JEE Main 2021MathematicsBinomial TheoremEasyNumerical

JEE Main 2021 — Binomial Theorem Question with Solution

JEE Main 2021 (31 Aug Shift 1)

Question

If 3644k is the term, independent of x, in the binomial expansion of x4-12x212, then k is equal to

Enter your answer

Show full solutionCorrect answer: 55
Correct answer
55

Step-by-step explanation

Given that x4-12x212

rth term of an expression is Tr+1 =Crnxn-ryr Tr+1=Cr12x412-r-12x2r=Cr121412-r(-12)r·x12-r-2r
⇒  12-3r=0
⇒  r=4

So term independent from x is T5=C412·148·34·44=C412·3444

We know that Crn=n!n-r!r!

=55×3644

They given that it is =k 3644

So required value of  k = 55.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Binomial Theorem chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.