Dear priyenga

              The minimum cutoff needed for a government engineering College depend upon the state where the college is present.

Many states have good government engineering College so their cut-off is high where as other have low cut-off.
In states like Maharashtra and Utter Pradesh there are good government engineering College so there cutoff is high where as in state like Madhya Pradesh the cutoff is low as the quality of education is low and even the colleges are not good.

But you want to play on safe side if your rank is under 30000 in JEE mains means you have scored more then 140 you can get a good college in which ever state you want a minimum you can get upto the qualifying marks.

Regards

Anna University, Chennai

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Government Engineering College, Jagdalpur

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