Q50 / 75 · JEE Main 2020 (07 Jan Shift 2) · Mathematics

Let X=n∈N:1≤n≤50. If A=n∈X: n is a multiple of 2 and B=n∈X: n is a multiple of 7, then the number of elements in the smallest subset of X, containing both A and B, is.

Correct answer: 29

Solution

Here, A=2,4,6,....50 and B=7,14,...49

Required smallest subset is A∪B.

So, nA∪B=nA+nB-nA∩B
=25+7-3
=29.

Hence, the correct answer is 29.

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