Hello aspirant , congratulations for getting 686 rank. Yes you have probability of getting MIT Muzaffarpur and BCE Bhagalpur . It also depends that which stream you would like to pursue , if you are okay with opting core branches , then surely you would get into one of them ( MIT or BCE ) . If you want CS ,ECE etc then also you have chances of being there. Apply for counseling and keep track of it.

Best wishes