Pune

Chitkara university is best among these for CSE.

The order would be -
IIT Bombay - JEE Advanced
NIT Nagpur - JEE Mains
COEP / VJTI - MHCET
Walchand - MHCET
PICT (if it becomes autonomous this year) - MHCET
VIT - MHCET

Admission takes place through CAP rounds (common admission process).
Most probably, there are 3-4 CAP rounds.

The best college for MBA in Pune is Symbiosis International University, you should take admission in this university without any doubt and you also have good marks MAH-CET, so I think you can't face any kind of problem.
All the best.

Vishwakarma Institute of Technology
College of Engineering Pune
Sinhgad College of Engineering
Bharati Vidyapeeth University College of Engineering
Maharashtra Institute of Technology Academy Of Engineering
Rajarshi Shahu College of Engineering,
And the procedure is LEET entrance exam.

For induction program, you need to contact the college administration.