B.Sc

Go through the link below for details:
https://www.shiksha.com/it-software/colleges/b-sc-colleges-Delhi.

Hey,
First make it clear in which university and course you want to take admission.

Yes, there is an entrance test, check out the details below:
Entrance Test:
Eligible candidates need to appear for the Intelligence and Design Evaluation and Assessment entrance exam conducted by the institute.
Final Selection:
Candidates are selected based on academic qualification and performance in entrance exam conducted by the institute.

Syllabus generally includes English language comprehension, Maths (upto class 12th), reasoning ability and general awareness.

It is a 3 year course.

The career after integrated M.Sc seems to be very high. A number of industries recruit the candidates who have pursued their degree in Integrated M.Sc. The career opportunities after M.Sc are also huge. One can perform in various roles such as scientist, researcher, lecturer or a consultant. These job profiles offer high remunerations compared to other jobs of the same kind.

A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years, or a person holding such a degree. Whether a student of a particular subject is awarded a Bachelor of Science degree or a Bachelor of Arts degree can vary between universities. Hope this helps you.

Mentioned below are the top colleges for B.Sc. Anesthesia technology in India:
Jawaharlal Institute of Post Graduate Medical Education and Research - [JIPMER], Pondicherry
KLE University, Belgaum
Jain University - [JU], Bangalore
Sumandeep Vidyapeeth, Vadodara.

It offers Neuropsychology at post graduate level. It doesn't offer Bachelor's degree.