Is it compulsory to repeat the practical exam if one fails to clear theory?

You need not reappear as your previous practical marks will be accounted for.

Is it compulsory for a student to repeat the practical examination also if he/she fails to clear theory?
— Gayatri Rawat

The candidate shall appear only in the theory part and his/her previous practical marks will be carried forward and accounted for if he/she has already cleared the practical.

What is the procedure to reappear as a private candidate? Can one appear for the Class 10 and 12 exams without joining school at all?
— Nita Sharma
Refer to the procedure for submission of applications of private candidates provided in the Secondary Curriculum (pg 8-9) and the Senior School Curriculum (pg 10-12) documents brought out by the Board for the Board examination 2014. A private candidate is a person who is not a regular candidate but, under the provisions of the examination bylaws, is allowed to undertake and/or appear in the All India/Delhi Senior School Certificate Examination or All India/Delhi Secondary School Examination of the Board. A candidate who has failed to qualify at the All India/Delhi Secondary School Examination/Senior School Certificate Examination of the Board will be eligible to reappear at the subsequent examination as a private candidate in the syllabi and textbooks as prescribed for the examination of the year in which he will reappear. Similarly, teachers serving in educational institutions affiliated to the Board; and women candidates who are bonafide residents of the National Capital Territory of Delhi and satisfy the following additional conditions are also eligible to appear as private candidates:
(a) that they have privately pursued the prescribed course of study under proper guidance; and
(b) that they are unable to join a secondary school affiliated to the Board or there are such other reasons compelling them to appear at the examinations as a private candidate. For more details please refer to the examination bylaws of the Board.

Does the Board provide any supplementary material for students preparing for Class 10 and Class 12 examinations?
— Ishita Bhatt
For Class 10, NCERT textbooks are the only books prescribed by the Board. For Class 12, in addition to the NCERT/CBSE textbooks (in subjects where NCERT books are not available) prescribed by the Board, supplementary reading material has been developed by the Board in economics, psychology, philosophy, business studies, accountancy, physics, chemistry and mathematics. This supplementary material is available on www.cbse.nic.in.