In the first year, all the freshmen will be doing common courses, in all of which you will be able to find the prescribed books with ease at the local book stores. You could refer to the 'First year courses' post under the 'Academic' section for greater details regarding the same. The only 2 books that I could think of, which you could carry from home from your list are Inorganic Chemistry by Dr R. K. Gupta and Integral Calculus by Amit Agarwaal for mainly reference use. Generally all first year courses have lectures slides and tutorials which cover most of all which is required.
As for the rest of the books that you will need in your next four years, I am sure you will figure it out when the time comes. We do have a massive library and you should be able to find a lot of reference books in there. Find it out at
www.library.iitb.ac.inDon't worry for the first day as you will be told about the books required for the individual courses respectively. After that, you can get it from the local book stores.
