The key phrase in the sentence is "laid-back demeanor." The correct answer choice will reflect the "laid-back" approach. Only "ambivalence," which means state of being undecided and not caring, has the appropriate connotation in the sentence.

The principal, in his authoritarian capacity, would be trying to calm down troubles at the school. The person the principal is locating is the "ringleader" or cause of the trouble, ruling out "passerby," "bystander," "follower," and "hermit." The correct answer choice, "instigator," means person who started something.

"Linguists" study languages (notice the similarity in the words). In this case, we are looking for a type of person who would work with old languages, so this fits perfectly.

"Proximity" means simply nearness to something. Here, we are given contextual clues that tell us that their restaurant choice had something to do with their apartment. All the answers would be reasons to choose the place, but "proximity" is the only one that has to do with their apartment.

"Negligence" is a noun which means act of choosing not to (neglecting to) do something. Here, it is clear that not tending the garden is what has led it to become chaotic.

The correct answer will point out the incredible bout of good fortune that allowed the general's scouts to find the plans, something that wasn't planned at all. The incorrect answers will either misinterpret the episode as a case of bad luck ("mischance"), poor circumstances ("adversity"), or a failure to address the topic at hand ("temerity"). "Spontaneity" comes close by referring to the seeming randomness of the event, but is not as good of a fit as "serendipity."

Since the girl is afraid of the dark, it would be very important to bring a flashlight on Halloween. This importance is stressed by the sentence's use of "absolute." The only answer choice that conveys this sense of importance is "necessity," making it the correct answer.

The sentence describes a speech given following someone’s death that is moving; this indicates that the correct answer is eulogy. A eulogy is a tribute or speech given for someone who has died. Of the four incorrect answer choices only presentation is even a little correct; but is a far inferior answer choice to eulogy. Satire refers to a use of wit to critique something. 

The second clause reveals that the first blank must refer to the “loyal companionship” of dogs. The correct answer is therefore fidelity (which means loyalty). One of the most common names for a dog, Fido, comes from the same Latin root if this helps you to remember. Nuisance and intractability both describe something that is difficult to deal with; discretion means judgment or prudence; jubilance means happiness.

From the words used in the second clause of the sentence you know that the blank must describe a brief relationship. Of the five answer choices dalliance most closely matches this meaning. Dalliance refers to an affair or flirtatious episode or frivolous experience. Discernment describes good judgment; arrogance means cockiness; fright refers to fear; cruelty describes the deliberate causing of pain or anguish.