Yes, you can join India Navy after 12th. Just perform well in your borads and write NDA exam by fulfilling their basic Eligibility criteria.

If you score more than 60% marks in PCM in 12 th standard and qualify JEE MAINS exam with minimum 45 marks you will be shortlisted to appear before services selection board under NAVY 10+2 BTECH ENTRY SCHEME. This is one of the two ways you can become an officer in Indian Navy after 12th standard, other being NDA .

If you talk about sailor entry in Indian Navy

For SENIOR SECONDARY RECRUITMENT (SSR) you must have qualified 10+2 with physics, mathematics and at least one of these subjects -Chemistry/Biology/Computer Science.

All the best!!