JEE Main 2022 · MathsMultiple choiceSingle correctEasyConceptual

JEE Main 28 June 2022, Shift 2, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let

R_1 = \{(a, b) \in \mathbf{N}\times\mathbf{N} : |a-b| \leq 13\}

and

R_2 = \{(a, b) \in \mathbf{N}\times\mathbf{N} : |a-b| \neq 13\}

. Then on

\mathbf{N}

(1)Both $R_1$ and $R_2$ are equivalence relations
(2)Neither $R_1$ nor $R_2$ is an equivalence relationOfficial answer
(3) $R_1$ is an equivalence relation but $R_2$ is not
(4) $R_2$ is an equivalence relation but $R_1$ is not

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 10× in all

2 Apr 2025, Shift 1 · Q12Let A be the set of all functions $f:\mathbf{Z}\to\mathbf{Z}$ and R be a relation on A such that…EasySingle correct
1 Feb 2024, Shift 2 · Q2Consider the relations $R_1$ and $R_2$ defined as $aR_1b \Leftrightarrow a^2+b^2=1$ for all $a, b\in\mathbf{R}$ and…MediumSingle correct
31 Jan 2024, Shift 1 · Q21Let $A=\{1,2,3,4\}$ and $R=\{(1,2),(2,3),(1,4)\}$ be a relation on A. Let S be the equivalence relation on A such that $R\subset S$ and…MediumNumerical value
27 Jul 2022, Shift 1 · Q1Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $a\,R_1\,b \Leftrightarrow ab \ge 0$ and…EasySingle correct
28 Jul 2022, Shift 1 · Q8For $\alpha\in\mathbf{N}$ , consider a relation $R$ on $\mathbf{N}$ given by $R=\{(x,y):3x+\alpha y\text{ is a multiple of }7\}$ . The…MediumSingle correct
29 Jun 2022, Shift 1 · Q11Let a set $A = A_1 \cup A_2 \cup \ldots \cup A_k$ , where $A_i \cap A_j = \phi$ for $i \ne j$ , $1 \le i, j \le k$ . Define the relation R…EasySingle correct
26 Feb 2021, Shift 1 · Q72Let $R=\{(P, Q)\mid P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of $(1, -1)$ is the…EasySingle correct
16 Mar 2021, Shift 2 · Q71Let $A=\{2,3,4,5,\ldots,30\}$ and ' $\simeq$ ' be an equivalence relation on $A\times A$ , defined by $(a,b)\simeq(c,d)$ , if and only if…MediumSingle correct

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.