The cost i am mentioning is what it will take from Hyderabad. I opted flight to delhi and to hyderabad from delhi. Default flight rate to Delhi will be 1997 INR if you book it in advance. So the to and fro cost will be about 4000 bucks, We can roam around delhi in a cheap way using Delhi Metro. Delhi metro is one of the best things in Delhi to roam.
Exploring Delhi can be done in just one day with the help of Delhi metro, after reaching delhi the first thing you need to do is to go to the nearest metro station and get a Metro Tourist pass (this cost about 150 bucks, it will have a balance of 100 rupees). You can recharge the pass at every metro station.