It is possible to acquire an MBA in India even if you don't have work experience! I know you will be surprised by this because what with all the big shots of IIMs wanting people who at least have some brief experience under their belt. But yes, there are programs that welcome fresh graduates with open arms….
Most of the universities take students regardless of experience. So, with this focus of colleges on academical records and higher entrance exam scores like CAT or MAT, it's seen enough to judge potential. Therefore, you need not have great experience with leadership in India if your CAT or MAT scores are excellent.
That aside, any bit of work experience does bring a more vibrant perspective to class discussions and group projects. Even if you don't have this, highlight any kind of internships, part-time jobs, or even group projects in studies and showcase your skills there. I can give my word of assurance when you demonstrate capability, no matter how slight, in anything.
And finally, consider what you would like your future to look like. If getting right into the business world after college fills that void, then pursue it! Be prepared to drink in as much information as possible, however. Take that bright-eyed zeal and curious mind with you, though, and you'll be just fine.
