Yes you can join Indian Navy after class 12 by appearing in IMU CET ( Indian Maritime University Common Entrance Test) .

For more details about dates, eligibility, application form, syllabus check-

engineering.career360.com/articles/imu-cet

Yes you can definitely join Indian Navy or Naval Academy after class 12th. For that you must have Physics and Mathematics as your subjects in 10+2 curriculum. After that while your class 12 terminates appear for NDA exam conducted by UPSC, which is conducted twice a year, prepare for it well. The full format for NDA/Naval Academy selection is:

• Written Examination (Mathematics+English+General Studies)
• SSB Interview
• Physical+Medical Tests

To gain information regarding appearing for NDA Examination follow the link; NDA Exam