The word “ubiquitous” comes from the Latin word "ubi,” meaning where. When something is “ubiquitous,” it exists everywhere, in all places. In contrast to this, something “rare” does not occur very often, so this is the best option for an antonym. Do not be fooled into thinking that “ubiquitous” is “iniquitous,” which means morally wrong. This mistake could lead you to choose either “acceptable” or “legal.”

Something "redundant" is repetitive and perhaps unnecessary. This is not always the case, for a building could be provided with redundant power supplies, meaning that it has extra sources of power that are not always used. Perhaps there is a danger that one set of power lines will be knocked down. An extra set is installed just in case of such an accident. These lines are “redundant” in the sense of being extra and superfluous, but they certainly are not useless; however, in general use, something that is redundant—so long as it is redundant—is extra and could be removed without causing any immediate changes to the situation. In contrast to this, something essential cannot be so easily changed.

When someone acts in an objective manner, that person does not allow his or her personal opinions to sway what he or she thinks about something. They allow the known “object” to express itself independently of any subjective biases or dispositions. In contrast to this, a bias is a type of prejudice on behalf of something, so someone who is “biased” is prejudiced on behalf of some outcome or interpretation. (Note that “prejudice” can be considered as “pre-judging”). This is the best option for an antonym among those provided.

Something that is delighting is not merely enjoyable but instead causes great joy. While "sadness," "annoyance," and "vexation" are all in some way opposed to delight, none of these options provide the direct contrast to “great joy” as does “disgust.” Interestingly, the word “disgust,” is related to “gustatory,” which means pertaining to the sense of taste. Something that is “dis-gusting” is literally something that has a horrible taste, though the term is generally used in its broad sense of meaning, a feeling of displeasure or revulsion. Still, roots like this can help you to remember less common words like “gustatory.”

As you likely suspect, the word “radiant” does come from the same roots in Latin as does the English word “ray” and “radiation.” When something is “radiant,” it is as though that thing emits rays of some sort (often light). A person can have “radiant” smile (one that is intense and very visible), or someone can be said to “radiate confidence” (once again, very visibly). Among the options provided, “dingy” is the only one that captures an antonym—here one to the very literal sense of “shining or radiating light.” Something that is “dingy” lacks brightness and is dull.

A "rhapsody" is an expression of great feeling in a very enthusiastic manner. “Rhapsodize” is a verb form related to this kind of expression. To “rhapsodize” means to discuss or write about something in a manner that expresses great pleasure. In comparison with this, the only potential answer that offers an antonym is “denounce.” To “denounce” something is to declare in a public forum that the thing is bad or wicked.

When someone lacks “taste,” this does not merely have to do with the sensory power of taste. Instead, the term is used here as indicating that someone is unable to make appropriate discriminations regarding things of culture—as when someone says, “Bob has good taste in wine,” implying that Bob knows and enjoys good wines, not cheap ones of low quality; therefore, the best option among those provided is “cultured,” which is a suitable antonym for “tasteless.” Someone who is “cultured” has refined tastes.

Although we often use the word “damp” in the sense of indicating being wet, to "dampen" can also mean to make less intense. For instance, we could say, “The spongy pads helped to dampen the force of the impact, thus preventing a great deal of harm.” In contrast to such decrease, the simple word “increase” is an excellent antonym.

The word “audacious” comes from the Latin for to dare. It describes something that is bold or daring and can be used to describe a personality trait of someone who is both bold and daring. This is quite the opposite of “apprehensive,” which means anxious or fearful.

The word “vitriolic” describes something that is critical and nasty in character. For instance, one could say, “The article was filled with vitriolic criticism of the current coaching staff, criticizing every one of their actions with the most scathing of words.” In contrast to such nastiness, “affectionate” is the only antonym among the options provided.