In each function of List-I, $[x]$ is the greatest integer less than or equal to $x$. For each function, decide how it behaves at the single point $x = 0$: whether it is continuous there, whether it is differentiable there, and, if it is, what $f'(0)$ is and whether $f'$ is continuous at $0$. Match each function in List-I with the one entry of List-II that describes it. One entry of List-II is not used. List-I P. $f(x) = x^2\,[x]$ Q. $f(x) = x^2 \cos\dfrac1x$ for $x \ne 0$, and $f(0) = 0$ R. $f(x) = x\,[x]$ S. $f(x) = x\,e^{|x|}$ List-II 1. $f$ is continuous at $x = 0$ but not differentiable there 2. $f$ is differentiable at $x = 0$, but $f'$ is not continuous at $x = 0$ 3. $f$ is differentiable at $x = 0$ with $f'(0) = 0$, and $f'$ is continuous at $x = 0$ 4. $f$ is not continuous at $x = 0$ 5. $f$ is differentiable at $x = 0$ with $f'(0) = 1$