Hi shashank, yes you can surely apply for Indian navy after completing your class 12.

You can apply for:- 

1.)Artificer Aprrentice:-  Minimum requirement to qualify is that you should have to score atleast 60% in class 12th board and you should have maths and physics as your subject.

Age :- 17 to 20 years

Syllabus:-Science, Maths, English and General Awareness.

This recruitment is for technical jobs.

2.)SSR:-you should have to qualify class 12th with maths and physics as compulsory subject.

This is a non-tech entry.

Syllabus is same as above.

3.)You can also apply for NDA AND NA Examination.

For that you have to NDA Examination and after qualifying you have to qualify the SSB Interview.

4.)Through 10 + 2 TES (Techanical entry scheme). On the basis of class 12th percentage, candidates are shortlisted for SSB Interview.

For more  information you can visit below link:-

https://www.joinindiannavy.gov.in/en/page/artificer-apprentice.html

https://www.google.com/amp/s/competition.careers360.com/articles/nda-eligibility-criteria/amp

Sorry dear to say,As per your age you are not eligible for NDA/NA because of the age limit for NDA is 16-20 age for sailor entry and 16 1/2 - 19 1/2 is for Naval academy (Officer entry), but you can apply after graduation for officer entry by CDS and INET (B.Tech/B.E. degree only).

All the best