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  • The coefficient of the middle term in the binomial expansion in powers of x of n

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  equals

Option: 1

\frac{3}{5}


Option: 2

\frac{10}{3}


Option: 3

\frac{-3}{10}


Option: 4

\frac{-3}{10}


Answers (1)

best_answer

Middle term in expansion of \left(1+\alpha x^4\right)={ }^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 \quad \alpha=-3 / 10
 

Posted by

vishal kumar

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