Mathematics · Sets and Relations

JEE Advanced 2025 — Paper 1 — Question 22

Let the set of all relations $R$ on the set $\{a, b, c, d, e, f\}$ , such that $R$ is reflexive and symmetric, and $R$ contains exactly 10 elements, be denoted by $S$ . Then the

number of elements in $S$ is $\qquad$

Answer: 105

Numerical answer — enter this value.

Step-by-step solution

For relation to be reflexive all the diagonal elements must be taken and out of remaining

30 elements there are 15 pairs and we need 2 pairs such that R contains exactly 10

elements and is both reflexive and symmetric.

$\therefore$ number of ways $={ }^{15} \mathrm{C}_{2}=105$

Answer key and solution verified before publishing.

Practise Sets and Relations

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Advanced 2025
Paper: Paper 1
Subject: Mathematics
Chapter: Sets and Relations
Topic: Types of Relations