JEE Main · Maths · Relations and Functions
Sets and Relations: JEE Main previous year questions
61 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 24 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 61
- in 59 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.5
- model; history: 0.5 a shift on average, typically 0.3–0.7
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 59 of 108 shifts: 61 questions, #40 of 196 topics.
- 02
34% of its questions since 2020 tested an idea no earlier year had asked; 34 repeated an idea from the year before.
- 03
The most repeated idea is Counting Relations, asked 14 times in 14 shifts (2021, 2022, 2023, 2024, 2025, 2026), most often as “count elements of relation”.
- 04
JEE Main has asked 15 of the 50 ideas in this topic; 27 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (57%); 36% need a numerical answer, 30% are easy and 13% hard. It went up from 0.4 to 0.6 questions a shift since 2024.
- 06
The skill tested most is multi-step (33%), then calculation (23%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 5 in 12 shifts · 2021: 11 in 24 shifts · 2022: 11 in 24 shifts · 2023: 10 in 12 shifts · 2024: 15 in 18 shifts · 2025: 6 in 8 shifts · 2026: 3 in 9 shifts.
- Up to 2023
- 0.4
- a shift, of 25
- Since 2024
- 0.6
- 0.2
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 59/108
- 55% of analysed shifts
Recent framings
- statement I/II on a relation
- numerical: elements to add for transitivity
- numerical: count elements of relation
Revise first
- Counting Relations · asked 2021, 2022, 2023, 2024, 2025, 2026
- Relation Types · asked 2020, 2021, 2023, 2024, 2025
- Equivalence Relations · asked 2021, 2022, 2024, 2025
How it is asked
Difficulty, format and skill
Across all 61 questions on Sets and Relations since 2017.
Difficulty
QUESTIONS- Easy18 · 30%
- Medium35 · 57%
- Hard8 · 13%
Format
SHARE- Single correct · 35 Q57%
- Numerical value · 22 Q36%
- Other · 2 Q3%
- Two statements · 1 Q2%
- Diagram based · 1 Q2%
Skill tested
SHARE- Multi-step · 20 Q33%
- Calculation · 14 Q23%
- Conceptual · 14 Q23%
- Application · 12 Q20%
- Diagram reading · 1 Q2%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 15 of the 50 ideas in this topic. 27 have never been asked yet.
- Asked directly15 · 30%
- Touched inside another question8 · 16%
- Never asked27 · 54%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
15 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
15 different ideas were tested; 10 came more than once.
count elements of relation
Numerical value · 14 shifts · 8 numericalcount elements of relation
Single correct · 12 shifts · 2 numericalcount elements of relation
Single correct · 10 shifts · 1 numericalrange of intersection from percentages of two sets
Single correct · 5 shiftscount elements in exactly two of three sets
Numerical value · 4 shifts · 3 numericalset operations on intervals of reals
Single correct · 3 shifts · 1 numericalcount elements of relation and closures
Numerical value · 2 shifts · 1 numericalcount elements of relation
Single correct · 2 shiftscount subsets with intersection condition
Numerical value · 2 shifts · 2 numericalset operations on solution sets of equations
Numerical value · 2 shifts · 1 numericalcount elements of relation
Numerical value · 1 shift · 1 numericalelements to add for transitivity
Numerical value · 1 shift · 1 numericalleast and most in intersection of three sets
Numerical value · 1 shift · 1 numericalcompare sets defined by inequalities
Single correct · 1 shiftcount elements of relation
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Counting Relationscount elements of relation | 14 | 14 | Numerical valueCalculation | 8 | |
| Relation Typescount elements of relation | 12 | 12 | Single correctConceptual | 2 | |
| Equivalence Relationscount elements of relation | 10 | 10 | Single correctConceptual | 1 | |
| Venn Diagramsrange of intersection from percentages of two sets | 5 | 5 | Single correctApplication | – | |
| Inclusion-Exclusion for Three Setscount elements in exactly two of three sets | 4 | 4 | Numerical valueApplication | 3 | |
| Intervals as Subsets of Rset operations on intervals of reals | 3 | 3 | Single correctApplication | 1 | |
| Counting Reflexive and Symmetric Relationscount elements of relation and closures | 2 | 2 | Numerical valueMulti-step | 1 | |
| Cartesian Productscount elements of relation | 2 | 2 | Single correctCalculation | – | |
| Subsets and Proper Subsetscount subsets with intersection condition | 2 | 2 | Numerical valueCalculation | 2 | |
| Set Operationsset operations on solution sets of equations | 2 | 2 | Numerical valueApplication | 1 | |
| Divisibility Relationcount elements of relation | 1 | 1 | Numerical valueCalculation | 1 | |
| Transitive Closureelements to add for transitivity | 1 | 1 | Numerical valueMulti-step | 1 | |
| Min-Max Cardinality Boundariesleast and most in intersection of three sets | 1 | 1 | Numerical valueMulti-step | 1 | |
| Roster and Set-Builder Formscompare sets defined by inequalities | 1 | 1 | Single correctMulti-step | – | |
| Inverse Relationscount elements of relation | 1 | 1 | Single correctApplication | – |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Sets and Relations questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20263 questions in 3 shifts
- 5 Apr, Shift 2Q21Let and . Then the number of elements, in the relation…
Idea: Divisibility Relation
New ideaMediumNumerical value - 6 Apr, Shift 2Q21Let . Then the minimum number of elements, required to be added in R to make it…
Idea: Transitive Closure
New ideaHardNumerical value - 8 Apr, Shift 2Q1Consider the relation R on the set defined by if and only if . Then, among the statements…
Idea: Counting Relations
Asked the year beforeMediumOther
JEE Main 20256 questions in 6 shifts
- 2 Apr, Shift 1Q12Let A be the set of all functions and R be a relation on A such that…
Idea: Equivalence Relations
Asked the year beforeEasySingle correct - 3 Apr, Shift 1Q1Let . Let R be a relation on A defined by if and only if . Let be…
Idea: Counting Relations
Asked the year beforeMediumSingle correct - 3 Apr, Shift 2Q1Let . Let R be a relation on defined by if and only if . Let be the number of…
Idea: Counting Reflexive and Symmetric Relations
MediumSingle correct - 4 Apr, Shift 2Q2Let and R be a relation on A defined by if and only if . Let be the number of elements…
Idea: Relation Types
Asked the year beforeMediumSingle correct - 7 Apr, Shift 1Q24The number of relations on the set , containing at most 6 elements including , which are reflexive and transitive…
Idea: Counting Relations
Asked the year beforeHardNumerical value - 8 Apr, Shift 2Q1Let . Let be a relation on defined by if and only if . Then…
Idea: Relation Types
Asked the year beforeMediumOther
JEE Main 202415 questions in 14 shifts
- 4 Apr, Shift 1Q21In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at…
Idea: Min-Max Cardinality Boundaries
New ideaHardNumerical value - 4 Apr, Shift 2Q1Let a relation R on be defined as: if and only if or…
Idea: Relation Types
Asked the year beforeMediumTwo statements - 6 Apr, Shift 1Q1Let the relations and on the set be given by and…
Idea: Relation Types
Asked the year beforeMediumSingle correct - 6 Apr, Shift 1Q7Let is neither a multiple of 3 nor a multiple of 4. Then the number of elements in is
Idea: Venn Diagrams
EasySingle correct - 6 Apr, Shift 2Q2Let . Let be a relation on defined by if and only if . Let be the number of elements in …
Idea: Counting Relations
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2Q1Let and . Let R be a relation on defined by if and only…
Idea: Relation Types
Asked the year beforeHardSingle correct - 9 Apr, Shift 1Q21Let and . Let R be a relation defined on by if and only if…
Idea: Counting Relations
Asked the year beforeMediumNumerical value - 1 Feb, Shift 1Q21Let . Let and two relation on A such that is divisible by is an…
Idea: Counting Relations
Asked the year beforeMediumNumerical value - 1 Feb, Shift 2Q2Consider the relations and defined as for all and…
Idea: Equivalence Relations
MediumSingle correct - 27 Jan, Shift 1Q1Let . Suppose M is the set of all the subsets of S, then the relation is :
Idea: Relation Types
Asked the year beforeEasySingle correct - 29 Jan, Shift 1Q2Let R be a relation on defined by if and only if is divisible by 5. Then R is
Idea: Relation Types
Asked the year beforeMediumSingle correct - 30 Jan, Shift 1Q29A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students…
Idea: Inclusion-Exclusion for Three Sets
Asked the year beforeHardNumerical value - 30 Jan, Shift 2Q21The number of symmetric relations defined on the set which are not reflexive is ________.
Idea: Counting Relations
Asked the year beforeMediumNumerical value - 31 Jan, Shift 1Q21Let and be a relation on A. Let S be the equivalence relation on A such that and…
Idea: Equivalence Relations
MediumNumerical value - 31 Jan, Shift 2Q21Let . Let be a relation on defined by if and only if . Let be a symmetric…
Idea: Relation Types
Asked the year beforeMediumNumerical value
JEE Main 202310 questions in 9 shifts
- 6 Apr, Shift 1Q1Let ,…
Idea: Roster and Set-Builder Forms
New ideaMediumSingle correct - 6 Apr, Shift 1Q21Let and . The number of elements in the relation…
Idea: Counting Relations
Asked the year beforeMediumNumerical value - 8 Apr, Shift 1Q21Let and be the relation defined on such that is odd positive integer or…
Idea: Counting Relations
Asked the year beforeMediumNumerical value - 8 Apr, Shift 2Q1Let . Then the relation is
Idea: Relation Types
EasySingle correct - 10 Apr, Shift 2Q1Let and . Then the number of elements in the relation…
Idea: Cartesian Products
New ideaMediumSingle correct - 11 Apr, Shift 1Q1An 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…
Idea: Inclusion-Exclusion for Three Sets
Asked the year beforeEasySingle correct - 11 Apr, Shift 2Q1Let and . Let be a relation defined on such that…
Idea: Cartesian Products
New ideaMediumSingle correct - 12 Apr, Shift 1Q21The number of relations, on the set containing and , which are reflexive and transitive but not symmetric, is…
Idea: Counting Relations
Asked the year beforeHardNumerical value - 13 Apr, Shift 2Q21Let and be a relation on A. Then the minimum number of…
Idea: Counting Reflexive and Symmetric Relations
New ideaMediumNumerical value - 15 Apr, Shift 1Q21Let and R be a relation on the set defined by . Then the number…
Idea: Relation Types
MediumNumerical value
JEE Main 202211 questions in 11 shifts
- 25 Jul, Shift 2Q21Let . Define and…
Idea: Subsets and Proper Subsets
New ideaHardNumerical value - 26 Jul, Shift 2Q21Let and . Then the number of elements in the set is ________
Idea: Subsets and Proper Subsets
New ideaEasyNumerical value - 27 Jul, Shift 1Q1Let and be two relations defined on by and…
Idea: Equivalence Relations
Asked the year beforeEasySingle correct - 28 Jul, Shift 1Q8For , consider a relation on given by . The…
Idea: Equivalence Relations
Asked the year beforeMediumSingle correct - 29 Jul, Shift 1Q1Let R be a relation from the set to itself such that , where are prime…
Idea: Counting Relations
Asked the year beforeMediumSingle correct - 25 Jun, Shift 2Q1Let and . Then which one of the following statements is…
Idea: Intervals as Subsets of R
Asked the year beforeEasySingle correct - 26 Jun, Shift 1 · Q27Inclusion-Exclusion for Three SetsAsked the year beforeMedium
- 28 Jun, Shift 1 · Q21Counting RelationsAsked the year beforeMedium
- 28 Jun, Shift 2 · Q1Equivalence RelationsAsked the year beforeEasy
- 29 Jun, Shift 1 · Q11Equivalence RelationsAsked the year beforeEasy
- 29 Jun, Shift 2 · Q16Counting RelationsAsked the year beforeMedium
JEE Main 202111 questions in 11 shifts
- 3 Aug, Shift 1 · Q61Set OperationsNew ideaEasy
- 26 Aug, Shift 1 · Q61Venn DiagramsAsked the year beforeMedium
- 27 Aug, Shift 1 · Q81Intervals as Subsets of RAsked the year beforeMedium
- 27 Aug, Shift 2 · Q61Counting RelationsNew ideaMedium
- 31 Aug, Shift 1 · Q61Relation TypesAsked the year beforeMedium
- 24 Feb, Shift 1 · Q85Set OperationsNew ideaHard
- 26 Feb, Shift 1 · Q72Equivalence RelationsNew ideaEasy
- 22 Jul, Shift 2 · Q86Inclusion-Exclusion for Three SetsNew ideaMedium
- 16 Mar, Shift 2 · Q71Equivalence RelationsNew ideaMedium
- 17 Mar, Shift 1 · Q61Venn DiagramsAsked the year beforeEasy
- 18 Mar, Shift 2 · Q78Equivalence RelationsNew ideaEasy
JEE Main 20205 questions in 5 shifts
- 9 Jan, Shift 2 · Q51Intervals as Subsets of RNew ideaEasy
- 2 Sep, Shift 1 · Q51Inverse RelationsNew ideaEasy
- 3 Sep, Shift 2 · Q51Relation TypesNew ideaMedium
- 4 Sep, Shift 1 · Q51Venn DiagramsNew ideaEasy
- 5 Sep, Shift 1 · Q51Venn DiagramsNew ideaEasy
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.