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Q.

Suppose A1,A2,A3,…….,A30  are thirty sets each having 5 elements and  B1,B2,……,Bn,  are n sets each with 3 elements. Let  ∪i=130Ai=∪j=1nBj=S and each elements of S belongs to exactly 10 of the  Ai′s and exactly 9 of the  Bj′s. Then n is equal to

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a

15

b

3

c

45

d

None of these

answer is C.

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Detailed Solution

O(S)=O(∪i=130Ai)=110(5×30)=15Since, element in the union S belongs to 10 of Ai′sAlso, O(S)=O(∪j=1nBj)=3n9=n3,∴n3=15⇒n=45
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