The blank precedes the noun 'knowledge', so it must be filled with the adjective/determiner that can modify the noun. Among the given options, only 'their' is the adjective/determiner (possessive) which can be used in the blank to modify the given noun.
So, the correct sentence is: Their knowledge in this field is really profound.
Hence, option (b) is the answer.
Note: Possessive Determiners/Adjectives: Words like 'my', 'our', 'your', 'his', 'her', 'its', and 'their' are known as possessive adjectives (or possessive determiners). They come before nouns and indicate ownership of the noun. Example: "The teacher asked the students to open their drawing books."
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