Let R be a relation from the set $\{1,2,3 \ldots \ldots \ldots, 60\}$ to itself such that $\mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}=\mathrm{pq}$, where $\mathrm{p}, \mathrm{q} \geq 3$ are prime numbers $\}$. Then, the number of elements in R is :

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Sets Relations and Functions

Let R be a relation from the set

{1, 2, 3 \dots\dots\dots, 60}

to itself such that

R = {(a, b) : b = pq

, where

p, q \geq 3

are prime numbers

}

. Then, the number of elements in R is :

Answer: (B)

For each value of

a

from 1 to 60, we count the possible values of

b = pq

where

p, q \geq 3

are primes.

Prime pairs:

Total distinct

b

values = 11.

Since

a

can take 60 values independently, total elements in R =

60 \times 11 = 660

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Single correct option