Match List-I with List-II

Choose the correct answer from the options given below :

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

Match each expression with its type.

(A) $x=2at^{2},\; y=at^{4}$

Both $x$ and $y$ are expressed in terms of a parameter $t$.

So it is a parametric function.

(A) → (III).

(B) $f(x)=(2x-3)^{3}$

This is a composition of functions: $2x-3$ and $(\cdot)^3$.

So it is a composite function.

(B) → (IV).

(C) $xy+y^{2}=\tan(x+y)$

$y$ is not explicitly expressed in terms of $x$.

So it is an implicit function.

(C) → (II).

(D) $y=\tan^{-1}\!\left(\frac{3x-x^{3}}{1-3x^{2}}\right)$

This involves an inverse trigonometric function.

(D) → (I).

final answer: (A)–(III), (B)–(IV), (C)–(II), (D)–(I)