Match List - I with List - II.

	List - I		List - II
(A)	$x = 2at^2, y = at^4$	(I)	Inverse trignometric function
(B)	$f(x) = (2x + 3)^3$	(II)	Implicit function
(C)	$xy + y^2 = \tan(x + y)$	(III)	Parametric function
(D)	$y = \tan^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right), -\frac{1}{\sqrt{3}} < x < \frac{1}{\sqrt{3}}$	(IV)	Composite function

Choose the correct answer from the options given below :

If $f(x)$, defined by $f(x)=\left\{\begin{array}{lll}k x+1 & \text { if } & x \leq \pi \\ \cos x & \text { if } & x>\pi\end{array}\right.$ is continuous at $x=\pi$, then the value of $k$ is :

If $t=e^{2 x}$ and $y=\log _{e} t^{2}$, then $\frac{d^{2} y}{d x^{2}}$ is :

A function $f(x) = \begin{cases} \frac{kx^3}{4} & \text{if } x \leq 1 \\ 8 & \text{if } x > 1 \end{cases}$ for some constant $k$, then $\frac{d^2f(x)}{dx^2}$ at $x = -1$ is

Function $f(x)=[x]$, greatest integer function is

(A) Continuous at $x=2.5$

(B) Continuous at $x=1$

(C) Differentiable at $x=2$

(D) Differentiable at $x=-1.2$

Choose the correct answer from the options given below:

The second order derivative of which of the following functions is $5^{\mathrm{x}}$ ?

If $y = \sin^{-1} x + \sin^{-1} \sqrt{1-x^2}, x \in (-1, 0)$, then $\frac{dy}{dx}$ is equal to