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Hello student,
Based on your percentile, it will be tough to get into colleges through the JoSAA Counselling. I suggest you appear for the second attempt to improve your score so that you are able to get top colleges like top core branches in NITs.
However, you do have the option of applying to private colleges. Many private colleges don't base your admission on JEE scores, and the ones that do, many of them don't have a specific fixed cutoff. For reference, you can check out some good private colleges for B.Tech in India in this article: https://engineering.careers360.com/colleges/list-of-private-engineering-colleges-in-gurgaon
If you want to check your rank range based on your percentile, then you can refer to the Careers360 JEE Main Rank Predictor: https://engineering.careers360.com/jee-main-rank-predictor?
If you need more information regarding which colleges you would be eligible for based on your marks and details, then you can refer to the Careers360 JEE Main College Predictor: https://engineering.careers360.com/jee-main-college-predictor?
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