Let $f_1 : \mathbb{R} \to \mathbb{R}$, $f_2 : \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \to \mathbb{R}$, $f_3 : (-1, e^{\pi/2} - 2) \to \mathbb{R}$ and $f_4 : \mathbb{R} \to \mathbb{R}$ be functions defined by (i) $f_1(x) = \sin\left(\sqrt{1 - e^{-x^2}}\right)$(ii) $$f_2(x) = \left\{ \begin{array}{ll} \dfrac{|\sin x|}{\tan^{-1} x} & \text{if } x \ne 0 \\ 1 & \text{if } x = 0 \end{array} \right.$$ where the inverse trigonometric function $\tan^{-1} x$ assumes values in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$(iii) $f_3(x) = [\sin(\log_e(x + 2))]$, where for $t \in \mathbb{R}$, $[t]$ denotes the greatest integer less than or equal to $t$ (iv) $$f_4(x) = \left\{ \begin{array}{ll} x^2 \sin\left(\dfrac{1}{x}\right) & \text{if } x \ne 0 \\ 0 & \text{if } x = 0 \end{array} \right.$$ | LIST-I | LIST-II | |--------|--------| | P. The function $f_1$ is | 1. NOT continuous at $x = 0$ | | Q. The function $f_2$ is | 2. continuous at $x = 0$ and NOT differentiable at $x = 0$ | | R. The function $f_3$ is | 3. differentiable at $x = 0$ and its derivative is NOT continuous at $x = 0$ | | S. The function $f_4$ is | 4. differentiable at $x = 0$ and its derivative is continuous at $x = 0$ |