Hello,
First of all I want to tell you that being from Bihar and studying in Maharashtra doesn't stops you to study in any of the college in India. If you are a diploma student then after completion of you diploma you can give Bihar Lateral Entry Entrance Exam. This exam is conducted for the students who want to change their college or if they want to go for B-Tech after their diploma.
Now the number of seats depends on the colleges, there is not a definite number for the intake of students. But if you have secured a decent rank in the exam, then there are chances that you'll get admission in the lateral entry. There are some private colleges also which gives lateral entry to the students, for a particular college you have to visit their websites or you can contact them.
Now you are asking for civil engineering, the cutoff for civil engineering for lateral entry admission for the previous years is near about 600. Every year the last rank fluctuates but it does not deviates much from 600. So there is a good competition for getting admission. But if worked hard its not tough to achieve that.
Hope this answers your question. Feel free to ask if have doubts.
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