IIIT

Hi,
The National Testing Agency (NTA) relaxed the 75 per cent marks in class 12 as an eligibility criterion for admission to NITs, IIITs and other Centrally Funded Technical Institutions (CFTIs) in which admission is done on the basis of Joint Entrance Exam (JEE) main scores. In an official notification issued late on Tuesday, the Testing Agency said that it is in receipt of numerous representations from the stakeholders regarding changing the criteria of 75 per cent marks in the Class 12 examination. The agencys official communique said, in view of these representations, it has decided to change the eligibility conditions for Admission to NITs, IIITs, and CFTIs participating through Central Seat Allocation Board (CSAB). For the candidates who qualify for admission in the NITs, IIITs and such other CFTIs whose admissions are based on the JEE (Main) ranks, they should have secured at least 75 per cent marks in the Class 12 examination or be in the top 20 percentile in Class 12 examination conducted by respective Boards.

It depends upon the JEE Main and JEE Advance cut offs, If You manage to qualify the exam by achieving the cut off, You can apply for JoSAA Counselling. It should be noted that the cut off for EWS/SC/ST/FEMALES/OBC category is lower than the general category.
If you manage to qualify JEE Main Cutoff, You would be eligible for JEE Advance which is the intake exam for IITs as mentioned above. However It is usually advised to fill the choices as per the preference of colleges and departments, for example CSE in NIT Trichy is your priority followed by CSE in NIT Warangal, you can fill CSE at NIT Trichy at serial number 1 and CSE at NIT Warangal at serial number 2 and so on and so forth. However, to get any NIT, you must have qualified JEE Mains and to get any IIT, you must have qualified JEE Advanced
But the previous cut offs of colleges should be taken in consideration, it is better to research over the cut off of colleges then make a preference list of colleges and fill accordingly.
According to past year you have very low chances to get admissions in NIT or IIIT.

On such OBC rank you have no chances to get any of the NITs or IIITs or GFTIs as the OBC rank closes around 30000 -33000 till final round of JoSAA counselling. But you can go for some other colleges that are discussed below. If we go through previous year's data of seat allotment On the basis of data mentioned in the question by you, you can go for the enlisted colleges :-
R. H. Sapat College of Engineering, Management Studies and Research, Nashik
A. C. Patil College of Engineering, Navi Mumbai
Rajkiya Engineering College, Mainpuri
KIPM College of Engineering and Technology (KIPM), Gorakhpur
Zeal College of Engineering and Research, Pune
And some more.