Option 1 -> "live by" means to follow principles or live near something, not asking about residence location.
Option 2 -> "put out" means to extinguish or inconvenience, completely unrelated to asking about residence.
Option 3 -> "put up" is a phrasal verb meaning to stay or reside temporarily or permanently at a place.
Option 4 -> "live with" means to cohabit with someone or tolerate something, requires an object after it.
Hence, Option 3: put up -> "Where do you put up in Delhi?" is the idiomatic way to ask where someone is staying or residing, making it the most appropriate phrasal verb for this context -> correct