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 the cut off for EWS/SC/ST/FEMALES/OBC category is lower than the general category
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 qualifies 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

For the college preferences and the courses provided by these colleges and to know which colleges participate in the JOSAA counselling, please go to the below mentioned link: https://engineering.careers360.com/articles/josaa-participating-institutes/amp

For college prediction as per your marks and rank, please go through the below mentioned link:

Hi Shaun,

Congratulations on that amazing result! Very well done. 

Now coming to the probable colleges, can you please tell me what category do you belong to so I can help you out with the cutoffs accordingly. 

Alternatively, I advise you to kindly go through our link ok JEE Paper 2 Cutoff 2019, that lists in detail the various NITs, IIITs and other colleges with their respective, category based expected cutoffs.

Link - http://engineering.careers360.com/articles/jee-main-cutoff-for-b-arch-b-planning. 

I am sure this will help you out. All the very best.