Let $f: R \rightarrow R$ be a continuous function such that for any two real numbers $x$ and $y$,$|f(x)-f(y)| \leq 10|x-y|^{201}$,then

If $f(x) = \begin{cases} \frac{1}{|x|} & ; |x| \geq 1 \\ ax^2 + b & ; |x| < 1 \end{cases}$ is differentiable at every point of the domain,then the values of $a$ and $b$ are respectively

The function $f(x) = e^{-|x|}$ is

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be respectively given by $f(x)=|x|+1$ and $g(x)=x^2+1$. Define $h: R \rightarrow R$ by $h(x)=\begin{cases} \max \{f(x), g(x)\} & \text{if } x \leq 0 \\ \min \{f(x), g(x)\} & \text{if } x > 0 \end{cases}$. The number of points at which $h(x)$ is not differentiable is

Let $f(x) = x^{2} - x + k - 2$,where $k \in R$. Find the complete set of values of $k$ for which $y = |f(|x|)|$ is non-derivable at $5$ distinct points.

$f(x) = ||x| - 1|$ is not differentiable at