Hello there!

According to your rank in JEE mains, your general rank would be around 35k. You can get some newer NITs and GFTIs. As you are from EWS category, you can get some good branches, but for core branches like CSE, mechanical, EEE you have very less chances.

Also, you can get the benefit of home state quota to get some good branches till the last round and the final CSAB counselling.
You can practice more and try to improve your percentile in the jee mains in July. You can go for the JEE mains crash course by Careers 360.

Here's the link for that https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/articles/careers360-jee-main-crash-course/amp&ved=2ahUKEwiw1bT92ZfqAhUKb30KHZ4iA08QFjAAegQIBhAB&usg=AOvVaw2qqSyBCop2N7ziMSe61Y3S&ampcf=1

Hope it helps

goodluck!

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96.69 percentile means your expected rank would be around 28,764. This would be your rank in Common Rank List. As both the sessions not yet conducted, we don't have category rank for now. Now if the number of candidates in September session  increases then your rank would also increase. Also the cutoffs depend on various factors like if you are applying through All India Quota or if it is your home state quota. But going by last few years' data and cutoffs, it might be difficult to get top NITs like NIT Trichy, Warangal, Surathkal as the cutoffs of these institutes are very high. But you can expect NIT Jalandhar, Patna, Jaipur, Durgapur, Raipur  etc. You can check the cutoffs here http://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches

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