The sentence is looking for an adjective to modify "aluminum" that helps to explain why casual cooks might prefer it to a cast iron skillet. Aluminum is already lighter than iron, so the missing word probably has something to do with the coating that is mentioned. 

Since the word is preceded by "an" rather than "a," it must begin with a vowel, so "cumbersome" isn't correct (and besides, it means the opposite of lightweight). "Amalgamated" means "put together from several parts." That could potentially describe this aluminum pan, except the sentence doesn't say anything about what the alumnimum might have been put together with. "Ossified" means turned to bone, which seems like a bad way to improve an aluminum pan. "Undiluted" refers to a concentrated liquid and is nonsensical when applied to a metal pan. "Anodized" specifically means to apply a coating to a metal surface using electricity, so that is definitely the best word here.

The traditionalist politican proposed an "uncompromising solution," while the dissident voices of the public felt differently. The blank follows the phrase "not as . . .", thus, "unequivocal" is the correct choice, as the public felt the issue was more ambiguous than the politican made it out to be.  

The sentence indicates that the way she speaks is outdated. "Anachronistic" conveys that her speaking is more fitting for a different time.

The subject wishes to be a "fair judge," therefore "her chief obligation" would be something indicating fairness. The correct answer should mean neutral or objective, the definition of "dispassionate."

The sentence describes a legal proceeding and notes that the prosecution had circumstantial evidence. The correct answer will indicate certain or secure evidence. "Forensic," meaning specific legal processes and standards, is the best answer choice.

The subject picks up "percussion instruments easily" as a result of the kind of "sense of rhythm" she possesses. This means the correct answer will show she has a natural "sense of rhythm." "Innate," meaning present from birth, inherent, or ingrained, is the best choice.

The subject routinely gets beaten by "more creative" players, which means he is not very creative. The correct answer needs to mean common or mundane, the definition of pedestrian.

The dislike of "any kind of unfamiliar" cuisine means the subject is unsophisticated or unwilling to change. "Provincial," literally meaning from the outskirts, but also meaning unsophisticated or narrow minded, is the correct answer.

The sentence states that "outlandish stories" were widely believed. The correct answer will indicate a similar absurdity of the "rumors." "Specious," meaning false or unreliable, is the best fit among the answers.

If the "formerly religious" feel the groups they left have a "problematic concern," it is reasonable they view the sins lightly. The correct answer should mean minor or unimportant, the definition of "venial."