Hello Nithin!

Well it is very rare for NASA to recruit IIT graduates directly from placements. NASA along with other space exploration companies like blue origin and spaceX comes under their defense department. So, foreigners can not be allowed to work in it directly due to national security reasons. Hence, they only recruit US employess with a US degree and international students with a valid US Masters degree(and those who eventually get a green card). You can complete your graduation from any top IIT(be it Bombay, Delhi,etc.)  and then head to the US to pursue Masters if your dream for NASA is to be fulfilled. Go for Masters in subjects like Orbital Mechanics, Propulsion systems, Thermodynamics, Aerodynamics, Aviationsystems, and Quantum mechanics.

You can try to get internships in CalTech which has a strong connection with JPL(Jet Propulsion Laboratory). This may eventually lead you to a project at CalTech associated with JPL or NASA.

Only 3% employees of NASA are Asians(Indians, Chinese, Japanese, etc.) and they do not even work directly for them. Companies like Boeing, Lockheed, Raytheon, etc hire them for buliding rockets for NASA.

Hope you understood.