Hii!
You haven't mentioned or tagged the name of the  subject stream for which you want to know the HSC exam dates 2021. However, let me tell you that the exams are expected to start in the month of May, 2021 and end till June, 2021. You can visit the following link for more information.

https://www.google.com/amp/s/school.careers360.com/articles/maharashtra-hsc-time-table/amp

Hope this helps.
Good luck!