“Ostracize” means banish from a community, or "exclude." As for the other answer choices, “include” means make part of a whole; “involve” means allow to be a part of; “hallow” means make sacred or consecrate; and "suggest" means put forward an idea directly or indirectly.

“Feign” means pretend, simulate, or "fake." As for the other answer choices, “suspend” means pause or stop; “preempt” means take action to prevent something from happening; “pursue” means chase after; and “rouse” means awaken or motivate.

To “pry” means to force two things apart, most often using some sort of lever; it can also mean to question, to become involved in by asking about, or to "inquire." As for the other answer choices, “expire” means run out, die, or stop being binding (in the case of formal documents); “embroil” means get mixed up in or involve someone or oneself in a conflict; “dismay,” when used as a verb, means or cause one to feel shocked, sad, and hopeless; and "bind" means attach securely, tie together the hands and feet in order to restrain, unite, or make something mandatory for someone, as in a "binding contract."

When someone feigns illness, he or she pretends to be sick. The word "feign" most directly signifies the act of pretending or dissimulating. Often (likely most of the time), this is done so as to lie. The actual act of pretending is the "feigning." The lying may well just be the reason for the pretending. The two are not the same, so do not be tricked by several of the options that try to lead you to say that they are. Thus, the best option is the simple, "pretend."

The word "modulate" contains the same roots that are found in the related word "moderate." The "mod-" prefix has a rich history, though it generally indicates that something has been measured. Thus, a "moderate" temper is one that has just the right amount of anger, excitement, sadness, and so forth.  To "accomodate" is to match the needs of someone else (thus, to meet his or her "measure"). When someone modulates his or her voice, he or she adjusts it to a given situation—thus "measuring" the voice to match the situation.  Thus, the best option for this question is "regulate."

The word "recant" comes from two somewhat common roots. The "re-" prefix can mean again. It can also indicate that something turns around (as in re-verse, for instance). The "-cant" portion of the word is derived from the Latin for to sing. Thus, we have words like "chant" and "cantor." When someone recants something, he or she takes back a remark made in the past. Thus, when we say that someone "recants his allegiance to the king of Spain", that person denies that he has such allegiance, though he did have it once upon a time. Although "renounce" would be an even better synonym, the option "deny" is sufficient for this question.

"Befuddle" means to cause someone to think unclearly. Of the answer choices only "confuse" is related to unclear thoughts. "Enlarge" and "diminish" both refer to changes in size, getting bigger and smaller respectively. "Explaining" makes a concept clearer which makes it an antonym of "befuddle." "Obscure" is the most similar word after "confuse," but it often refers to physical obstruction of a view rather than making an idea unclear.

"Rebut" means to prove a claim is false in the course of an argument.

"Contradict" is closer than "argue" because a "rebuttal" is a rhetorical device often used within an argument rather than the argument itself, "agree" is an antonym of "rebut," "slip" means to fall or trip, and "exclaim" means to say something excitedly.

"Peddle" means to sell or to travel around selling something. To provide further help, "sentence" means determine the punishment for; "portray" means depict, show. 

To "swindle" someone means to cheat him or her out of money. To provide further help, "mollify" means sooth, calm, relieve; "redeem" means make right something done wrong; "plead" means beg, urge.