Correct option is D
Option (d) contains an error. The correct form should be "taken" instead of "take" to match the past participle needed in the passive voice construction. Thus, the corrected sentence should read, "The protesters were badly beaten and taken into custody by the authorities."
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Grammatical rule used: In a passive voice construction, the verb form should be in the past participle when combined with a form of the verb "to be" to denote the action being performed on the subject.
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Example: The book was written by the author. (Here, "written" is the past participle form of "write").