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

If the greatest divisor of $30 \cdot 5^{2n} + 4 \cdot 2^{3n}$ is $p, \forall n \in N$ and that of $2^{2n+1} - 6n - 2$ is $q, \forall n \in N$, then $p+q=$

Let $n \in \mathbb{N}$. Which one of the following is true?

If $X = \{ 8^n - 7n - 1 : n \in N \}$ and $Y = \{ 49(n - 1) : n \in N \}$,then

If the remainder when $x$ is divided by $4$ is $3$,then the remainder when $(2020+x)^{2022}$ is divided by $8$ is ....... .

Using the binomial theorem,prove that $6^{n} - 5n$ always leaves a remainder of $1$ when divided by $25$ for all $n \in N$.