MNNIT Allahabad - Motilal Nehru National Institute of Technology

It all depends on your JEE Mains rank and rank is different for different category.
If you belong to general category, your rank must be under 4.5k(240 marks)(for both HM and OS).
You are OBC then your OBC rank must be approximate 1.5K[220 marks] to get CSE/IT in NIT, Allahabad and if you belong SC/ST category, your SC/ST rank must be approximate under 1K[170 marks].

It's quite difficult, but you can get biotechnology or production and then you can change your branch if your CPI is good in the 1st year.

I think it's difficult for you to get MNNIT CSE if you belong to general category. According to me, both are good, but in MNNIT, you can opt for IT and after 1st year if your CPI is good (above 8.5) then you can change your branch to CSE.

If you want a good coding culture, then you should go for IIIT, Allahabad.

Well, if your general rank is 96500 then you won't be getting any government college. You should instead go for private colleges with a desirable branch.

NIT, Trichy is one of the best institutes for CSE. It is top among the NITs and placements for CSE are pretty good here. The only issue you might have is of adjusting to the new environment. Also, Delhi is much better to live than Trichy. So take your decision considering all the facts.

It think there is no chance.

Yes, but in chemical or biotech or production branch.

I think there is hope according to your category.