Indian Institute of Technology, IIT Bombay

Hello Vaskar Das, it's very nice to hear from you that your dream is to work at NASA. Like our own ISRO, NASA too requires specialists in different streams like mathematics, physics, mechanical engineering, medicine, metallurgy, etc. So frankly speaking you don't have to be an aeronautical engineer from IIT Mumbai to get a job in NASA. Don't feel pity for yourself for being physically challenged. There is a large number of such people who have achieved greatness in this world by sheer dint of hard work and determination. Of course, being a Govt institute, IIT Mumbai also reserves seats for physically challenged students and offers all help for them to be comfortable on their campus.
Best wishes to you.