Hey Simran,
Congratulations on qualifying JEE-MAINS. As per your score you can get into government colleges in Bihar in core branches with lower cutoff. I can't say about any particular College. It depends on there cutoff for specific Category. Or you can wait for Spot round.
Here is a link you could try for predicting College
https://engineering.careers360.com/jee-main-college-predictor?ici=search_trending
Best of luck
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