Hello dear student, 
Greetings
I am sorry to tell you but you cannot appear in improvement exam as improvement exam is only for those students who have passed their exam but are not satisfied with their marks and want to improve it.
Improvement exams are for students who have passed but are not satisfied with their marks and are willing to take the exams again. CBSE Improvement Exam can be taken in one or more subjects in the succeeding year only after passing the subject in Class XII.
you can give Improvement exam only after clearing compartment exam , if you failed in any 1 subject in class 12th but in case you failed compartment exam then you are not eligible for it.
thankyou
Good luck