JEE Main 2021MathematicsBinomial TheoremHardMCQ

JEE Main 2021Binomial Theorem Question with Solution

JEE Main 2021 (24 Feb Shift 2)

Question

If n2 is a positive integer, then the sum of the series C2n+1+2C22+C23+C24++C2n is

Choose an option

Show full solutionCorrect option: B
Correct answer
Bnn+12n+16

Step-by-step explanation

C2n+1+2C22+C23+C24++C2n

C2n+1+2C33+C23+C24++C2n

{use Cr+1n+Crn=Crn+1}

=C2n+1+2C34+C24+C35++C2n

=C2n+1+2C35+C25++C2n

=C2n+1+2C3n+C2n

=C2n+1+2·C3n+1

=n+1n2+2·n+1nn-12.3

=nn+12n+16

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About this question

This is a previous-year question from JEE Main 2021, covering the Binomial Theorem 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.