Yes,you can apply for the Indian Navy after completing Bsc Nautical science with 60% aggregate marks from any recognized University/institute of India.

Some renowned colleges offering B. Sc. Nautical Science degree are as follows:

1) T.S. Rahman

2) IMU Campuses - Chennai, Kolkata, Mumbai, Kochi, Vishakhapatnam, Navi Mumbai

3) Hindustan Institute of Maritime Training

4) T. S. Chanakya

5) Maharashtra Academy of Naval Education and Training

6) AMET

7) VELS Maritime

Hope this helps. Good Luck