['Biology', 'Evolution']
options: None
correct_option: None
source_db: MarksBatch2_P2.db
title:
the-evolutionary-story-of-moths-in-england-during-industrialisation-reveals-that-evolution-is-apparently-reversible-clarify-this-statement

slug:
the-evolutionary-story-of-moths-in-england-during-industrialisation-reveals-that-evolution-is-apparently-reversible-clarify-this-statement-90124

question:
<div class="question">The evolutionary story of moths in England during industrialisation reveals, that 'evolution is apparently reversible'. Clarify this statement.</div>

answer:
<div class="solution">The peppered moths were initially white coloured, then black coloured due to industrialisation. In recent years, the light coloured moths are increasing in population.<br/>During the 20th century a light coloured peppered moth Biston betularia was found on the bark of trees in the industrial regions of England. The tree bark was covered by whitish lichens, so the light coloured moths escaped unnoticed from predatory birds.<br/>The barks after industrialisation got covered by smoke, so the white moths were selectively picked up by birds. The black coloured moths however, escaped unnoticed against a dark background and became abundant gradually.<br/>However, in recent years, reduction in industrial pollution has led to the growth of lichens again and thus, the population of light coloured moths is increasing again. The evolutionary story of moths in England, thus reveals, that 'evolution is apparently reversible'.</div>


tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-expansion-of-x-y-n-n-5-is-done-in-the-descending-powers-of-x-if-the-sum-of-the-fifth-and-sixth-terms-is-zero-then-y-x-is-equal-to

slug:
the-expansion-of-x-y-n-n-5-is-done-in-the-descending-powers-of-x-if-the-sum-of-the-fifth-and-sixth-terms-is-zero-then-y-x-is-equal-to-91917

question:
<div class="question">The expansion of $(\mathrm{x}-\mathrm{y})^{\mathrm{n}}, \mathrm{n} \geq 5$ is done in the descending powers of $x$. If the sum of the fifth and sixth terms is zero,<br/>then $\frac{\mathrm{x}}{\mathrm{y}}$ is equal to</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{n}-4}{5}$</span> </div>

answer:
<div class="solution">$(x-y)^{n}, n \geq 5$<br/>General term, $T_{r+1}=n_{c_{r}} x^{n-r}(-y)^{r}$<br/>$T_{5}+T_{6}=0$<br/>$\Rightarrow\left[n_{c_{4}} x^{n-4}(-y)^{4}\right]+\left[n_{c_{5}} x^{n-5}(-y)^{5}\right]=0$<br/>$\Rightarrow n_{c_{4}} x^{n-4} y^{4}-n_{c_{5}} x^{n-5} y^{5}=0$<br/>$\Rightarrow n_{c_{4}} x^{n-4} y^{4}=n_{c_{5}} x^{n-5} y^{5}$<br/>$\Rightarrow \quad \frac{x^{n-4-n+5}}{y}=\frac{n_{c_{5}}}{n_{c_{4}}} \Rightarrow \frac{x}{y}=\frac{x !}{5 !(n-5) !} \times \frac{4 !(n-4) !}{\not x !}$<br/>$=\frac{\not !(n-4)(n-5) !}{5 \times \not 1 !(n-5) !}=\frac{n-4}{5}$</div>


tags: ['Physics', 'Ray Optics', 'JEE Main', 'JEE Main 2021 (27 Jul Shift 2)']
answer: <div class="solution">Standard graph between angle of deviation and<br/>incident angle.</div>
source_db: MarksBatch2_P2.db
title:
the-expected-graphical-representation-of-the-variation-of-angle-of-deviation-with-angle-of-incidence-i-in-a-prism-is

slug:
the-expected-graphical-representation-of-the-variation-of-angle-of-deviation-with-angle-of-incidence-i-in-a-prism-is-79581

question:
<div class="question">The expected graphical representation of the variation of angle of deviation ' <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi></math> ' with angle of incidence 'i' in a prism is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/43da3379-46a3-468a-9878-4d0f4acb7183-image.png" style="width: 162px; height: 158px;"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/fea8d568-2cde-4d52-8e41-a528e985ec35-image.png" style="width: 167px; height: 168px;"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/ca9fc679-f9cf-4a62-b885-ab3a7823c91f-image.png" style="width: 166px; height: 165px;"/></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/5baf540d-b671-44be-99d6-146fe3cfa3fb-image.png" style="width: 162px; height: 164px;"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/fea8d568-2cde-4d52-8e41-a528e985ec35-image.png" style="width: 167px; height: 168px;"/></span> </div>


tags: ['Chemistry', 'Chemical Kinetics', 'NEET']
answer: <div class="solution">Correct Option is : (B)<br/>1450 seconds</div>
source_db: MarksBatch2_P2.db
title:
the-experimental-data-for-decomposition-of-n-2-o-5-2n-2-o-5-4no-2-o-2-in-gas-phase-at-318k-are-given-below-which-of-the-following-options-is-closest-t

slug:
the-experimental-data-for-decomposition-of-n-2-o-5-2n-2-o-5-4no-2-o-2-in-gas-phase-at-318k-are-given-below-which-of-the-following-options-is-closest-t-28844

question:
<div class="question">The experimental data for decomposition of N<sub>2</sub>O<sub>5</sub>:   [ 2N<sub>2</sub>O<sub>5</sub>â 4NO<sub>2</sub>+ O<sub>2</sub>] in gas phase at 318K are given below: <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/2YG1fOQipQihTfRY2bNIRqdtnDaGTcm6fd1qdJEfIL9o4RQVck..png"/><br/>  Which of the following options is closest to the half-life period for the reaction?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">864 seconds</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1450 seconds</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">2863 seconds</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3320 seconds</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">1450 seconds</span> </div>


title: the-expression-c-o-s-c-o-s-s-i-n-s-i-n-is-equal-to
slug: the-expression-c-o-s-c-o-s-s-i-n-s-i-n-is-equal-to-28047
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The expression $\frac{\sin \alpha+\sin \beta}{\cos \alpha+\cos \beta}$ is equal to</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\tan \left(\frac{\alpha+\beta}{2}\right)$</span> </div>

answer:
<div class="solution">$\begin{aligned} &amp; \frac{\sin \alpha+\sin \beta}{\cos \alpha+\cos \beta}=\frac{\not 2 \sin \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)}{\not 2 \cos \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)} \\ &amp;=\tan \left(\frac{\alpha+\beta}{2}\right) \end{aligned}$</div>


title: the-expression-c-o-t-x-cosecx-1-c-o-t-x-cosecx-1-is-equal-to
slug: the-expression-c-o-t-x-cosecx-1-c-o-t-x-cosecx-1-is-equal-to-98237
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The expression $\frac{\cot x+\operatorname{cosecx}-1}{\cot x-\operatorname{cosecx}+1}$ is equal to:</div>

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

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

answer:
<div class="solution">$\frac{\cot x+\operatorname{cosecx}-\left(\operatorname{cosec}^{2} x-\cot ^{2} x\right)}{\cot x-\operatorname{cosec} x+1}$<br/>$=\frac{\cot x+\operatorname{cosecx}-[(\operatorname{cosec} x-\cot x)(\operatorname{cosec} x+\cot x)]}{\cot x-\operatorname{cosecx}+1}$<br/>$=\frac{(\cot x+\operatorname{cosecx})(1+\cot x-\operatorname{cosec} x)}{(\cot x-\operatorname{cosec} x+1)}$<br/>$=\cot x+\operatorname{cosec} x$<br/>$=\frac{\cos x}{\sin x}+\frac{1}{\sin x}=\frac{1+\cos x}{\sin x}$</div>


title: the-extinct-subspecies-of-zebra-quagga-was-originally-found-in
slug: the-extinct-subspecies-of-zebra-quagga-was-originally-found-in-67152
question: <div class="question">The extinct subspecies of zebra, Quagga, was originally found in</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Russia</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">South Africa</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Mauritius</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">India</span> </li> </ul>

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

answer:
<div class="solution">The quagga was a subspecies of the plain zebras which was found abundantly in the areas of Cape Province and South Africa.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">41.2</span> </div>
source_db: MarksBatch2_P2.db
title:
the-f-h-for-c-o-2-g-c-o-g-and-h-2-o-g-are-3935-1105-and-2418-k-j-m-o-l-1-respectively-the-standard-enthalpy-change-in-kj-for-the-reaction-c-o-2-g-h-2-

slug:
the-f-h-for-c-o-2-g-c-o-g-and-h-2-o-g-are-3935-1105-and-2418-k-j-m-o-l-1-respectively-the-standard-enthalpy-change-in-kj-for-the-reaction-c-o-2-g-h-2-76614

question:
<div class="question">The <math><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><mi mathvariant="normal">H</mi><mo>Â°</mo></math> for <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>,</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">O</mi><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo></math> and <math><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo></math> are -393.5, -110.5 and -241.8 <math><mi mathvariant="normal">k</mi><mi mathvariant="normal">J</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> respectively. The standard enthalpy change (in kJ) for the reaction <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>+</mo><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>â</mo><mi mathvariant="normal">C</mi><mi mathvariant="normal">O</mi><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>+</mo><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mo>(</mo><mi mathvariant="normal">g</mi><mo>)</mo></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">524.1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">41.2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">-262.5</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">-41.2</span> </li> </ul>

answer:
<div class="solution"><math><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">r</mi></mrow></msub><mi mathvariant="normal">H</mi><mo>=</mo><munder><mrow><mtext>Î£</mtext><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><msup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></mrow><mrow><mfenced separators="|"><mrow><mtext>Products</mtext></mrow></mfenced></mrow></munder><mo>-</mo><munder><mrow><mtext>Î£</mtext><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><msup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></mrow><mrow><mfenced separators="|"><mrow><mtext>Reactants</mtext></mrow></mfenced></mrow></munder></math><br/><math><mo>=</mo><mfenced close="]" open="[" separators="|"><mrow><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><msubsup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">O</mi><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup><mo>+</mo><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><msubsup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup></mrow></mfenced><mo>-</mo><mfenced close="]" open="[" separators="|"><mrow><msub><mrow><mi mathvariant="normal">Î</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow></msub><msubsup><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup></mrow></mfenced></math><br/><math></math> <math><mo>=</mo><mfenced close="]" open="[" separators="|"><mrow><mfenced separators="|"><mrow><mo>-</mo><mn>110.5</mn></mrow></mfenced><mo>+</mo><mfenced separators="|"><mrow><mo>-</mo><mn>241.5</mn></mrow></mfenced></mrow></mfenced><mo>-</mo><mfenced close="]" open="[" separators="|"><mrow><mo>-</mo><mn>393.5</mn></mrow></mfenced></math><br/><math> <mrow> <mo>=</mo><mo>+</mo><mn>41.2</mn><mtext> </mtext><mtext>kJ</mtext></mrow></math></div>


title: the-false-statement-about-the-terror-of-bengal-is
slug: the-false-statement-about-the-terror-of-bengal-is-19968
question: <div class="question">The false statement about the Terror of Bengal is:</div>
tags: ['Biology', 'Environmental Issues', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">It has been a native of India since hundreds of years.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">It is commonly called water hyacinth and have mauve flowers.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Its scientific name is <em>Eichhornia crassipes</em>.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">It causes disturbance in ecosystem dynamics of water body in a short span of time.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It has been a native of India since hundreds of years.</span> </div>

answer:
<div class="solution">Plant of water hyacinth <em>Eichhornia crassipes</em> is known by 'Terror of Bengal'. It grows abundantly in eutrophic water bodies and can cause blocks in waterways. They give distinct colour to water, deteriorate the quality of water and are extremely harmful to fishes. They grow rapidly and are responsible for imbalance in water body ecosystem. They are native to Brazil and were introduced in India by the British</div>


tags: ['Chemistry', 'General Organic Chemistry', 'VITEEE', 'VITEEE 2015']
source_db: MarksBatch2_P2.db
title:
the-false-statements-among-the-following-are-i-a-primary-carbocation-is-less-stable-than-a-tertiary-carbocation-ii-a-secondary-propyl-carbocation-is-l

slug:
the-false-statements-among-the-following-are-i-a-primary-carbocation-is-less-stable-than-a-tertiary-carbocation-ii-a-secondary-propyl-carbocation-is-l-48842

question:
<div class="question">The false statements among the following are
<br/>I. A primary carbocation is less stable than a tertiary carbocation.
<br/>II. A secondary propyl carbocation is less stable than allyl carbocation.
<br/>III. A tertiary free radical is more stable than a primary free radical.
<br/>IV. Isopropyl carbanion is more stable than ethyl carbanion.</div>

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

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

answer:
<div class="solution">Since $2^{\circ}$ propyl carbocation is little more stable than allyl carbocation and ethyl carbanion is more stable than isopropyl carbanion.</div>


title: the-feeding-of-cattle-should-be-carried-out-in-a-scientific-manner-with-special-emphasis-on
slug: the-feeding-of-cattle-should-be-carried-out-in-a-scientific-manner-with-special-emphasis-on-70518
tags: ['Biology', 'Strategies for Enhancement in Food Production', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The feeding of cattle should be carried out in a scientific manner with special emphasis on</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Quality of fodder.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Quantity of fodder.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Both the quality and quantity of fodder.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Neither the quality nor the quantity of fodder.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both the quality and quantity of fodder.</span> </div>

answer:
<div class="solution">In dairy farm management:<br/><br/>a. Processes and systems are involved that increase milk yield and improve quality.<br/><br/>b. Proper care is given to the cattle: well housed, well-fed (A. Clean water, B. Fodder with quality and quantity), and maintaining a disease-free environment.<br/><br/>c. Cleanliness and hygiene of the handler and animal are also maintained while milking storage and transport of the milk and its products.<br/><br/>d. Regular inspections and visits by a veterinary doctor are mandatory.</div>


title: the-ferns-conifers-gnetales-and-ginkgo-all-are-direct-descendants-of
slug: the-ferns-conifers-gnetales-and-ginkgo-all-are-direct-descendants-of-32352
tags: ['Biology', 'Evolution', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The ferns, conifers, gnetales and <em>Ginkgo</em> all are direct descendants of</div>

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

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

answer:
<div class="solution"><em>Psilophyton</em> is a genus of extinct vascular plants. Described in 1859, it was one of the first fossil plants to be found which was of Devonian age. Plants lacked leaves or true roots; spore-forming organs or sporangia were born on the ends of branched clusters.</div>


title: the-fifth-term-of-an-apof-n-terms-whose-sum-is-n-2-2-n-is
slug: the-fifth-term-of-an-apof-n-terms-whose-sum-is-n-2-2-n-is-48060
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The fifth term of an APof n terms, whose sum is $\mathrm{n}^{2}-2 \mathrm{n}$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">7</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">15</span> </li> </ul>

answer:
<div class="solution">Given, $\mathrm{S}_{\mathrm{n}}=\mathrm{n}^{2}-2 \mathrm{n}$.<br/>We know, $T_{n}=S_{n}-S_{n-1}$<br/>So, $T_{5}=S_{5}-S_{4}$<br/>$S_{5}=5^{2}-2(5)=25-10=15$<br/>$S_{4}=4^{2}-2(4)=16-8=8$<br/>So, $T_{5}=15-8=7$</div>


title: the-figure-shows-a-human-blood-cell-identify-it-and-give-its-characteristics
slug: the-figure-shows-a-human-blood-cell-identify-it-and-give-its-characteristics-60450
tags: ['Biology', 'Body Fluids and Circulation', 'NEET', 'NEET 2013 (Karnataka)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The figure shows a human blood cell. Identify it and give its characteristics.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/iDqul4sGkxNBhk_8PYaHPB3gUmul30cu6_qkOLB_YSM.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\begin{array}{|l|l|} \hline \text{ Basophil } &amp; \text{ Secretes } \\ \text{ inflammatory } &amp; \text{ serotonin }, \end{array}$</span> </div>

answer:
<div class="solution">Basophils have three lobed nucleus and a smaller number of coarse granules. They secrete histamine, serotonin, heparin, etc., and are involved in inflammatory reactions. Lymphocytes are smaller in size having round nucleus. They are of two major types - ' $B$ ' and ' $T$ ' lymphocytes. Both $\mathrm{B}$ and $T$ lymphocytes are responsible for immune responses of the body. Neutrophils are the most abundant cells and are phagocytic in nature which destroy foreign organisms entering the body. They are polymorphic and have multi-lobed nucleus. Monocytes are the largest of all WBCs. They are motile, phagocytic in nature. Their life span is about $10-20 \mathrm{hrs}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/8P-OL812r7GdykUfIurGCq9Wu-w3d5B3LNSo4lV_Ocw.original.fullsize.png"/><br/><br/>Related Theory<br/>There are two types of $W B C$ - granulocytes and agranulocytes. Neutrophils, eosinophils and basophils are different types of granulocytes, while lymphocytes and monocytes are the Agranulocytes.</div>


tags: ['Biology', 'Human Reproduction', 'NEET', 'NEET 2013 (Karnataka)']
source_db: MarksBatch2_P2.db
title:
the-figure-shows-a-section-of-human-ovary-select-the-option-which-gives-the-correct-identification-of-cither-a-or-b-with-functioncharacteristic

slug:
the-figure-shows-a-section-of-human-ovary-select-the-option-which-gives-the-correct-identification-of-cither-a-or-b-with-functioncharacteristic-84581

question:
<div class="question">The figure shows a section of human ovary. Select the option which gives the correct identification of cither A or B with function/characteristic.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/ywHDtJefcBn8DRutHrJBSJmxupFntvdMuC2-zfof-Bg.original.fullsize.png"/><br/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">b- Corpus luteum - Secretes progesterone</span> </div>

answer:
<div class="solution">The zona pellucida and thecal cells of Graafian follicle in the ovary after ovulation forms corpus luteum, which produce progesterone. The tertiary follicle changes into the mature follicle or Graafian follicle and forms a new membrane called zona pellucida surrounding it. The Graafian follicle now ruptures to release the secondary oocyte (ovum) from the ovary. During oogenesis in embryonic development, oogonia start division and enter into prophase-I of the meiotic division and get temporarily arrested at that stage, called primary oocytes. Each primary oocyte then gets surrounded by a layer of granulosa cells and is called the primary follicle<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/kNjyhmr0f7dC0IqOdZ6KtY4NttEolh0O3FRabGX8Nkw.original.fullsize.png"/><br/><br/>Related Theory<br/>The secondary follicle transforms into a tertiary follicle characterized by a fluid filled cavity called antrum. The theca layer organize into an inner theca interna and an outer theca externa. At this stage (puberty) the primary oocyte within the tertiary follicle grows in size and completes its first meiotic division. It is an unequal division resulting in the formation of a large haploid secondary oocyte and a tiny first polar body.<img src="https://cdn-question-pool.getmarks.app/pyq/neet/TPZhViQolnWMiBA0-yFgsX6ZwjxUMtsLcCHnWNBXsMo.original.fullsize.png"/><br/></div>


tags: ['Biology', 'Structural Organisation in Animals', 'AIIMS', 'AIIMS 2017']
source_db: MarksBatch2_P2.db
title:
the-figure-shows-different-human-tissues-labelled-as-a-to-d-which-option-gives-the-correct-identification-of-the-label-its-location-and-one-feature

slug:
the-figure-shows-different-human-tissues-labelled-as-a-to-d-which-option-gives-the-correct-identification-of-the-label-its-location-and-one-feature-67806

question:
<div class="question">The figure shows different human tissues labelled as $\mathrm{A}$ to $\mathrm{D}$. Which option gives the correct identification of the label, its location and one feature?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/aiims/r2ZekZMz6y2XnH9RxPvFoAgP0DG13VfKhu7Tv8ORI18.original.fullsize.png"/><br/></div>

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

answer:
<div class="solution">The given figure $\mathrm{A}$ is squamous epithelium, found in walls of blood vessels and air sacs of lungs and is involved in functions like forming a diffusion layer. B is cuboidal epithelium, found in ducts of glands and tubular parts of nephrons of kidney and its main functions are secretion and absorption. $\mathrm{C}$ is columnar epithelium, found in lining of stomach and intestine and helps in secretion and absorption. D is ciliated columnar epithelium, present in inner surface of hollow organs like bronchioles and Fallopian tubes and helps to move particles or mucus in a specific direction over the epithelium.</div>


tags: ['Biology', 'Animal Kingdom', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-figure-shows-four-animals-a-b-c-and-d-select-the-incorrect-answer-with-respect-to-a-common-characteristic-of-these-animals-a-b-c-d

slug:
the-figure-shows-four-animals-a-b-c-and-d-select-the-incorrect-answer-with-respect-to-a-common-characteristic-of-these-animals-a-b-c-d-70205

question:
<div class="question">The figure shows four animals <math><mfenced separators="|"><mrow><mi mathvariant="normal">A</mi></mrow></mfenced><mo>,</mo><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mi mathvariant="normal">B</mi></mrow></mfenced><mo>,</mo><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mi mathvariant="normal">C,</mi></mrow></mfenced></math> and <math><mfenced separators="|"><mrow><mi mathvariant="normal">D</mi></mrow></mfenced></math>. Select the incorrect answer with respect to a common characteristic of these animals.<br/> <br/> <math><mfenced separators="|"><mrow><mi mathvariant="normal">A</mi></mrow></mfenced></math> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/11_opt_1_bio.JPG" style="max-width:100%; object-fit:contain"/> <math><mfenced separators="|"><mrow><mi mathvariant="normal">B</mi></mrow></mfenced></math> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/11_opt_2_bio.JPG" style="max-width:100%; object-fit:contain"/> <br/> <math><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi></mrow></mfenced></math> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/11_opt_3_bio.JPG" style="max-width:100%; object-fit:contain"/> <math><mfenced separators="|"><mrow><mi mathvariant="normal">D</mi></mrow></mfenced></math> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/11_opt_4_bio.JPG" style="max-width:100%; object-fit:contain"/></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Aurelia-Polyp form, stinging capsules are present on body.</span> </div>

answer:
<div class="solution">Tapeworms belong to Platyhelminthes, which are triploblastic and show false segmentation. Octopus belongs to Molluscs which have an unsegmented body. Prawns belong to Arthropods and thus have jointed appendages. Aurelia have umbrella shaped body and belong to phylum Colenterates. Umbrella shaped body is the medusa form. Being a Coelenterate, it shows the presence of cnidocytes, which are stinging cells present on the body and are used for anchorage, defense, capturing the prey.</div>


title: the-first-biosphere-reserve-established-in-india-is
slug: the-first-biosphere-reserve-established-in-india-is-48619
question: <div class="question">The first biosphere reserve established in India is</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Pachmarhi Biosphere Reserve</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Nokrek Biosphere Reserve</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Sundarbans Biosphere Reserve</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Nilgiri Biosphere Reserve</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Nilgiri Biosphere Reserve</span> </div>

answer:
<div class="solution">In 1986, India established its first biosphere reserve called the Nilgiri Biosphere Reserve which covers Tamilnadu, Kerala and Karnataka. Gulf of Mannar biosphere reserve in Tamilnadu is India's largest biosphere reserve spanning an area of 10,500 sq. km.</div>


title: the-first-meiotic-division-during-oogenesis-is-completed-at-the-stage-of
slug: the-first-meiotic-division-during-oogenesis-is-completed-at-the-stage-of-98399
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The first meiotic division during oogenesis is completed at the stage of</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">primary oocyte within the tertiary follicle</span> </div>

answer:
<div class="solution">Oogenesis is the process of formation of oocyte involving the process of folliculogenesis. Oogenesis begins before birth and the ovaries before birth consist of many primary oocytes. At birth these oocytes are surrounded by follicular cells and this is primary follicle. These remain in the ovary till puberty. As puberty is attained one oocyte completes its cycle. At the beginning primary oocyte is within primary follicle. Oocyte begins its Meiosis I and arrests at Prophase-I. Primary follicle then develops into secondary and further into tertiary follicle but the follicle remains in the arrested prophase-I phase. When tertiary follicle is formed the primary oocyte finally completes its meiosis I and forms secondary oocyte and first polar body after which the tertiary follicle forms the Graffian follicle.</div>


title: the-first-meiotic-division-during-spermatogenesis-takes-place-when
slug: the-first-meiotic-division-during-spermatogenesis-takes-place-when-19967
question: <div class="question">The first meiotic division during spermatogenesis takes place when:</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary spermatocytes divide to form secondary spermatocytes</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 spermatocytes divide to form spermatids</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Spermatogonia divide to form primary spermatocytes</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Spermatids to spermatozoa</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primary spermatocytes divide to form secondary spermatocytes</span> </div>

answer:
<div class="solution">Spermatogenesis is a highly specialized process of cellular differentiation resulting in the formation of functional spermatozoa. Spermatogenesis begins with a diploid spermatogonium in the seminiferous tubules, which divides mitotically to produce two diploid primary spermatocytes.<br/><br/>The primary spermatocyte then undergoes meiosis I to produce two haploid secondary spermatocytes.<br/><br/>The haploid secondary spermatocytes undergo meiosis II to produce four haploid spermatids.</div>


title: the-first-overtone-in-a-closed-pipe-has-a-frequency
slug: the-first-overtone-in-a-closed-pipe-has-a-frequency-37162
question: <div class="question">The first overtone in a closed pipe has a frequency</div>
tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Same as the fundamental frequency of an open tube of same length</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Twice the fundamental frequency of an open tube of same length</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Same as that of the first overtone of an open tube of same length</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">First overtone for closed pipe $=\frac{3 v}{4 l}$<br/>Fundamental frequency for open pipe $=\frac{v}{2 l}$<br/>First overtone for open pipe $=\frac{2 v}{2 l}$.</div>


title: the-focal-distance-of-a-point-on-the-parabola-y-2-12-x-is-4-what-is-the-abscissa-of-the-point
slug: the-focal-distance-of-a-point-on-the-parabola-y-2-12-x-is-4-what-is-the-abscissa-of-the-point-83418
tags: ['Mathematics', 'Parabola', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The focal distance of a point on the parabola $y^{2}=12 x$ is 4 . What is the abscissa of the point?</div>

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

answer:
<div class="solution">Focal distance of a point $\left(x_{1}, y_{1}\right)$ on the parabola is $y^{2}=4 a x$ is equal to its distance from directrix $x+a=0$ is<br/>$\mathrm{x}_{1}+\mathrm{a}$<br/>For $y^{2}=12 x$, comparing with $y^{2}=4 a x$.<br/>$4 a=12 \Rightarrow a=3$<br/>so, $x_{1}+3=4$<br/>$\Rightarrow \quad x_{1}=1$</div>


title: the-foci-of-the-hyperbola-4-x-2-9-y-2-1-0-are
slug: the-foci-of-the-hyperbola-4-x-2-9-y-2-1-0-are-41122
question: <div class="question">The foci of the hyperbola $4 x^{2}-9 y^{2}-1=0$ are</div>
tags: ['Mathematics', 'Hyperbola', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(\pm \sqrt{13,0})$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left(\pm \frac{\sqrt{13}}{6}, 0\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(0, \pm \frac{\sqrt{13}}{6}\right)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\pm \frac{\sqrt{13}}{6}, 0\right)$</span> </div>

answer:
<div class="solution">$4 x^{2}-9 y^{2}=1$<br/>$\frac{x^{2}}{\left(\frac{1}{2}\right)^{2}}-\frac{y^{2}}{\left(\frac{1}{3}\right)^{2}}=1$<br/>eccentricity, $\mathrm{e}=\sqrt{1+\frac{\left(\frac{1}{3}\right)^{2}}{\left(\frac{1}{2}\right)^{2}}}=\frac{\sqrt{13}}{3}$<br/>foci $=\left(\pm \frac{1}{2} \times \frac{\sqrt{13}}{3}, 0\right)=\left(\pm \frac{\sqrt{13}}{6}, 0\right)$</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-following-anatomical-features-belong-to-a-hypodermis-made-by-collenchyma-b-pericycle-in-patches-of-parenchyma-and-sclerenchyma-c-bundle-cap-is-pre

slug:
the-following-anatomical-features-belong-to-a-hypodermis-made-by-collenchyma-b-pericycle-in-patches-of-parenchyma-and-sclerenchyma-c-bundle-cap-is-pre-16462

question:
<div class="question">The following anatomical features belong to<br/> <br/>
A. Hypodermis made by collenchyma.<br/>
B. Pericycle in patches of parenchyma and sclerenchyma<br/>
C. Bundle cap is present.<br/>
D. Vascular bundle open.<br/>
 </div>

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

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

answer:
<div class="solution"><table border="1"> <tbody> <tr> <td>Features</td> <td>Dicot stem</td> </tr> <tr> <td>1. Epidermis</td> <td>Single layered with trichomes (hair)</td> </tr> <tr> <td>2. Hypodermis</td> <td>Collenchymatous</td> </tr> <tr> <td>3. Cortex</td> <td>Parenchymatous</td> </tr> <tr> <td>4. Pericycle</td> <td>Sclerenchymatous.</td> </tr> <tr> <td>5. Medullary rays</td> <td>Parenchymatous</td> </tr> <tr> <td>6. Vascular bundles</td> <td>Vascular bundles are conjoint, open and with endarch protoxylem. These are arranged in a ring-like manner.</td> </tr> <tr> <td>7. Pith</td> <td>Parenchymatous</td> </tr> </tbody></table></div>


tags: ['Biology', 'Body Fluids and Circulation', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-following-are-some-statements-about-leucocytes-which-of-these-is-incorrect-i-the-most-abundant-leucocyte-is-a-granulocyte-whereas-the-least-abunda

slug:
the-following-are-some-statements-about-leucocytes-which-of-these-is-incorrect-i-the-most-abundant-leucocyte-is-a-granulocyte-whereas-the-least-abunda-88351

question:
<div class="question">The following are some statements about leucocytes. Which of these is incorrect?<br/> <br/>
I. The most abundant leucocyte is a granulocyte, whereas the least abundant leucocyte is an agranulocyte.<br/>
II. The largest leucocyte is a granulocyte, whereas the smallest leucocyte is an agranulocyte.<br/>
III. Phagocytic leucocytes may be agranulocyte or granulocyte.<br/>
IV. Polymorphonuclear leucocytes are the largest granulocyte, whereas the largest agranulocyte has a kidney-shaped nucleus.</div>

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

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

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


tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-following-diagrams-represent-the-types-of-aestivation-in-corolla-identify-the-correct-combination-of-labelling

slug:
the-following-diagrams-represent-the-types-of-aestivation-in-corolla-identify-the-correct-combination-of-labelling-17067

question:
<div class="question">The following diagrams represent the types of aestivation in corolla. Identify the correct combination of labelling.<br/> <br/> <u><strong><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/EM0037139_Ques2222.jpg" style="max-width:100%; object-fit:contain"/></strong></u></div>

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

answer:
<div class="solution">The mode of arrangement of sepals or petals in floral bud with respect to the other members of the same whorl is known as aestivation. The main types of aestivation are valvate, twisted, imbricate and vexillary.<br/>In valvate, sepals or petals just touch one another at the margin, without overlapping, <em>e.g., Calotropis.</em><br/>In twisted, one margin of sepal or petal overlaps that of the next one and so on, e.g., China rose, ladyâs finger, cotton, etc.<br/>In imbricate, The margins of sepal or petals overlap one another but not in any particular direction<em> e.g., Cassia,</em> Goldmohur.<br/>In vexillary, the largest posterior petal (vexillum or standard) overlaps two lateral petals (alae or wings) which in turn overlaps the two smallest, anterior but united petals (keel or carina), <em>e.g</em>., pea, bean etc.</div>


tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch2_P2.db
title:
the-following-is-the-record-of-goals-scored-by-team-a-in-a-football-session-for-the-team-b-mean-number-of-goals-scored-per-match-was-2-with-a-standard

slug:
the-following-is-the-record-of-goals-scored-by-team-a-in-a-football-session-for-the-team-b-mean-number-of-goals-scored-per-match-was-2-with-a-standard-43733

question:
<div class="question">The following is the record of goals scored by team A in a football session.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/HepJGpg8cyDRJ4mMRG9cADwbjLr8As6dh7afWEUh5i4.original.fullsize.png"/><br/><br/>For the team $B$, mean number of goals scored per match was 2 with a standard deviation $1.25$ goals.<br/>Find which team may be considered more consistent?</div>

answer:
<div class="solution">For Team A:<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/mHrk1yJ1rAjwZr0hGHEKLQWo6zZp04cwZqmn1StTjQw.original.fullsize.png"/><br/><br/>$\bar{x}=\frac{50}{25}=2$<br/>S.D. $=\sqrt{\frac{\Sigma f_i x_i^2}{n}-\left(\frac{\Sigma f_i x_i}{n}\right)^2}=\sqrt{\frac{130}{25}-\left(\frac{50}{25}\right)^2}$<br/>$=\sqrt{5.2-4}=\sqrt{1.2}=1.09$<br/>For team $B, \bar{x}=2$, S.D. $=1.25$<br/>Since their means are same, $\therefore \sigma_{\mathrm{A}}$ is less than that $\sigma_B$, therefore team $A$ is more consistent than team $B$.</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-following-item-consists-of-two-statements-one-labelled-the-assertion-a-and-the-other-labelled-the-reason-r-you-are-to-examine-these-two-statements-1

slug:
the-following-item-consists-of-two-statements-one-labelled-the-assertion-a-and-the-other-labelled-the-reason-r-you-are-to-examine-these-two-statements-1-79624

question:
<div class="question">The following item consists of two statements, one labelled the Assertion (A) and the other labelled the Reason (R). You are to examine these two statements carefully and decide if the Assertion (A) and Reason (R) are individually true and if so, whether the reason is a correct explanation of the Assertion. Select your answer using the codes given below. Assertion (A) : The work done when the force and displacement are perpendicular to each other is zero.<br/><br/>Reason (R) : the dot product $\vec{A} \cdot \vec{B}$ vanishes, if the vector<br/>$\vec{A}$ and $\vec{B}$ are perpendicular.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both A and $\mathrm{R}$ are true but $\mathrm{R}$ is not the correct explanation of A</span> </div>

answer:
<div class="solution">(A) We know that<br/>Work done $=\overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathbf{d}}=|\overrightarrow{\mathbf{F}}| \cdot|\overrightarrow{\mathbf{d}}| \cos \theta$<br/>Since, $\theta=90^{\circ}$<br/>$\Rightarrow$ work done $=|\overrightarrow{\mathbf{F}}| \cdot|\overrightarrow{\mathbf{d}}| \cos 90^{\circ}=0$<br/>(R) $\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}=0$<br/>$\Rightarrow \overrightarrow{\mathbf{A}}$ and $\overrightarrow{\mathbf{B}}$ are perpendicular. Both $\mathrm{A}$ and $\mathrm{R}$ are true but $\mathrm{R}$ is not correct explanation of<br/>A.</div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-following-item-consists-of-two-statements-one-labelled-the-assertion-a-and-the-other-labelled-the-reason-r-you-are-to-examine-these-two-statements-2

slug:
the-following-item-consists-of-two-statements-one-labelled-the-assertion-a-and-the-other-labelled-the-reason-r-you-are-to-examine-these-two-statements-2-15806

question:
<div class="question">The following item consists of two statements, one labelled the Assertion $(A)$ and the other labelled the Reason $(R) .$ You are to examine these two statements carefully and decide if the Assertion $(A)$ and Reason $(R)$ are individually true and if so, whether the reason is a correct explanation of the Assertion. Select your answer using the codes given below.<br/>Assertion (A): $M=\left[\begin{array}{cc}5 &amp; 10 \\ 4 &amp; 8\end{array}\right]$ is invertible. <br/>Reason (R): M is singular.</div>

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

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

answer:
<div class="solution">(A) Consider $M=\left[\begin{array}{rr}5 &amp; 10 \\ 4 &amp; 8\end{array}\right]$<br/>Now, $|M|=\left|\begin{array}{rr}5 &amp; 10 \\ 4 &amp; 8\end{array}\right|=40-40=0$<br/>Since, $|M|=0$<br/>$\therefore M$ is not invertible.<br/>(R) Since, determinant of $M$ is zero therefore $M$ is singular matrix. Therefore, $\mathrm{A}$ is false and $\mathrm{R}$ is true.</div>


tags: ['Mathematics', 'Indefinite Integration', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-following-item-consists-of-two-statements-one-labelled-the-assertion-a-and-the-other-labelled-the-reason-r-you-are-to-examine-these-two-statements

slug:
the-following-item-consists-of-two-statements-one-labelled-the-assertion-a-and-the-other-labelled-the-reason-r-you-are-to-examine-these-two-statements-37022

question:
<div class="question">The following item consists of two statements, one labelled the Assertion $(A)$ and the other labelled the Reason $(R) .$ You are to examine these two statements carefully and decide if the Assertion (A) and Reason $(R)$ are individually true and if so, whether the reason is a correct explanation of the Assertion. Select your answer using the codes given below.<br/>$Assertion (A)$: $\int \frac{e^{x}}{x}(1+x \log x) d x+c=e^{x} \log x$<br/>$Reason$ $(\mathbf{R}): \int e^{x}\left[f(x)+f^{\prime}(x)\right] d x=e^{x} f(x)+c$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both A and $\mathrm{R}$ are true but $\mathrm{R}$ is not the correct explanation of $\mathrm{A}$</span> </div>

answer:
<div class="solution">(A) Consider $\int \frac{e^{x}}{x}(1+x \log x) d x$<br/>$=\int \frac{e^{x}}{x} d x+\int e^{x} \log x d x$<br/>$=e^{x} \log x-\int e^{x} \log x d x+\int e^{x} \log x d x=e^{x} \log x$<br/>(R) $\int e^{x}\left[f(x)+f^{\prime}(x)\right] d x$<br/>$=\int e^{x} f(x) d x+\int e^{x} f^{\prime}(x) d x$<br/>$=e^{x} f(x)-\int e^{x} f^{\prime}(x) d x+\int e^{x} f^{\prime}(x) d x=e^{x} f(x)+c$<br/>Both Aand $\mathrm{R}$ are true but $\mathrm{R}$ is not the correct explanation of $\mathrm{A}$.</div>


title: the-following-organic-compound-in-living-tissue-is
slug: the-following-organic-compound-in-living-tissue-is-68880
tags: ['Chemistry', 'Biomolecules', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">lipid</span> </div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The following organic compound in living tissue is<br/> <br/> <img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/85_bio_CAdio.JPG" style="max-width:100%; object-fit:contain"/></div>

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

answer:
<div class="solution">The structure is of cholesterol. This is a derived lipid as it does not contain any fatty acids but are lipids as these have fat-like properties. This is composed of four fused carbon rings. Cholesterol is the most abundant steroid in the animal tissues whose precursor is acetic acid. It is essential component of animal plasma membrane too.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2011 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4500</span> </div>
answer: <div class="solution">Required $=7500-3000=4500$</div>
source_db: MarksBatch2_P2.db
title:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b--1

slug:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b-1-93219

question:
<div class="question">The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures:<br/>Agriculture(A), Industry (B), Education (C), Employment (D) and Miscellaneous (E) The total allocation is 36,000 (in crores of rupees).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Eh8pBqfdSM5DosNPoXkGzyLX0PlssvuKdrMWKkyXuZU.original.fullsize.png"/><br/><br/>How much excess money (in crores) is allocated to Miscellaneous over Education? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3600</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4200</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">4500</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">4800</span> </li> </ul>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b--2

slug:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b-2-12952

question:
<div class="question">The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures:<br/>Agriculture(A), Industry (B), Education (C), Employment (D) and Miscellaneous (E) The total allocation is 36,000 (in crores of rupees).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Eh8pBqfdSM5DosNPoXkGzyLX0PlssvuKdrMWKkyXuZU.original.fullsize.png"/><br/><br/>$\quad$ Which head is allocated maximum funds? $\quad$</div>

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

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

answer:
<div class="solution">Agriculture : $\frac{90}{360} \times 36000=9000$ Miscellaneous : $\frac{75}{360} \times 36000=7500$<br/>Industry: $\frac{45}{360} \times 36000=4500$<br/>Education:3000 $\quad$ Employment : 12000 Hence, funds.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2011 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3000</span> </div>
answer: <div class="solution">Education: 3000</div>
source_db: MarksBatch2_P2.db
title:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b--3

slug:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b-3-11896

question:
<div class="question">The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures:<br/>Agriculture(A), Industry (B), Education (C), Employment (D) and Miscellaneous (E) The total allocation is 36,000 (in crores of rupees).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Eh8pBqfdSM5DosNPoXkGzyLX0PlssvuKdrMWKkyXuZU.original.fullsize.png"/><br/><br/>How much money (in crores) is allocated to $\begin{array}{ll}\text { Education? } &amp; {}\end{array}$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">3000</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">6000</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">9000</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">10800</span> </li> </ul>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2011 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">21000</span> </div>
answer: <div class="solution">Required $=9000+12000=21000$</div>
source_db: MarksBatch2_P2.db
title:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b-

slug:
the-following-pie-chart-gives-the-distribution-of-funds-in-a-five-year-plan-under-the-major-heads-of-development-expenditures-agriculturea-industry-b-51547

question:
<div class="question">The following pie chart gives the distribution of funds in a five year plan under the major heads of development expenditures:<br/>Agriculture(A), Industry (B), Education (C), Employment (D) and Miscellaneous (E) The total allocation is 36,000 (in crores of rupees).<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Eh8pBqfdSM5DosNPoXkGzyLX0PlssvuKdrMWKkyXuZU.original.fullsize.png"/><br/><br/>How much money (in crores) is allocated to both Agriculture and Employment? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">20000</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">21000</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">24000</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">27000</span> </li> </ul>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-1

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-1-42541

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion $(A)^{\prime}$ and the other as 'Reason $(R)^{\prime}$. You are to examine these two statements carefully and select the answer.<br/>Assertion (A): We cannot find out the regression of $x$ on $y$ from that of y on $\mathrm{x}$. Reason (R): In one equation $x$ is dependent variable and $y$ is independent whereas in other equation $\mathrm{y}$ is dependent variable and $\mathrm{x}$ is independent.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both $\mathbf{A}$ and $\mathbf{R}$ are individually true, and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$.</span> </div>

answer:
<div class="solution">All are correct statement and $\mathrm{R}$ is correct explanation<br/>of $\mathrm{A}$.</div>


tags: ['Mathematics', 'Trigonometric Equations', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-2

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-2-17384

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion $(A)^{\prime}$ and the other as 'Reason $(R):$ You are to examine these two statements carefully and select the answer.<br/>Let $X=\{\theta \in[0,2 \pi] \cdot \sin \theta=\cos \theta\}$<br/>Assertion (A): The number of elements in $X$ is 2. Reason (R) : $\sin \theta$ and $\cos \theta$ are both negative both in second and fourth quadrants.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathbf{A}$ is true but $\mathbf{R}$ is false.</span> </div>

answer:
<div class="solution">$\quad(\mathrm{A}): \mathrm{X}=\{\theta \in[0,2 \pi]: \sin \theta=\cos \theta\}$<br/>Number of elements in $\mathrm{X}$ is 2 . Since, $\sin \theta=\cos \theta$ is possible at $\theta=45^{\circ}$ and $225^{\circ}$ Since, $\cos \theta$ is negative in IInd quadrant but $\sin \theta$ is positive, $R$ is false.</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-3

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-3-57188

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason $(R)^{\prime} .$ You are to examine these two statements carefully and select the answer.<br/>Assertion (A): $\left\{x \in R \mid x^{2}   &lt; 0\right\}$ is not a set. Here $R$ is the set ofreal numbers. Reason (R): For every real number $\mathrm{x}, \mathrm{x}^{2}&gt;0 .$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both A and $\mathbf{R}$ are individually true, and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$.</span> </div>

answer:
<div class="solution">Since $x^{2}   &lt; 0$ is not possible for real numbers. A is true Since $x^{2}&gt;0$ for $\forall x \in R$. Both $($ A $)$ and $(R)$ are true and<br/>(R) is the correct explanation of ( $\mathrm{A}$ ).</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-4

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-4-41717

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answer.<br/><br/>Assertion (A): $1 / 8, \log _{a^{2}} a \rightarrow$ exponent should be to the base, $\log ^{2}$ are in GP but not in AP<br/>Reason: $(\mathbf{R}): \mathrm{x}, \mathrm{y}, \mathrm{z}$ are in APas well as in GPif $\mathrm{x}=\mathrm{y}=\mathrm{z}$.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Both A and $\mathrm{R}$ are individually true and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$</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">B</span> <span class="option-data">Both A and $\mathrm{R}$ are individually true but $\mathrm{R}$ is not the correct explanation $\mathrm{A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{A}$ is true but $\mathrm{R}$ is false</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$A$ is false but $R$ is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both A and $\mathrm{R}$ are individually true and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$</span> </div>

answer:
<div class="solution">If $x, y, z$ are in GP then $x \cdot z=y^{2}$<br/>Here $x=\frac{1}{8}, z=\log _{a} a^{2}, y=\left(\log _{a}^{2} a\right)$<br/>$\frac{1}{8} \times \log _{a} a^{2}=\frac{1}{8} \cdot 2=\frac{1}{4}$<br/>and $\left(\log _{\mathrm{a} 2} \mathrm{a}\right)^{2}=\left(\frac{1}{2}\right)^{2}=\frac{1}{4}$<br/>Hence, $\frac{1}{8}, \log _{\mathrm{a} 2} \mathrm{a}, \log _{\mathrm{a}} \mathrm{a}^{2}$ arein GP.<br/>Thus, both A and Rare individuallytrue and Ris correct explanation of $\mathrm{A}$</div>


tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-5

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-5-80374

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answer.</div>

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

answer:
<div class="solution">$\frac{z_{1}}{z_{2}}=\frac{3+4 i}{3+5 i}=\frac{(3+4 i)(3-5 i)}{3^{2}-5^{2}}=\frac{9-3 i+20}{9-25}=\frac{29-3 i}{-16}$<br/>which is complex number. Both A and R are individually true and $\mathrm{R}$ is correct explanation of $\mathrm{A}$.</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2006 (Phase 1)']
answer: <div class="solution">A is true, but R is false.</div>
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-6

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-6-92705

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)' You are to examine these two statements carefully and select the answer.<br/>Assertion $(\mathbf{A}):$ If $\overrightarrow{\mathrm{a}}=2 \overrightarrow{\mathrm{i}}+\overrightarrow{\mathrm{j}}-2 \overrightarrow{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{i}}+\overrightarrow{\mathrm{j}}-\overrightarrow{\mathrm{k}}$<br/>then $|\overrightarrow{\mathrm{a}}| \neq|\overrightarrow{\mathrm{b}}|$<br/>Reason (R) : Two unequal vectors can never have same magnitude.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A is false but R is true.</span> </div>


tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-7

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-7-34967

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answer.<br/>Assertion $(\mathbf{A}): \int_{0}^{\pi} \sin ^{7} x d x=2 \int_{0}^{\pi / 2} \sin ^{7} x d x$<br/>Reason(R) $: \sin ^{7} x$ is an odd function</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both $\mathrm{A}$ and $\mathrm{R}$ are individually true but $\mathrm{R}$ is not the conect explamation A</span> </div>

answer:
<div class="solution">$\int_{0}^{\pi} \sin ^{7} x d x=2 \int_{0}^{\pi / 2} \sin ^{7} x d x$<br/>$\sin x$ is an odd function and for an odd function<br/>$\int_{0}^{a} f(x) d x=2 \int_{0}^{a / 2} f(x) d x$<br/>Hence, $\int_{0}^{\pi} \sin ^{7} x d x=2 \int_{0}^{\pi / 2} \sin ^{7} x d x$ is true.<br/>So, A and $\mathrm{R}$ both are individually true but $\mathrm{R}$ is not the correct explanation of A.</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-8

slug:
the-following-question-consist-of-two-statements-one-labelled-as-the-assertion-a-and-the-other-as-reason-r-you-are-to-examine-these-two-statements-car-8-43324

question:
<div class="question">The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason $(R)^{\prime} .$ You are to examine these two statements carefully and select the answer.<br/>Assertion $(\mathbf{A}): 0.3+0.03+0.003+\ldots=\frac{1}{3}$<br/>Reason $(\mathbf{R}):$ For each $(+)$ ve integer $\mathrm{n}$, let $\mathrm{a}_{\mathrm{n}}=\mathrm{a}+\mathrm{nd}, \mathrm{a}$ and<br/>dare real numbers. Then, $\mathrm{a}_{1}+\ldots .+\mathrm{a}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}+1) \mathrm{d}] .$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both $\mathrm{A}$ and $\mathrm{R}$ are individually true but $\mathrm{R}$ is not the correct explanation of $\mathrm{A}$</span> </div>

answer:
<div class="solution">(A): $0.3+0.03+0.003+\ldots=\frac{1}{3}$<br/>Let $\mathrm{S}=0.3+0.03+0.003+\ldots$<br/>This is geometric series with<br/>first term, $\mathrm{a}=0.3$ and common ration, $\mathrm{r}=\frac{1}{10}$.<br/>So, $S=\frac{a}{1-r}=\frac{0.3}{1-\frac{1}{10}}=\frac{0.3 \times 10}{9}$<br/>$$<br/>\begin{array}{l}<br/>\quad=\frac{3}{9}=\frac{1}{3} \cdot \text { So },(\mathrm{A}) \text { is true. } \\<br/>(\mathrm{R}): \text { As given }: \mathrm{a}_{\mathrm{n}}=\mathrm{a}+\mathrm{nd} \\<br/>\Rightarrow \mathrm{a}_{1}+\mathrm{a}_{2}+\ldots+\mathrm{a}_{\mathrm{n}} \\<br/>=\mathrm{a}+\mathrm{d}+\mathrm{a}+2 \mathrm{~d}+\ldots+\mathrm{a}+\mathrm{nd} \\<br/>=\mathrm{n} \mathrm{a}+(1+2+\ldots+\mathrm{n}) \mathrm{d} \\<br/>=\mathrm{na}+\frac{\mathrm{n}(\mathrm{n}+1) \mathrm{d}}{2}=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}+1) \mathrm{d}]<br/>\end{array}<br/>$$<br/>So, $(\mathrm{R})$ is also true Hence, both (A) and (R) are true. but $\mathrm{R}$ is not the correct explanation of (A)</div>


