Hi,
Aerospace engineering is a upcoming field. IITs are better compared to private universities. Private universities tution fee are very high. On average most of colleges fee are 8- 12 lakh for 4 years. If you're very much passionate about aerospace engineering then go for it.  But,  if you are thinking some other branches, do apply for Electrical  or mechanical.  They are highly blooming field. Even you can do master in aerospace engineering with graduation in mechanical.