If $125^{x}=\frac{25}{5^{x}},$ then find the value of $x$.

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$\left(5^{-2}\right)^{3}=\ldots \ldots \ldots$

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

The rationalising factor of $4-\sqrt{5}$ is...........

Find the value of $b$ :

$\frac{\sqrt{2}+\sqrt{3}}{3 \sqrt{2}-2 \sqrt{3}}=2-b \sqrt{6}$

In each of the following numbers rationalise the denominator

$\frac{n^{2}}{\sqrt{m^{2}+n^{2}}+m}$

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$0.3 \overline{6}=$