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Mathematics - Sets and Relations

Practise 149 NDA previous year questions on Sets and Relations, compiled from papers spanning 2010 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 NDA tests.

Sets and Relations has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 149 questions in all. 37% of them were easy, 60% moderate and 3% tough. Most of its questions came from 2013, with 19 questions that year. In the last three years (2024–2026) it had 13 questions across 5 papers, about 2.6 per paper.

The chapter's 3 topics are not weighted equally: Questions on Venn Diagram (65 questions, 44%), Questions on number of relations and sets (58 questions, 39%), and Questions on Symmetric Transitive and Reflexive Properties (26 questions, 17%) have been asked the most. Over the last five years the most frequent topics have been Questions on number of relations and sets (12), Questions on Venn Diagram (11), and Questions on Symmetric Transitive and Reflexive Properties (6). Questions on Venn Diagram has produced the most tough questions (4).

  1. 1What is equal to ?2026 (Phase 1)Questions on Venn Diagram
  2. 2Let and be two sets. For some set , both and are empty sets and . Which of the following is/are true ? I. II. III. Select the answer using t2026 (Phase 1)Questions on Venn Diagram
  3. 3Let be a relation on the set of natural numbers defined by . Which of the following statements is/are correct ? I. is symmetric relation II.2026 (Phase 1)Questions on Symmetric Transitive and Reflexive Properties
  4. 4If and are non-empty subsets of a set, and and represent their complements, then which of the following is/are correct? I. II. Select the an2025 (Phase 2)Questions on Venn Diagram
  5. 5In a class of 45 students, 34 like to play cricket and 26 like to play football. Further, each student likes to play at least one of the two2025 (Phase 2)Questions on Venn Diagram
  6. 6Set contains elements and set contains elements, and they have elements in common. How many elements does have?2025 (Phase 2)Questions on number of relations and sets
  7. 7Let and . How many elements does the subset of corresponding to the relation have, where and ?2025 (Phase 2)Questions on number of relations and sets
  8. 8Let R be a relation on the open interval and is given by . Then which one of the following is correct?2024 (Phase 1)Questions on Symmetric Transitive and Reflexive Properties
  9. 9For any three non-empty sets what is equal to?2024 (Phase 1)Questions on Venn Diagram
  10. 10Consider the following statements : A. The set of all irrational numbers between and is an infinite set. B. The set of all odd integers less2024 (Phase 2)Questions on number of relations and sets
  11. 11Let P and Q be two non-void relations on a set A . Which of the following statements are correct? A. and are reflexive is reflexive. B. and 2024 (Phase 2)Questions on Symmetric Transitive and Reflexive Properties
  12. 12If A and B are two non-empty sets having 10 elements in common, then how many elements do and have in common?2024 (Phase 2)Questions on number of relations and sets
  13. 13In a class of 240 students, 180 passed in English, 130 passed in Hindi and 150 passed in Sanskrit. Further, 60 passed in only one subject, 12024 (Phase 2)Questions on Venn Diagram
  14. 14The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/ are correct? 1. It is p2023 (Phase 2)Questions on number of relations and sets
  15. 15Let . Define a relation R from A to A by , where . Which of the following statements is/are correct? 1. The domain of R is {1, 4, 7, 10, 13,2023 (Phase 2)Questions on number of relations and sets
  16. 16Consider the following statements: 1. 2. 3. Which of the statements given above are correct?2023 (Phase 2)Questions on Venn Diagram
  17. 17If , then how many elements are there in the power set of ?2022 (Phase 1)Questions on number of relations and sets
  18. 18Consider all the subsets of the set . How many of them are supersets of the set ?2022 (Phase 1)Questions on number of relations and sets
  19. 19Consider the following statements in respect of two nonempty sets and : 1. or 2. and Which of the above statements is/are correct?2022 (Phase 1)Questions on Venn Diagram
  20. 20Consider the following statements in respect of two nonempty sets and : 1. iff 2. iff Which of the above statements is/are correct?2022 (Phase 1)Questions on number of relations and sets
  21. 21Consider the following statements in respect of the relation in the set IN of natural numbers defined by if : 1. is reflexive 2. is symmetri2022 (Phase 1)Questions on Symmetric Transitive and Reflexive Properties
  22. 22Consider the following statements in respect of any relation on a set : 1. If is reflexive, then is also reflexive 2. If is symmetric, then 2022 (Phase 1)Questions on Symmetric Transitive and Reflexive Properties
  23. 23Consider the following statements : 1. If is the subset of defined by , , then is a function from to . 2. If is the subset of defined by ; ,2022 (Phase 2)Questions on number of relations and sets
  24. 24Consider the following statements : 1. The set of all irrational numbers between and is an infinite set. 2. The set of all odd integers less2022 (Phase 2)Questions on number of relations and sets
  25. 25Let be a relation from to defined by and . Which of the following are not correct? 1. for all 2. 3. and Select the correct answer using the 2022 (Phase 2)Questions on Symmetric Transitive and Reflexive Properties
  26. 26Consider the following : 1. 2. Which of the above is/are correct?2022 (Phase 2)Questions on number of relations and sets
  27. 27Paragraph: A university awarded medals in basket ball, football and volleyball. Only students got medal in all the three sports and the meda2022 (Phase 2)Questions on Venn Diagram
  28. 28Paragraph: A university awarded medals in basket ball, football and volleyball. Only students got medal in all the three sports and the meda2022 (Phase 2)Questions on Venn Diagram
  29. 29Paragraph: A university awarded medals in basket ball, football and volleyball. Only students got medal in all the three sports and the meda2022 (Phase 2)Questions on Venn Diagram
  30. 30Consider the following statements : 1. and are equivalent sets. 2. and are equal sets. Which of the above statements is/are correct?2021 (Phase 1)Questions on number of relations and sets
  31. 31Consider the following statements : 1. The null set is a subset of every set. 2. Every set is a subset of itself. 3. If a set has 10 element2021 (Phase 1)Questions on number of relations and sets
  32. 32Let be a relation defined as if and only if , where . How many elements of the form are there in ?2021 (Phase 1)Questions on number of relations and sets
  33. 33Consider the following statements in respect of sets : 1. The union over intersection of sets is distributive. 2. The complement of union of2021 (Phase 2)Questions on Venn Diagram
  34. 34Consider three sets and having 6,5 and 4 elements respectively. All these 15 elements are distinct. Let . How many proper subsets does have?2021 (Phase 2)Questions on number of relations and sets
  35. 35Consider the following statements in respect of relations and functions : 1. All relations are functions but all functions are not relations2021 (Phase 2)Questions on number of relations and sets
  36. 36Suppose set consists of first 250 natural numbers that are multiples of 3 and set consists of first 200 even natural numbers. How many eleme2021 (Phase 2)Questions on Venn Diagram
  37. 37Consider the proper subsets of . How many of these proper subsets are superset of the set ?2020Questions on number of relations and sets
  38. 38Paragraph: Read the following information and answer: Consider the following Venn diagram, where and are three sets. Let the number of eleme2020Questions on Venn Diagram
  39. 39Paragraph: Read the following information and answer: Consider the following Venn diagram, where and are three sets. Let the number of eleme2020Questions on Venn Diagram
  40. 40Paragraph: Read the following information and answer: Consider the following Venn diagram, where and are three sets. Let the number of eleme2020Questions on Venn Diagram
  41. 41Let }. A relation R on is defined by if when . Then the relation is2020Questions on Symmetric Transitive and Reflexive Properties
  42. 42Suppose and is a relation on . If , then which one of the following is correct?2019 (Phase 1)Questions on Symmetric Transitive and Reflexive Properties
  43. 43relation is defined on the set of natural numbers as , Then which one of the following is correct?2019 (Phase 1)Questions on Symmetric Transitive and Reflexive Properties
  44. 44Consider the following statements for the two non-empty sets and : (1) (2) Which of the above statements is/are correct ?2019 (Phase 1)Questions on Venn Diagram
  45. 45Let be a non-empty set and let be subsets of . Consider the following statments : (1) (2) for all sets (3) for all sets Which of the above s2019 (Phase 1)Questions on number of relations and sets
  46. 46If , then the power set of is2019 (Phase 1)Questions on number of relations and sets
  47. 47Paragraph: In a school, all the students play at least one of three indoor games - chess, carrom and table tennis, 60 play chess, 50 play ta2019 (Phase 1)Questions on Venn Diagram
  48. 48Paragraph: In a school, all the students play at least one of three indoor games - chess, carrom and table tennis, 60 play chess, 50 play ta2019 (Phase 1)Questions on Venn Diagram
  49. 49If and are subsets of a given set, then which one of the following relations is not correct?2019 (Phase 2)Questions on Venn Diagram
  50. 50If a set contains 3 elements and another set contains 6 elements, then what is the minimum number of elements that can have?2019 (Phase 2)Questions on Venn Diagram

Frequently Asked Questions

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

This chapter includes 149 questions compiled from NDA papers spanning 2010 to 2026.

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

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

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

Sets and Relations has appeared in 17 of the 17 years of NDA papers covered here, with 149 questions across 30 papers - about 5 per paper it appears in.

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

Of the 149 questions analysed for this chapter, 37% are easy, 60% moderate and 3% tough. 2013 had the most, with 19 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 Venn Diagram - 65 questions (44%)
  • Questions on number of relations and sets - 58 questions (39%)
  • Questions on Symmetric Transitive and Reflexive Properties - 26 questions (17%)
  • Questions on Venn Diagram has produced the most tough questions (4).
6.Is Sets and Relations's weightage in NDA going up or down?

Across all 30 papers analysed, Sets and Relations has averaged about 5.0 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.