Basic Maths — NDA Mathematics PYQs

If $k<(\sqrt{2}+1{)}^3<k+2$, where $k$ is a natural number, then what is the value of $k$?

Let $y=x!$ and $z=(2x)!$. If $\frac{z}{y}=120$, then what is the value of $(3x)!$?

Let $n$ be a natural number. The number of consecutive zeros at the end of the expansion of $n!$ is exactly $2$. How many values of $n$ are possible?

What is the remainder when $5^{99}$ is divided by $13$?