Match List-I with List-II

List-I (Function $y=$)	List-II ($\dfrac{dy}{dx}$ at $x=0$)
(A) $x+e^x$	(I) 1
(B) $\tan^{-1}x-\dfrac{x}{2}$	(II) $\dfrac{1}{2}$
(C) $\tan^{-1}x$	(III) 0
(D) $x+\cos^{-1}x$	(IV) 2

Choose the correct answer from the options given below:

Let $f(x) = |x-1| + |x-2|, x \in R$. Then which of the following statements is/are TRUE?

(A) $f$ is continuous everywhere.

(B) $f$ is continuous everywhere except at $x = 1$ and $x = 2$

(C) $f$ is not differentiable at $x = 1$ and $x = 2$

(D) $f$ is differentiable at $x = 1$ and $x = 2$

Choose the correct answer from the options given below:

If $y = \left(x + \sqrt{x^2+1}\right)^m$, then $\frac{dy}{dx}$ is

Let $f(x) = |3-x| + (3+x)$ be a function, then which of the following statements are TRUE?

A. $f(x)$ is continuous at $x=3$

B. $f(x)$ is continuous at $x=-3$

C. $f(x)$ is differentiable at $x=3$

D. $f(x)$ is differentiable at $x=-3$

Choose the correct answer from the options given below:

If $x = a\sec^3 \theta$, $y = a \tan^3 \theta$, then $\frac{dy}{dx}$ at $\theta = \frac{\pi}{3}$ is

The value of k for which the function, defined by, $f(x) = \begin{cases} \frac{3x + 4 \tan x}{x} & : x \neq 0 \\ k & : x = 0 \end{cases}$ is continuous at $x = 0$, is

If $x = at^2$ and $y = 4at$, then the value of $\frac{d^2y}{dx^2}$ at $t = 1/a$, is