Answer : Option B

Explanation :

$MF#%\begin{align}&\left[\dfrac{\dfrac{1}{\sqrt{9}}-\dfrac{1}{\sqrt{11}}}{\dfrac{1}{\sqrt{9}}+\dfrac{1}{\sqrt{11}}}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{\sqrt{11}-\sqrt{9}}{\sqrt{11}+\sqrt{9}}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{\left(\sqrt{11}-\sqrt{9}\right)\left(\sqrt{11}-\sqrt{9}\right)}{\left(\sqrt{11}+\sqrt{9}\right)\left(\sqrt{11}-\sqrt{9}\right)}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{\left(\sqrt{11}-\sqrt{9}\right)^2}{11-9}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{11-2\sqrt{11}\sqrt{9}+9}{2}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{20-2\sqrt{99}}{2}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left(10-\sqrt{99}\right)+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \dfrac{\left(10-\sqrt{99}\right) \left(10+\sqrt{99}\right)}{x}=\dfrac{1}{2}\\\\
&\Rightarrow \dfrac{\left(100-99\right)}{x}=\dfrac{1}{2}\\\\
&\Rightarrow \dfrac{1}{x}=\dfrac{1}{2}\\\\
&\Rightarrow x=2\end{align}$MF#%