Algebra

Relations & Functions

Medium

core

Let S be the set of all real numbers and let R be a relation on S, defined by $aRb \Leftrightarrow |a-b| \leq 1$ . Then, R is

reflexive and symmetric but not transitive.

reflexive and transitive but not symmetric

symmetric and transitive but not reflexive

an equivalence relation

✅ Correct Option: 1

$|a-a|=0\le1$ , so R is reflexive; $|a-b|=|b-a|$ , so it is symmetric. It fails transitivity: $|1-2|\le1$ and $|2-3|\le1$ but $|1-3|=2>1$ . Hence reflexive and symmetric but not transitive.

2026: 31 May Shift 2

A relation $R$ on set of real numbers $(\mathbb{R})$ is defined as $R = \{(a,b): a \le b, a,b \in \mathbb{R}\}$ . The relation is :

2023: 22 May Shift 3

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 :

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:

2022: 7 Aug Shift 2

Let L be the set of all lines in a plane and R be the relation in L defined as $R = \{(l_1, l_2) : l_1 \text{ is perpendicular to } l_2, \text{ where } l_1, l_2 \in L\}$ . Choose the correct answer :

2025: 2 June Shift 1

Relation R on the set $A = \{1, 2, ..., 15\}$ defined as $R = \{(x, y): y - 4x = 0\}$ is

2026: 18 May Shift 2

For the relation R defined below, where $\mathbb{R}$ and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II

LIST-I Relation	LIST-II Properties of relation hold by R
A. $R=\{(a,b): a,b\in \mathbb{R}; a^2+b^2=4\}$	I. Neither reflexive, nor symmetric, nor transitive
B. $R=\{(a,b): a,b\in \mathbb{R}; 1+ab>0\}$	II. Equivalence relation
C. $R=\{(a,b): a,b\in N; a+2b=8\}$	III. Symmetric but neither reflexive nor transitive
D. On N×N, relation R defined by $(a,b)R(c,d) \Leftrightarrow a+d=b+c$	IV. Reflexive and symmetric, but not transitive

Choose the correct answer from the options given below:

Let S be the set of all real numbers and let R be a relation on S, defined by aRb⇔∣a−b∣≤1aRb \Leftrightarrow |a-b| \leq 1aRb⇔∣a−b∣≤1. Then, R is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let S be the set of all real numbers and let R be a relation on S, defined by $aRb \Leftrightarrow |a-b| \leq 1$ . Then, R is