Context Free Grammar: at least 2 1's, at most 2 0's
Hint

If $L_{i j}$ is the language with at least $i$ $1$s and at most $j$ $0$s 

$$\begin{align}
L_{2 2} &amp;= 1 \, L_{1 2} \, | \,?\\
... \\
L_{0 0} &amp;= \,?
\end{align}$$



Edited to answer the correct question.