JEE Main 2016 — Binomial Theorem Question with Solution
From: JEE Main 2016 (Online) 9th April Morning Slot
Question
For x R, x -1,
if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + . . . . + x2016 =
then a17 is equal to :
if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + . . . . + x2016 =
then a17 is equal to :
Choose an option
Show full solutionCorrect option: A
Correct answer
A
Step-by-step explanation
Assume,
P = (1 + x)2016 + x(1 + x)2015 + . . . . .+ x2015 . (1 + x) + x2016 . . . . .(1)
Multiply this with
x(1 + x)2015 + x2(1 + x)2014 +
. . . . . . + x2016 + . . . . . (2)
Performing (1) (2), we get
(1 + x)2016
P = (1 + x)2017 x2017
a17 = coefficient of x17 2017C17
P = (1 + x)2016 + x(1 + x)2015 + . . . . .+ x2015 . (1 + x) + x2016 . . . . .(1)
Multiply this with
x(1 + x)2015 + x2(1 + x)2014 +
. . . . . . + x2016 + . . . . . (2)
Performing (1) (2), we get
(1 + x)2016
P = (1 + x)2017 x2017
a17 = coefficient of x17 2017C17
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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.