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  • The greatest value of the term independent of x in the expansion of  (x sin<

The greatest value of the term independent of x in the expansion of  (x sina + x-1cosa)10 , is

Option: 1

25


Option: 2

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


Option: 3

\frac{1}{2^5 }\cdot \frac{10 !}{(5!)^2 }


Option: 4

none of these 


Answers (1)

best_answer

T_{r+1} = ^{10 } C_r (x \sin \alpha )^{10 - r } \cdot \left ( \frac{\cos \alpha }{x} \right )^r

It is independent of x if r = 5.

The term independent of x = 10C5 . sin5a . cos5a

= ^{10 } C _5 \cdot \frac{1}{2^5 } (\sin 2 \alpha ) ^5 \leq ^{10}C_5 \cdot \frac{1}{2^5} .

Posted by

Irshad Anwar

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