First of all, there is no minimum percentage criteria to be eligible for Jee Main. The minimum qualification required for Jee Main is that the candidate must has passed 10+2 with Physics, Mathematics or any of these subjects such as Chemistry or Biology or Biotechnology or Technical or Vocational subject from a recognized board. Final year candidates which means who are going to appear for 12th board exams are eligible to appear for Jee Main. There is no minimum percentage reuqired to be eligible for Jee Main. However for admission to NITs, IIITs, CFTIs, and IITs one needs to have at least 75% aggregate marks in 12th or being in top 20 percentile of the respective boards. There is relaxation in marks for reserved category students.
Along with qualifying Jee Main, candidates have to secure at least 75% aggregate marks in 12th final examination or being in top 20 percentile of their respective boards to be eligible for Jee Advanved. So with 60% marks you can surely appear for Jee Main but appearance in Jee Jee Advanced depends on other criteria. For this year, MHRD has withdrawn the 75% marks criteria. But for next year i.e. 2021 it is not yet announced.
For now you can check the below link for more details in Jee Main eligibility criteria http://engineering.careers360.com/articles/jee-main-eligibility-criteria

Joint Entrance Examination (Main)

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