Secretly is the opposite of openly, and silently is the opposite of noisily. Choices a and b are clearly not the opposites of silently. (Choice d) means the same thing as silently.
Careful and cautious are synonyms (they mean the same thing). Boastful and arrogant are also synonyms. The answer is not (choice b) because humble means the opposite of boastful. The answer is not choice c or d because neither means the same as boastful.
EXAMIANS