Prove EXPTIME \ NP is not a subset of NP-Hard?
Hint: note co-NP $\subseteq$ EXPTIME, and co-NP-complete $\cap$ NP = $\emptyset$ since NP $\neq$ co-NP, it remains to prove co-NP-complete $\nsubseteq$ NP-hard. 


   Further hint: if co-NP-complete $\subseteq$ NP-hard, try to show for each language $L\in$ NP, you can build a NTM deciding $\bar L$, thus NP $\subseteq$ co-NP, a contradiction.