If the coefficients of the middle terms in the binomial expansions of (1 + α x) 26 and (1 - α x) 28 , α≠0, are equal, then the value of α is:

Mathematics · Binomial Theorem

JEE Main 2026 — 6 April, Morning Shift — Question 28

If the coefficients of the middle terms in the binomial expansions of $(1 + \alpha x)^{26}$ and $(1 - \alpha x)^{28}$ , $α≠0,$ are equal, then the value of $α$ is:

Option A:
1
Option B:
$\frac{14}{13}$
Option C:
$\frac{27}{7}$
Option D:
$\frac{7}{27}$
Correct

Answer: D

Step-by-step solution

$(1+\alpha x)^{26}$ Middle term, $\mathrm{T}_{14}={ }^{26} \mathrm{C}_{13} \alpha^{13}$ For $(1-\alpha \mathrm{x})^{28}$ Middle term $={ }^{28} \mathrm{C}_{14} \alpha^{14}$ $\Rightarrow{ }^{26} \mathrm{C}_{13} \alpha^{13}={ }^{28} \mathrm{C}_{14} \alpha^{14}$ $\Rightarrow{ }^{26} \mathrm{C}_{13}={ }^{28} \mathrm{C}_{14} \alpha$ $\Rightarrow{ }^{26} \mathrm{C}_{13}=\frac{28}{14} \times \frac{27}{14} .{ }^{26} \mathrm{C}_{13} \alpha$ $\Rightarrow \alpha=\frac{7}{27}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 6 April, Morning Shift
Subject: Mathematics
Chapter: Binomial Theorem
Topic: Introduction to Binomial Theorem