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Saturday, 31 October

JEE Main · Maths · Relations and Functions

Equivalence Relations

JEE Main asked Equivalence Relations 10 times in 10 of the 108 shifts Lumi analysed, in 2021, 2022, 2024 and 2025. It belongs to Sets and Relations, in Relations and Functions (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
10
in 10 shifts
Years
4 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.10’210.14’220’230.09’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 4 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20251 of 8
  • 20242 of 18
  • 20230 of 12
  • 20224 of 24
  • 20213 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: conceptual.

  • Count elements of relation
  • Classify relation on set of functions

Difficulty

Easy 6Medium 4Hard 0

1 of the 10 questions had a numerical answer.

Every question

All 10 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 2 Apr 2025, Shift 1 · Q12Let A be the set of all functions f:Z→Zf:\mathbf{Z}\to\mathbf{Z} and R be a relation on A such that…EasySingle correct
  2. 31 Jan 2024, Shift 1 · Q21Let A={1,2,3,4}A=\{1,2,3,4\} and R={(1,2),(2,3),(1,4)}R=\{(1,2),(2,3),(1,4)\} be a relation on A. Let S be the equivalence relation on A such that R⊂SR\subset S and…MediumNumerical value
  3. 1 Feb 2024, Shift 2 · Q2Consider the relations R1R_1 and R2R_2 defined as aR1b⇔a2+b2=1aR_1b \Leftrightarrow a^2+b^2=1 for all a,b∈Ra, b\in\mathbf{R} and…MediumSingle correct
  4. 29 Jun 2022, Shift 1 · Q11Let a set A=A1∪A2∪…∪AkA = A_1 \cup A_2 \cup \ldots \cup A_k, where Ai∩Aj=ϕA_i \cap A_j = \phi for i≠ji \ne j, 1≤i,j≤k1 \le i, j \le k. Define the relation R…EasySingle correct
  5. 28 Jun 2022, Shift 2 · Q1Let R1={(a,b)∈N×N:∣a−b∣≤13}R_1 = \{(a, b) \in \mathbf{N}\times\mathbf{N} : |a-b| \leq 13\} and…EasySingle correct
  6. 28 Jul 2022, Shift 1 · Q8For α∈N\alpha\in\mathbf{N}, consider a relation RR on N\mathbf{N} given by R={(x,y):3x+αy is a multiple of 7}R=\{(x,y):3x+\alpha y\text{ is a multiple of }7\}. The…MediumSingle correct
  7. 27 Jul 2022, Shift 1 · Q1Let R1R_1 and R2R_2 be two relations defined on R\mathbb{R} by a R1 b⇔ab≥0a\,R_1\,b \Leftrightarrow ab \ge 0 and…EasySingle correct
  8. 18 Mar 2021, Shift 2 · Q78Define a relation R over a class of n×nn\times n real matrices A and B as "ARB iff there exists a non-singular matrix P such that…EasySingle correct
  9. 16 Mar 2021, Shift 2 · Q71Let A={2,3,4,5,…,30}A=\{2,3,4,5,\ldots,30\} and '≃\simeq' be an equivalence relation on A×AA\times A, defined by (a,b)≃(c,d)(a,b)\simeq(c,d), if and only if…MediumSingle correct
  10. 26 Feb 2021, Shift 1 · Q72Let R={(P,Q)∣PR=\{(P, Q)\mid P and QQ are at the same distance from the origin}\} be a relation, then the equivalence class of (1,−1)(1, -1) is the…EasySingle correct

Shifts: 26 Feb 2021, Shift 1, 16 Mar 2021, Shift 2, 18 Mar 2021, Shift 2, 28 Jun 2022, Shift 2, 29 Jun 2022, Shift 1, 27 Jul 2022, Shift 1, 28 Jul 2022, Shift 1, 31 Jan 2024, Shift 1, 1 Feb 2024, Shift 2, 2 Apr 2025, Shift 1.

Same topic

Other ideas in Sets and Relations

Sets and Relations has 15 ideas JEE Main has asked; 10 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas