As per your marks in jee main, your probable rank will be 14,701 - 16,301 with a percentile of 97.7 - 99.7%.
So, it's true that you could barely get any branch but there are chances that you might get yourself a decent branch named " Metallurgical and material engineering", " Production engineering", " Instrumentation and control engineering ".
So, we cannot deny the fact that you will not get any branch but above mentioned are some branches that you might crack. Now, the main point is whether you are well versed with this branches and you want to select one or not.
Hope your query is resolved. If you face any queries in future do inform me. I wish you best of luck in your future endeavor.
At this score, there is hardly any chances of getting admission in NIT TRICHY but you can get admission in other top NITs like NIT DURGAPUR,PATNA,JAMSHEDPUR,etc.