Let $R_1, R_2, R_3, R_4$ be the relations defined on the set $A=\{1,2,3\}$. then

Match List-I with List-II

List-I (Relation)	List-II (Type)
(A) $R_1=\{(1,1),(2,2),(3,3)\}$	(I) Only transitive
(B) $R_2=\{(1,2),(2,3),(1,3)\}$	(II) Equivalence relation
(C) $R_3=\{(1,2),(2,1),(1,1),(2,2)\}$	(III) Reflexive and symmetric but not transitive
(D) $R_4=\{(1,1),(2,2),(3,3),(2,3),(3,2),(1,2),(2,1)\}$	(IV) Symmetric and transitive but not reflexive

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Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \frac{x}{x^2+1}$ then

Let A = {1, 2, 3}. The number of equivalence relations containing (1, 3) is

Let R be the relation over the set A of all straight lines in a plane such that $l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1}$ is parallel to $l_{2}$. Then R is :

Match List-I with List-II

Where ℝ is set of real numbers

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The function $f: [-1, 1] \rightarrow R$ is given by $f(x) = \frac{x}{x + 2}$

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