This set of words is a bit strange, but given that both “opaque” and “translucent” are found among the options, let us realize that it must have something to do with how light passes through a surface. The other three words all relate to the state of being soiled or dirty, indicating that in such a case there would be little light that could pass through an otherwise clean surface (e.g. a piece of glass). Something “opaque” completely prevents light from passing through; therefore, the word “translucent” is the best option among those provided, as it means allowing light to pass through. The “trans-” prefix, meaning across, is added to “-lucent,” which means pertaining to light. It therefore literally means letting light across.

This whole set of words is related to being clean, however, not to the same degree. To be “sterile” is to be completely free of any dirt or potentially infectious material. Even something “sanitary” (clean and generally safe with regard to health) is not necessarily as clean as something that is completely sterile; therefore, “sterile” is the word least related to the others.

"Philanthropic" means charitable. If a person is "haughty," "conceited," "pompous," or "pretentious," she is arrogant, or thinks her abilities are superior to everyone else's. All four of these words describe more than just confidence. Also, all four of these terms are pejorative, and philanthropic has positive connotations.

"Devoid" is an adjective meaning entirely lacking. I might say, "The terrorist was devoid of all emotion." "Brilliant," "clever," "canny," and "astute" are all synonyms for the word "intelligent."

"Mutinous" means to refuse the orders of a superior. It is usually applied to people in the armed forces. "Disgusting," "revolting," "abhorrent," and "vile" all imply something that creates a feeling of strong disgust. For example: "Cleaning the outhouse was completely vile." You could substitute any of the other three words for "vile" and have the same basic meaning.

Although all of these words mean "silent," four of them are adverbs and one is an adjective. Adverbs describe how a verb is performed. For instance, HOW does Johnny run?  He runs quickly. Quickly is the adverb. Most adverbs end in -ly. "Inaudible" is an adjective. Adjectives describe nouns. For instance, "The actor was inaudible over the noise of the crowd." Inaudible is the adjective describing the actor, a noun. 

All five words can be used to describe a person. "Beautiful," however, is generally used to describe a person's physical appearance. "Deranged," "curious," "brilliant," and "methodical" are generally used to describe a person's personality or state of mind.

Each of these words are adjectives, so we can't make a distinction based on the part of speech. "Elderly," "juvenile," "youthful," and "senior" all describe age. "Glorious" is a synonym for "wonderful," or "superb." "Glorious" does not describe age.

All five words are adjectives that describe a person's ability. "Inept" means incompetent, or unskilled. The "inept" teacher might routinely lose her students' papers. "Competent," "proficient," "skilled," and "qualified" are all synonyms meaning capable, or able to complete the assigned tasks. These words are all antonyms of "inept." 

When someone is “indolent,” he or she is lazy. The word “dolor” means “sadness or distress,” and “indolent” literally means “wishing to avoid any distress (hence, any work).” The other options all indicate personality aspects that are full of energy. The only word among them that might be a bit unknown is “vigorous,” which means “healthy and full of energy or strength.”