Coefficient of middle term in binomial expansion in powers of x of {(1 + α x)^4} and of {(1 - α x)

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7.Binomial Theorem

hard

The coefficient of the middle term in the binomial expansion in powers of $x$ of ${(1 + \alpha x)^4}$ and of ${(1 - \alpha x)^6}$ is the same if $\alpha $ equals

A

$\frac{3}{5}$

B

$\frac{{10}}{3}$

C

$\frac{{ - 3}}{{10}}$

D

$\frac{{ 3}}{{10}}$

(AIEEE-2004)

Solution

(c) Middle term in expansion of $(1 + \alpha {x^4}) = {\,^4}{C_2}{(\alpha x)^2}$

Middle term in expansion of ${(1 – \alpha x)^6} = {\,^6}{C_3}{( – \alpha x)^3}$

According to question, $^4{C_2}{\alpha ^2} = \, – \,{\,^6}{C_3}{\alpha ^3}$

$ \Rightarrow $ $\alpha = – 3/10$.

Standard 11

Mathematics

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