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Hi Aryaman,
Based on your category rank, under All India seat you might NOT be able to get into majority of NITs under Other State quota. However, you may have a good chance in Home State quota depending on the state. I will advice you to use our College Predictor tool for JEE Mains to help you in finding college and branch of your choice based on your merits in the exam.
Good Luck
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With 96.67 Percentile, assuming you are from General Category, your CRL will be anywhere around 35-36k. With this Rank, you have fair chances in securing Electronics, Mechanical or Chemical Engineering at VIT Pune. You need to secure atleast between 20-25k, to have fair chances in securing IT/CS/AI Branches at VIT Pune.
For more information about VIT Pune Cutoffs do follow the link below https://www.careers360.com/colleges/vishwakarma-institute-of-technology-pune/cut-off
However, I would advise you to target anywhere around 98 Percentile in JEE Main over the next 2 Attempts and target securing a seat at some of the NITs, IIITs or Top GFTIs.
For more information and College Prediction do follow the link below
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
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