Choose the sentence that has the incorrect preposition in it:

The correct answer is Option (1) → The train is running off time.

A train runs on time (punctually) or behind time (late); "off time" is not an English expression for punctuality. The preposition is wrong: the sentence should read "The train is running on time" or "behind time".
Corrected: The train is running on time.
Example: Our flight left on time.

Why the Other Options are Incorrect?

Option 2: It has been five years since I have seen my mother. — Incorrect. Correct use: "since" marks the point of time from which the period is counted. (The verb would read better as "since I last saw", but the preposition is right.)

Option 3: Sheela left for the station an hour ago. — Incorrect. Correct use: "leave for" a place is right, meaning to set out towards it.

Option 4: Vineet studied till 1am for his upcoming exam. — Incorrect. Correct use: "till" marks the point of time up to which an action continues, and "for" gives the purpose; both are correct.