Is there a scope for biomedical engineering in India having studied in a good private college in Mumbai?

Yes, It has a scope.

Scope of Biomedical Engineering in India

1- After doing Biomedical Engineering, you can be employed in some MNC's as Sales, Service and Application Specialists.
2- You can work as a Research Engineer as well in some OEM Manufacturing Companies
3- You can work as a Biomedical Engineer in the Hospitals
4- You can pursue Masters from any of the IIT's, IIT Bombay, Madras, Hyderabad and Kharagpur. Thus escalating your Salary figures
5-You can be a Biomedical Entrepreneur, Biomedical Engineering offers the best scope for the same among any other branch of engineering
6- You can pursue MBA in Hospital management or Hospital Administration and become a Hospital manager in which you control all the aspects of hospitals