The correct answer is "gloom is to depression."

This is an analogy that expresses a synonym relationship. "Alarmed and frightened" have a similar meaning, making them synonyms. "Gloom and depression" also have similar definitions, which correctly completes the analogy. 

"Monologue" and "soliloquy" are synonyms, both words refer to a speech given by one single actor during a play. So, to solve this analogy you need to determine which of these words has the same meaning as "underling" (a person of lower-rank, a subordinate). The correct answer is "subaltern." Additionally, "lassitude" is exhaustion, weariness; a "philistine" is an uncultured person; a "syndicate" is a collection of people who have a similar interest and are working together to further that interest; a "repository" is a place for storing things.

Since "novelty" means "the quality or state of being new, different, and interesting," and "outdatedness" means "the quality of no longer being useful, acceptable, modern, or current," "novelty" and "outdatedness" are antonyms, and we need to pick out an answer choice that is the opposite of "dull." While "ennui" may look like a good answer choice, "ennui" means "a lack of spirit, enthusiasm, or interest," so while one might feel ennui at the prospect of doing something dull, "ennui" does not mean the opposite of "dull," so it can't be the correct answer. "Sharp," however, is an antonym of "dull" when "dull" is used to mean "having an edge or point that is not sharp," so "sharp" is the correct answer.

Since someone who is generous is not miserly ("hating to spend money"), the two words are antonyms, so we need to pick out a word that means the opposite of "incorrigible." "Incorrigible" is an adjective that refers to people or their tendencies, and means "not able to be corrected, improved, or reformed." While "corrugated" sounds somewhat like "incorrigible," "corrugated" means "shaped into alternate ridges and grooves" and is used with materials, surfaces, and structures. Since "corrugated" is not an opposite of "incorrigible," it can't be the correct answer. "Correctable," however, means the opposite of "incorrigible," so "correctable" is the correct answer.

"Candor" is a noun that means "the quality of being open and honest in expression; frankness," so it is an antonym of "falsehood." That means that we need to pick out an answer choice that consists of a pair of antonyms. While "anger is to fury" might look like a potentially correct answer, "anger" and "fury" are synonyms, not antonyms, so it cannot be the correct answer. "Happiness is to misery," however, is the correct answer, because just as "candor" is an antonym of "falsehood," "happiness" is an antonym of "misery."

"Hazy" and "clear" are antonyms, so we need to pick out an answer choice that is an antonym of "livid." "Livid" is an adjective that means "furiously angry." So, "mad" cannot be the correct answer, because while "mad" and "livid" are synonyms, we are not looking for synonyms, but antonyms. "Pleased," however, is an adjective that means "feeling or showing pleasure and satisfaction, esp. at an event or a situation," and because "pleased" is the answer choice that is most nearly an antonym of "livid," "pleased" is the correct answer.

“Doubt” is a word that when used as a verb can mean “ feel uncertain about,” “question the truth or fact of (something),” or “disbelieve (a person or their word).” “Trust,” on the other hand, when used as a verb, means “believe in the reliability, truth, ability, or strength of.” So, “doubt” and “trust” are antonyms, and we need to pick out an answer choice which consists of a pair of antonyms. While “hurry is to hustle” might look like a potentially correct answer choice, “hurry” means “move or act with haste; rush” when used as a verb, and “hustle” can be used as a verb that means “hurry; bustle,” so the two words are synonyms, not antonyms, and “hurry is to hustle” cannot be the correct answer. “Heal is to wound,” however, consists of a pair of antonyms, because “wound” can mean “inflict an injury on (someone)” whereas heal can mean “cause (a wound, injury, or person) to become sound or healthy again” when used of a person or treatment. So, because “heal” and “wound” are opposites just as “doubt” and “trust” are opposites, “heal is to wound” is the correct answer.

"Corpulent" means fat, so it is an antonym of skinny. In order to solve this analogy you have to determine the best available antonym for comely. "Comely" means cute, so the best antonym is “ugly.”

"Penurious" means stingy or not very generous and is an antonym of "generous." To solve this analogy you have to identify the most accurate antonym for feral. "Feral" means wild, untamed, so the correct antonym is “domesticated,” which means house-trained; a dog is an example of a domesticated animal.

"Unbelievable" is an antonym of plausible, so to solve this analogy you have to determine the best antonym for robust. "Robust" means in good shape, healthy, so the correct antonym is unhealthy.