If the local maximum value of the function f ( x ) = ( 3 e 2 sin x ) sin 2 x , x ( 0 , 2 ) is k e , then ( k e ) 8 + k 8 e 5 + k 8 is equal to [2023]

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Solution

Q.
If the local maximum value of the function $f (x) = {(\frac{\sqrt{3 e}}{2 \sin x})}^{\sin^{2} x}, x \in (0, \frac{π}{2})$ is $\frac{k}{e}$ , then ${(\frac{k}{e})}^{8} + \frac{k^{8}}{e^{5}} + k^{8}$ is equal to [2023]

1 $e^{3} + e^{5} + e^{11}$

2 $e^{3} + e^{6} + e^{10}$

3 $e^{5} + e^{6} + e^{11}$

4 $e^{3} + e^{6} + e^{11}$

Ans.
(4)

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