Hii Harsh!
There are a number of government Colleges across India offering the marine engineering course. Some of them are-
* Marine engineering and research institute, Kolkata
* Tolani Maritime Institute, Pune
* Mohamed sathak engineering College, Tamil Nadu
* Cochin University of science and technology, Kochi
* Vels academy of maritime studies, Chennai etc.,
Hope this helps.
Good luck!

The best government Marine Engineering College in India is IMU, Kolkata. IMU Kolkata has been ranked no.1 in Asia. The placement record is very good in IMU. Other government marine engineering Institutes are - IMU, Mumbai; Tolani Maritime Institute, Pune; Vels Academy of Maritime Studies, Chennai; Cochin University of Science and Technology.