Exam

Yes, the entry for B.Sc in NIMHANS is through an entrance exam called the National Eligibility cum Entrance Test for B.Sc. (Hons.) in Nursing (NEET-B.Sc.N) conducted by the National Board of Examinations in Nursing (NBEB). The exam is held once a year in June.

Observing the statistics of last year cut offs and results I feel you will play a safer side. Since this is a decent rank  seeing the previous cutoffs. So, yes, you have a pretty good chance of getting selected in the merit list for the course in the institute. Along with it may be having the state domicile will also benefit you.

I find your question incomplete. You should specify the entrance exam you are talking about. Only in that case, I will be giving you specific advice in that domain. but mostly in all the entrance exams basic mathematics is asked. Also as you have mentioned that you have opted for Science please mention the stream you opted for. If biology, then mathematics will not be your core subject but mathematics is a powerful tool applicable in physics and chemistry. 

Generally, there is a common exam for this course you have to apply for the exams of different institute in which you want to take admission then you have to pass that exam, get the required cutoff to get admission and must score 60 percent marks in class.

Yes, you can join Amrita school of Engineering, coimbatore without JEE. You have to appear for AEEE. AEEE is conducted twice a year to get admission in Amrita school of Engineering.

If students have a good rank in JEE MAIN they can get a direct admission in Amrita school of Engineering.

Direct admission for GATE qualified students is also available, but no interview is required.

Yes, there is an entrance test for admission to the College of Engineering, Trivandrum (CET)'s undergraduate (UG) and postgraduate (PG) programs. The Kerala Engineering, Architecture, and Medical admission Examination (KEAM) is the admission test for undergraduate programs. The KEAM is a state-level admission test administered by the Kerala Commissioner of admission Exams (CEE). 

CAT is not a mandatory requirement for admission to College of Engineering, Trivandrum. CAT scores are required only for admission to the MBA program offered by the college.

Candidates must take one of the CMAT, CAT, or KMAT tests in order to be considered for enrollment in the M.B.A. programme offered by the CET.

Based on their exam results, they will be shortlisted and contacted for the group discussion and personal interview rounds.

Yes, students can pursue Diploma anytime only the criteria is you must pass 10 with 50 percent marks if you are Diploma in engineering then your maths has to be good, you must score 60 marks in 10 exams as well for taking the admission.