The remainder when $(2021)^{2022} + (2022)^{2021}$ is divided by $7$ is:

The remainder,when $3^{2003}$ is divided by $28$,is

The remainder,when $7^{103}$ is divided by $23$,is equal to:

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 $........$.

If $n \in N$,then ${11^{n + 2}} + {12^{2n + 1}}$ is divisible by

If $2(4^{2n+1}) + 3^{3n+1}$ is divisible by $k$,where $k > 1$,for all $n \in N$,then the value of $k$ is: