Yes you can. But you are going to have 4 years gap in your 12th board marksheet after 10th board, which is normally 2 years in other students marksheets.

Hello Student
There is no such rules as to take admission in class 11 from class 12.Most possibly in any Secondary education board in India has the provision to take such admission from class 12 to class 11.The idea is an absurdity views of mind.The main intension is possibly to create a hapzard situation in education system doing such attempt for due to simple curiosity of neglecting the policy if education.
Hope this helps