JEE Math Practice Question

If the local maximum value of the function $$f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0, \frac{\pi}{2}\right)$$ , is $$\frac{k}{e}$$, then $$\left(\frac{k}{e}\right)^{8}+\frac{k^{8}}{e^{5}}+k^{8}$$ is equal to

1. A.$$e^{3}+e^{6}+e^{10}$$
2. B.$$e^{3}+e^{5}+e^{11}$$
3. C.$$e^{3}+e^{6}+e^{11}$$
4. D.$$e^{5}+e^{6}+e^{11}$$