The word “vacuity” is related to the words “vacuum,” meaning empty space, and “vacate,” meaning, “to empty out an area.” “Vacuity” can be used to describe a mere empty physical space, though it usually is used to indicate intellectual emptiness. For instance, one could say, “After years of listening to the vacuity of his classmates’ opinions, the student was glad to graduate and be freed from their unthinking opinions.”

The word “vibrant” is related to words like “vibrate” and “vibrato.” In a sense, something that is “vibrant” is “shaking with energy.” Often, the word is used to describe something that is dynamic, lively, or energetic. It can mean more than physical energy, for one can speak of a “stimulating, vibrant work environment” or a “vibrant imagination.” The word can also mean “colorful.”

The word “simultaneous” comes from the Latin root “simul,” meaning “together.” Though in some ways related to the word “similar,” it indicates this notion of two things being “together” or “at the same time.” The word “concurrent” literally means “current with” or “happening / existing at the same time as something else.” The “con-” prefix is the same as “cum” found in “cumulative” and “com-” as found in “community.” It means “with.”

When something is “restrained,” it is kept within limits or “held tight.” The word is taken from the Latin root meaning “to squeeze or hold.” It is related to English words such as “constrict” or “constrain.” A “restraint” is something that keeps things within boundaries; hence, it can be called a “restriction” (a word that is similarly derived from the same Latin roots).

The “-ious” ending helps us to see that “sagacious” is likely an adjective. Here, this leaves us with “saga-”. Be careful, however! This is not about a “saga” in the literary sense. The question is trying to trick you into picking “folklore” or “mythological” (or even “breathtaking”). Instead, the “saga-” prefix is derived from the common base of “sage”, meaning a wise person. Someone who is “sagacious” is wise. “Clever” is the best option that we have for something close to “wise.” (They are not exactly the same, but it works given our options.)

The word “induce” comes from two Latin components. The prefix “in-” is rather simple, meaning in or into. You likely know “-duce” as well, though not under this form. A “duke” is a kind noble in British society (a leader of sorts), and a “con-ductor” leads a band. Indeed, to “introduce” (intro-duce) is to bring someone “into the group," so to speak. The “-duce” comes from the Latin "dux," meaning leader or commander. To “induce” is to influence or arouse some action. You might say, “I induced him into running, contrary to his lazy temperament.” When you “instigate,” you initiate an action. This is an excellent synonym.

When something is “tactile,” it relates to touch. The “-tact” portion of “intact” is derived from a similar Latin root. Other related words are “tangible” and “tangent.” Something that is “in-tact” is together and not broken apart. An “intact” building has all of its major structural parts “touching.” Such a thing is still a “whole” (even if it is perhaps somewhat damaged).

The word “trivial” has an interesting history. It comes from the Latin "trivium," which referred to part of the curriculum undertaken by young students. The “trivium” was comprised of three subjects—grammar, logic, and rhetoric. It was so called because it was made up of these three topics. (The prefix “tri-” means three, recall.) These were basic subjects, needed for the others. The word thus came to mean “unimportant” or “simple.” Something “banal” is unoriginal and, in a manner of speaking, simplistic to the point of being boring. This is the best option among those offered. “Elementary” would be the only other tempting option, but that word does not carry with it the negative connotations that come with “trivial” in today’s use of the word.

The word “dolor” means sad, coming from Latin roots regarding sadness and pain. The “in-” prefix sometimes means in or into but can also mean not. Someone who is indolent wishes to avoid sadness and pain—by doing nothing. The word thus comes to mean something like “lazy.” While “depressed” might seem correct, that has more to do with being “dolorous” than being “indolent.” An indolent person is much more like a sloth—slow-moving. Thus, “slothful” (meaning lazy) is an excellent synonym.

The word “fidelity” is derived from the Latin roots for “faith” and is found in other words like “confident” and “infidel.” When someone shows fidelity, that person is faithful to someone or something. For instance, to say, “Raul showed fidelity to his wife all throughout their marriage, never once breaking the trust of their marriage vows.”