$f(x) = \begin{cases} -x & \text{ if } x < 0 \\ +x & \text{ if } x \geq 0 \end{cases}$
Continuity at $ x=0 $
$\begin{align*} \lim_{x \rightarrow 0^{-}}f(x)\ &= \lim_{x \rightarrow 0^{+}}f(x)\\ 0 &= 0\\ \end{align*}$
So $ f(x) = |x|$ is continous at x = 0
Differentiability at $x=0$
$\begin{align*} \lim_{h \rightarrow 0}\frac{f(0)-f(0-h)}{0-(0-h)} &= \lim_{h \rightarrow 0}\frac{f(0+h)-f(0)}{(0+h)-(0)}\\ \lim_{h \rightarrow 0}\frac{0-(-0+h)}{h)} &= \lim_{h \rightarrow 0}\frac{(0+h)-0}{h} \\ -1 &= 1\\ \end{align*}$
So $ f(x) = |x|$ is not differentiable at x = 0
P is true and Q is false
Option $A$ is the aswer