I'm a little confused on the verb tense. Is karenge in oblique form here or is this the spelling always used for third person? If it is oblique, why?
As far as I understand, verbs do not take the oblique form - only nouns do. Here, Delhi would be the noun taking the oblique, as it is followed by the post position Mein. Karenge is in the respectful third person future tense - with the एगें ending
तुम दिल्ली में क्या करेगा? what is wrong in this sentence ?
My guess is that it's not in the formal form karengé. Just masculine single karenga
As of this time there is no correct option. Of the three choices given the "correct" one is "आप दिल्ली में क्या करोगी?"