The difference between an integer and its cube is divisible by

For all positive integers $k$, if the greatest divisor of $25^k+12k-1$ is $d$, then $4\sqrt{d}=$

The remainder when $(11)^{1011} + (1011)^{11}$ is divided by $9$ is

The remainder on dividing $1+3+3^{2}+3^{3}+\ldots+3^{2021}$ by $50$ is

The remainder when $7^{2022} + 3^{2022}$ is divided by $5$ is:

Given below are two statements:
Statement $I$: $25^{13} + 20^{13} + 8^{13} + 3^{13}$ is divisible by $7$.
Statement $II$: The integral part of $(7 + 4\sqrt{3})^{25}$ is an odd number.
In the light of the above statements, choose the correct answer from the options given below: