With a UR rank of 2700 and a BC (Backward Caste) rank of 1100 in the BCECE (Bihar Combined Entrance Competitive Examination), you have a good chance of securing admission in various government engineering and medical colleges in Bihar. The exact college and branch you might get depend on factors like the number of available seats, the cut-off for different branches, and the specific preferences for the current year.

Possible Engineering Colleges:

1. Government Engineering College, Bhagalpur
2. Government Engineering College, Siwan
3. Bihar College of Engineering, Patna (now part of NIT Patna)

Branches You Might Get:

• Computer Science and Engineering
• Electrical Engineering
• Mechanical Engineering
• Civil Engineering

The exact availability can vary, so it's a good idea to check the previous year’s cut-off ranks and get in touch with the BCECE board or visit their official website for the most recent and specific information regarding seat allocation and branch availability.