B.Sc Forensic Science

BE and B.Sc both are different courses. You should opt for a course as per your interest. But I would suggest you do B.Tech which is most developing and growing field in the modern era and will be more demanded in future as well.
All the best.

Duration: 3 years
1st-year non-sponsored semester fee (Rs. in Lacs): 0.58
1st-year non-sponsored semester fee (Rs. in Lacs): 0.87
This is per semester fee.

Both are the same, but B.Sc. in forensic sciences will get you jobs in the government sector (forensic dept).
Gujarat Forensic Science University is the best.

B.Sc in Forensic Sciences:
Admission Process:
Admission to the course is based on the candidates performance at the 10+2 level. Institutes offering the course admit students based on whether they meet the minimum, set cut- off scores at the 10+2 level. A few institutes however, shortlist students based on their performance in an additional entrance test conducted at their own level. Top B.Sc entrance exams in India are mentioned at the link provided below:
https://www.shiksha.com/science/articles/top-bsc-msc-entrance-exams-in-india-blogId-13484

No, you have to register for the course you want to take admission in.

Both are good options, but B.Sc in forensic science is a better option as you can get good career prospects in India as well as abroad.