The slope of the tangent|Differential Equations|JEEMAIN 2022

JEE MAIN 2022

25-07-22 S1

Question

The slope of the tangent to a curve $C: y=y(x)$ at any point $[x, y)$ on it is $\frac{2 e^{2 x}-6 e^{-x}+9}{2+9 e^{-2 x}}$. If $C$ passes through the points $\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right)$ and $\left(\alpha, \frac{1}{2} \mathrm{e}^{2 \alpha}\right)$ then $\mathrm{e}^\alpha$ is equal to :

Select the correct option:

$\frac{3+\sqrt{2}}{3-\sqrt{2}}$

$\frac{3}{\sqrt{2}}\left(\frac{3+\sqrt{2}}{3-\sqrt{2}}\right)$

$\frac{1}{\sqrt{2}}\left(\frac{\sqrt{2}+1}{\sqrt{2}-1}\right)$

$\frac{\sqrt{2}+1}{\sqrt{2}-1}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution