JEE Main 2020MathematicsBinomial TheoremHardNumerical

JEE Main 2020 — Binomial Theorem Question with Solution

JEE Main 2020 (07 Jan Shift 1)

Question

If the sum of the coefficients of all even powers of x in the product 1+x+x2+…+x2n1-x+x2-x3+…+x2n is 61, then n is equal to

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Show full solutionCorrect answer: 30
Correct answer
30

Step-by-step explanation

Let 1-x+x2..1+x+x2…=a0+a1×a2x2+…
Put x=1,
12n+1=a0+a1+a2+..a2n  …2
Put x=-1
2n+1×1=a0-a1+a2+..a2n  …2
From 1+2
4n+2=2a0+a2+…
=2×61
⇒2n+1=61⇒n=30

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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.