Mechanical Engineering

Amrita school of Business Bangalore campus offers an executive MBA-MS course. The classes are held on Saturdays and Sundays. Please do visit the following link to ascertain your eligibility and to find out about the application process
https://www.amrita.edu/program/emba-ms-management-university-buffalo-usa

You can try for Amity, Jaipur also

As is understandable from the name. Automobile is focused on Automobiles. But Mechanical Is a very diverse core brance. Everything you can see feel around you is mechanical in nature. Or requires concepts of mechanical engineering.
Thus i would advice as you to keep otions open and take Mechanical Enginnering from good colleges like BITS, Lovely Professional University, SRM etc. Once you get in final year you can choose specialization as Automobile engineering.

Both are almost same in terms of both carriculam as well as importance. automobile engg. in one hand specialises you in a particular field of mech. engg but at the same time you can have a much broader field after mech.engg. including the automobile sector.
hope that helps :-)

International students will not be accepted for part time courses. You have to take up full time course to get the student visa to enter into Singapore. You may not have aerospace or aeronautical courses in Singapore. you can try in Ireland where you will get up to 50% schorlaship in Limerick University

Your JEE Mains Score is too low for NITs. Insted try for some other colleges.

If you do BTech Automobile your career is restricted to Automobile industry only. Where as as Mechanical engineer you can work in all industries including Automobile. By the Automobile Engineering is a specialisation under Mechanical engineering.