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If the greatest value of the term independent of ' x ' in the expansion of \left(x \sin \alpha+a \frac{\cos \alpha}{x}\right)^{10} is \frac{10 !}{(5 !)^{2}}, then the value of ' a ' is equal to
Option: 1 -1
Option: 2 1
Option: 3 -2
Option: 4 2

Answers (1)

best_answer

General \, Term= \, ^{10}C_{r}\, x^{10-r}\left ( \sin \alpha \right )^{10-r}\, ( \frac{a^{r}.\left ( \cos \alpha \right )^{r}}{x^{r}})

For  term independent of x

10-r-r= 0\Rightarrow r= 5

Term\, is\, ^{10}C_{5}\cdot a^{5}\left ( \sin \alpha \cos \alpha \right )^{5}
As\, \sin \alpha \cos \alpha = \frac{1}{2}\sin 2\alpha,so\, its\, greatest\, value\, is\, \frac{1}{2}
\therefore greatest\, value\, of\, the\, term= \, ^{10}C_{5}\cdot \frac{a^{5}}{2^{5}}
Comparing with given max value a^{5}= 2^{5}\Rightarrow a= 2

Posted by

Kuldeep Maurya

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