Colleges in Pune

The eligibility criteria of LLM course of SPPU is LLB/ BA LLB/ BSL LLB. As per the other colleges regulations Integrated LLB students are eligible for LLM courses, So BBA LLB, B.Com LLB or even B.Sc. LLB should be there. So it better to talk to SPPU directly for more clarifications.
For queries, please contact PG Admissions Section, BOD, University of Pune.

Yes, you can get admission for MCA without giving the entrance exam by going for direct admission process.
the only requirements are that you should have already passed BCA or other equivalent examination.
for merit based direct admission you should have the specified minimum aggregate by the institute which is generally 60% in you BCA.
You can also try for the college's reserved management Quota Seats but it could cost you dearly.