Let $f(x) = 3x^3 + 4e^{\frac{x}{2}}$ and $g(x) = f^{-1}(x)$. Then the value of $g'(4)$ is equal to...

If the function $f(x) = ax^3 - bx^2 - 8x - 4$ satisfies Roll's theorem in $[1,3]$, if $f'(2) = 0$ then $a - b$ is equal to...

The co-ordinates of the point on the curve $y = x\log x$ at which the normal is parallel to the line $2x - 2y = 3$ are...

If $\int \dfrac{1}{\cos^3 x \sqrt{\sin 2x}}\, dx = p(\tan^2 x + q)\sqrt{\tan x} + c$, then the values of $p$ and $q$ respectively are