JEE Main Maths · Relations and Functions

Sets and Relations in JEE Main

Name: Sets and Relations: JEE Main previous year questions
Creator: Lumi

Sets and Relations (Maths, Relations and Functions) came 25 times in 24 of the 42 JEE Main shifts Lumi analysed, across 10 distinct ideas. 15 of them came in 2024–26; it was last asked in 2026.

Questions: 25; in 24 shifts
Ideas asked: 10; 4 asked more than once
Numerical answer: 9; 36% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 6Medium 17Hard 2

Format

Single correct14 Q
Numerical value9 Q
Other2 Q

Ideas inside the topic

10 ideas

Counting Relations7 Q
Equivalence Relations5 Q
Relation Types5 Q
Counting Reflexive and Symmetric Relations2 Q
Divisibility Relation1 Q
Inclusion-Exclusion for Three Sets1 Q
Intervals as Subsets of R1 Q
Inverse Relations1 Q
Roster and Set-Builder Forms1 Q
Transitive Closure1 Q

Where it sits

Part of Relations and Functions, which had 60 questions in all. Sets and Relations accounts for 42% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Every question

All 25 Sets and Relations questions

Newest first, each with its options and official answer.

5 Apr 2026, Shift 2 · Q21Let $A=\{1, 4, 7\}$ and $B=\{2, 3, 8\}$ . Then the number of elements, in the relation…MediumNumerical value
6 Apr 2026, Shift 2 · Q21Let $R=\{(x,y)\in\mathbf{N}\times\mathbf{N}:\log_e(x+y)\le2\}$ . Then the minimum number of elements, required to be added in R to make it…HardNumerical value
8 Apr 2026, Shift 2 · Q1Consider the relation R on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab > 0$ . Then, among the statements…MediumOther
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
3 Apr 2025, Shift 1 · Q1Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$ . Let R be a relation on A defined by $x\mathrm{R}y$ if and only if $0 \le x^2 + 2y \le 4$ . Let $l$ be…MediumSingle correct
3 Apr 2025, Shift 2 · Q1Let $A = \{-2, -1, 0, 1, 2, 3\}$ . Let R be a relation on $A$ defined by $xRy$ if and only if $y = \max\{x, 1\}$ . Let $l$ be the number of…MediumSingle correct
4 Apr 2025, Shift 2 · Q2Let $A=\{-3,-2,-1,0,1,2,3\}$ and R be a relation on A defined by $xRy$ if and only if $2x-y\in\{0,1\}$ . Let $l$ be the number of elements…MediumSingle correct
7 Apr 2025, Shift 1 · Q24The number of relations on the set $A = \{1, 2, 3\}$ , containing at most 6 elements including $(1, 2)$ , which are reflexive and transitive…HardNumerical value
8 Apr 2025, Shift 2 · Q1Let $A = \{0, 1, 2, 3, 4, 5\}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $\max\{x, y\} \in \{3, 4\}$ . Then…MediumOther
6 Apr 2024, Shift 2 · Q2Let $A=\{1,2,3,4,5\}$ . Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x\le 5y$ . Let $m$ be the number of elements in $R$ …MediumSingle correct
9 Apr 2024, Shift 1 · Q21Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$ . Let R be a relation defined on $A\times B$ by $(a_1,b_1)\,R\,(a_2,b_2)$ if and only if…MediumNumerical value
29 Jan 2024, Shift 1 · Q2Let R be a relation on $\mathbb{Z}\times\mathbb{Z}$ defined by $(a, b)\,R\,(c, d)$ if and only if $ad-bc$ is divisible by 5. Then R isMediumSingle correct
30 Jan 2024, Shift 2 · Q21The number of symmetric relations defined on the set $\{1, 2, 3, 4\}$ which are not reflexive is ________.MediumNumerical value
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
31 Jan 2024, Shift 2 · Q21Let $A=\{1,2,3,\ldots,100\}$ . Let $R$ be a relation on $A$ defined by $(x,y)\in R$ if and only if $2x=3y$ . Let $R_1$ be a symmetric…MediumNumerical value
6 Apr 2023, Shift 1 · Q1Let $A=\{x\in\mathbb{R}:[x+3]+[x+4]\le 3\}$ ,…MediumSingle correct
6 Apr 2023, Shift 1 · Q21Let $A=\{1,2,3,4,\ldots,10\}$ and $B=\{0,1,2,3,4\}$ . The number of elements in the relation…MediumNumerical value
8 Apr 2023, Shift 2 · Q1Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ . Then the relation $R = \{(x, y) \in A \times A : x + y = 7\}$ isEasySingle correct
11 Apr 2023, Shift 1 · Q1An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five…EasySingle correct
13 Apr 2023, Shift 2 · Q21Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R=\{(a,b)\in A\times A: b=|a| \text{ or } b^2=a+1\}$ be a relation on A. Then the minimum number of…MediumNumerical value
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
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
9 Jan 2020, Shift 2 · Q51If $A=\{x\in\mathbf{R}:|x|<2\}$ and $B=\{x\in\mathbf{R}:|x-2|\ge 3\}$ ; then :EasySingle correct
2 Sep 2020, Shift 1 · Q51If $R=\{(x, y) : x, y\in \mathbf{Z},\ x^{2}+3y^{2}\le 8\}$ is a relation on the set of integers $\mathbf{Z}$ , then the domain of $R^{-1}$ …EasySingle correct