"Is there an air-conditioner in this room?"
Translation:יש מזגן בחדר הזה?
These are common words, they're not formal usage. יש is not quite equivalent:
When your object has the definite article, only the long form is acceptable:
״המזגן ישנו״ אבל לא ״המזגן יש״
However, when there is no definite article, both short and long forms are acceptable, and neither is more high-brow than the other.
״ישנן בנות״ בסדר אבל גם ״יש בנות״