When something "meanders" it moves in a way that is not direct but, instead, zigzags from one point to another. Now, this can be used to describe physical motion ("meandering in the fields"). It can also be used to describe something physical and motionless, like a path that zigzags and thus is said to "meander." Finally, it can be used to describe things like thought processes.  Someone's "meandering thoughts" circle about, considering different things for some time before finally resting in a conclusion. Thus, the word "circuitous" works well as a synonym. This word comes from roots meaning circle or around. "Circuitous" reasoning is a kind of thinking that takes a much longer time to arrive at its end than is strictly necessary. A circuitous path is one that meanders quite a bit before reaching its destination. 

The word "minuscule" is related to very familiar words like "miniature" and the often-used prefix "mini-". This cluster of words generally designates that a given things is small.  Something that is "minuscule" is very small or tiny. Hence, the best option among those provided is "microscopic." The options "shrunken" or "short" do not express the tininess involved in being "minuscule."

When something is "engrossing," it is very interesting, drawing someone's attention completely. It comes from roots that are related to the word "gross" that describes twelve dozen of something. To be "engrossed" is to be entirely taken in an interested by something. Thus, the only appropriate option among those offered here is "engaging."

The word "vague" comes from the same root that we find in "vagabond," which describes a person who wanders around. (Likewise, there is "vagrant", which has a similar meaning.) Something that is "vague" is not clear—as though it "wanders around" clarity but never actually settles on a single meaning or appearance. Among the options given here, the only one that describes such a state of imprecision is "indefinite." Something that is "in-definite" is not well defined or certain. It is hazy and thus "vague."

When something is "arduous" it is difficult, thus requiring a lot of work and effort to be completed. Thus, if we were to say, "The yardwork was an arduous affair", we would mean by this that it was very difficult to complete. Do not confuse this with "ardor," which indicates enthusiasm. These come from different Latin roots.  "Arduous" comes from "difficult," while "ardor" comes from "to burn." The best option for this question is "strenuous". Think of this as meaning, "Requiring a lot of straining (i.e. a lot of difficult work)."

When we describe something as being "manifold," we mean that it involves many different aspects or elements. Thus, the word "numerous" is the best synonym. When we say, "The requirements for the position were manifold", we mean, "There were numerous requirements for the position."

When something is exhilarating, it is exciting or thrilling. This does not mean that it is dangerous, though dangerous things are often exhilarating precisely because of their dangerous nature. Thus, the best option is "invigorating." "Vigor" is energy or enthusiasm. To say that something is "invigorating" is to say that it fills one with energy. Something that is exhilarating does this insofar as it is exciting. Thus, this is the best option among those provided.

When something is "inferior," it is beneath something else. (That "higher" thing is said to be "superior.") The word can be used to describe people. Thus a worker is the "inferior" to his or her boss. The word can also be used to describe things that are deficient in quality. Thus, you could say, "The corn that I bought yesterday was of inferior quality." This means that it was not as good as it could be. The options "minimalistic" and "simple" attempt to have you choose incorrectly. Something that is inferior is subpar or sub-standard. Neither "minimalistic" nor "simple" express this kind of deficiency. Hence, "deficient" is by far the best option among those provided.

Something that is "revolting" is disgusting. Now, this could also be the present participle of the verb "revolt," meaning to rebel, but none of the options presented match that meaning. Therefore, we are looking for something that is akin to "disgusting." While something that is "rotting" is likely to be disgusting, this is not the same being revolting, as "rotting" refers to a specific process of organic decay, not the feeling produced by that process. The only option that provides a direct synonym is "nauseating," which describes something that is sickening (in the way that something revolting is sickening).

The word "progressive" can be used as an adjective to describe a process that changes one step at a time. To make progress literally means "to step forward." (The word "gradual" comes from the same Latin root.) Additionally, the word can also be used to describe something that has already made such progress—a progressive idea is one that is forward-thinking. For this question, the only option that functions as an adequate synonym is "developing." If someone has a progressive disease it is "developing" (in the sense of increasing in its strength and the damage that it is doing).