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

Question

Accepted Answer

"$${T_{r + 1}} = {}^{10}{C_r}{(x\sin \alpha )^{10 - r}}{\left( {{{a\cos \alpha } \over x}} \right)^r}$$

r = 0, 1, 2, ......., 10

T_{r + 1} will be independent of x when 10 $-$ 2r = 0 $\Rightarrow$ r = 5

$${T_6} = {}^{10}{C_5}{(x\sin \alpha )^5} \times {\left( {{{a\cos \alpha } \over x}} \right)^5}$$

$= {}^{10}{C_5} \times {a^5} \times {1 \over {{2^5}}}{(\sin 2\alpha )^5}$

will be greatest when sin2$\alpha$ = 1

$\Rightarrow {}^{10}{C_5}{{{a^5}} \over {{2^5}}} = {}^{10}{C_5} \Rightarrow a = 2$"

If the greatest value of the term independent of 'x' in the

expansion of ${\left( {x\sin \alpha + a{{\cos \alpha } \over x}} \right)^{10}}$ is ${{10!} \over {{{(5!)}^2}}}$, then the value of 'a' is equal to :

Solution

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

Solution

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More Binomial Theorem questions

Drill 25 more like these. Every day. Free.

If the greatest value of the term independent of 'x' in the

expansion of ${\left( {x\sin \alpha + a{{\cos \alpha } \over x}} \right)^{10}}$ is ${{10!} \over {{{(5!)}^2}}}$, then the value of 'a' is equal to :