The word "equanimity" means calmness and composure, especially in difficult situations. Therefore, the word that is most nearly the opposite in meaning to "equanimity" is option B, "excitement."

When someone displays "equanimity," they remain calm and composed, even in challenging or stressful situations. In contrast, "excitement" usually involves a feeling of enthusiasm, eagerness, or arousal, which is the opposite of calmness and composure.

Option A, "duplicity," means deceitfulness or dishonesty, which is not directly related to "equanimity." Option C, "dubiousness," means uncertainty or doubt, which is also not directly related to "equanimity." Option D, "resentment," means bitterness or anger towards someone or something, which is also not directly related to "equanimity." Therefore, B is the best choice as the opposite of "equanimity."