11. Find the smallest integer $n$ such that $n(\sqrt{101}-10)>1$.
11. Answer: 21
Solving the inequality $n(\sqrt{101}-10)>1$, we obtain
$$
n>\frac{1}{\sqrt{101}-10}=\frac{\sqrt{101}+10}{1}=\sqrt{101}+10 .
$$

As $n$ is an integer and $10<\sqrt{101}<11$, we have $n \geq 21$.