JEE Main 2021 — Binomial Theorem Question with Solution
From: JEE Main 2021 (Online) 24th February Morning Shift
Question
The value of
-15C1 + 2.15C2 – 3.15C3 + ... - 15.15C15 + 14C1 + 14C3 + 14C5 + ...+ 14C11 is :
-15C1 + 2.15C2 – 3.15C3 + ... - 15.15C15 + 14C1 + 14C3 + 14C5 + ...+ 14C11 is :
Choose an option
Show full solutionCorrect option: D
Correct answer
D213 - 14
Step-by-step explanation
We know,
214 - 1
213
Also let, S = 14C1 + 14C3 + 14C5 + ...+ 14C11
S + 14C13 = 14C1 + 14C3 + 14C5 + ...+ 14C11 + 14C13
S + 14C13 = 213
S + 14 = 213
S = 213 - 14
Other Method :
We know,
Differentiating both sides with respect to x,
Put
We know,
214 - 1
213
Also let, S = 14C1 + 14C3 + 14C5 + ...+ 14C11
S + 14C13 = 14C1 + 14C3 + 14C5 + ...+ 14C11 + 14C13
S + 14C13 = 213
S + 14 = 213
S = 213 - 14
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This is a previous-year question from JEE Main 2021, 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.