Match List - I with List - II.

	List - I		List - II
(A)	$y = \log(\sin x)$	(I)	$\frac{d^2y}{dx^2} = -\frac{1}{x^2}$
(B)	$y = e^{(1 + \log x)}$	(II)	$\frac{d^2y}{dx^2} = 2$
(C)	$y = \log\lvert x \rvert$	(III)	$\frac{d^2y}{dx^2} = 0$
(D)	$y = x^2 + 4x - 1$	(IV)	$\frac{d^2y}{dx^2} = -\csc^2 x$

Choose the correct answer from the options given below :

If $y = \frac{1}{x+1}$, then $\frac{d^2y}{dx^2}$ at $x = 2$ is:

If $x = 4t$ and $y = \frac{4}{t}$, then $\frac{d^2y}{dx^2}$ is

If $y = \sqrt{12^x(3x^2+2)}$, then $\dfrac{dy}{dx}$ will be

(consider $\log_e x = \log x$)

The point('s) at which the function $f$ given by $f(x) = \begin{cases} \dfrac{|x|}{2x}, & x<0 \\ -\dfrac{1}{2}, & x\geq0 \end{cases}$ is continuous is (are)

Let $x = t^2, y = t^3$. Then $\frac{d^2y}{dx^2}$ is equal to

If $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, then $\frac{d^2y}{dx^2}$ is equal to