NIT

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.

I don't think so, in my course there is no any option like this may be others allow .

Yes, in IIIT Manipur easily after participating in CSAB round.

With 83 percentile in JEE Mains, admission to CSE in top NITs or IIITs is unlikely for General category. However, you may get lower GFTIs or North East NITs and CSE-related branches like IT, AI/DS, or ECE in newer IIITs or GFTIs through JoSAA/CSAB rounds.

Options depends upon you category and homestate, so complete your question. 

You JEE MAIN rank is too good . It guarantees you good seat in good college.

For IIT seat it will vary from category.

Appear in JEE main, score good percentile and participate in JOSSA AND CSAB counseling and get admission.