see apart from aerospace engineering, you could look at aeronautical engineering offered I think by Manipal University, SRM to name some. You could apply to IISt - they have avionics too. However admissions to IIST is through JEE Advanced. 

The next option in case these dont pan out should be

Cuttoff doesn't matter here. you need to have minimum of 95% in +2 to get into merit list of sastra 

There is no entrance test to get into MIT as you will have to attend the single window counseling conducted by Anna University as seats will be filled on the basis on TNEA score.

To know more about MIT, you can go through the below link-

All about MIT

Good

Aerospace branch is new branch in Sastra university. 

Generally, there is a less scope of this branch at UG level mostly companies preffered to take students from IITs. 

In private Amrita and SRM provides good placements. 

Sastra University provides good placements for other core branches. 

According, to careers 360 it

Aerospace is offered in some IITs like Bombay, Madras, Kharagpur and Kanpur so JEE Advanced. SRM also offers it so SRMJEEE. Manipal offers aeronautical so that is another option. If you write COMEDK,you could check private colleges in Karnataka. IIEST shibpur also offers this so JEE Main. Amrita also offers

No, NITs don't provide Aerospace engineering.

You can check the top colleges for Aerospace engineering below

Indian Institute of Technology Madras

Indian Institute of Technology Bombay

Indian Institute of Technology Kharagpur

Indian Institute of Technology, Kanpur

SRM University, Chennai

To check complete list you can refer below link

Top Engineering

Aeronautical Engineering is a division of aerospace engineering. Aerospace is much broader branch in comparison to aeronautical engineering. 

If you are interested in aircrafts designing you can opt for Aeronautical Engineering. 

If you are interested in the space research and related topics like space crafts and aircrafts, then you can