JEE Main 2021MathematicsBinomial TheoremEasyMCQ

JEE Main 2021 — Binomial Theorem Question with Solution

JEE Main 2021 (25 Jul Shift 2)

Question

The sum of all those terms which are rational numbers in the expansion of 213+31412 is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D43

Step-by-step explanation

rth term in the expansion of 213+31412 is 

Tr+1=Cr122r3·312-r4

Since, Tr+1 will be rational number, when r = 0,3,6,9,12 and r = 0,4,8,12 

⇒r=0,12 for rational term of the expansion

Therefore, T1+T13=1×33+1×24×1

=27+16

=43.

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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.