JEE Main 2022 (Online) 29th July Morning ShiftQuestion 1
Let $R$ be a relation from the set $\{1,2,3,\ldots,60\}$ to itself such that $R=\{(a,b):b=pq$, where $p,q\ge3$ are prime numbers$\}$. Then, the number of elements in $R$ is :
Sets, Relations and Function
Solution
Possible $b=pq\le60$ with primes $p,q\ge3$: $9,15,21,25,33,35,39,49,51,55,57$ (11 values). Each such $b$ pairs with any $a\in\{1,\dots,60\}$, so $|R|=11\times60=660$. Option (B).