JEE Main 2023 — Binomial Theorem Question with Solution
From: JEE Main 2023 (Online) 13th April Morning Shift
Question
Let be the constant term in the binomial expansion of . If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of is , then is equal to _____________.
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Show full solutionCorrect answer: 36
Correct answer
36
Step-by-step explanation
Given expression . Here, and .
The -th term of the binomial expansion of is given by
.
Substitute and in this formula, we get:
.
The constant term in the binomial expansion is obtained when the power of in the terms equals zero.
This happens when , which gives .
Now, for coefficient of
The -th term of the binomial expansion of is given by
.
Substitute and in this formula, we get:
.
The constant term in the binomial expansion is obtained when the power of in the terms equals zero.
This happens when , which gives .
Now, for coefficient of
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This is a previous-year question from JEE Main 2023, 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.