A) 2
B) 3
C) 4
D) None of these
Correct Answer: A
Solution :
\[\frac{\frac{1}{\sqrt{9}}-\frac{1}{\sqrt{11}}}{\frac{1}{\sqrt{9}}+\frac{1}{\sqrt{11}}}\times \frac{10+\sqrt{99}}{x}=\frac{1}{2}\] \[\Rightarrow \] \[\frac{11\sqrt{9}-9\sqrt{11}}{11\sqrt{9}+9\sqrt{11}}\times \frac{10+\sqrt{99}}{x}=\frac{1}{2}\] \[\Rightarrow \] \[\frac{{{(11\sqrt{9}-\sqrt{11})}^{2}}}{1089+891}\times 10+\sqrt{99}\times 2=x\] \[\Rightarrow \] \[x=\frac{2(1089+891)-198\sqrt{99})(10+\sqrt{99)}}{198}\] \[\Rightarrow \] \[x=(10-\sqrt{99})(10+\sqrt{99})\] \[=2(100-99)=2\]
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