Sentence I: Correct usage. "Gate" refers to a physical barrier that opens and closes, especially for safety or access control. In this context, it is correctly used to refer to a lift's safety mechanism.
Sentence II: Correct usage. In event-related or entertainment industry contexts, "gate" can informally refer to the amount of money earned from ticket sales or attendance. The usage here, though less common in everyday speech, is correct and idiomatic in industry parlance.
Sentence III: Correct usage. "Gated" is an adjective derived from the noun "gate", describing a residential area that is enclosed and access-controlled, usually for enhanced security. The sentence uses the word appropriately.
All three sentences reflect accurate contextual and grammatical usage of the word in its noun or adjective forms.
Hence, option (d) is the answer.
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