Sets & Relations
75 NDA Mathematics previous year questions (PYQs) from 17 papers, 2017 to 2026, with answers and worked solutions.
About this chapter
- Difficulty: 24 easy · 42 moderate · 9 hard.
- Most-asked subtopics: Counting Sets, Subsets, and Inclusion-Exclusion (28), Set Operations, Identities, and Cartesian Products of Sets (25), Relations — Properties, Cartesian Product, and Counting (22).
- Updated 14 September 2026.
- NDA · Sep 2026 · Q46Moderate
#1Set Operations, Identities, and Cartesian Products of Sets
- NDA · Sep 2026 · Q48Moderate
#2Set Operations, Identities, and Cartesian Products of Sets
- NDA · Apr 2017 · Q23Moderate
#3Set Operations, Identities, and Cartesian Products of Sets
#4Set Operations, Identities, and Cartesian Products of Sets
- NDA · Sep 2017 · Q6Moderate
#5Set Operations, Identities, and Cartesian Products of Sets
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#6Set Operations, Identities, and Cartesian Products of Sets
- NDA · Apr 2018 · Q6Moderate
#7Set Operations, Identities, and Cartesian Products of Sets
#8Set Operations, Identities, and Cartesian Products of Sets
#9Set Operations, Identities, and Cartesian Products of Sets
#10Set Operations, Identities, and Cartesian Products of Sets
- NDA · Sep 2019 · Q3Moderate
#11Set Operations, Identities, and Cartesian Products of Sets
#12Set Operations, Identities, and Cartesian Products of Sets
- NDA · Sep 2019 · Q28Moderate
#13Set Operations, Identities, and Cartesian Products of Sets
- NDA · Apr 2020 · Q47Moderate
#14Set Operations, Identities, and Cartesian Products of Sets
#15Set Operations, Identities, and Cartesian Products of Sets
#16Set Operations, Identities, and Cartesian Products of Sets
- NDA · Apr 2022 · Q42Moderate
#17Set Operations, Identities, and Cartesian Products of Sets
- NDA · Apr 2022 · Q43Moderate
#18Set Operations, Identities, and Cartesian Products of Sets
- Set · 1 questionConsider the following: 1. A∩B = A∩C ⟹ B = C 2. A∪B = A∪C ⟹ B = C
- NDA · Sep 2022 · Q15Moderate
#19Set Operations, Identities, and Cartesian Products of Sets
- NDA · Apr 2026 · Q24Moderate
#20Set Operations, Identities, and Cartesian Products of Sets
#21Set Operations, Identities, and Cartesian Products of Sets
- NDA · Sep 2025 · Q2Moderate
#22Set Operations, Identities, and Cartesian Products of Sets
#23Set Operations, Identities, and Cartesian Products of Sets
#24Set Operations, Identities, and Cartesian Products of Sets
- NDA · Apr 2024 · Q24Moderate
#25Set Operations, Identities, and Cartesian Products of Sets
#26Counting Sets, Subsets, and Inclusion-Exclusion
#27Counting Sets, Subsets, and Inclusion-Exclusion
- Set · 2 questionsConsider the information given below and answer the two items (02) that follow: In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.
- NDA · Apr 2018 · Q13Moderate
#28Counting Sets, Subsets, and Inclusion-Exclusion
#29Counting Sets, Subsets, and Inclusion-Exclusion
#30Counting Sets, Subsets, and Inclusion-Exclusion
- Set · 2 questionsConsider the information given below and answer the two (02) items that follow: A survey was conducted among 300 students. It was found that 125 students like to play cricket, 145 students like to play football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.
#31Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Sep 2018 · Q9Moderate
#32Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Apr 2019 · Q15Moderate
#33Counting Sets, Subsets, and Inclusion-Exclusion
- Set · 2 questionsConsider the following for the next 02 (two) items that follow: In a school, all the students play at least one of three indoor games – chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.
- NDA · Apr 2019 · Q16Moderate
#34Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Apr 2019 · Q17Moderate
#35Counting Sets, Subsets, and Inclusion-Exclusion
#36Counting Sets, Subsets, and Inclusion-Exclusion
#37Counting Sets, Subsets, and Inclusion-Exclusion
- Set · 3 questionsDirections for the following three (03) items: Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z) which is equal to 90.
- NDA · Apr 2020 · Q16ModerateHas image
#38Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Apr 2020 · Q17ModerateHas image
#39Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Apr 2020 · Q18ModerateHas image
#40Counting Sets, Subsets, and Inclusion-Exclusion
#41Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Sep 2021 · Q38Moderate
#42Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Sep 2021 · Q43Moderate
#43Counting Sets, Subsets, and Inclusion-Exclusion
#44Counting Sets, Subsets, and Inclusion-Exclusion
#45Counting Sets, Subsets, and Inclusion-Exclusion
- Set · 1 questionConsider the following statements: 1. The set of all irrational numbers between and is an infinite set. 2. The set of all odd integers less than 100 is a finite set.
#46Counting Sets, Subsets, and Inclusion-Exclusion
- Set · 3 questionsConsider the following for the next three (03) items that follow: A university awarded medals in basketball, football and volleyball. Only x students (x < 6) got medal in all the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x + 15) medals in football and (x + 25) medals in volleyball.
#47Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Sep 2022 · Q35Moderate
#48Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Sep 2022 · Q36Moderate
#49Counting Sets, Subsets, and Inclusion-Exclusion
- NDA · Apr 2026 · Q7Moderate
#50Counting Sets, Subsets, and Inclusion-Exclusion
Showing the first 50 of 75.
See all 75 questionsMore chapters in this subject
- 3D Geometry94
- Application of Derivatives76
- Applications of Integration27
- Binomial Distribution31
- Binomial Theorem56
- Circles28
- Complex Numbers76
- Conics40
- Definite Integration69
- Differential Equations67
- Differentiation89
- Functions115
- Height & Distance26
- Indefinite Integration42
- Inverse Trigonometry36
- Limits & Continuity87
- Lines104
- Logarithms27
- Matrices & Determinants181
- Permutation & Combination80
- Probability176
- Properties of Triangle52
- Quadratic Equations67
- Sequence & Series93
- Statistics165
- Trigonometric Equations34
- Trigonometric Identities145
- Vectors102