If $g(x) = (x^2 + 2x + 1)\cdot f(x)$ such that $f(0) = 5$ and $\lim\limits_{x \to 0}\dfrac{f(x)-5}{x} = 4$ then $g'(0) = $

If the line $x + By + C = 0$ is the normal to the curve given by $x = a\sin^3 t$, $y = b\cos^3 t$, (where $a, b \neq 0$) at a point $t = \dfrac{\pi}{2}$, then $B - C = $

If the tangent to the curve $xy + ax + by = 0$ at $(1,1)$ makes an angle of $\tan^{-1}2$ with positive direction of the $x$-axis, then the value of $\dfrac{ab}{a+b}$ is...

If the side of an equilateral triangle increases at the rate of $\sqrt{3}\ \text{cm/sec}$, then the rate of change of increase of its area when the side is $12\ \text{cm}$ is ____