The number of points of discontinuity of $f(x)$ where $f(x) = | | |x + [x]| - 3[x] | - 5[x] |$ on $[-2, 2]$ is (where $[ \cdot ]$ denotes the greatest integer function).

Let $f(x) = [x^2] \sin(\pi x)$, for $x > 0$. Then:

For $a \neq 0$ and $b \neq 0$,if the real valued function $f(x) = \frac{\sqrt[5]{a(625+x)} - 5}{\sqrt[4]{625+bx} - 5}$ is continuous at $x = 0$,then $f(0) =$

If $f(x) = \operatorname{sgn} \left( 3\cos x - \frac{a}{3} \right)$ is continuous for all $x$,then the least positive integral value of $a$ is - (where $\operatorname{sgn}(x)$ denotes the signum function of $x$)

If $f(x)$ defined as given below is continuous on $R$,then the value of $a+b$ is equal to: $f(x) = \begin{cases} \sin x, & x \leq 0 \\ x^2+a, & 0 < x < 1 \\ b x+3, & 1 \leq x \leq 3 \\ -3, & x > 3 \end{cases}$

If $f(x)= \begin{cases}-2 \sin x & , \quad x \leqslant-\frac{\pi}{2} \\ a \sin x+b & , \quad \frac{-\pi}{2} < x < \frac{\pi}{2} \\ \cos x & , \quad x \geqslant \frac{\pi}{2}\end{cases}$ is continuous at $x=-\frac{\pi}{2}$ and $x=\frac{\pi}{2}$,then the value of $2a+b$ is