Hello Eqtedar,

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india-accepting-bcece

The above link will give you the list of colleges accepting the BCECE score and rank.

876 rank is quite a good rank and considering previous year cut-offs, you may easily get branches such as ECE and CSE at Bhagalpur College of Engineering, Bhagalpur. Whereas, you may even get the mechanical branch at Muzaffarpur Institute of Technology, and Nalanda Institute of Technology. AT Gaya College of engineering, there is a chance that you may get Electrical or Mechanical.

Hope this helps

Regards.