JEE Main 2022MathematicsSets and RelationsMediumMCQ

JEE Main 2022 — Sets and Relations Question with Solution

JEE Main 2022 (29 Jul Shift 1)

Question

Let R be a relation from the set 1,2,3………,60 to itself such that R={a,b:b=pq, where p,q≥3 are prime numbers}. Then, the number of elements in R is

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Show full solutionCorrect option: B
Correct answer
B660

Step-by-step explanation

Given b=pq where p & q are prime numbers ≥3 and 1≤pq≤60

If p=3,q=3,5,7,11,13,17,19

And if p=5   q=5,7,11 and so on,

So, b will be 3×3,3×5,3×7,3×11,3×13,3×17,3×19,5×5,5×7,5×11,7×7

i.e. total 11 possibilities

Now a can be 1,2,⋯,60

i.e. total 60 possibilities

Hence, the number of relations =60×11=660

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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.