Relations & Mappings Questions with Solutions

6 questions3 easy2 medium1 hard

A relation from set A to set B is a subset of the Cartesian product A x B. A mapping, or function, is a special relation in which every element of A is related to exactly one element of B. This topic covers types of relations (reflexive, symmetric, transitive and equivalence relations), domain, codomain and range, and types of functions such as one-one (injective), onto (surjective) and bijective functions, along with composition and inverse functions. Exam questions test identifying the type of a given relation or function, counting the number of relations or functions between two sets, and finding the domain or range of a function. Useful counting facts: if A has m elements and B has n elements, there are 2^(mn) relations and n^m functions from A to B. Practise the relations and mappings questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
$R_{1} = (x, y) ∣ x, y \in R, x^{2} + y^{2} \leq 25$ and $R_{2} = (x, y) ∣ x, y \in R, 9 y \geq 4 x^{2}$ . Then $R_{1} \cap R_{2}$ is
A. One–oneB. OntoC. One–one and ontoD. None of these
hardAsked in MAH MCA CET 2023View solution ›
Q2.
Define a relation $\sim$ on the set $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$ by $a \sim b$ if $a - 2 b$ is divisible by 3. Then:
A. $\sim$ is not symmetric, not reflexive and not transitiveB. $\sim$ is reflexive but neither symmetric nor transitiveC. $\sim$ is symmetric but neither transitive nor reflexiveD. $\sim$ is transitive but neither reflexive nor symmetric
mediumAsked in NIMCET 2026View solution ›
Q3.
Let R be the set of real numbers. If $f : R \to R$ is a function defined by $f (x) = x^{2}$ . then $f$ is
A. Injective but not surjectiveB. Surjective but not injectiveC. BijectiveD. Neither injective nor surjective
easyAsked in MAH MCA CET 2024View solution ›
Q4.
Let R be a reflexive relation on a finite set A having 10 elements, and let m be the number of ordered pairs in R. Then
A. $m \geq 10$ B. $m = 100$ C. $m = 10$ D. $m \leq 10$
easyAsked in NIMCET 2023View solution ›
Q5.
The total number of relations that exist from a set $A$ with $m$ elements into the set $A \times A$ is:
A. $m^{2}$ B. $m^{3}$ C. $m$ D. None of these
mediumAsked in NIMCET 2009View solution ›
Q6.
Let $A = 1, 2, 3, \dots, 20$ . Let $R \subseteq A \times A$ such that $R = (x, y) : y = 2 x - 7$ . Then the number of elements in $R$ is equal to
A. 10B. 13C. 7D. 17
easyAsked in NIMCET 2025View solution ›