Mumbai

You can check on the link:
https://goo.gl/DjUK6X

Welingkar and NMIMS are very good and certainly the best possible for great deal of learning and grooming via distance mode and is considered valid degree amongst companies.

Total 480 seats for all specialisation including for PGDM:
https://www.shiksha.com/Itm-Itm-Business-School-Navi-Mumbai-institute-college-listingoverviewtab-35619

There are no such colleges with direct admission, you need to go through first year of studies, else it may impact your placements and internship opportunities.

Dear Avi Kapoor,
Amity Global Business School is following some different concept in the management education. They have collaborations with foreign business schools and classes, international study tours, etc. Coming to the specialisation, in the curriculum itself, they focus on international business papers. Therefore, it is a good option for you.
All the best.

Kindly refer to the link mentioned below B.Tech in mechanical engineering colleges:
https://engineering.shiksha.com/be-btech-in-mechanical-engineering-courses-in-mumbai-all-ctpg

You have a very good chance.
Good luck.