What should be my college preference and branch with general rank 41640 and obc rank 10540 and UP domicile in JoSAA.

Log in to JoSAA with your JEE credentials. Then you would need to list your preferred institutes and branches in order of priority. Mention IIIT Vadodara (Institute Code 308) and your desired branch (CSE or IT) higher in your list to increase allotment chances based on your rank.

The NIT Srinagar BTech seat allotment is first done through the JoSAA counseling. The allotment of seats is based on a candidate's JEE Mains score. However, if after the seat allotment, there are still some vacant seats for the BTech course, they are filled through the CSAB counseling.

Candidates interested in NIT Patna BTech admissions are required to appear for the JoSAA counseling round to get a seat alloted in the course. Only if there are any vacant seats remaining after JoSAA counseling at NIT Patna, then the candidates are selected during the CSAB counseling. Thus, all cand

Yes, you can participate in the CSAB special rounds even after accepting a JoSAA seat in the NIT+ system, provided you follow the specific rules. 

No, you need to fill fresh choices for CSAB rounds. The choices filled in JoSAA will not be carried to the CSAB counselling.