The related set of words all pertain to some character trait that is identifying or at least rather unique. An idiosyncrasy is a character trait that is only had by a single person. If someone has a particular way clicking his or her tongue while talking, that could be called an idiosyncrasy. An oddity is something that is out of the ordinary—an odd person “just doesn’t fit in.” A quirk is an odd type of behavior or occurrence. Only “conventional” indicates something that is “normal” or generally known or accepted. A “societal convention” is a normal pattern of behavior that is found in some society as a whole.

All of the related words assert some sort of belief that there is meaning (or at least hope thereof). "Nihilism" generally means the state of believing that there is no meaning in the world or life. In comparison with this, being faithful or believing is quite different—for faith and belief of any type imply that some meaning is anticipated. Also, to be hopeful is to look for something to come about—which likewise signifies some hope of meaning. Certainly, meaningful is quite different than believing that there is no meaning at all.

Each of the related words here indicates something akin to a fad—a trend, style, or idea that is currently popular, though perhaps just for this moment. Such things come and go rather fluidly, as do whims. (To do something “on a whim” is to do so in response to a sudden change of opinion but not with any deep convictions). To be “in the vogue” is to be “fashionable right now.” Such things likely will be relegated to the time period of their popularity. When something is “novel,” however, it is merely being described as being new. While such a thing could perhaps be a mere fad, the word “novel” merely designates that the things is new and heretofore unheard of.

Note that all of these words pertain to being bad or unacceptable in some way; however, the wrong options all indicate being bad in some very strong way. “Turpitude” is depravity or wickedness. To be “depraved” is to be greatly perverse or wicked. A sociopath is someone who has such bad morals that he or she cannot even function in society. Something “vile” is very disgusting, and, when applied to moral matters, very bad or wicked. In comparison with all of these, “bad” is much weaker.

It might be tempting in this question to be distracted by “blaze” and “ablaze,” the latter being an adjective form of the former; however, note that all the words—including “ablaze”—describe the state of being on fire; however, the incorrect answers all share the fact that they all pertain to strong or large fires. In contrast to this, the simple case of “fire” is much weaker and thus differs from the rest of the words.

All of these words pertain to closeness and could be read merely as applying to spatial closeness. The “vicinity” of something is the area around it. The word comes from the Latin for “neighbor.” The word “proximate” does mean “close” but it can be used more strictly in the sense of being the closest thing in space or time. Since all of our words have this general sense of being close, this one stronger word is the one that does not fit with the others.

The set of related words all indicate some sort of damaging remark that someone can make. To cast “aspersions” on others is to attack that person’s reputation. A denigrating remark is one that is unfairly critical. When someone defames another person, he or she damages that person’s reputation. A slanderous statement is a spoken statement that is false and intentionally damaging. By contrast, to “magnify” someone is to praise him or her greatly.

The similar words indicate something related to aiding or helping. The word “alleviate” means “to make lighter or to remove.” (“Levity” means “light-hearted humor.” Likewise, the word “relieve” is related to the same root meaning “to make lighter or remove”). When something is “detrimental,” it is harmful or at least tends to cause harm. This is quite the opposite of the other words pertaining to helping and thus does not fit with the rest of the group.

Something “arbitrary” is something that is chosen randomly or on a whim. It comes from the Latin for “judge” but likewise has relations to the notion of “will” and “free will.” To choose things arbitrarily is to do so without any “rhyme or reason” (as is popularly said). The other options all indicate some state of affairs that is planned and sensible to various degrees. This is certainly the case with “scheduled,” “plan,” and “agenda.” Likewise, an “itinerary” is the route that is planned for some journey, being taken from the Latin for “road, path, or journey.”

The related words must be seen as sharing the general notion of “being certain and determined.” This shared meaning becomes very obvious when you realize that tentative is different from the others, even if they themselves differ in degrees. The word “tentative” means “not certain or temporary.” Sometimes, when we are asked a question, we must provide a “provisional answer,” meaning an answer that is temporary—a first hunch, though requiring follow-up thought and research. All of the other words indicate some kind of certainty. A resolution is a decision to do something, usually made with firm conviction. A “resolute attitude” is one that is so resolved to do a given resolution. An “unwavering devotion” to something is a devotion that does not stray (waver) from the metaphorical “path” of that devotion. If you are inflexible, you will not change from your choices. Perhaps this is a bad attitude, but for this question, it merely matters that we see the fact that it is quite different from “tentative.”