JEE Main 2020 — Binomial Theorem Question with Solution
From: JEE Main 2020 (Online) 7th January Morning Slot
Question
If the sum of the coefficients of all even powers of x in the product
(1 + x + x2 + ....+ x2n)(1 - x + x2 - x3 + ...... + x2n) is 61, then n is equal to _______.
(1 + x + x2 + ....+ x2n)(1 - 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
(1 + x + x2
+ ....+ x2n)(1 - x + x2 - x3 + ...... + x2n)
= a0 + a1x + a2x2 + …..
put x = 1
(2n + 1)1 = a0 + a1 + a2 + …… (1)
put x = –1
1(2n + 1) = a0 – a1 + a2+ …….. (2)
Adding (1) and (2)
4n + 2 = 2(a0 + a2 + ….. )
4n + 2 = 2 61
n = 30
= a0 + a1x + a2x2 + …..
put x = 1
(2n + 1)1 = a0 + a1 + a2 + …… (1)
put x = –1
1(2n + 1) = a0 – a1 + a2+ …….. (2)
Adding (1) and (2)
4n + 2 = 2(a0 + a2 + ….. )
4n + 2 = 2 61
n = 30
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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.