Which elements have zero valency?in which group of the periodic table have they been placed?

First you go to google.com and search "valency".
www.google.com/#q=valency

After looking at a couple of links you come to this one:
www.freechemistryonline.com/what-is-valency.html

It's a rather long explanation, but it's complete. So you study it until it seems obvious and then you know it.