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

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Sets Relations and Functions

Let

A = {2, 3, 4, 5, 6}

. Let R be a relation on the set

A \times 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 ______.

Answer: 120

For each

x \in A

count the

z \in A

with

x ∣ z

x = 2

gives

{2, 4, 6}

(3),

x = 3

gives

{3, 6}

(2), and

x = 4, 5, 6

give one each, so there are

3 + 2 + 1 + 1 + 1 = 8

ordered pairs

(x, z)

. Independently, the number of pairs

(y, w)

with

y \leq w

drawn from a

5

-element set is

(2 5) + 5 = 15

. The two conditions are independent, so

R

has

8 \times 15 = 120

elements.

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Integer answer