Match List - I with List - II.

	List - I		List - II
(A)	$f(x) = \frac{1}{x}, f : \mathbf{R} - \{0\} \to \mathbf{R} - \{0\}$	(I)	neither injective nor surjective
(B)	$f(x) = x^2, f : \mathbf{N} \to \mathbf{N}$	(II)	surjective but not injective
(C)	$f(x) = x^2, f : \mathbf{R} \to \mathbf{R}$	(III)	injective but not surjective
(D)	$f : \{1, 2, 3\} \to \{1, 2\}$ defined as $f : \{(1, 1), (2, 2), (3, 1)\}$	(IV)	injective and surjective

Choose the correct answer from the options given below :

Let $R : \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers and R be a relation. An element $(x, y) \in R$ if $x + y - \sqrt{2}$ belongs to the set of irrational numbers. Then the relation R is :

If $f: R \to R$ is defined by $f(x) = \sin x + x$, then $f(f(x))$ is:

Let X be a non-empty set and let P be the collection of all subsets of X. Let R be a relation in P, defined by $R = \{(A, B): A \text{ is subset of } B\}$. Then, R is

A. Reflexive relation

B. Symmetric relation

C. Not a transitive relation

D. Transitive relation

Choose the correct answer from the options given below:

If n(A) = 3 and n(B) = 2, then number of non-empty relations from A to B is

Let R be a relation on the set of natural numbers N defined by nRm if n divides m. Then R is :

(A) Reflexive Relation

(B) Symmetric Relation

(C) Transitive Relation

(D) Identity Relation

Choose the correct answer from the options given below :

If $A = \{x: x \in R, -\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\}$ and $B = \{y: y \in R, -1 \leq y \leq 1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \sin x$, then $f$ is