Dear Rakeshri,
To appear for the civil services, you should have a degree from universities or educational institute that which are recognized as universities by The University Grants Commission Act 1956 or an equivalent qualification. In that case you can appear for the civil services exam even if you are awaiting your final year results. In general, it is not important that the course is a regular, contact course or a distance learning course. What matters is that the university you have got your degree from is a deemed University as per the UGC ACT 1956 and therefore you can sit for the UPSC exam. The choice of an optional subject in the civil service examination does not necessarily have to do with your subjects in graduation. Many a students do take up completely different subjects as well because they are more scoring and the candidates are able to master them easily.