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Mathematics - Sets and Relations

Practise 18 NEST (NISER) previous year questions on Sets and Relations, compiled from papers spanning 2012 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 NEST (NISER) tests.

Sets and Relations has been asked in 11 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 18 questions in all. 22% of them were easy, 72% moderate and 6% tough. Most of its questions came from 2021, with 4 questions that year. In the last three years (2024–2026) it had 2 questions across 4 papers, about 0.5 per paper.

The chapter's 3 topics are not weighted equally: Questions on number of relations and sets (10 questions, 56%), Questions on Venn Diagram (4 questions, 22%), and Questions on Symmetric Transitive and Reflexive Properties (4 questions, 22%) have been asked the most. Questions on number of relations and sets has also led over the last five years, with 5 questions. Questions on number of relations and sets has produced the most tough questions (1).

  1. 1Let be a set. Let be the equivalence relation on defined by if and only if . Then the number of equivalence classes of on is2026Questions on number of relations and sets
  2. 2Let be the equivalence relation on defined by if . Then2024 (Session 1)Questions on number of relations and sets
  3. 3Let and be a function. Let be a subset of such that the following conditions are satisfied: (i) if then , and (ii) if then . Then it follows2023 (Session 2)Questions on Symmetric Transitive and Reflexive Properties
  4. 4Let . Let be the equivalence relation on defined by if . For let denote the equivalence class of . Then2023 (Session 2)Questions on number of relations and sets
  5. 5For sets and , define Let and be distinct sets. Then2022 (Session 1)Questions on Venn Diagram
  6. 6For , let denote the fractional part of . Suppose is a relation defined on by if and only if . Then the number of equivalence classes of is2022 (Session 2)Questions on number of relations and sets
  7. 7Let be subsets of a set such that for all . If , then2022 (Session 2)Questions on number of relations and sets
  8. 8Five friends have the following hobbies : Akshay likes singing and cooking, Bharati likes singing and painting, Charu likes painting and coo2021 (Session 1)Questions on Venn Diagram
  9. 9If and , then the number of elements in is2021 (Session 2)Questions on number of relations and sets
  10. 10A group of 5 students, X, Y, Z, P, Q, have the following combination of two subjects each in their first year of college. X studies Physics 2021 (Session 2)Questions on number of relations and sets
  11. 11Let be a function. If and , define and . Then the true statement/statements is/ are2021 (Session 2)Questions on number of relations and sets
  12. 12Let be a set of elements. It is defined that - a relation on is symmetric if then for ; - a relation on is antisymmetric if then for . Let a2020 (Session 1)Questions on Symmetric Transitive and Reflexive Properties
  13. 13Let be a relation on given by Then is2020 (Session 2)Questions on Symmetric Transitive and Reflexive Properties
  14. 14Let and be two equivalence relations on a set . Then the relation on is2018Questions on Symmetric Transitive and Reflexive Properties
  15. 15There are 100 students in a class. It is found that 60 students study Mathematics, 45 students study Physics and 35 students study Chemistry2016Questions on Venn Diagram
  16. 16Let be a nonempty set and be the set of all subsets of . Define a function such that for and , Then, for and is not equal to2015Questions on Venn Diagram
  17. 17The probability that a randomly chosen relation from a set to itself is a symmetric relation is2013Questions on number of relations and sets
  18. 18Let denote the set . Then,2012Questions on number of relations and sets

Frequently Asked Questions

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

This chapter includes 18 questions compiled from NEST (NISER) papers spanning 2012 to 2026.

2.Are these questions only from NEST (NISER), or from other exams too?

These are NEST (NISER) 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 NEST (NISER) Mathematics?

Sets and Relations has appeared in 11 of the 16 years of NEST (NISER) papers covered here, with 18 questions across 14 papers - about one per paper it appears in.

4.What is the difficulty level of Sets and Relations questions in NEST (NISER)?

Of the 18 questions analysed for this chapter, 22% are easy, 72% moderate and 6% tough. 2021 had the most, with 4 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 number of relations and sets - 10 questions (56%)
  • Questions on Venn Diagram - 4 questions (22%)
  • Questions on Symmetric Transitive and Reflexive Properties - 4 questions (22%)
  • Questions on number of relations and sets has produced the most tough questions (1).
6.Is Sets and Relations's weightage in NEST (NISER) going up or down?

Across all 14 papers analysed, Sets and Relations has averaged about 1.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.5 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.