JEE Main 2023 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 8 April 2023, Shift 1, Maths Q21

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

Let

A=\{0,3,4,6,7,8,9,10\}

and

R

be the relation defined on

A

such that

R=\{(x,y)\in A\times A: x-y

is odd positive integer or

x-y=2\}

. The minimum number of elements that must be added to the relation

R

, so that it is a symmetric relation, is equal to ____________.

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.