"Influential" means having a powerful effect on people or events. "Important," which means significant or valuable, is closest in meaning to "influential," so it is the correct answer.

Incorrect answers:

"Miraculous" means inexplicable or occurring through or as if through divine intervention, as in the sentence, "The sick child made a miraculous recovery that the doctors did not think was possible."

"Approving" means thinking favorably of, as in the sentence, "The teacher had an approving look on her face as she told the students she was proud of their hard work."

"Cautious" means careful, as in the sentence, "You must be cautious when you cross the busy street."

The word "authoritative" means trustworthy or self-assured and commanding. So, the best answer choice is "commanding."" "Power" is not the best choice because it is a noun that refers to the strength of something. Since "authoritative" is an adjective, the answer must also be an adjective.

Severe is defined as something that is unnecessarily extreme, which can also define harsh. 

"Feeble" means lacking strength because of age or sickness. Weak also means not strong, so "weak" is the correct answer. As for the other answer choices, to "saunter" means to walk slowly, at a relaxed pace, to "revert" means to return to a previous state, an "avalanche" is a dangerous event in which snow and rocks fall quickly down the side of a mountain, and a "banquet" is a large meal or a feast.

"Feeble" means weak or ineffectual. To further help you, "robust," "sturdy," and "brawny" are synonyms and all mean strong.

"Dominant" means in control, in charge, on top.

When something is "intense," it is very strong. For instance, "intense emotions" are strong emotions, and "intense heat" is very hot. When we increase the "intensity" of something, we make it to be more extreme—stronger, louder, brighter, and so forth. The best option provided is "extreme," which means to a high degree. This is similar in meaning to "intense."

The closest word in meaning to "feeble" is "frail." If someone or something is "feeble," it means that it is frail or weakened.

Drastic means likely to have a strong or far-reaching effect, and can mean radical or "extreme."

"Futile" is an adjective that means "incapable of producing any useful result; pointless." So, we need to pick out an adjective that means something like "pointless." "Successful," then, cannot be the correct answer, because "successful" is an adjective that can mean "accomplishing an aim or purpose," making it an antonym, not a synonym, of "futile." "Useless," however, is an adjective that can mean "not fulfilling or not expected to achieve the intended purpose or desired outcome," and because "useless" is the answer choice closest in meaning to "futile," "useless" is the correct answer.