Algebra

Relations & Functions

Easy

core

Let A = {1,2,3}. Consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is

reflexive only

reflexive and transitive

symmetric and transitive

neither symmetric nor transitive

✅ Correct Option: 2

Reflexive: $(1,1),(2,2),(3,3)$ all present, yes.

Symmetric: $(1,2)$ in R but $(2,1)$ not in R, so not symmetric.

Transitive: $(1,2)$ and $(2,3)$ give $(1,3)$ , present. All transitive checks pass.

Hence R is reflexive and transitive.

2026: 18 May Shift 1

Let a relation $R$ be defined on a set $A = \{1,2,3,4,5\}$ as $R = \{(a,b): |a-b| \text{ is even or zero}\}$ . Then which of the following statements is not TRUE?

2025: 22 May Shift 2

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

2026: 18 May Shift 1

If $f(x) = \sin^{-1}\left(\dfrac{2^{x+1}}{1+4^x}\right)$ , then

Match List-I with List-II

List-I	List-II
Value of $x$	$\dfrac{1}{2}f(x)$
(A) $x = 0$	(I) $\tan^{-1}\sqrt{2}$
(B) $x = \dfrac{1}{2}$	(II) $\tan^{-1}4$
(C) $x = 1$	(III) $\dfrac{\pi}{4}$
(D) $x = 2$	(IV) $\tan^{-1}2$

Choose the correct answer from the options given below:

2025: 30 May Shift 2

The relation R on the set of real numbers defined by $R = \{(a, b): a \leq b^2\}$ is

(A) Reflexive

(B) Not symmetric

(D) Transitive

Choose the correct answer from the options given below:

2025: 13 May Shift 1

Let $A = \{a, b, c\}$ . Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is

2023: 30 May Shift 3

Which of the following graphs represent a function ?

Let A = {1,2,3}. Consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)