Am I eligible for the IAS exam with degree in correspondence???????????

Yes, you are eligible for the IAS exam with degree in correspondence, no matter whether your degree is correspondence or the regular, only a recognized degree required to apply for this examination.

You need to appear in the Civil Service Examination, this examination is conducted by the UPSC. Here I am giving you the details of this examination:

Nationality:
A citizen of India, or
A subject of Nepal, or
A subject of Bhutan, or
A Tibetan refugee who came over to India before 1st January, 1962 with the intention of permanently settling in India, or
A person of Indian origin who has migrated from Pakistan, Burma, Sri Lanka, East African countries of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawi, Zaire, Ethiopia and Vietnam with the intention of permanently settling in India.

Required qualification:
The applicant should hold a degree of any of Universities incorporated by an Act of the Central or State Legislature in India

Optional subjects of Civil Service Exam mains:
Agriculture
Animal Husbandry and Veterinary Science
Botany
Chemistry
Civil Engineering
Mathematics
Mechanical Engineering
Medical Science
Commerce
Economics
Geography
Geology
Indian History
Law
Philosophy
Physics
Political Science
Psychology
Public Administration
Electrical Engineering
Sociology
Statistics
Zoology