NIT

With a 73 percentile in the JEE Main and belonging to the ST category, admission to NITs for B.Arch is unlikely for top-tier NITs, but there's a chance for some NITs and other good architecture colleges. You should explore other colleges and consider participating in the JoSAA/CSAB counseling process. 

Your OBC NCL rank 7000 in JEE Mains puts you in a favorable position for admission in the following NITs: NIT Calicut, NIT Jamshedpur, NIT kurukshetra and NIT Silchar. Another good IIIT is IIIT Sri City, Chittoor which is on par with IIIT Nagpur. Your chances at NIT Jamshedpur are good.

No, You can not get admission for B.Tech (any branch) in NIT with 52.34 percentile. It's because the cutoffs of NITs are set between 85-90 percentile for reserved categories and above 95 percentile for general category. However, you can try for State Government Colleges and Private Universities/Colleges that either have their own state level exams or lower cutoffs respectively.

Yes, you can get admission in engineering colleges like IIIT or NIT, but it depends on your entrance exam performance.

For M.Sc Mathematics admissions in NITs, the entrance exam is typically IIT JAM, not JEE Mains.

You particularly have to give IIT JAM for M.Sc.

Your chances of getting a top NiT are very slim .

If you get a NIT it will not be a top and also you will not get your desired or good branch like CSE entc .

In my opinion you could try to get admission in local government engineering colleges which are available .

If you got 78% in JEE mains, the estimated rank in DASA will be more than 8000 according to trends and they are based on JEE Mains actual scores.

You might not get an admission in NIT for CS programme because there is so much difference in DASA rank according to your JEE main percentile. NIT Warangal, Surathkal requires DASA ranks in between 150-400, NIT Calicut requires between 800-1000 and all lower tier NITs requires nearly between 2000-2500. So, it is nearly impossible to get CS in NITs with your JEE 78 percentile.

Yes, it is possible to get admission to IIIT Sri City with a rank of 30000. IIIT Sri City JEE Main cutoff 2025 for the General AI category was ranged between 24802 and 30681. Looking at the cutoff range, we can say that getting at IIIT Sri City at 30000 rank is possible among the General AI category candidates.