Choose the option that correctly transforms the given sentence from A…

The correct answer is Option (3) → Let the door be shut and you be asked to go to sleep.

Active	Passive
Please shut the door and go to sleep.	Let the door be shut and you be asked to go to sleep.

Passive voice of an imperative sentence:

• Deciding clue: the sentence is an order ("Please shut ... and go"), so the passive is built with Let.
• Object becomes subject: the object "the door" comes after Let, followed by be + past participle: "shut the door" → "Let the door be shut".
• Tense kept: the sentence stays an order. "Go to sleep" has no object to turn round, so it is reported with you be asked / requested to + verb: "you be asked to go to sleep"; the two orders stay joined by and.
• Agent (by ...): the doer is the listener, "you", who is understood, so no "by you" is added.
• Other passive forms: is/am/are + V3 (present), was/were + V3 (past), has/have been + V3, had been + V3, will be + V3, is/was being + V3.
  Example: Close the window and sit down. → Let the window be closed and you be asked to sit down.

Why the Other Options are Incorrect?

Option 1: The door is to be shut while you go to sleep. — Incorrect.

• "while" makes the two actions happen at the same time; the active sentence gives two orders, one after the other.
• The order to go to sleep is lost; it becomes only a time clause.

Option 2: Let the door get shut and you be asleep. — Incorrect.

• "get shut" is informal; the passive of an order uses "be + past participle".
• "be asleep" describes a state; the active sentence asks the listener to go to sleep.

Option 4: You are requested to close the door while you go to sleep. — Incorrect. "while" changes the meaning: the listener is asked to close the door during the act of going to sleep, not to shut it and then go to sleep.

Contrast: the passive of an order is built with Let ... be + past participle; "while" (Options 1 and 4) turns the two orders into one time clause.