Let  $f_1:R\to R;f_2:(\frac{-\pi }{2},\frac{\pi }{2})\to R; f_3:(-1,e^{\pi /2}-2)\to R,$  and  $f_4:R\to R$ be functions defined by 

i)   $f_1\left(x\right)=\sin \left(\sqrt{1-e^{-x^2}}\right)$        
ii) $\begin{array}{l}{f}_2\left(x\right)=\frac{\left|\sin x\right|}{Ta{n}^{-1}x},x\ne 0\\ =1,x=0\end{array}$  Where the inverse trigonometric function  $Ta{n}^{-1}x$  assumes values in  

      $(\frac{-\pi }{2},\frac{\pi }{2})$
iii) $f_3\left(x\right)=\left[\sin \left({\log }_e(x+2)\right)\right],$ Where $t\in R,\left[t\right]$  denotes the greatest integer less than or equal to ‘t’

iv)  $\begin{array}{l}{f}_4\left(x\right)=x^2\sin \left(\frac{1}{x}\right),x\ne 0\\ =0,x=0\end{array}$
 

	LIST-I		LIST-II
	The function  $f_1$ is		Not Continuous at $x=0$
	The function is $f_2$  is		Continuous at  $x=0$ and not differentiable at $x=0$
	The function  $f_3$  is		Differentiable at $x=0$ but its derivative is not Continuous at  $x=0$
	The function $f_4$  is		Differentiable at $x=0$ and its derivative is Continuous at $x=0$

The correct option is: