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

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

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Application +4 | -1

The coefficient of the middle term in the binomial expansion in powers of

x

{(1 + \mathrm{\alpha }x)^4}

and of

{(1 - \mathrm{\alpha }x)^6}

is the same, if

\alpha

equals

View answer and explanation

Correct option: C

- \frac{3}{{10}}

Option C (

- \frac{3}{{10}}

) is correct because it is the value of

\alpha

that makes the coefficients of the middle terms in the two binomial expansions equal.

Practice All Chapter MCQs →

\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n