Mathematics · Sets and Relations

JEE Main 2026 — 23 January, Evening Shift — Question 16

Let $\mathrm{A}=\{0,1,2, \ldots .9)$ . Let R be a relation on A defined by $(\mathrm{x}, \mathrm{y}) \in \mathrm{R}$ if and only if $|\mathrm{x}-\mathrm{y}|$ is a multiple of 3 . Given below are two statements:

Statement I: $n(R)=36$

Statement II: $R$ is an equivalence relation.

In the light of the above statements, choose the correct answer from the options given below

Option A:
Both Statement I and Statement II are correct
Option B:
Statement I is incorrect but Statement II is correct
Correct
Option C:
Statement I is correct but Statement II is incorrect
Option D:
Both Statement I and Statement II are incorrect

Answer: B

Step-by-step solution

Number of form $3 \mathrm{~K}=4$

Number of form $3 \mathrm{~K}+1=3$

Number of form $3 \mathrm{~K}+2=4$

$4 \times 4+3 \times 3+3 \times 3=34$

relations $\Rightarrow x R y \Rightarrow y R x$

$\Rightarrow(\mathrm{x}-\mathrm{y})=3 \lambda,(\mathrm{y}-\mathrm{z})=3 \mu$

$\Rightarrow(\mathrm{x}-\mathrm{z})=3(\lambda+\mu)$ R is reflexive, symmetric and transitive

$\mathrm{S}_{2}$ is ture Ans. $S_{1}$ is false but $S_{2}$ is ture

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 23 January, Evening Shift
Subject: Mathematics
Chapter: Sets and Relations
Topic: Types of Relations