If the greatest value of the term independent of in the expansion of ${\left( {{\rm{x sin}}\alpha + a\frac{{\cos \alpha }}{{\rm{x}}}} \right)^{10}}$ is $\frac{{10!}}{{{{(5!)}^2}}},$ then the value of $a$ is equal to

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

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Application +4 | -1

If the greatest value of the term independent of in the expansion of

{\left( {\mathrm{x sin}\alpha + a\frac{{\cos \alpha }}{\mathrm{x}}} \right)^{10}}

\frac{{10!}}{{{{(5!)}^2}}},

then the value of

a

is equal to

View answer and explanation

Correct option: D

Option D (2) is correct because the greatest value of the term independent of x is achieved when sin(2α)=1, leading to a=2 after solving the equation.

More Questions from BINOMIAL THEOREM

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\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

equals If

a

and

d

are two complex numbers, then the sum to

\left( {n + 1} \right)

terms of the following series

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

is The number of different terms in the expansion of

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

is The sum of the coefficient of the binomial expansion of

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

is equal to 6561 . The constant term in the expansion is The coefficient of

{x^5}

in the expansion of

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

is If

\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

, then

n

equals