"Is your house intact?"
Translation:Ваш дом цел?
I believe «целый» should also be a possible alternative.
«Цел» is the short form of the adjective. Short forms are almost dead in modern Russian, however, some adjectives still have it. There's only one position when they are still used: when they are the predicate (i.e. in sentences "X is Y' or "is X Y", where Y is the adjective). I.e. they are only used in the nominative case, and not used as a subject.
The choice between short and long forms depends on the adjective. For most adjectives it's interchangeable (снег белый = снег бел 'snow is white'). However, for some adjectives short form sounds better than a long form (e.g. нужен often can't be replaced with the long form нужный).
I believe for the word «целый», both «целый» and «цел» sound OK (although «целый» sounds more colloquial).
This sentence is not likely to be used every day. It literally means that you want to ask if something happened to the house. E.g.:
- Я слы́шала, у вас бы́ло си́льное землетрясе́ние. Ваш дом цел? I've heard there was a strong earthquake at your place. Is your house intact?
It can also be used jokingly, when you suggest someone is so hopeless that they can destroy the house:
— Я вчера́ реши́л испе́чь пиро́г, но забы́л его во́время вы́тянуть... 'I decided to bake a cake yesterday, but I forgot to take it out in time...'
— Ну и как, ваш дом цел? 'So, is your house intact?'