IIT

yes
IIT Kanpur, roorkee, kharagpur,madras offers aeronautical and aerospace engineering

You are adviced to appear for JEE Mains examination and if you make it in cutoff list you will be required to appear for JEE Advance to seek admission in IIT. Syllabus for JEE I based on CBSE +2 stage syllabus. Following are JEE preparation options: Self Preparation, Correspondence or contact classes by JEE training institutes. You may chose based on your own strength and weaknesses analysis and your personal conditions.

If you have not got job in campus placement after completing your B.Tech CSE you will face challenges in getting appropriate job directly. Therefore, M.Tech in CSE in IITs is an excellent option. MS abroad is an expensive option, therefore, you may do ROI analysis before taking a decision.

Why private college.?
U can get nit easily
Go for counselin

Try for core branches at old iits
Iit kanpur kharagpur bombay roorkee madras are best

Aerospace engineering is the primary field of engineering which deals with the engineering aspects of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering. AE graduates have job opportunities in DRDO, ISRO, HAL and other aeronautical manufacturing companies and it's ancillaries, Airlines in Maintenance engineer roles, Indian Air Force, IT companies with Engineering vertical, acedmics etc. AE graduates also have job opportunities abroad.

According to placement and other facilities iim is better but where do you want to go its your's choice.