Jump to a section

Mathematics - Sets and Relations

Practise 120 JEE Main previous year questions on Sets and Relations, compiled from papers spanning 2004 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Sets and Relations has been asked in 20 of the 25 years of JEE Main papers analysed (2002–2026), with 120 questions in all. 36% of them were easy, 52% moderate and 13% tough. Most of its questions came from 2023, with 21 questions that year. In the last three years (2024–2026) it had 44 questions across 49 papers, about 0.9 per paper.

The chapter's 3 topics are not weighted equally: Questions on Symmetric Transitive and Reflexive Properties (59 questions, 49%), Questions on number of relations and sets (43 questions, 36%), and Questions on Venn Diagram (18 questions, 15%) have been asked the most. Questions on Symmetric Transitive and Reflexive Properties has also led over the last five years, with 41 questions. Questions on number of relations and sets has produced the most tough questions (7).

  1. 1Consider the relation R on the set defined by if and only if . Then, among the statements: I. The number of elements in R is 17 II. R is an 08 Apr, 2026 (E)Questions on Symmetric Transitive and Reflexive Properties
  2. 2Let . Then the minimum number of elements, required to be added in to make it a transitive relation, is __________.06 Apr, 2026 (E)Questions on Symmetric Transitive and Reflexive Properties
  3. 3Let and . Then the number of elements, in the relation is _______.05 Apr, 2026 (E)Questions on number of relations and sets
  4. 4Let . Let R be a relation on the set given by if and only if divides and . Then the number of elements in R is _______.02 Apr, 2026 (E)Questions on number of relations and sets
  5. 5Let R be a relation defined on the set by . Then the number of elements in R is24 Jan, 2026 (M)Questions on number of relations and sets
  6. 6Let . Let R be a relation on A defined by if and only if . Let be the number of elements in R. Let m and n be the minimum number of elements23 Jan, 2026 (M)Questions on Symmetric Transitive and Reflexive Properties
  7. 7Let . Let R be a relation on A defined by if and only if is a multiple of 3. Given below are two statements: Statement I : . Statement II : 23 Jan, 2026 (E)Questions on Symmetric Transitive and Reflexive Properties
  8. 8Let the relation R on the set be given by . Then the minimum number of elements required to be added in R, in order to make the relation sym22 Jan, 2026 (M)Questions on Symmetric Transitive and Reflexive Properties
  9. 9The number of elements in the relation is22 Jan, 2026 (E)Questions on number of relations and sets
  10. 10Let be the set of the first 11 natural numbers. Then the number of elements in and the product of all elements of is even is .22 Jan, 2026 (E)Questions on number of relations and sets
  11. 11The number of relations, defined on the set , which are both reflexive and symmetric, is equal to:21 Jan, 2026 (M)Questions on number of relations and sets
  12. 12Let and . Then21 Jan, 2026 (E)Questions on Venn Diagram
  13. 13Let . Let R be the relation on A defined by if and only if . Let be the number of elements in R, and m be the minimum number of elements req21 Jan, 2026 (E)Questions on Symmetric Transitive and Reflexive Properties
  14. 14Let . Let be a relation on A defined by if and only if max . Then among the statements : The number of elements in R is 18 , and : The relat08 Apr, 2025 (E)Questions on Symmetric Transitive and Reflexive Properties
  15. 15The number of relations on the set containing at most 6 elements including , which are reflexive and transitive but not symmetric, is ______07 Apr, 2025 (M)Questions on Symmetric Transitive and Reflexive Properties
  16. 16Let and R be a relation on defined by if and only if . Let be the number of elements in R. Let and be the minimum number of elements require04 Apr, 2025 (E)Questions on Symmetric Transitive and Reflexive Properties
  17. 17Let , be a relation on A defined by if and only if . Let be the number of elements in R and be the minimum number of elements required to be03 Apr, 2025 (M)Questions on Symmetric Transitive and Reflexive Properties
  18. 18Let . let R be a relation on A defined by if and only if . Let be the number of elements in R. Let m and n be the minimum number of elements03 Apr, 2025 (E)Questions on Symmetric Transitive and Reflexive Properties
  19. 19Let A be the set of all functions and R be a relation on A such that and . Then R is:02 Apr, 2025 (M)Questions on Symmetric Transitive and Reflexive Properties
  20. 20Let and R be a relation on A such that . Let , be a sequence of elements of R such that the second entry of an ordered pair is equal to the 02 Apr, 2025 (E)Questions on number of relations and sets
  21. 21Define a relation R on the interval \( [0, { }{2} )\) by \(x {R} y\) if and only if \( ^2 x- ^2 y=1\). Then R is :29 Jan, 2025 (M)Questions on Symmetric Transitive and Reflexive Properties
  22. 22Let . Define a relation from to by : Then, the sum of all the elements in the range of is equal to :29 Jan, 2025 (E)Questions on number of relations and sets
  23. 23The relation and is even is:28 Jan, 2025 (M)Questions on Symmetric Transitive and Reflexive Properties
  24. 24Let be the set of first ten prime numbers. Let , where is the set of all possible products of distinct elements of . Then the number of all 24 Jan, 2025 (M)Questions on number of relations and sets
  25. 25Let and . Then is equal to :24 Jan, 2025 (E)Questions on number of relations and sets
  26. 26Let be a relation defined on the set . Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relatio23 Jan, 2025 (M)Questions on number of relations and sets
  27. 27Let and . If or , then is :23 Jan, 2025 (E)Questions on number of relations and sets
  28. 28Let . Define a relation on as : Statement I : is an equivalence relation. Statement II : For some , the set represents a line parallel to . 23 Jan, 2025 (E)Questions on Symmetric Transitive and Reflexive Properties
  29. 29The number of non-empty equivalence relations on the set is :22 Jan, 2025 (M)Questions on number of relations and sets
  30. 30Let and and . Then is equal to :22 Jan, 2025 (M)Questions on number of relations and sets
  31. 31Let . The number of relations on , containing and , which are reflexive and transitive but not symmetric, is ______ -22 Jan, 2025 (E)Questions on Symmetric Transitive and Reflexive Properties
  32. 32Let and . Let be a relation defined on by if and only if . Then the number of elements in is _________09 Apr, 2024 (M)Questions on number of relations and sets
  33. 33Let and . Let be a relation on defined by if and only if is an even integer. Then the relation is08 Apr, 2024 (E)Questions on Symmetric Transitive and Reflexive Properties
  34. 34Let the relations and on the set be given by and . If and be the minimum number of elements required to be added in and , respectively, in o06 Apr, 2024 (M)Questions on Symmetric Transitive and Reflexive Properties
  35. 35Let . Let be a relation on defined by if and only if . Let be the number of elements in and be the minimum number of elements from that are 06 Apr, 2024 (E)Questions on Symmetric Transitive and Reflexive Properties
  36. 36Let the set be partitioned into 3 sets with equal number of elements such that and . The maximum number of such possible partitions of is eq05 Apr, 2024 (E)Questions on number of relations and sets
  37. 37In 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 le04 Apr, 2024 (M)Questions on Venn Diagram
  38. 38Let a relation on be defined as: if and only if or . Consider the two statements: (I) is reflexive but not symmetric. (II) is transitive The04 Apr, 2024 (E)Questions on Symmetric Transitive and Reflexive Properties
  39. 39The number of elements in the set S = x , y , z : x , y , z ∈ Z , x + 2 y + 3 z = 42 , x , y , z ≥ 0 equals ________01 Feb, 2024 (M)Questions on number of relations and sets
  40. 40Let A = 1 , 2 , 3 , . ..20 . Let R 1 and R 2 two relation on A such that R 1 = { a , b : b is divisible by a } R 2 = { a , b : a is an integ01 Feb, 2024 (M)Questions on number of relations and sets
  41. 41Consider the relations R 1 and R 2 defined as a R 1 b ⇔ a 2 + b 2 = 1 for all a , b , ∈ R and a , b R 2 c , d ⇔ a + d = b + c for all a , b 01 Feb, 2024 (E)Questions on Symmetric Transitive and Reflexive Properties
  42. 42Let 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 ⊂ S 31 Jan, 2024 (M)Questions on Symmetric Transitive and Reflexive Properties
  43. 43Let A = 1 , 2 , 3 , . ...100 . Let R be a relation on A defined by x , y ∈ R if and only if 2 x = 3 y . Let R 1 be a symmetric relation on A31 Jan, 2024 (E)Questions on number of relations and sets
  44. 44A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics Chemistry. It was found that all students passed in a30 Jan, 2024 (M)Questions on Venn Diagram
  45. 45The number of symmetric relations defined on the set { 1 , 2 , 3 , 4 } which are not reflexive is _______.30 Jan, 2024 (E)Questions on number of relations and sets
  46. 46Let R be a relation on Z × Z defined by ( a , b ) R ( c , d ) if and only if a d - b c is divisible by 5 . Then R is29 Jan, 2024 (M)Questions on Symmetric Transitive and Reflexive Properties
  47. 47If R is the smallest equivalence relation on the set { 1 , 2 , 3 , 4 } such that { ( 1 , 2 ) , ( 1 , 3 ) } ⊂ R , then the number of elements29 Jan, 2024 (E)Questions on Symmetric Transitive and Reflexive Properties
  48. 48Let S = { 1 , 2 , 3 , … , 10 } . Suppose M is the set of all the subsets of S , then the relation R = { ( A , B ) : A ∩ B ≠ ϕ ; A , B ∈ M } 27 Jan, 2024 (M)Questions on Symmetric Transitive and Reflexive Properties
  49. 49The number of elements in the set { n : 10 n 100 and 3 n - 3 is a multiple of 7 } is _______.15 Apr, 2023 (M)Questions on number of relations and sets
  50. 50Let A = 1 , 2 , 3 , 4 and R be a relation on the set A A defined by R = a , b , c , d : 2 a + 3 b = 4 c + 5 d . Then the number of elements 15 Apr, 2023 (M)Questions on number of relations and sets

Frequently Asked Questions

1.How many questions are available for Sets and Relations?

This chapter includes 120 questions compiled from JEE Main papers spanning 2004 to 2026.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Sets and Relations chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Sets and Relations an important chapter for JEE Main Mathematics?

Sets and Relations has appeared in 20 of the 25 years of JEE Main papers covered here, with 120 questions across 110 papers - about one per paper it appears in.

4.What is the difficulty level of Sets and Relations questions in JEE Main?

Of the 120 questions analysed for this chapter, 36% are easy, 52% moderate and 13% tough. 2023 had the most, with 21 questions.

5.Which topics in Sets and Relations should I focus on?

These topics have carried the most weightage in Sets and Relations:

  • Questions on Symmetric Transitive and Reflexive Properties - 59 questions (49%)
  • Questions on number of relations and sets - 43 questions (36%)
  • Questions on Venn Diagram - 18 questions (15%)
  • Questions on number of relations and sets has produced the most tough questions (7).
6.Is Sets and Relations's weightage in JEE Main going up or down?

Across all 110 papers analysed, Sets and Relations has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.9 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.