Correct option is B
The correct sentences, to use the given word correctly, are (A) & (B).
The term “ eminently” to a great degree, as in extremely.
The sentence (A) uses "eminently" correctly. It describes the professor's high level of qualification with a wealth of knowledge and research experience, indicating an exceptional degree of qualification.
The sentence (B) also uses "eminently" correctly. It describes the politician's highly charismatic personality, indicating an outstanding or exceptional level of charisma.
The sentence (C) is incorrect. "Eminently" is not suitable in this context. A more suitable word in this context might be "effectively" or "successfully."