JEE Main 2021MathematicsSets and RelationsMediumMCQ

JEE Main 2021 — Sets and Relations Question with Solution

JEE Main 2021 (27 Jul Shift 2)

Question

Let N be the set of natural numbers and a relation R on N be defined by R=x,y∈N×N:x3-3x2y-xy2+3y3=0. Then the relation R is

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Show full solutionCorrect option: B
Correct answer
Breflexive but neither symmetric nor transitive

Step-by-step explanation

x3-3x2y-xy2+3y3=0

⇒xx2-y2-3yx2-y2=0

⇒x-3yx-yx+y=0

Now, x=y ∀x,y∈N×N so its a reflexive relation.
But not symmetric & transitive

Since, 3,1 satisfies but 1,3 does not.

Also 3,1&1,-1 satisfies but 3,-1 does not.

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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.