Number of points of non-differentiability of the function $g\left(x\right)=\left[x^2\right]\left\{{\cos }^{2}4x\right\}+\left\{x^2\right\}\left[{\cos }^{2}4x\right]+$$x^2{\sin }^{2}4x+\left[x^2\right]\left[{\cos }^{2}4x\right]+\left\{x^2\right\}\left\{{\cos }^{2}4x\right\}\text{ in }(-50,50)\text{ where }\left[x\right]\text{ and }\left\{x\right\}\text{ denotes the }$$\text{ greatest integer function and fractional part function of }x\text{ respectively, is equal to }$

$$\begin{gathered} \mathrm{co}nsider, \\ \begin{array}{l}g\left(x\right)=\left[x^2\right]\left\{{\cos }^{2}4x\right\}+\left[x^2\right]\left[{\cos }^{2}4x\right]+\\ \left\{x^2\right\}\left\{{\cos }^{2}4x\right\}+\left\{x^2\right\}\left[{\cos }^{2}4x\right]+x^2{\sin }^{2}4x\\ =\left(\left[x^2\right]+\left\{x^2\right\}\right)\left(\left\{{\cos }^{2}4x\right\}+\left[{\cos }^{2}4x\right]\right)+x^2{\sin }^{2}4x\\ =x^2{\cos }^{2}4x+x^2{\sin }^{2}4x (for eg. \left[2.25\right]=2 and \left\{2.25\right\}=0.25 then \left[2.25\right]+ \left\{2.25\right\} =2.25)\\ =x^2\end{array} \end{gathered}$$

$\text{ Clearly }g\left(x\right)\text{ is continuous and differentiable }\mathrm{\forall }x\in \mathrm{ℝ}$

Number of points of non-differentiability is ‘0’
Therefore, the correct answer is 0.00.