JEE Main 2020MathematicsBinomial TheoremMediumMCQ

JEE Main 2020 — Binomial Theorem Question with Solution

JEE Main 2020 (04 Sep Shift 2)

Question

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of 1+xn+5 are in the ratio 5:10:14, then the largest coefficient in the expansion is :

Choose an option

Show full solutionCorrect option: A
Correct answer
A462

Step-by-step explanation

Let three consecutive terms are Tr, Tr+1, Tr+2
So, Cr-1n+5Crn+5=510 and Crn+5Cr+1n+5=1014

Using property CrnCr-1n=n-r+1r, we have

n+5-r+1r=2 and n+5-r+1+1r+1=75

⇒n-3r+6=0 and 5n-12r+18=0

Solving both equations, n=6, r=4
Hence, the greatest coefficient will be of middle term, which is =C5n+5=C511=462

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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.