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Hi Sarvani,
IIT's and NIT's offer B.Tech / BE courses and not B.Sc. However, to help you with more information, I would request gopal sharma. Nikhlesh Mathur to share their expertise.
Eligibility for NIT:
Admission to undergraduate programs is based on All India ranks of JEE (Joint Entrance Examination). The candidates need to have a minimum pass percentage in Class XII examination in order to apply for NITs.
Eligibility for BITS:
Admission are done on the basis of BITSAT.
Eligibility for BITSAT 2013 –
For admission, students must have passed the 12th class examination of 10+2 system from a recognized Central or State board or its equivalent with physics, chemistry and mathematics.
Further, the candidate should have obtained a minimum of aggregate 75% marks in physics, chemistry and mathematics subjects in XII examination, at least 60% marks in each of the physics, chemistry and mathematics subjects and should have adequate proficiency in English.
Only Students who are appearing for 12th examination in 2013 or who have passed 12th Examination in 2012 are eligible to appear in the BITSAT-2013 test.
If a candidate has taken more than one attempt in 12th class or its equivalent, only his latest performance is considered, provided this attempt has been for the full component of subjects/courses prescribed.
Students who have passed 12th examination in 2011 or earlier are NOT eligible to appear in BITSAT-2013. Students who are presently studying in BITS at any of its campuses are not eligible to appear in BITSAT-2013.
Admissions will be made purely on merit. The merit position of the candidate for admission will be based on the score obtained by the candidate in the
BITSAT-2013. However, their eligibility for admission is subject to fulfilling the requirement of minimum marks in 12th examination, as mentioned above.
Birla Institute of Technology and Science Admission Test (BITSAT 2013), which will be conducted in May and June 2013. BITSAT will be held from Tuesday, May 14, 2013 to Saturday, June 01, 2013.
Hope this helps.
Thanks
All The Best.!

Hi Shashank,
Candidates aspiring for a degree course at TS Chanakya, Mumbai and Marine Engineering Research Institute Kolkata, should qualify the Joint Entrance Examination conducted by the Indian Institute of Technology (IIT), which assesses the candidate’s knowledge of physics, chemistry and mathematics.
The examination is followed by personal interviews/counseling, where the interviewers assess the degree of alertness, and awareness of the external environment in the candidates and their suitability for such a career.
However, some of the institutes might conduct their own entrance examination. For exact details, you need to get in touch with the institute authorities.
For the list of institutes, refer to the below link:
https://science.shiksha.com/be-marine-engineering-colleges-in-india-categorypage-2-62-1-0-0-1-1-2-0-none-1-0
Hope this helps.
Thanks
All The Best