Simplify the following expression: $(\sqrt{11}-\sqrt{3})^{2}$

Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{\frac{9}{27}}$
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}$

Find the value of $a$ :
$\frac{3-\sqrt{5}}{3+2 \sqrt{5}}=a \sqrt{5}-\frac{19}{11}$

For each question,select the proper option from four options given,to make the statement true: $\frac{\sqrt{50}}{\sqrt{98}}$ is a $\ldots \ldots \ldots$ number.

Simplify: $\frac{7 \sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2 \sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3 \sqrt{2}}{\sqrt{15}+3 \sqrt{2}}$

The value of $1.999...$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0,$ is