"Athletic," "frisky," and "limber" are synonyms of agile. "Agile" means to be quick and well coordinated in movement.

"Lethargic" means to be drowsy or slugglish.

"Inert," "lethargic," and "lackadaisical" are synonyms of indolent. "Indolent" means slow or lazy, while "energetic" means full of energy.

"Nimble," "agile," and "limber" are synonyms of lithe. "Lithe" means moving or bending with ease, while "clumsy" means awkward in movement or action.

Something that is erratic has no pattern and happens at unknown intervals. The word is related to the word “err” and “error,” as these words all come from a Latin base that means “to stray.” When we make an “error,” we “stray from the right path.” Something “erratic” strays from any pattern—which would be like a straight line. In contrast to something “erratic,” “steady” is an excellent antonym.

To fasten something is to latch or attach it to something else. When you fasten a chest-strap on a book bag, you latch together two clips, joining them together at one connection point. The opposite of such an action of fastening is “unlatching,” which quite obviously means “to remove a latch or undo a latching.”

When someone is in haste, that person acts in a very speedy manner, often in an over-hurried manner. To “make haste” is to act rapidly to accomplish something. “To delay” is the opposite of making haste. While someone who is slothful or slacking might be less likely to make haste, the only direct antonym among the possible answers is “delay.”

A torrent is a very forceful movement of water. When something flows “torrentially,” it does so with great speed and quantity. In contrast to this, a trickle is a small flow of water—an apt antonym. The options “river” and “flow” mean to trap you by mere association with water. The options “illegal” and “licit” likewise are traps since the word “torrent” is associated with a type of computer file sharing method that is sometimes used in a legally questionable manner.

For this word, following your hunch likely will help if you do not know the vocabulary. The primary sense of the word “variegated” is “multicolored,” particularly meaning that those colors are arranged in an irregular pattern. This is often used to describe certain types of multicolored leaves.  If you saw the word “varied” in the word “variegated,” you would potentially be able to answer this without having direct knowledge of “variegated.” Only “monotonous” is sufficiently opposed to the notion of variety for our needs. Something monotonous has a single character—a single tone (color, sound, etc). It can describe a voice that does not change its pitch as well as a picture that has a single color.

When something is “dormant” it could be said to be “sleeping.” A closer meaning to the standard English usage of the word would be “inactive.” It does have a relation, however, to the notion of sleeping, as could be inferred by its relationship to the word “dormitory,” which means “sleeping room” or “building for sleeping.” In contrast with inactivity or “dormancy,” only “active” functions as an adequate antonym.

When something lingers, it remains in a given area, as when a smell lingers in the kitchen after cooking or a guest lingers for some time after dinner, talking about many things and not leaving the house; therefore, in a very broad sense, you could say that “to linger” means “to stay.” The best contrast with this among the options provided is “depart,” meaning “to leave.”