JEE Main 2021MathematicsSets and RelationsHardMCQ

JEE Main 2021 — Sets and Relations Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

Let Z be the set of all integers,
A=(x,y)∈Z×Z:(x−2)2+y2≤4

B=(x,y)∈Z×Z:x2+y2≤4 and 

C=(x,y)∈Z×Z:(x−2)2+(y−2)2≤4
If the total number of relations from A∩B to A∩C is 2p, then the value of p is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A25

Step-by-step explanation

A=(x,y)∈Z×Z;(x−2)2+y2≤4

B=(x,y)≤Z×Z;x2+y2≤4

C=(x,y)∈Z×Z;(x−2)2+(y−2)2≤4

Here, we can see from the above diagram A∩B={(0,0),(1,0),(2,0),(1,1),(1,-1)}⇒n(A∩B)=5

Similarly n(A∩C)=5

Relation from A∩B to A∩C=25×5=2p

⇒p=25

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About this question

This is a previous-year question from JEE Main 2021, 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.