JEE Main 2020MathematicsBinomial TheoremMediumNumerical

JEE Main 2020 — Binomial Theorem Question with Solution

JEE Main 2020 (05 Sep Shift 1)

Question

The natural number m, for which the coefficient of x in the binomial expansion of  xm+1x222 is 1540, is

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Show full solutionCorrect answer: 13
Correct answer
13

Step-by-step explanation

The general term in the binomial expansion,

Tr+1=Cr22xm22-rx-2r

⇒Tr+1=Cr22xm(22-r)-2r

For the coefficient of x

22 m-m r-2 r=1

⇒22 m-1=r(m+2)

⇒r=22m-1m+2

⇒r=22m+44-45m+2

r=22-3.3.5m+2⇒22-r=3·3·5m+2

Since, Cr22=C22-r22

So possible values of m=1,3,7,13,43, but C322=1540⇒22-r=3⇒m=13

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About this question

This is a previous-year question from JEE Main 2020, 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.