JEE Main 2022MathematicsSets and RelationsHardNumerical

JEE Main 2022 — Sets and Relations Question with Solution

JEE Main 2022 (26 Jun Shift 1)

Question

Let A=n∈ N:H.C.F. n,45=1 and let B=2k:k∈1,2,…,100. Then the sum of all the elements of A∩B is _____.

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Show full solutionCorrect answer: 5264
Correct answer
5264

Step-by-step explanation

Here B=2,4,6,8....,200

Sum of elements in A∩B

=2+4+6+…+200⏟Multiple of 2-6+12+…+198⏟Multiple of 2 & 3 i.e. 6

-10+20+…+200⏟Multiple of 5 & 2 i.e. 10+30+60+…+180⏟Multiple of 2,5 & 3 i.e. 30

=2100×1012-633×342-1020×212+306×72

=5264

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About this question

This is a previous-year question from JEE Main 2022, 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.