JEE Main 2016MathematicsBinomial TheoremHardMCQ

JEE Main 2016 — Binomial Theorem Question with Solution

JEE Main 2016 (09 Apr Online)

Question

For x ∈R, x≠-1, if 1+x2016+x1+x2015+x21+x2014+…+x2016= ∑ i=0 2016 a i x i , then a17 is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A2017!17!2000!

Step-by-step explanation

S=1+x2016+x1+x2015+x21+x2014+……+x20151+x+x2016  ...i

x1+x S=x 1+x2015+x21+x2014+…+x2016+x20171+x  ...ii

ii-i

S1+x=1+x2016-x20171+x

∴ S=1+x2017-x2017

Coefficient a17=2017C17 =2017!17!2000!

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 2016, 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.