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Hello Mudavath,
Since you got 66.7 percentile in JEE Mains and you also belong to an ST category , you will get a seat in NIT. This years JEE cutoff for NIT for ST students is 44.33 percent . So , yes you will get a seat in NIT.
Here is a link you can go through to check the cutoff patterns for the previous years : https://engineering.careers360.com/articles/jee-main-cutoff
Hope I have solved your doubt. If still there are any queries the do ask us.
All the best !!!
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