It is difficult to predict the actual rank or admission possibilities as JEE Main is being conducted twice by NTA for the first time and rank will be based on NTA percentile score.

Based on your score your probable rank will be 268,520 - 298,520 and your probable category rank range will be 90221 - 97721, With this rank the chances seems less to get Mechanical branch in NIT Patna. 

NOTE: The Rank Predicted is on the basis of the expected total number of students i.e. 1152650 appearing in the JEE Mains April Session.

Good Luck!