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

If $\int \sqrt{2}\sqrt{1+\sin x}\, dx = -4\cos(ax+b) + c$, then the value of $a, b$ respectively are...