<div class="question-component md:card md:rounded-lg md:py-4 flex flex-col gap-2 lg:gap-4 svelte-1pnvkqi"><div class="flex flex-col gap-2 max-md:card max-md:pt-3"><div class="flex items-center justify-between gap-3 px-4 pb-2 border-b-gray-100 dark:border-opacity-20" style="border-bottom-width: 1px; border-bottom-style: solid;"><div class="flex items-center gap-3"><div class="flex items-center justify-center text-white dark:text-blue-400 bg-blue-600 dark:bg-opacity-10 text-sm shrink-0" style="width: 25px; height: 25px; border-radius: 50%;">1</div> <div class="flex flex-col gap-1.5"><div class="font-semibold text-sm max-md:text-xs">JEE Advanced 2015 Paper 2 Offline</div> <div class="flex items-center gap-1.5 text-xs"><div class="px-1.5 py-0.5 bg-opacity-10 rounded-sm text-blue-700 bg-blue-600 dark:text-blue-400 text-ellipsis overflow-hidden whitespace-nowrap">MCQ (More than One Correct Answer)</div> <div class="px-1.5 py-0.5 bg-opacity-5 rounded-sm text-green-700 bg-green-600 dark:text-green-400 ">+4</div> <div class="px-1.5 py-0.5 bg-opacity-5 rounded-sm text-red-700 bg-red-600 dark:text-red-400 ">-1</div> </div></div></div> <div class="flex justify-end gap-2"> <button class="shrink-0"><img class="border-2" src="/image/warning.png" alt="Report Question" style="width: 30px;height: 30px;padding: 4px;border-radius: 50%"></button></div></div>   <div class="question xl:text-lg px-4 py-2.5">Let <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>1</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> and <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>2</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> be two ellipses whose centres are at the origin. The major axes of <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>1</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> and <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>2</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> lie along the <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></mjx-assistive-mml></mjx-container>-axis and the <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D466 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></mjx-assistive-mml></mjx-container>-axis, respectively.  Let <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D446 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></mjx-assistive-mml></mjx-container> be the circle <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msup><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: 0.363em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-texatom><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-texatom space="3" texclass="ORD"><mjx-msup><mjx-mrow><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-texatom texclass="ORD"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D466 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2212"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="3"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-texatom><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-mrow><mjx-script style="vertical-align: 0.477em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msup><mi>x</mi><mn>2</mn></msup></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mi>y</mi><mo>−</mo><mn>1</mn></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mn>2</mn></msup></mrow><mo>=</mo><mn>2</mn></math></mjx-assistive-mml></mjx-container>. The straight line <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D465 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="3"><mjx-c class="mjx-c1D466 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c33"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>3</mn></math></mjx-assistive-mml></mjx-container> touches the curves <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D446 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></mjx-assistive-mml></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>1</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> and <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>2</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> at <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D443 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n"><mjx-c class="mjx-c2C"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="2"><mjx-c class="mjx-c1D444 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>,</mo><mi>Q</mi></math></mjx-assistive-mml></mjx-container> and <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D445 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></mjx-assistive-mml></mjx-container> respectively. Suppose that <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D443 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D444 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D443 TEX-I"></mjx-c></mjx-mi><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D445 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-texatom space="4" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-msqrt><mjx-sqrt><mjx-surd><mjx-mo class="mjx-n"><mjx-c class="mjx-c221A"></mjx-c></mjx-mo></mjx-surd><mjx-box style="padding-top: 0.174em;"><mjx-mn class="mjx-n"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-box></mjx-sqrt></mjx-msqrt></mjx-texatom></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c33"></mjx-c></mjx-mn></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>Q</mi><mo>=</mo><mi>P</mi><mi>R</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow><mn>3</mn></mfrac></mrow></math></mjx-assistive-mml></mjx-container>. If <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mn>1</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> and <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mn>2</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> are the eccentricities of <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>1</mn></msub></mrow></math></mjx-assistive-mml></mjx-container> and <mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D438 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.026em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>E</mi><mn>2</mn></msub></mrow></math></mjx-assistive-mml></mjx-container>, respectively, then the correct expression(s) is (are) </div></div> <div class="options md:px-4 flex flex-col gap-2 lg:gap-4"><div role="button" class="flex items-center gap-2 max-md:card md:rounded px-4 py-4 dark:border-gray-500 md:border-2 cursor-pointer select-none transition-all relative bg-opacity-20   hover:border-2   "><div class="shrink-0 flex items-center justify-center text-white text-sm rounded-[50%] w-[25px] h-[25px] bg-blue-600  ">A</div>  <div class="grow question xl:text-lg"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msubsup><mjx-texatom texclass="OP"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi></mjx-texatom><mjx-script style="vertical-align: -0.288em; margin-left: 0px;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-spacer style="margin-top: 0.18em;"></mjx-spacer><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msubsup><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-msubsup space="3"><mjx-texatom texclass="OP"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi></mjx-texatom><mjx-script style="vertical-align: -0.288em; margin-left: 0px;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-spacer style="margin-top: 0.18em;"></mjx-spacer><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msubsup><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-texatom space="4" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c><mjx-c class="mjx-c33"></mjx-c></mjx-mn></mjx-texatom></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-texatom></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mrow data-mjx-texclass="OP"><mi>e</mi></mrow><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mrow data-mjx-texclass="OP"><mi>e</mi></mrow><mn>2</mn><mn>2</mn></msubsup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>43</mn></mrow><mrow data-mjx-texclass="ORD"><mn>40</mn></mrow></mfrac></mrow></math></mjx-assistive-mml></mjx-container> </div> </div><div role="button" class="flex items-center gap-2 max-md:card md:rounded px-4 py-4 dark:border-gray-500 md:border-2 cursor-pointer select-none transition-all relative bg-opacity-20   hover:border-2   "><div class="shrink-0 flex items-center justify-center text-white text-sm rounded-[50%] w-[25px] h-[25px] bg-blue-600  ">B</div>  <div class="grow question xl:text-lg"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-texatom space="4" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-texatom size="s" texclass="ORD"><mjx-msqrt><mjx-sqrt><mjx-surd><mjx-mo class="mjx-n"><mjx-c class="mjx-c221A"></mjx-c></mjx-mo></mjx-surd><mjx-box style="padding-top: 0.158em;"><mjx-mn class="mjx-n"><mjx-c class="mjx-c37"></mjx-c></mjx-mn></mjx-box></mjx-sqrt></mjx-msqrt></mjx-texatom></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-texatom size="s" texclass="ORD"><mjx-mn class="mjx-n"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-msqrt><mjx-sqrt><mjx-surd><mjx-mo class="mjx-n"><mjx-c class="mjx-c221A"></mjx-c></mjx-mo></mjx-surd><mjx-box style="padding-top: 0.163em;"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-box></mjx-sqrt></mjx-msqrt></mjx-texatom></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mn>1</mn></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mn>2</mn></msub></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msqrt><mn>7</mn></msqrt></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn><msqrt><mn>10</mn></msqrt></mrow></mfrac></mrow></math></mjx-assistive-mml></mjx-container> </div> </div><div role="button" class="flex items-center gap-2 max-md:card md:rounded px-4 py-4 dark:border-gray-500 md:border-2 cursor-pointer select-none transition-all relative bg-opacity-20   hover:border-2   "><div class="shrink-0 flex items-center justify-center text-white text-sm rounded-[50%] w-[25px] h-[25px] bg-blue-600  ">C</div>  <div class="grow question xl:text-lg"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mrow><mjx-mo class="mjx-n"><mjx-stretchy-v class="mjx-c7C" style="height: 1.168em; vertical-align: -0.334em;"><mjx-ext><mjx-c></mjx-c></mjx-ext><mjx-mark></mjx-mark></mjx-stretchy-v></mjx-mo><mjx-texatom texclass="ORD"><mjx-msubsup><mjx-texatom texclass="OP"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi></mjx-texatom><mjx-script style="vertical-align: -0.288em; margin-left: 0px;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-spacer style="margin-top: 0.18em;"></mjx-spacer><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msubsup><mjx-mo class="mjx-n" space="3"><mjx-c class="mjx-c2B"></mjx-c></mjx-mo><mjx-msubsup space="3"><mjx-texatom texclass="OP"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi></mjx-texatom><mjx-script style="vertical-align: -0.288em; margin-left: 0px;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn><mjx-spacer style="margin-top: 0.18em;"></mjx-spacer><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msubsup></mjx-texatom><mjx-mo class="mjx-n"><mjx-stretchy-v class="mjx-c7C" style="height: 1.168em; vertical-align: -0.334em;"><mjx-ext><mjx-c></mjx-c></mjx-ext><mjx-mark></mjx-mark></mjx-stretchy-v></mjx-mo></mjx-mrow><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-texatom space="4" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c35"></mjx-c></mjx-mn></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c38"></mjx-c></mjx-mn></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="ORD"><msubsup><mrow data-mjx-texclass="OP"><mi>e</mi></mrow><mn>1</mn><mn>2</mn></msubsup><mo>+</mo><msubsup><mrow data-mjx-texclass="OP"><mi>e</mi></mrow><mn>2</mn><mn>2</mn></msubsup></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mn>5</mn><mn>8</mn></mfrac></mrow></math></mjx-assistive-mml></mjx-container> </div> </div><div role="button" class="flex items-center gap-2 max-md:card md:rounded px-4 py-4 dark:border-gray-500 md:border-2 cursor-pointer select-none transition-all relative bg-opacity-20   hover:border-2   "><div class="shrink-0 flex items-center justify-center text-white text-sm rounded-[50%] w-[25px] h-[25px] bg-blue-600  ">D</div>  <div class="grow question xl:text-lg"><mjx-container class="MathJax" jax="CHTML" style="font-size: 119.5%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom><mjx-texatom texclass="ORD"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D452 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-texatom><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-texatom space="4" texclass="ORD"><mjx-mfrac><mjx-frac><mjx-num><mjx-nstrut></mjx-nstrut><mjx-texatom size="s" texclass="ORD"><mjx-msqrt><mjx-sqrt><mjx-surd><mjx-mo class="mjx-n"><mjx-c class="mjx-c221A"></mjx-c></mjx-mo></mjx-surd><mjx-box style="padding-top: 0.164em;"><mjx-mn class="mjx-n"><mjx-c class="mjx-c33"></mjx-c></mjx-mn></mjx-box></mjx-sqrt></mjx-msqrt></mjx-texatom></mjx-num><mjx-dbox><mjx-dtable><mjx-line></mjx-line><mjx-row><mjx-den><mjx-dstrut></mjx-dstrut><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c34"></mjx-c></mjx-mn></mjx-den></mjx-row></mjx-dtable></mjx-dbox></mjx-frac></mjx-mfrac></mjx-texatom></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mn>1</mn></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mn>2</mn></msub></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msqrt><mn>3</mn></msqrt></mrow><mn>4</mn></mfrac></mrow></math></mjx-assistive-mml></mjx-container> </div> </div></div>  <div class="text-center"><button class="shadow drop-shadow-sm bg-blue-600 text-white px-4 py-2 rounded hover:font-bold transition-all select-none" aria-label="Check Answer Button">Check Answer</button></div> </div>