Answer : 1. "proficiency"
Explanation :

The appropriate word to fill in the blank is:

A) proficiency

So the sentence would be: "She is known for her proficiency in mathematics."

Explanation:

"Proficiency" is a noun that means a high degree of skill or expertise in a particular area.

"Proficient" is an adjective, so it wouldn’t fit the blank that needs a noun.

"Proficients" is not a standard word in this context.

"Proficiently" is an adverb and does not fit as it describes how something is done rather than a noun indicating skill.