JEE Main 2026 · 6 Apr · Shift 1 · Mathematics Q8

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If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}$ , $\alpha\ne0$ , are equal, then the value of $\alpha$ is:

\dfrac{14}{13}

\dfrac{27}7

\dfrac7{27}

Answer and worked solution

Official answer: D

Middle terms.

$(1+\alpha x)^{26}$ : $T_{14}$ , coefficient $\binom{26}{13}\alpha^{13}$ .
$(1-\alpha x)^{28}$ : $T_{15}$ , coefficient $\binom{28}{14}\alpha^{14}$ .

Equate.
$\alpha=\frac{\binom{26}{13}}{\binom{28}{14}}=\frac{14\cdot14}{28\cdot27}=\frac7{27}.$

(D)

Topics:General and middle terms

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JEE Main 2026 · 6 Apr · Shift 1, Mathematics question 8