JEE Main 2020MathematicsSets and RelationsHardNumerical

JEE Main 2020 — Sets and Relations Question with Solution

JEE Main 2020 (07 Jan Shift 2)

Question

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.

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Show full solutionCorrect answer: 29
Correct answer
29

Step-by-step explanation

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.

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About this question

This is a previous-year question from JEE Main 2020, covering the Sets and Relations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.