How to privately appear for class 11 arts stream

Dear Minal 

As a private candidate, you can complete Class 12 from two routes, depending upon your case in question.

If you haven't appeared for Class 12 exams ever and you wish to study Class 12 and appear in the said exams, you can enroll yourself as an NIOS student with NIOS. You can get all the information about this on their website. The link is given below.

NIOS Website: http://www.nios.ac.in

In case you have appeared/studied for Class 12 from CBSE before (either under Delhi Scheme or All India), but failed some exams or wish to improve some subject score or you wish to take up an additional subject, you can appear for the subject's exam as a private candidate from CBSE board. For that, you will need to submit an application to the Regional Officer to the Board within the prescribed limit an application in the form prescribed together with the prescribed fee for the examination and three copies of passport size photographs duly signed by the candidate and countersigned in case of teacher by the authorities and in case of others a member of the Governing Body of the Board or Head of a School affiliated to the Board. In case of any queries, you can call CBSE Helpline No. 1800-11-8002/011-22509256/ 011-22509258/ 011-22509259/ 011-22041807/011-22041808 or contact concerned CBSE Regional Office on all working days. 

Hope it helps. 
All the best!