The difference between an integer and its cube is divisible by

The remainder when $5^{99}$ is divided by $13$ is

The $50^{\text{th}}$ root of a number $x$ is $12$ and the $50^{\text{th}}$ root of another number $y$ is $18$. Then the remainder obtained on dividing $(x + y)$ by $25$ is $........$.

The remainder obtained when $5^{99}$ is divided by $13$ is

If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$,then $k$ is equal to

$\sqrt {\underbrace {111........1}_{200\,\text{digits}} - \underbrace {222.......2}_{100\,\text{digits}}} $ equals :-