Indian Institute of Science

You have to crack NTSE or KVPY Olympiad. Else, your JEE Mains score has to be more than 60%. If by any chance you miss out on mains score, your JEE Advanced score has to be more than 60%, after which you have to apply and then you will be called for a short interview.
The above mentioned procedure is to get admitted in IISC if you are a 12th pass out from MPC.

Hi Akshay,
The cut-off varies every year according to the number of students applying for examination and number of seats available. It would be advisable that you get in touch with college authorities/official page directly for accurate cutoff which can help you in getting a seat in IISc-Bangalore.

Please refer to the link provided below for details regarding top colleges offering a course in B.Sc.
https://www.shiksha.com/science/articles/top-10-bsc-msc-colleges-in-india-blogId-13473

Hello Siddharth,
Integrated Ph.D programme begins after graduation. I am attaching the link so that you can get all the details:
http://www.iisc.ac.in/admissions/ph-d-integratedprogrammes/#ffs-tabbed-11

Both are the colleges are of national importance and very reputed colleges of India but if any one has to choose among these, give first priority to the IITs.

Hello Priya,
In India, it's not possible to jump branch. For doing PG in Aeronautical engineering, you need to have done graduation in that branch.