List of top Mathematics Questions on Relations asked in JEE Main

If $A=\{1,2,3,4\}$. A relation from set $A$ to $A$ is defined as $(a,b)\,R\,(c,d)$ such that $2a+3b=3c+4d$. Find the number of elements in the relation.

Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $ and $ R $ be a relation on $ A $ defined by $ xRy $ if and only if $ 2x - y \in \{0, 1\} $. Let $ l $ be the number of elements in $ R $. Let $ m $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to:

The number of relations on the set $ A = \{1, 2, 3\} $ containing at most 6 elements including $ (1, 2) $, which are reflexive and transitive but not symmetric, is:

Define a relation $ R $ on the interval $ [0, \frac{\pi}{2}] $ by $ xRy $ if and only if $ \sec^2 x - \tan^2 y = 1 $. Then $ R $ is:

Let $ R $ be a relation on $ \mathbb{Z} \times \mathbb{Z} $ defined by $(a, b) R (c, d)$ if and only if $ad - bc$ is divisible by 5.
Then $ R $ is:

Let S = {1,2,3,..., 20}, R₁ = {(a, b): a divide b}, R₂ = {(a, b): a is integral multiple of b} and a, b ∈ S. n(R₁ - R₂) = ?

If $A = {1, 2, 3, … 100}$, $R = {(x, y) | 2x = 3y, x, y ∈ A}$ is symmetric relation on $A$ and the number of elements in $R$ is $n$, the smallest integer value of $n$ is

A = {1, 2, 3, 4} minimum number of elements added to make an equivalence relation on set A containing (1, 3) & (1, 2) in it.

A = {1, 2, 3, 4} , R = {(1, 2), (2, 3), (2, 4)} R ⊆ S and S is an equivalence relation then the minimum number of elements to be added to R is n, then the value of n is?

The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c)\}$ on the set $\{ a , b , c \}$ so that it becomes symmetric and transitive is :

The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c),(b, d)\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is _______

Among the relations
$S=\left\{(a, b): a, b \in R -\{0\}, 2+\frac{a}{b}>\right\}$
and $T=\left\{(a, b): a, b \in R , a^2-b^2 \in Z\right\}$,

Let $ A = \{1, 2, 3, 4, 5, 6, 7\} $. Then the relation $ R = \{(x, y) \in A \times A : x + y = 7\} $ is:

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B) : a₁ divides b₂ and a₂ divides b₁} is

Let R₁ and R₂ be relations on the set {1, 2, ….., 50} such that R₁ ={(p, pⁿ) : p is a prime and n≥ 0 is an integer} and R₂ = {(p, pⁿ) : p is a prime and n = 0 or 1}. Then, the number of elements in R₁ – R₂ is ______.

Let $R =\{( P , Q ) | P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of (1,-1) is the set: