List of top Mathematics Questions on types of relations asked in KEAM

Let \(R\) be a relation in \(\mathbb{N}\) defined by \(\{(x,y): x + 3y = 10, x,y \in \mathbb{N}\}\). Then the range of \(R\) is

Let $X = \{a_1, a_2, a_3, \ldots, a_n\}$ be a set consisting of $n$ elements. The relation $R = \{(a_1,a_1),(a_2,a_2),(a_3,a_3),\ldots,(a_n,a_n)\}$ on the set $X$ is:

Given \( y = \frac{1}{1 + \tan x} \), find \( f^{-1}(x) \), where \( 0<x<\frac{\pi}{2} \).

The relation \( R = \{(1,3), (2,3), (2,4), (3,1), (4,4), (4,1)\} \) on the set \( X = \{1,2,3,4\} \) is:

Let \(A\) and \(B\) be two finite sets. If \(n(A) = 7\) and the number of relations from \(A\) into \(B\) is 128, then \(n(B) =\)

Let $A=\{2,3,4,5\}$, $B=\{36,45,49,60,77,90\}$ and let $R$ be the relation 'is factor of' from $A$ to $B$. Then the range of $R$ is the set

Consider the set $A = \{1,2,3\}$ along with the relation $R = \{(1,1),(2,2),(1,2),(2,1),(3,3)\}$. Which of the following statements is true?

Let $R = \{(a,b): a \leq b^2\}$ be a relation on the set of all real numbers. Then $R$ is

Consider the set \( M = \{1,2,3\} \) along with the relation \( R = \{(1,2), (1,1), (3,1), (3,4), (3,3), (4,3)\ \). Which of the following statements is true?