India

IISC, Bangalore,
IISER, Pune
IITD, IITKGP, IITK, IITB, IITR, IITM, BITS Pilani, etc. are some top universities for B.Sc and M.Sc Physics.
All these Institutes have three Entrance Exam. You can find their details on their respective websites. Also check out the link below for some other top Colleges for

Annamalai University is enacted by Annamalai University Act, 2013 (Tamil Nadu Act 20 of 2013), approved by President of India. Degrees awarded by university are valid for higher studies and government jobs in India.

Cut-off for government college for general categories can be 500 plus and for private college, it can be 400 plus.

I believe ASCO provides better placements. But, my personal recommendation would be for you to pursue higher studies.

I think it is not possible to change the college from state to state, because the universities are changing, they do not accept this type of migration.

You may refer to the following link for ranking of top engineering colleges in India including NITs based on multiple criteria such as faculty, facilities, academic records, placement records etc: https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0.

Admission in National Institute of Engineering, Mysore in B.E. (Lateral Entry) is based on Karnataka CET.