Exam

If you are asking about International Institute of Information Technology (IIIT) Hyderabad, Than you have to fill the forms by using IIIT Hyderabad website only. Because IIIT Hyderabad is not the part of JEE Main counselling conducted by JOSSA. The admission portal of IIIT Hyderabad will be activated in the month of April 2020.

CLAT exam is for admissions in BA+LLB and BBA+LLB five years of duration courses in NLUs. So, there is no need for CLAT entrance exam for the BBA course. However, if you are asking about the BBA+LLB course at NMIMS School of Law, then admission in the asked course is based on CLAT or ISAT scores. So, if you have not given CLAT exam, then you can go with the ISAT exam.

The registration process of CAT 2021 will be begin in the 1st week of August 2020 and exam will be conducted in 4th week of November 2020. So candidates those are appearing in final year of exams in 2020 will be eligible for CAT 2021. Hence you can not apply for CAT 2021.

You have not written about the home state you belong. However, your expected JEE Main AIR is below 31825. The last year closing rank in the asked branch was 26535 at NIT Nagaland. Hence your chances are moderate for CSE in NITs. However, you can get the following branches.
1. Civil Engineering at NIT Sikkim, Meghalaya, Manipur, Patna, Mizoram, Durgapur, Arunachal Pradesh, Srinagar, Puducherry, Nagaland, Silchar
2. EEE at NIT Meghalaya, Manipur, Mizoram, Nagaland
3. Electrical engineering at NIT Manipur, Arunachal Pradesh, Srinagar.