Let A = \ 2,3,4,5,6\ . Let R be a relation on the set A × A given by ( x , y ) R ( z , w ) if and only if x divides z and y leq w . Then the number of elements in R is

Mathematics · Sets and Relations

JEE Main 2026 — 2 April, Evening Shift — Question 43

Let $\mathrm{A} = \{2,3,4,5,6\}$ . Let R be a relation on the set $\mathrm{A}\times \mathrm{A}$ given by $(\mathbf{x},\mathbf{y})\mathbf{R}(\mathbf{z},\mathbf{w})$ if and only if $\mathbf{x}$ divides $\mathbf{z}$ and $\mathbf{y}\leq \mathbf{w}$ . Then the number of elements in R is

Answer: 120

Numerical answer — enter this value.

Step-by-step solution

For $\mathrm{x}=2, \mathrm{z}=2,4,6$

\begin{array}{cl} x=3 & z=3,6 x=4 & z=4 x=5 & z=5 x=6 & z=6 \end{array}

Total case $=8$ and no. of combination of $y$ and $w$ satisfying $y \leq w$ $=1+2+3+4+5=15$ No. of relations satisfying ( $\mathrm{x}, \mathrm{y}$ ) $\mathrm{R}(\mathrm{z}, \mathrm{w})$ is $8 \times 15=120$ .

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Exam: JEE Main 2026
Paper: 2 April, Evening Shift
Subject: Mathematics
Chapter: Sets and Relations
Topic: Relations