What! Your teacher is crazy - half of those things will catch on fire if they are mixed! You should double check to make sure you have them written down right or you could really get hurt!
If you mix HNO3 and HCl you will get a brown gas (don't light it or smell it!). The one that is heavier is the HNO3, because it has more atoms in it. Then, mix the silver one (AgNO3) with KOH - it will give a silver coating to the plastic (search for Tollins Test to see what it looks like). DI water will absorb CO2 from the air and make carbonic acid, so the one that is acidic will be the water.
Good luck!