The relationship between FAULTFINDER and CRITICISE is that a faultfinder is someone who actively engages in criticizing. Similarly, an arbitrator is someone who actively engages in mediation to resolve disputes. Both pairs indicate the primary action performed by the subject.

The relationship between MUTTER and INDISTINCT is that muttering is speaking in a way that is indistinct or unclear. Similarly, drone refers to a continuous, dull sound that is monotonous. Both pairs describe an action or sound with its defining characteristic.

The relationship between FRAGILE and BREAK is that something fragile is prone to breaking. Similarly, something flammable is prone to burning. Both pairs indicate a characteristic that leads to a specific outcome.

The relationship between ESCAPE and CAPTURE is one of opposition: escape is the act of avoiding capture. Similarly, invest (putting money into something) is in opposition to bankruptcy (losing all money). Both pairs represent conflicting outcomes.

The relationship between CHOREOGRAPHY and DANCE is that choreography is the planned structure or design that organizes a dance. Similarly, a plot is the structured framework or design that organizes a story. Both represent the blueprint or foundation of the respective outcome.

The relationship between STUDY and LEARN is that studying is an action taken to achieve learning. Similarly, searching is an action undertaken to achieve finding something. Both relationships represent a process leading to an outcome.

The relationship between NUMB and INSENSIBLE is that "numb" describes a state of being "insensible" or unable to feel. Similarly, "repulse" is a reaction to something that is "odious" or repulsive, as "odious" describes the quality that causes repulsion.

A mercenary is motivated by money to fight, just as a vindictive person is motivated by revenge. Both relationships show that the second term is the driving force behind the actions of the first term. The other options do not clearly establish such a motivation-action connection.

The relationship between DIVIDE and UNITE is one of opposites (divide means to separate, and unite means to bring together). Similarly, Fission (splitting) and Fusion (joining) are opposites in the context of physical processes. The other options either involve synonyms or are not as directly related to the concept of division and unity.

The relationship is that a gourmet is someone who has refined taste and expertise in food. Similarly, a connoisseur is someone with refined taste and expertise in art. The other options don't reflect this subject-to-expert connection as clearly.