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Yes ,BIT Patna is costly.All the private engineering colleges worth high cost.So for better and cheaper options you have to go with government colleges.As you didnot mention your category I consider you as general category student.Here I am providing some of my known government options which you can go for with your rank:
1.Mizoram University :Civil ,ECE,Electrical
2. Assam University : Agriculture and farm Engineering
3.School of Engineering ,Tezpur : Civil ,Food technology
All the best!!!
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