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Suppose, A(1),A(2),"……..",A(30) are thir...

Suppose, `A_(1),A_(2),"……..",A_(30)` are thirty sets each having 5 elements and `B_(1), B_(2), B_(n)` sets each with 3 elements, let `underset(i=1)overset(30)(uu) A_(i) = underset(j=1)overset(n)(uu) B_(j) =S` and each element of S belongs to exactly 10 of the `A_(i)'s` and exactly 9 of the ` B_(j)'s`. Then, n is equal to

A

pm=nq

B

`alphapm=betanq`

C

`betapm=alphanq`

D

`(pm)^(beta)=(nq)^(alpha)`

Text Solution

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The correct Answer is:
C
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  • Suppose A_(1),A_(2),……,A_(20) are twenty sets each having 5 elemennts and B_(1),B_(2),………..,B_(n) are n sets each having 2 elements. Let U_(i=1)^(20)A_(i)=S=U_(f=1)^(n)B_(f) . If each element of S belong to exactly 10 of the A_(i)^(')s and to exactly 4 of the B_(i)^(')s then n is (i) 10 (ii) 20 (iii) 100 (iv) 50

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