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You will definitely get mechanical branch in NIT Jaipur and NIT Allahabad . I am not sure about NITs of warangal and trichy and mechatronics is taught within mechanical. I study in MNIT and my friend from mechanical has got rank around 9000 . For more information you may look at opening and closing ranks of nechanical branch in these NITs from campus career360s list.
All the best!
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