Aerospace engineering is offered by many government and private college ... Like iit madras , iit kanpur ,amrita university , for iits you have to give jee mains and advance .. and for private colleges they have their own exam test . Amrita university takes the exam for the admission

Aerospace Engineering is available at some IITs like IIT Madras, IIT Bombay,  IIT Kanpur,  IIT Kharagpur which can be entered through JEE advanced  and IIST through JEE main.