JEE Main 2014MathematicsSets and RelationsMediumMCQ

JEE Main 2014 — Sets and Relations Question with Solution

JEE Main 2014 (06 Apr)

Question

If X=4n-3n-1 : n∈N  and Y=9n-1 : n∈N, where N is the set of natural numbers, then X∪Y is equal to

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Show full solutionCorrect option: B
Correct answer
BY

Step-by-step explanation

X=4n-3n-1:n∈N

4n-3n-1=3+1n-3n-1

=nC03o1n+nC1311n-1+.....+nCn3n-3n-1

=1+n3+nC232+.....+3n-3n-1

=nC232+nC333+.....+3n

=32nC2+nC331+nC432+.....+3n-2

=9k, where k is a natural number.

Y=9n-1 : n∈N

∴  X⊆Y

∴  X∪Y=Y

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About this question

This is a previous-year question from JEE Main 2014, 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.