CUET Mathematics 2025 29 May Shift 2 PYQs

If $y = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right), 0 < x < 1$, then $\frac{dy}{dx}$ is equal to

If $y = e^{acos^{-1}x}, -1 < x < 1$, then $(1-x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx}$ is equal to

If the function

$f(x) = \begin{cases} k\cos x & , x \neq \frac{\pi}{2} \\ \pi - 2x & , x = \frac{\pi}{2} \\ 3 & , x = \frac{\pi}{2} \end{cases}$

is continuous at $x = \frac{\pi}{2}$, then $k$ is equal to