Mathematics · 2022
JEE Main · 25 July 2022, Shift 1 · Q10
The slope of the tangent to a curve C: y=y(x) at any point (x, y) on it is (2 e^2 x-6 e^-x+9)/(2+9 e^-2 x). If C passes through the points (0,…
The slope of the tangent to a curve $\displaystyle \mathrm{C}: y=y(x)$ at any point $\displaystyle (x, y)$ on it is $\displaystyle \frac{2 \mathrm{e}^{2 x}-6 \mathrm{e}^{-x}+9}{2+9 \mathrm{e}^{-2 x}}$. If C passes through the points $\displaystyle \left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right)$ and $\displaystyle \left(\alpha, \frac{1}{2} \mathrm{e}^{2 \alpha}\right)$, then $\displaystyle \mathrm{e}^\alpha$ is equal to :
Official answer
(2)
$\displaystyle \frac{3}{\sqrt{2}}\left(\frac{3+\sqrt{2}}{3-\sqrt{2}}\right)$
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.