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Saturday, 31 October

JEE Main · Maths · Relations and Functions

Counting Relations

JEE Main asked Counting Relations 14 times in 14 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Sets and Relations, in Relations and Functions (Maths). The longest wait between two years asking it was 1 year. In 2022, 2023, 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
14
in 14 shifts
Years
6 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210.11’220.21’230.19’240.25’250.11’26

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

Shift by shift

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

  • 20261 of 9
  • 20252 of 8
  • 20244 of 18
  • 20233 of 12
  • 20223 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Count elements of relation
  • Count relations with given properties

Difficulty

Easy 0Medium 12Hard 2

8 of the 14 questions had a numerical answer.

Every question

All 14 questions

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

  1. 8 Apr 2026, Shift 2 · Q1Consider the relation R on the set {−2,−1,0,1,2}\{-2, -1, 0, 1, 2\} defined by (a,b)∈R(a, b) \in R if and only if 1+ab>01 + ab > 0. Then, among the statements…MediumOther
  2. 7 Apr 2025, Shift 1 · Q24The number of relations on the set A={1,2,3}A = \{1, 2, 3\}, containing at most 6 elements including (1,2)(1, 2), which are reflexive and transitive…HardNumerical value
  3. 3 Apr 2025, Shift 1 · Q1Let A={−3,−2,−1,0,1,2,3}A = \{-3, -2, -1, 0, 1, 2, 3\}. Let R be a relation on A defined by xRyx\mathrm{R}y if and only if 0≤x2+2y≤40 \le x^2 + 2y \le 4. Let ll be…MediumSingle correct
  4. 30 Jan 2024, Shift 2 · Q21The number of symmetric relations defined on the set {1,2,3,4}\{1, 2, 3, 4\} which are not reflexive is ________.MediumNumerical value
  5. 1 Feb 2024, Shift 1 · Q21Let A={1,2,3,…,20}A=\{1,2,3,\ldots,20\}. Let R1R_1 and R2R_2 two relation on A such that R1={(a,b):bR_1=\{(a,b): b is divisible by a}a\} R2={(a,b):aR_2=\{(a,b): a is an…MediumNumerical value
  6. 9 Apr 2024, Shift 1 · Q21Let A={2,3,6,7}A=\{2,3,6,7\} and B={4,5,6,8}B=\{4,5,6,8\}. Let R be a relation defined on A×BA\times B by (a1,b1) R (a2,b2)(a_1,b_1)\,R\,(a_2,b_2) if and only if…MediumNumerical value
  7. 6 Apr 2024, Shift 2 · Q2Let A={1,2,3,4,5}A=\{1,2,3,4,5\}. Let RR be a relation on AA defined by xRyxRy if and only if 4x≤5y4x\le 5y. Let mm be the number of elements in RR…MediumSingle correct
  8. 12 Apr 2023, Shift 1 · Q21The number of relations, on the set {1,2,3}\{1,2,3\} containing (1,2)(1,2) and (2,3)(2,3), which are reflexive and transitive but not symmetric, is…HardNumerical value
  9. 8 Apr 2023, Shift 1 · Q21Let A={0,3,4,6,7,8,9,10}A=\{0,3,4,6,7,8,9,10\} and RR be the relation defined on AA such that R={(x,y)∈A×A:x−yR=\{(x,y)\in A\times A: x-y is odd positive integer or…MediumNumerical value
  10. 6 Apr 2023, Shift 1 · Q21Let A={1,2,3,4,…,10}A=\{1,2,3,4,\ldots,10\} and B={0,1,2,3,4}B=\{0,1,2,3,4\}. The number of elements in the relation…MediumNumerical value
  11. 29 Jun 2022, Shift 2 · Q16The probability that a relation R from {x,y}\{x, y\} to {x,y}\{x, y\} is both symmetric and transitive, is equal toMediumSingle correct
  12. 28 Jun 2022, Shift 1 · Q21Let R1R_1 and R2R_2 be relations on the set {1,2,....,50}\{1, 2, ...., 50\} such that R1={(p,pn):pR_1=\{(p, p^n): p is a prime and n≥0n\ge0 is an integer}\}…MediumNumerical value
  13. 29 Jul 2022, Shift 1 · Q1Let R be a relation from the set {1,2,3,…,60}\{1, 2, 3, \ldots, 60\} to itself such that R={(a,b):b=pqR = \{(a, b) : b = pq, where p,q≥3p, q \geq 3 are prime…MediumSingle correct
  14. 27 Aug 2021, Shift 2 · Q61Let Z\mathbb{Z} be the set of all integers, A={(x,y)∈Z×Z:(x−2)2+y2≤4}A = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : (x-2)^2 + y^2 \le 4\},…MediumSingle correct

Shifts: 27 Aug 2021, Shift 2, 28 Jun 2022, Shift 1, 29 Jun 2022, Shift 2, 29 Jul 2022, Shift 1, 6 Apr 2023, Shift 1, 8 Apr 2023, Shift 1, 12 Apr 2023, Shift 1, 30 Jan 2024, Shift 2, 1 Feb 2024, Shift 1, 6 Apr 2024, Shift 2, 9 Apr 2024, Shift 1, 3 Apr 2025, Shift 1, 7 Apr 2025, Shift 1, 8 Apr 2026, Shift 2.

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