The number of point / points where the function $f(x) = \dfrac{1}{x^2-5|x|+6}$ is discontinuous is......

If $x\,e^{xy} = y + \sin^2 x$, then the value of $\dfrac{dy}{dx}$ at $x = 0$ is equal to

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 = $