Which of the following is differentiable at $x=0$?

Let $f(x)=|1-2 x|$,then

$A$ function $f$ is defined on $[-3,3]$ as
$f(x) = \begin{cases} \min \{|x|, 2-x^{2}\} & , -2 \leq x \leq 2 \\ [|x|] & , 2 < |x| \leq 3 \end{cases}$
where $[x]$ denotes the greatest integer $\leq x$. The number of points,where $f$ is not differentiable in $(-3,3)$ is

Let $f(x) = |2x^2 + 5|x| - 3|$,$x \in R$. If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively,then $m + n$ is equal to:

If $f(x) = \begin{cases} \tan^{-1} x, & \text{when } |x| \leq 1 \\ \frac{1}{2}(|x|-1), & \text{when } |x| > 1 \end{cases}$,then the domain of $\frac{d}{dx} f(x)$ is

The left-hand derivative of $f(x) = [x]\sin(\pi x)$ at $x = k$,where $k$ is an integer and $[x]$ denotes the greatest integer function $\le x$,is: