After failing in CHAT or CET, can I apply separately for PGDM? If yes, which is a better college for PGDM in low fees?

I assume, you are talking about CAT and CET here. For applying in any college for the course of PGDM, you at least need to pass one MBA entrance exam, may it be CAT XAT CET, SNAP etc. And, if you want to get in a good college you need to score high in any of these exams. All the best.