Hey,
Yes , You can . Their are two procedure to join the Indian Navy. One is NDA (National Defence Academy) and another one is Technical Entry . For NDA you have to give exam conducted by UPSC , in which you will have two options to join Indian navy .One is of NDA and another is INA (Indian Naval Academy) , their test are same but you have to give choice between INA and NDA . Than after you passed the exam ,You will have SSB and Followed by Medical. But in technical entry you dont have exam you will be directly called for SSB . But for direct SSB you have to get Good marks in JEE Mains Exams as well as in 12th class. You have to fill your application on the Indian Navy Website and you will be call for SSB in your Eligible with your marks.