Algebra

Relations & Functions

Easy

core

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 :

(A) and (C) Only

(A) and (B) Only

(A) and (D) Only

(B) and (C) Only

✅ Correct Option: 1

Reflexive: $n$ divides $n$ , yes.

Symmetric: $2|4$ but $4\nmid 2$ , no.

Transitive: if $n|m$ and $m|p$ , then $n|p$ , yes.

Identity: requires $nRm$ only if $n=m$ ; here $2|4$ so no.

Reflexive and Transitive only.

2026: 29 May Shift 2

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

2025: 14 May Shift 2

Let a relation R = {(a, b) : a is a factor of b, a, b $\in$ N}. Then, R is ______.

2026: 18 May Shift 1

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

2025: 16 May Shift 1

Match List-I with List-II

Where ℝ is set of real numbers

List-I	List-II
(A) f: ℝ → ℝ s.t f(x) = x⁴ is	(I) one-one, Into
(B) f: ℝ → [0, ∞) s.t f(x) = x⁴ is	(II) many-one, into
(C) f: [0, ∞) → ℝ s.t f(x) = x⁴ is	(III) one-one, onto
(D) f: [0, ∞) → [0, ∞) s.t f(x) = x⁴ is	(IV) many-one, onto

Choose the correct answer from the options given below:

2026: 14 May Shift 2

Given the relation $R=\{(1,2),(2,3)\}$ on a set $A=\{1,2,3\}$ , then which of following statements are TRUE?

A. Minimum number of ordered pairs are added to R so that enlarged relation is reflexive is 3

B. Minimum number of ordered pairs are added to R so that enlarged relation is symmetric is 2

C. Minimum number of ordered pairs are added to R so that enlarged relation is an equivalence relation is 7

D. Minimum number of ordered pair are added to R so that enlarged relation is an equivalence relation is 6.

Choose the correct answer from the options given below:

2026: 29 May Shift 1

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

Choose the correct answer from the options given below:

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 :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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 :