Yes, you are eligible for the UPSC CSE after graduating with distance education from Annamalai or any other university.
The UPSC administers this exam once a year.
CRITERIA FOR ELIGIBILITY:
The candidate must be an Indian citizen.
The candidate must have a bachelor's degree from a recognized university.
There is no required minimum percentage of marks to be eligible for this exam.
Candidates in their final year of study are also eligible for this exam.