Hello,
Your percentile in JEE mains paper is quite good but as you have not secured minimum of 75% in your boards, you won't be eligible for admission into NITs, IIITs and GFTIs. This criteria is applicable for only general category students. For ST, SC and OBC and PwD category the minimum marks in 12 boards is 65% .
You can go for some top private engineering colleges in India which accept the JEE mains score. Also based on your Rank in JEE mains, you will get a good amount of fees concession.
Here's a list of top private engineering colleges in India which accept JEE mains score https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/colleges/list-of-private-engineering-colleges-in-india-accepting-jee-main&ved=2ahUKEwj20IDA28DqAhW_wzgGHeQZD6EQFjADegQIAxAC&usg=AOvVaw24m3lhnJnkiYxFQHt_5cXG

Hope it helps

There is no percentage barrier in Jee Main. The 75% criteria is only for getting admission in NITs, IIITs, CFTIs and IITs. As you haven't got 75% marks in Board or not in top 20 percentile of your board, you'll not be eligible for admission in these institutes. You can use our Jee Main college predictor tool to know about your admission possibilities - http://engineering.careers360.com/jee-main-college-predictor
But you have a good percentile score in Jee Main based on which you can get top engineering colleges. 95.6 percentile in Jee Main means your expected rank would be around 38,236. If the number of candidates in second phase increases your rank would also increase. Based on your score and last year's data, you can get- Sant Longowal Institute of Engineering and Technology, Institute of Technology - Guru Ghasidas Vishwavidyalaya, Tezpur University etc.

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