Let A = 2 , 3 , 4 , 5 , … . , 30 and ' ≃ ' be an equivalence relation on A × A ,…

Let A=2,3,4,5,….,30 and '≃' be an equivalence relation on A×A, defined by a,b≃c,d, if and only if ad=bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair 4,3 is equal to :
  1. 5
  2. 6
  3. 8
  4. 7

Solution

A=2,3,4,5,…,,30

a,b=c,d⇒ad=bc

4,3=c,d ⇒ 4d=3c

⇒43=cd

cd=43 & c,d∈2,3,……,30

c, d =4,3,8,6,12,9,16,12,20,15,24,18,28,21

No. of ordered pair =7

Asked in: JEE Main 2021 (16 Mar Shift 2)

Practice more Sets and Relations questions on Aicharya