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!!!

Dear Aspirant,
The fee structure of BIT Patna for b tech is around Rs 1,76,000 per year.
The minimum fee structure of any engineering college is around 1,50,000 p.a
BIT Patna is a nice College. You can take admission in that.fee is also not so high.
Don't choose college according the money.
If  fee of any college is less ,but you are not getting enough education facility.its not worth the money.
So think wisely.
You can take admission in BIT Patna
Thankyou
Hope it helps

BIT Patna

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