If number of points of discontinuity of the function $f\left(x\right)=\left[2+10\sin x\right],$ in $x\in \left[0,\frac{\pi }{2}\right]$is same as number of point non-differentiability of the function $g\left(x\right)=\left(x-1\right)\times (x-2)\left|(x-1)(x-2)\mathrm{....}(x-2m)\right|$ $(m\in N)$ in $x\in (-\infty ,\infty )$then the value of m is

$2+10\sin x\in [2,12]$

$$\begin{gathered} \text{ Clearly, }\mathrm{f}\left(\mathrm{x}\right)\text{ is discontinues where} \\ 2+10\sin \mathrm{x}=3,4,5,\dots 12\text{, i.e., at }10 Points \end{gathered}$$

Number of points of non – differentiability of
 $f\left(x\right)=(x-1)(x-2)$$\left|\right(x-1\left)\right(x-2)\dots (x-2m\left)\right|\text{ is }(2m-2) \mathrm{as} g\left(x\right)$ is differentiable at  $x=1\text{ and }x=2$

$\therefore 2m-2=10$

$\therefore m=6$