Suppose A and B are the coefficients of 30 th and 12 th terms respectively in the binomial expansion of (1+x) 2 n-1 . If 2 A=5 B , then n is equal to:

Mathematics · Binomial Theorem

JEE Main 2025 — 24 January, Evening Shift — Question 11

Suppose $A$ and $B$ are the coefficients of $30^{\text {th }}$ and $12^{\text {th }}$ terms respectively in the binomial expansion of $(1+x)^{2 n-1}$ . If $2 A=5 B$ , then $n$ is equal to:

Option A:
22
Option B:
21
Correct
Option C:
20
Option D:
19

Answer: B

Step-by-step solution

$\mathrm{A}={ }^{2 \mathrm{n}-1} \mathrm{C}_{29} \quad \mathrm{~B}={ }^{2 \mathrm{n}-1} \mathrm{C}_{11}$

$2{ }^{2 n-1} C_{29}=5{ }^{2 n-1} C_{11}$

$2 \frac{(2 n-1)!}{29!(2 n-30)!}=5 \frac{(2 n-1)!}{(2 n-12)!11!}$

$\frac{1}{29 \ldots 12 \cdot 5}=\frac{1}{(2 n-12)(2 n-13) \ldots(2 n-29).{2}}$

$\frac{1}{30 \cdot 29 \ldots 12}=\frac{1}{(2 n-12)(2 n-13) \ldots(2 n-29) 12}$

$2 \mathrm{n}-12=30$

$\mathrm{n}=21$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 24 January, Evening Shift
Subject: Mathematics
Chapter: Binomial Theorem
Topic: Binomial Coefficients