Hi Sanket,
You can apply for marine engineering by Clearing JEE MAINS into NITs and by JEE Advanced into IITs.
Also except this, there are many other institutions which constitute their own exam for admission into the respective institutions.
Some of the colleges are :

CV Raman College of Engineering, Bhubaneswar
Exam: JEE Mains, OJEE

Srinivas Institute of Technology, Mangalore
Exam: COMEDK UGET, KCET

School of Engineering, Cochin University of Science and Technology
Exam: CUSAT

Coimbatore Marine College, Coimbatore
Exam: IMU CET

For more detailed information, visit our page:
https://engineering.careers360.com/colleges/list-of-marine-engineering-colleges-in-india


Best Wishes

Dear Aspirant,

Top Marine Engineering Colleges in India includes-

1. Marine Engineering and Research Institute, Kolkata
2. Tolani Maritime Institute, Pune
3. Vels Academy of Maritime Studies, Chennai
4. BITS, Hyderabad

Admissions in Marine Engineering are either on merit bases or different entrance exam followed by personal interview.

JNEC Aurangabad

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