Select the option that expresses the given sentence in passive voice.

He opened the door for his mother.

The door was opened by him for his mother.

The correct passive voice form of the given sentence "He opened the door for his mother" is The door was opened by him for his mother.

The active voice of the sentence is "He opened the door for his mother." This sentence is in the simple past tense, which is used to describe an action that happened in the past. The passive voice of the sentence is formed by putting the subject of the active sentence after the verb "to be" and the past participle of the main verb. In this case, the subject of the active sentence is "he" and the main verb is "open." The past participle of "open" is "opened." So, the passive form of the sentence is "The door was opened by him for his mother."

The other options are incorrect because:

• The door was open by him for his mother. This sentence is in the past tense, but the verb "was" is in the singular form, even though the subject of the sentence is "door," which is plural.
• The door had been opened by him for his mother. This sentence is in the past perfect tense, which is used to describe an action that happened in the past before another action happened. However, in this case, the action of the door being opened is not relevant to the present.
• The door is opened by him for his mother. This sentence is in the present tense, but the action of the door being opened happened in the past.