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  • The greatest value of the term independent of x in the expansion of <img alt="\left(x \sin a+x^{-1} \cos a\right)^{10}" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28x%20%5Csin

The greatest value of the term independent of x in the expansion of \left(x \sin a+x^{-1} \cos a\right)^{10} is

Option: 1

\frac{10 !}{6 ! \cdot 4 !}


Option: 2

\frac{10 !}{5 ! \cdot 5 !}


Option: 3

{2^{5}} \cdot \frac{10 !}{5 ! \cdot 5 !}


Option: 4

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


Answers (1)

best_answer

On expansion we can see that for r=5 terms will be independent of x

^{10} C_{5}(x \sin a)^{5} \cdot\left(x^{-1} \cos a\right)^{5}=^{10} C_{5} \;(\sin a \cdot \cos a)^{5} 

The maximum value of sin a \times cos a = 1/2 (As it equals 1/2 * sin(2a))

hence,  ^{10} C_{5} \;(\sin a \cdot \cos a)^{5}=\frac{1}{2^{5}} \cdot \frac{10 !}{5 ! \cdot 5 !} is the answer.

 

option D is correct

Posted by

Devendra Khairwa

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