Answer : Option D

Explanation :

$MF#%\begin{align}&\dfrac{\sqrt{7}}{2} - \dfrac{10}{\sqrt{7}} + \sqrt{175}\\\\
&= \dfrac{\sqrt{7}}{2} - \dfrac{10}{\sqrt{7}} + \sqrt{7 \times 25}\\\\
&= \dfrac{\sqrt{7}}{2} - \dfrac{10}{\sqrt{7}} + 5\sqrt{7}\\\\
&=\dfrac{\left(\sqrt{7}\right)^2 - (2 \times 10) + (5\sqrt{7} \times 2\sqrt{7}) }{2\sqrt{7}}\\\\
&=\dfrac{7 - 20 + 70 }{2\sqrt{7}} = \dfrac{57}{2\sqrt{7}} \\\\&= \dfrac{28.5}{\sqrt{7}}
= \dfrac{28.5}{2.645} = \dfrac{28500}{2645} = 10.77\end{align}$MF#%

$MF#%\text{Please note that }\dfrac{57}{2\sqrt{7}}\text{ can be solved further in the below lines as well}
$MF#%

$MF#%\dfrac{57}{2\sqrt{7}} = \dfrac{57 \times \sqrt{7}}{2\sqrt{7} \times \sqrt{7}} = \dfrac{57\sqrt{7}}{14} \\\\
= \dfrac{57 \times 2.645}{14} = \dfrac{150.765}{14} = 10.77$MF#%