The definition of "mundane" is everyday or ordinary, making "common" the only possible choice.

The word “prodigious” is related to the same root word as “prodigy,” which is often used to describe a person who has great skills. For instance, many people talked of Mozart as a “child prodigy” because he could play the piano with great skill at a young age. When something is “prodigious,” it is impressive, magnificent, or at least grand in scope or degree. Among the options provided, “monumental” best captures this sense.

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.