Dear Aspirant Hope you are doing well Now let me go through your question

Till now nta has not released any date on its official website so recommends you to keep eye on official website oe careers360 website Link https://jeemain.nta.nic.in/webinfo2021/Page/Page?PageId=1&LangId=P

Iif you want to know more about it check out the link given in below https://www.google.com/amp/s/engineering.careers360.com/exams/jee-main/amp

Or you can try college predictor tool link given below which help out find to your college preferences government or private link in below

https://engineering.careers360.com/jee-main-college-predictor?utm_source=qna

Hope it helps

Thank you