Dear Student,

You can take admission in which ever board you want after completing 10th standard (High School) form state board as of 11th standard no you can't get admission in 12th standard (Intermediate) in different college or board to complete it you have to complete you intermediate form the college you are enrolled into 11th standard.

But there is a option you can drop the 11th standard and take the admission next year into 11th standard again into the board of your choice and complete your intermediate education.