Hello,

Yes, there is a physical test.

Admission is through an entrance followed by a screening test and a main written examination.

After clearing the test, there is an interview and a medical test.

The eligibility for joining merchant navy is finishing class 12 with Physics, Chemistry, and Mathematics. 

Other eligibility criteria are as follows:

Candidates have to be unmarried Indian citizens.

Normal vision is required but glasses up to plus or minus 2.5 may be allowed.

Hope this helps. You can contact for any further guidelines.