Greetings, 

Shivam so  after going through the stated problem I would suggest that according to your scores there are many private colleges which will provide you admission in any scores but of course they will be expensive and I will not recommend spending so much money on a BA degree . There are many option as you stated that you want to became and IAS officer and want to give UPSC so you can give some competition exams like CLAT ,etc now which will help you give a backup option also as we all admit this fact that UPSC is not a piece of cake . 

By giving any competition exam ; let's take example of CLAT at the end of 5 year course you will be an advocate and the course studies in law school will majorly help you pass UPSC . 

Secondly you should take admission in any BA college according to your score whose fee is also low because let's face another fact that the education, the books , the knowledge will always be same in every college whether it is top college or not so top college of delhi or elsewhere . So I would advise you to take admission there because in the end what matters is your scores /percentage in your degree .

While studying you can also take up some part -time job which will help you financially . You can go for a job as a teacher in some private school which will also help you clear out/remember  the concepts you forgot . You will get in touch with general knowledge everyday .  

If your end motive is giving UPSE then do not think about college ,you should only and only focus on getting the knowledge and the score/percentage in graduation degree. 

If you go for some competition exams as I have mentioned above CLAT would be the best option because of the courses involved in law school are almost the same as what UPSC exam paper pattern mostly demands . So this is best option also for the reason that CLAT exam will be conducted in may and you have almost 2 months to prepare . 

I hope this article might have helped you figure out what you should do according to the situation . Even after that you are not satisfied  or have further queries or doubts do drop a comment or post another question and I will surely be delighted to help you out .