Let $y = \sqrt[p]{x^3 y}$. If $\dfrac{dy}{dx} = \dfrac{3}{2}$ when $y = 1$, then the value of $p$ is equal to $\ldots$

If $f'(x) = \sin^2 x$ and $y = f\left(\dfrac{2x-1}{x^2+1}\right)$, then $\dfrac{dy}{dx}$ at $x = 1$ is

If $f : R \to R$ is an even function then

Let $g(x) = f(x) + f(1-x)$ and $f''(x) < 0, 0 \leq x \leq 1$, then $\ldots$