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

JEE Main 2022 Mathematics question

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

(1)600
(2)660Correct
(3)540
(4)720

Answer: (2)

Solution

The relation counts pairs (a, b) with b = pq, p, prime and . The possible values of b are 9, 15, 21, 33, 39, 51, 57 , 25, 35,

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Question ID VK-035136