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Hello aspirant!
If you are under home state quota then you will definitely get NIT Jamshedpur (Production engineering) otherwise it is very difficult.I am saying this on the basis of previous year opening and closing ranks given in the josaa website.
You can also go through this website
https://josaa.nic.in/Result/Result/OpeningClosingRankArchieve.aspx
Hope it answer your concerns.
The cutoff for core branches will not change much but for the branches like this you can expect change in the cutoff but six thousand is a great ask from you and we should hope for the best to get into the college you desired.
Hope you got the answer you are looking for thank you .
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