ATMA

The last date for registration was 17th July 2016.

Yes. It's definitely possible. All you need to do is paying an advance amount to book your seat. Admissions are almost over. We are left with very limited number of seats. You can apply through your UG MARKS for MBA Admissions

Sorry, as the admission process is close for the current academic year. You have a very good percentile score.

Percentile is calculated on the basis of following formula.
Total No. of students appeared- Your Rank/ Total No. of students appeared.
Multiply the above score by 100.
That is your percentile.

You can appear for exam like IIFT, I think in India no other college is as good as IIFT (Indian institute of foreign trade) for international business.

There are lots of colleges providing you MBA but according to MAT only few best colleges are there which accepts 95 above percentile.
It is better for you to check colleges by your percentile on Shiksha instead of asking others because no one will tell you the best college, but do MBA from Bangalore or Pune.

The following are some good colleges in and around Mumbai, which accept the ATMA exam score:
Vivekanand Education Society's Institute of Management Studies & Research (VESIM), Chembur
Thakur Institute of Management Studies and Research (TIMSR), Kandivali
Welingkar Institute of Management Development & Research (WeSchool), Matunga
SIES College of Management Studies (SIESCOMS), Nerul
Sydenham Institute of Management Studies, Research and Entrepreneurship Education (SIMSREE), Churchgate
MET Institute of Management (MET IOM), Bandra

KITSOM, AIMS are two good colleges where you have decent chances. Check list of top MBA colleges accepting ATMA scores.
https://www.shiksha.com/mba/ranking/top-mba-colleges-india-accepting-atma/2-2-0-0-9180