Let $[x]$ be the greatest integer $\leq x$. Then the number of points in the interval $(-2, 1)$,where the function $f(x) = |[x]| + \sqrt{x - [x]}$ is discontinuous,is $........$.

The function $f(x) = \begin{cases} x - 1, & x < 2 \\ 2x - 3, & x \ge 2 \end{cases}$ is a continuous function:

If the function $f(x) = \begin{cases} \frac{k\cos x}{\pi - 2x}, & x \neq \frac{\pi}{2} \\ 3, & x = \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}$,then $k = $

If $\lim _{x \rightarrow a^{+}} f(x)=p, \lim _{x \rightarrow a^{-}} f(x)=m$ and $f(a)=k$,then which one of the following is true?

For real $x$ with $-10 \leq x \leq 10$,define $f(x) = \int_{-10}^x 2^{[t]} dt$,where for a real number $r$,we denote by $[r]$ the greatest integer less than or equal to $r$. The number of points of discontinuity of $f$ in the interval $(-10, 10)$ is

Let $[t]$ denote the greatest integer less than or equal to $t$. If the function $f(x) = \begin{cases} b^2 \sin \left(\frac{\pi}{2} \left[\frac{\pi}{2}(\cos x + \sin x) \cos x\right]\right), & x < 0 \\ \frac{\sin x - \frac{1}{2} \sin 2x}{x^3}, & x > 0 \\ a, & x = 0 \end{cases}$ is continuous at $x = 0$, then $a^2 + b^2$ is equal to