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 $f(0) =$

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).

If the function $f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|\pi - x| + 3, & x > 5 \end{cases}$ is continuous at $x = 5$,then the value of $a - b$ is

If $f(x) = \begin{cases} \frac{\sin 5x \tan kx}{x^2} & , x \neq 0 \\ 1 & , x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is . . . . . . . $(\because k \neq 0)$

If $f(x) = \begin{cases} \frac{\log_{e} x}{x-1} & x \neq 1 \\ k & x=1 \end{cases}$ is continuous at $x=1$,then the value of $k$ is

If the real valued function $f(x) = \begin{cases} \frac{\cos 3x - \cos x}{x \sin x} & \text{if } x < 0 \\ p & \text{if } x = 0 \\ \frac{\log(1 + q \sin x)}{x} & \text{if } x > 0 \end{cases}$ is continuous at $x = 0$, then $p + q =$