Let $L = L_1 \cap L_2 $, where $L_1$ and $L_2$ are languages as defined below:
$L_1= \left \{ a^m b^mca^nb^n \mid m,n \geq 0 \right \}$
$L_2=\left \{ a^i b^j c^k \mid i,j,k \geq 0 \right \}$
Then $L$ is
- Not recursive
- Regular
- Context free but not regular
- Recursively enumerable but not context free.