Hello student with 60 percentile in Jee main its difficult to get admission in government colleges as we all know that seats are very limited and admission is directly based on merit rank.

I request you to please help me with the college you're concerned about so that I can check and provide you the exact information about cut off and admission process.

You can also use careers360 college predictor to predict college. - https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Feel free to comment if you've any doubt

Good luck