You can appear in MHT CET to take admission in private engineering colleges of Maharashtra but it is recommended to take admission through JEE Main as they are preffered over MHT CET.

To take admission in government engineering colleges of Maharashtra you need a domicile certificate. 

To appear in KCET exam you need a domicile certificate of Karnataka. 

If you want to take admission in private engineering colleges of Karnataka you can appear in COMEDK exam. 

Good Luck!!