IIT

Data Science is provided by IIT-Madras; JEE eligibility is not necessary. You can study of a data scientist in IIT without JEE. It is a 4 year degree course provided by the IIT Madras.

Tata Institute of Fundamental Research (TIFR)
International Center Theoretical Sciences
IISER Pune
IIT Kanpur
These are the best college for Quantum Related Masters programme.

Choose DTU for computer engineering. the placements of computer engineering, DTU are great, the average package is around 18-19 LPA. You may choose IIT, if you prefer the tag as it is one of the most prestigious institutes in india.

To get admission in IITs every student has to take iit jee exam conducted every year by NTA.JEE Main is the first stage of the IIT JEE entrance exam. It is conducted twice in a year (January and April) to offer admissions into various government and private colleges depending upon the rank of the candidate.

After JOSSA counselling you can leave your NIT college and take admission in IITs.

There are fee waiver in IITs for students whose family income is less than 1 Lacs, you will get 80-100% Fee waiver.