Hey ,

Considering your rank and preferred branch,  you have chances to get a seat in the following colleges : 

• Nalanda College of Engineering, Chandi
• Motihari College of Engineering, Motihari
• Bakhtiyarpur College of Engineering, Patna
• Darbhanga College of Engineering, Darbhanga
• Rastrakavi Ramdhari Singh Dinkar College of Engineering, Begusarai
• Shershah College of Engineering, Sasaram
• Sitamarhi Institute of Technology, Sitamarhi
• Gaya College of Engineering, Gaya
• Purnea College of Engineering, Purnea
• BP Mandal College of Engineering, Madhepura
• Saharsa College of Engineering, Saharsa
• Loknayak Jai Prakash Institute of Technology, Chhapra
• Katihar College of Engineering, Katihar
• Supaul College of Engineering, Supaul

Hope it helps!