NDA Sets, Relations and Functions questions with solutions
Set operations, relations and functions. 39 questions from our 2016–2025 NDA pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.
NDA 2025
- The number of subsets of the set A=\1,2,3,4,5\ having at least 3 elements is
- If n(A)=20, n(B)=15 and n(A∩ B)=8, then the number of elements in the symmetric difference Atriangle B is
- On mathbbR, the relation R is defined by xRy if and only if |x|=|y|. The equivalence class of -4 is
- Relations on the set of all straight lines in a plane: 1. "Is parallel to" (a line being parallel to itself) is an equivalence relation. 2. "Is…
- The number of relations on a set of 4 elements that are both reflexive and symmetric is
- For finite sets A,B, n(A∪ B)=n(A)+n(B) always. 2. The empty set is a subset of every set, and \∅\ has exactly one element.
NDA 2024
NDA 2023
- In a class of 48 students, 30 study Mathematics, 25 study Physics and 12 study neither subject. The number of students who study both subjects is
- Let A⊂ B with n(A)=3 and n(B)=6. The number of sets C such that A⊆ C⊆ B is
- If n(A)=20, n(B)=15 and n(A∩ B)=5, then the number of elements belonging to exactly one of the sets A and B is
- The number of symmetric relations that can be defined on a set with 3 elements is
- The number of relations on the set A=\1,2,3\ that are both reflexive and symmetric is
NDA 2022
NDA 2021
- Let A be the set of multiples of 3 and B the set of multiples of 5 among the integers 1,2,…,50. Then n(A∪ B) is
- If A⊂ B, then A∪ B=B. 2. The power set of a set with 3 elements has 6 elements.
- The relation aRbiff a-b is divisible by 3 on the set of integers is an equivalence relation. 2. The relation 'a divides b' on the set of natural…
- Every reflexive and symmetric relation on \1,2,3\ is transitive. 2. The identity relation on any non-empty set is an equivalence relation.
NDA 2020
- In a class, 20 students play cricket, 15 play hockey and 6 play both. How many students play exactly one of the two games?
- If n(A)=40, n(B)=35, n(C)=30, n(A∩ B)=15, n(B∩ C)=10, n(C∩ A)=12 and n(A∩ B∩ C)=5, then n(A∪ B∪ C) is
- For any sets A and B: 1. If A⊂ B, then A∪ B=B. 2. A-B=B-A always.
- A set has 64 subsets. How many of its subsets contain an odd number of elements?
- The number of symmetric relations on a set containing 4 elements is
- Let R be the relation on the set mathbbN defined by a R b if a divides b. Consider: 1. 2. R is antisymmetric.
NDA 2019
- Let A=\3,6,9,…,30\ and B=\5,10,15,…,30\. The number of elements in A∩ B is
- The number of subsets of \1,2,3,4,5,6\ that contain the element 1 but do not contain the element 6 is
- On the set \1,2,3,4\ the relation R=\(1,2),(2,3),(3,4)\ is given. The least number of ordered pairs that must be added to R to make it transitive is
- The number of equivalence relations on the set \1,2,3\ is
- If A⊂ B, then B'⊂ A' for subsets of a universal set U. 2. (A∪ B)-C=(A-C)∪(B-C) for any sets A,B,C.
NDA 2018
- How many reflexive relations can be defined on a set A having 4 elements?
- In a group of 100 students, 40 study Physics, 35 study Chemistry and 15 study both. How many study neither subject?
- On the set mathbbZ of integers a relation R is defined by aRb if and only if a-b is divisible by 3. 1. R is an equivalence relation. 2. R has exactly…
- If A has 2 elements, what is the number of elements in the power set of the power set of A, that is n(P(P(A)))?
- What is the domain of the real function f(x)=(√(x-2))/(x-5)?
NDA 2017
NDA 2016
Other Mathematics topics
Three Dimensional Geometry 48Vector Algebra 60Complex Numbers and Quadratic Equations 35Binomial Theorem 16Sequences and Series 36Quadratic Equations 27Permutations and Combinations 25Statistics 35Probability 27Matrices 37Determinants 13Binary Number System 11Logarithms 11Inverse Trigonometric Functions 22Trigonometric Functions and Identities 49Trigonometric Equations 16Properties of Triangles 18Heights and Distances 12Straight Lines 43Circles 21Conic Sections 28Limits 23Continuity and Differentiability 16Application of Derivatives 34Derivatives 33Integrals 16Definite Integrals 23Application of Integrals 12Differential Equations 30