Q.

Let  R  be a relation  from  the set  {1,2,3……..,60} to itself  such that  R ={(a,b): b=pq, where p,q3 are  prime numbers } .Then , the number  of   elements  in  R is

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a

660

b

600

c

720

d

540

answer is B.

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Detailed Solution

Now  numbers  of   possible  values   of  a =60,  for  b=pq
If    p=3, q=3,5,7,11,13,17,19
Total  cases =7 
If  p=  5q =5,7,11                  total case =3 
If p=7q  =7                            total case =1
Possible  value of    7+3+1=11 and a  =60
Total cases  a×b=60×11=660

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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