JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Sets Relations and Functions

Let

A = {2, 3, 5, 7, 9}

. Let R be the relation on A defined by x Ry if and only if

2 x \leq 3 y

. Let

ℓ

be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then

ℓ + m

is equal to:

Answer: (B)

Solution

The relation is

x R y

when

2 x \leq 3 y

, i.e.

y \geq \frac{2 x}{3}

. Counting the admissible

y

for each

x

A = {2, 3, 5, 7, 9}

: for

x = 2

and

x = 3

every element qualifies (

5

each); for

x = 5

and

x = 7

only

{5, 7, 9}

qualify (

3

each); for

x = 9

only

{7, 9}

qualify (

2

). Hence

ℓ = 5 + 5 + 3 + 3 + 2 = 18

. For symmetry every

(x, y) \in R

requires

(y, x) \in R

; the reverses that are absent are

(5, 2), (7, 2), (9, 2), (5, 3), (7, 3), (9, 3), (9, 5)

, so

m = 7

. Therefore

ℓ + m = 18 + 7 = 25

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Single correct option