It would be better to use 'base' as the main verb, and say "What did you base such conclusions on?" or "On what did you base such conclusions?"

Based on what did you make such conclusions? = OK On what did you base your conclusions? = a little more natural. what are your conclusions based on = alter sentence to use base based on what--? ---- based on. but although that is the logic we write it with the question tag at the end. what are ----------(x) -------based on?