NIT

Firstly admissions to National Institute of Technology are given based on the performance in examination called JEE Mains. As a matter of fact there is no other examination which is required to be cleared by the student to get admission in these institutes. On the other hand JEE Advanced examination will lead students for admission in IIT's. Thus we can SEE that these two examinations are required for taking admission in two different Sets of Institutions. Also there is no other examination that can get a student admission in either of these to Sets of institutions. In view of foregoing, we can conclude that these are the only two examinations required to be given and no other examination has any score for enabling admission in these two Sets of institutions.

All the colleges you have mentioned, namely VIT, Thapar University, BITS Pilani, Amity University, SRM, DTU, and NIT Bhopal, are considered to be among the top engineering colleges in India and are known for their quality education and infrastructure. However, based on the latest ranking reports, BITS Pilani is considered to be the best among the colleges you have mentioned for Computer Science Engineering (CSE) followed by VIT and DTU. Here are the details:
BITS Pilani: BITS Pilani is ranked #1 among private engineering colleges in India and is also ranked among the top engineering colleges in the country by various ranking agencies such as NIRF, QS World University Rankings, Times Higher Education Rankings, etc. VIT: VIT is ranked #2 among private engineering colleges in India and is also ranked among the top engineering colleges in the country by various ranking agencies such as NIRF, QS World University Rankings, Times Higher Education Rankings, etc. DTU: Delhi Technological University (DTU) is a government-funded university and is ranked #6 among all engineering colleges in India by NIRF. DTU is known for its strong research programs and industry collaborations.

SAT scores are indeed accepted for undergraduate BE/B.Tech admission under the DASA scheme in NITs. Under the DASA scheme, a certain percentage of seats are reserved for NRI/PIO/OCI students in NITs. The reservation criteria are as follows:
15% seats are reserved for applicants from the Non-SAARC countries.
2.5% seats are reserved for applicants from the SAARC countries.
27% seats are reserved for applicants from the PIO/OCI category. To be eligible for admission under the DASA scheme, the candidate must have passed the qualifying examination (12th grade or equivalent) with a minimum of 60% marks in aggregate or 6.50 CGPA on a 10-point scale or equivalent grade in the qualifying examination. For the admission process, DASA uses SAT scores (Scholastic Assessment Test) for shortlisting candidates. The candidates need to score a minimum of 1440 out of 1600 in the SAT Maths and Reading & Writing) and a minimum of 800 out of 800 in Maths in SAT Subject Test. The final selection is based on the SAT score, choice of the programme and availability of seats.