How are roommates decided at IIT Patna?

IIT Patna hostel is a 7-floor building and the distribution is branch-wise on every floor. Usually, the allotment is as follows

• Ground floor: Civil and Chemical Engineering students
• 1st floor: Civil and Electrical Engineering students
• 2nd floor: Mechanical Engineering and EEE students
• 3rd floor: ME and MME students
• 4th floor: CS and MME students
• The MTech and Ph.D. students stay in the top floors usually. 

As for the roommate allotment, roommates are allocated in alphabetical order within your branch. Branch. A room has 2-3 students of the same branch and usually the same first alphabet in their name.