JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 12 April 2023, Shift 1, Maths Q21

Question 21 of 90 in this shift, Maths question 21 of 30, Section B.

The number of relations, on the set

\{1,2,3\}

containing

(1,2)

and

(2,3)

, which are reflexive and transitive but not symmetric, is ____________.

Official answer

NTA final key.

Chapter: Relations and Functions
Topic: Sets and Relations
Idea tested: Counting Relations

Same idea in other shifts

Asked 14× in all

8 Apr 2026, Shift 2 · Q1Consider the relation R on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab > 0$ . Then, among the statements…MediumOther
3 Apr 2025, Shift 1 · Q1Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$ . Let R be a relation on A defined by $x\mathrm{R}y$ if and only if $0 \le x^2 + 2y \le 4$ . Let $l$ be…MediumSingle correct
7 Apr 2025, Shift 1 · Q24The number of relations on the set $A = \{1, 2, 3\}$ , containing at most 6 elements including $(1, 2)$ , which are reflexive and transitive…HardNumerical value
6 Apr 2024, Shift 2 · Q2Let $A=\{1,2,3,4,5\}$ . Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x\le 5y$ . Let $m$ be the number of elements in $R$ …MediumSingle correct
9 Apr 2024, Shift 1 · Q21Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$ . Let R be a relation defined on $A\times B$ by $(a_1,b_1)\,R\,(a_2,b_2)$ if and only if…MediumNumerical value
1 Feb 2024, Shift 1 · Q21Let $A=\{1,2,3,\ldots,20\}$ . Let $R_1$ and $R_2$ two relation on A such that $R_1=\{(a,b): b$ is divisible by $a\}$ $R_2=\{(a,b): a$ is an…MediumNumerical value
30 Jan 2024, Shift 2 · Q21The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is ________.MediumNumerical value
6 Apr 2023, Shift 1 · Q21Let $A=\{1,2,3,4,\ldots,10\}$ and $B=\{0,1,2,3,4\}$ . The number of elements in the relation…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.