JEE Main 2022 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 28 July 2022, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

For

\alpha\in\mathbf{N}

, consider a relation

R

\mathbf{N}

given by

R=\{(x,y):3x+\alpha y\text{ is a multiple of }7\}

. The relation

R

is an equivalence relation if and only if :

(1) $\alpha=14$
(2) $\alpha$ is a multiple of 4
(3)4 is the remainder when $\alpha$ is divided by 10
(4)4 is the remainder when $\alpha$ is divided by 7Official answer

Official answer

Option 4

NTA final key (2022 Session 2).

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

Same idea in other shifts

Asked 5× 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
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
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
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 42 of the 174 JEE Main shifts held from 2017 to 2026.