The correct answer is: A. He was refused admittance by the peon.
The peon is the subject of the sentence, and “admittance” is the direct object. The verb “refuse” takes a direct object and an indirect object, so the correct sentence structure is “The peon refused [direct object] [indirect object] admittance.” In this case, the indirect object is “him,” so the correct sentence is “The peon refused him admittance.”
The other options are incorrect because they do not follow the correct sentence structure. Option B, “Admittance is refused to him by the peon,” is in the passive voice. The passive voice is used when the focus of the sentence is on the action, rather than the person or thing doing the action. In this case, the focus of the sentence is on the fact that the peon refused admittance, not on the peon himself. Option C, “Admittance was refused by the peon to him,” is also in the passive voice. Option D, “Admittance is refused him by the peon,” is grammatically correct, but it is not the most natural way to say the sentence. The most natural way to say the sentence is “The peon refused him admittance.”