JEE Main 2013MathematicsBinomial TheoremHardMCQ

JEE Main 2013 — Binomial Theorem Question with Solution

JEE Main 2013 (07 Apr)

Question

The term independent of x in the expansion of x+1x2/3-x1/3+1-x-1x-x1/210  is

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Show full solutionCorrect option: A
Correct answer
A210

Step-by-step explanation

We know, x2/3-x1/3+1x1/3+1=x+1

⇒x+1x2/3-x1/3+1=x1/3+1

Also, x-1x-x=x-1x+1xx-1=x+1x=1+x-1/2

Hence, the given binomial becomes x1/3-x-1/210.

General term =10Cr-1rx10-r3x-r2

Hence, for term independent of x.

 We get 10-r3=r2

20-2r=3r

r=4
∴ Term Independent of x=10C4=210
 

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About this question

This is a previous-year question from JEE Main 2013, 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.