Simplify

$\frac{11^{\frac{1}{3}}}{11^{\frac{1}{5}}}$

Insert a rational number and an irrational number between the following:

$\frac{1}{3}$ and $\frac{1}{2}$

Convert following rational numbers in decimal form and state the kind of its decimal expansion

$\frac{37}{60}$

State whether the following statements are true or false

Every whole number is a rational number.

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 : (Final answer only)

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