Suppose A1,A2,…,A30are thirty sets each having 5 elements and B1,B2,…,Bn are n sets each with 3 elements let ∪i=130 Ai=∪j=1n Bi=S and each element of S belongs to exactly 10 of the Ai′s and exactly 9 of the Bi′s.Then n is equal to 

Suppose A1,A2,,A30are thirty sets each having 5 elements and B1,B2,,Bn are n sets each with 3 elements let i=130Ai=j=1nBi=S and each element of S belongs to exactly 10 of the Ais and exactly 9 of the Bis.Then n is equal to 

  1. A
  2. B
  3. C
  4. D

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    S=A1A2A30=B1B2Bn

    Since each Ai contains 5 elements, number of elements in S (with repetitions) = 5 x 30 = 150

    But each element of S appears exactly 10 times.

     Number of distinct elements in S=15010=15

    Similarly by other union of Bis number of distinct elements in S=3n9

    Now, 3n9=15n=45

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.