"Incontrovertible" is an adjective that means "not able to be denied or disputed," so we need to pick out an answer choice that means something like "undeniable." "Unbelievable," while beginning with a negative prefix like both "incontrovertible" ("in-") and "undeniable" ("un-") do, actually means "not able to be believed; unlikely to be true," so it is an antonym of "incontrovertible" and "undeniable." "Irrefutable," however, is an adjective that means "impossible to deny or disprove," and because "irrefutable" is the answer choice closest in meaning to "incontrovertible," "irrefutable" is the correct answer.

The word "equivocal" means unclear in meaning due to being able to be interpreted in multiple ways. The best choice is "ambiguous," which means having more than one meaning. Something that is ambiguous is unclear because it can have multiple meanings, as is an equivocal statement. Considering the other choices, "equal" means having the same value, "audible" means able to be heard, and "original" means new or the initial one of its kind.

The word "scurrilous" means offensive. The best choice is "offensive," as it is a part of the definition of "scurrilous." Considering the other choices, "scamper" means run about playfully, "gloomy" means saddened, and "clever" means quick-witted.

The word "vituperative" means abusive. So "abusive," a word that means characterized by treating someone badly, is the correct answer. Considering the other choices, "neglected" means not having received a suitable amount of attention, "criticized" means judged harshly by another when describing something, and "disorganized" means careless.

"Paltry" means having little meaning, importance, or worth or very small or meager. "Insignificant" is the only choice that has a definition similar to that of "paltry."

"Trivial" means unimportant, so "unimportant" is the synonym.

The word "crucial" refers to something that is necessary to achieve a certain end. For example, if one more loss will eliminate your team from the baseball championship, then winning the next game is crucial. Basically, we are looking for a word that implies great importance. "Vital," which means essential, is the best choice here. "Unimportant" is the opposite of the answer that we want, and "extra" implies that something is present in addition to a certain quantity and unnecessary, not that it is necessary. Finally, "diminutive" means short or unusually small.

If something is pivotal, it means that it is important.  For example, the last regular football game of a season is pivotal in determining whether the team will play in the semifinals.

Something that is “eminent” is well-known or important. This is opposed to something that is "imminent," which means about to happen. To provide further guidance, "futile" means pointless; "worthless" means not worth anything; "morose" means miserable and glum; "novelty" means innovation, something original.

"Tangential" is an adjective that means either "diverging from a previous course or line; erratic," or "hardly touching a matter; peripheral." So, we need to pick out an answer choice that means something like "erratic" or "peripheral." "Essential" cannot be the correct answer, then, because "essential" means "absolutely necessary; extremely important," making it an antonym of "tangential," not a synonym. "Nonessential," however, is an adjective that means "not absolutely necessary," and because "nonessential" is the answer choice closest in meaning to "tangential," "nonessential" is the correct answer.