JEE Main 2021 · MathsMultiple choiceSingle correctEasyConceptual

JEE Main 18 March 2021, Shift 2, Maths Q78

Question 78 of 90 in this shift, Maths question 18 of 30, Section A.

Define a relation R over a class of

n\times n

real matrices A and B as "ARB iff there exists a non-singular matrix P such that

PAP^{-1}=B

". Then which of the following is true ?

(1)R is reflexive, symmetric but not transitive
(2)R is reflexive, transitive but not symmetric
(3)R is symmetric, transitive but not reflexive,
(4)R is an equivalence relationOfficial answer

Official answer

Option 4

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
28 Jun 2022, Shift 2 · Q1Let $R_1 = \{(a, b) \in \mathbf{N}\times\mathbf{N} : |a-b| \leq 13\}$ and…EasySingle 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

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.