JEE Main 2026 Apr 6 Shift 1, Mathematics Q8: Properties Of Binomial Coefficient

JEE Main2026Apr 6, Shift 1Mathematics

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

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

Solution

In $(1 + α x)^{26}$ the middle term is the $1 4^{th}$ : coefficient is $(13 26) α^{13}$ .

In $(1 - α x)^{28}$ the middle term is the $1 5^{th}$ : coefficient is $(14 28) α^{14}$ .

Setting them equal: $(13 26) α^{13} = (14 28) α^{14}$ , so $α = \frac{( 13 26 )}{( 14 28 )}$ .

Using $(14 28) = \frac{28 \cdot 27}{14 \cdot 14} (13 26)$ , we get $α = \frac{14 \cdot 14}{28 \cdot 27} = \frac{7}{27}$ .

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JEE Main 2026 Apr 6 Shift 1, Mathematics Q8: Properties Of Binomial Coefficient

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