Let $[t]$ represent the greatest integer not exceeding $t$. Then the number of points of discontinuity of $f(x) = [10^x]$ in the interval $(0, 10)$ is:

If $f: R \rightarrow R$ is defined by $f(x) = \begin{cases} x-1, & \text{for } x \leq 1 \\ 2-x^2, & \text{for } 1 < x \leq 3 \\ x-10, & \text{for } 3 < x < 5 \\ 2x, & \text{for } x \geq 5 \end{cases}$,then the set of points of discontinuity of $f$ is

Discuss the continuity of the function $f$ given by $f(x) = x^{3} + x^{2} - 1$.

If the function $f(x) = \begin{cases} \frac{\tan 4x \times \cos 3x}{x} & , x \neq 0 \\ k & , x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is equal to . . . . . .

Let $[t]$ denote the greatest integer less than or equal to $t$. Let $f(x)=x-[x]$,$g(x)=1-x+[x]$,and $h(x)=\min \{f(x), g(x)\}$ for $x \in [-2, 2]$. Then $h$ is :

If $f(x) = [x]$ for $x \in (-1, 2)$,then $f$ is discontinuous at (where $[x]$ represents the floor function).