Hello,
For admission into NITs, IIITs and other government engineering colleges, you need to score minimum of 75% for General Category in your 12 boards or minimum 65% for ST/SC/OBC/PwD. Apart from that you also need to score good marks in JEE mains. If you belong to General category, and you have scored less than 75% in your 12 boards, then you won't be eligible for admission into NITs and IIITs.
You can go for some top private engineering colleges in India which offer a fees concession for students with exceptional marks in JEE mains.
Please visit this link to get a list of private engineering colleges in India accepting 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=2ahUKEwjgmbDVnM_qAhUzzTgGHaziDhQQFjADegQIAxAC&usg=AOvVaw24m3lhnJnkiYxFQHt_5cXG&cshid=1594814965272

Hope it helps

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