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:: Relation (Mathematics)

JEE Mains 29^{th\ }$ July $1^{st\ }$ Shift 2022 29th July Shift 1

Mathematics

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 \geq 3

are prime numbers\}. Then, the number of elements in

R

is:

600

660

540

720

Correct Answer:

(b) :

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

, where

p,q \geq 3

are prime numbers\}\\ Number of possible values of

a = 60

\\ For

b = pq

, if

p = 3,q = 3,5,7,11,13,17,19

\\ If

p = 5,q = 5,7,11

; if

p = 7,q = 7

\therefore\

Number of elements in

R = 60(7 + 3 + 1) = 660

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