I want to know that girls candidate are eligible for the Merchant Navy or not, can you tell me the same???

Yes, girls can join merchant Navy. You can join it by appearing Indian Maritime University (IMU) examination. here are the details of this examination:

Eligibility:
The applicant should have completed 10+2 or equivalent with Physics, Chemistry and Mathematics from a recognized Board or University.

Courses Offered
Category I:
Diploma in Nautical Science leading to B.Sc. Nautical Science

Category II:
B.Sc. Ship Building and Repair
B.Tech. (Marine Engineering)

Examination centers:
Agra
Ahmedabad
Allahabad
Bangalore
Bhopal
Bhubaneswar
Chandigarh
Chennai
Cochin
Coimbatore
Dehradun
Guwahati
Hubli
Hyderabad
Jabalpur
Jaipur
Jodhpur
Kolkata
Kota
Lucknow
Meerut
Mumbai
Patna
Port Blair
Pune
Raipur
Ranchi
Shimla
Siliguri
Srinagar
Trivandrum
Visakhapatnam