CUET Mathematics 2025 22 May Shift 1 PYQs

If $f(x) = x^3\log_e x$, Then $f''(e^2)$ is equal to

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

The value of k for which the function, defined by, $f(x) = \begin{cases} \frac{3x + 4 \tan x}{k} & ; x \neq 0 \\ k & ; x = 0 \end{cases}$ is continuous at $x = 0$, is