Hello Siddanth, Aerospace and aeronautics are completely different branches. Aircraft engineering as offered by IIAE and other colleges you have mentioned deals with aviation industry and civil, commercial or defence aircrafts and may have applications in aerospace but the reverse is not true.

for aerospace, there's IIST thiruvananthapuram, and other colleges like IIT mumbai etc. BIT mesra too has a programme in Rocket Propulsion at the masters level. 

Qualifications required for IIAE:

• 10+2 with PCM
• all India admission entrance examination popularly known as AIAEE (All India AME entrance examination) exclusively for the Indian Institute of Aircraft Engineering (IIAE) registered candidates only.