There are lot of schools that are considered "public ivys" which are very good. Why does the name "Ivy League" matter anyway?
Because it's the most storied athletic
conference in the United States.
Physics, probably not. Engineering, I have no idea. For Physics I'd apply to 4-5 schools in the 20-40 range, 3 in the 10-20 range, a top 10, and 2 safeties in the 60-80 range that fit your research interests. With that spread I'd say you have a 40% chance of going to a top 20 school, 90% top 40 school, will definitely get in somewhere.
Remember, there are MANY international applicants, and many of them from india. The strong competition for spots and the desire for cultural diversity means the application process for any indian student in america is a bit of a crap shoot, especially with funding issues schools are having regarding TAships. If you would have came in with a perfect GRE and a first authorship in Phys. Rev. D I'd only give you a 10% chance at a top 10 school.