Let the relation R on the set $\mathrm{M}=\{1,2,3, \ldots, 16\}$ be given by $\mathrm{R}=\{(\mathrm{x}, \mathrm{y}): 4 \mathrm{y}=5 \mathrm{x}-3, \mathrm{x}, \mathrm{y} \in \mathrm{M}\}$. Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal to

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Sets Relations and Functions

Let the relation R on the set

M = {1, 2, 3, \dots, 16}

be given by

R = {(x, y) : 4 y = 5 x - 3, x, y \in M}

.
Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal to

Answer: (B)

The condition

4 y = 5 x - 3

forces

5 x \equiv 3 (mod 4)

, i.e.

x \equiv 3 (mod 4)

, so

x \in {3, 7, 11, 15}

. Checking that

y

also lies in

M

x = 3 \Rightarrow y = 3

x = 7 \Rightarrow y = 8

x = 11 \Rightarrow y = 13

, while

x = 15 \Rightarrow y = 18 \in / M

. Thus

R = {(3, 3), (7, 8), (11, 13)}

. The pair

(3, 3)

is already symmetric, but

(7, 8)

and

(11, 13)

require their reverses

(8, 7)

and

(13, 11)

. The minimum number of elements to be added is

2

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option