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Solutions
The sentence implies that his parents did not agree with his plan of becoming a musician.
'Opposed' meaning 'anxious to prevent or put an end to; disagreeing with' is the apt fit for the blank.
The meanings of the other words are:
Contrasted: differed strikingly.
Contrary: opposite in nature, direction, or meaning.
Resisted: withstood the action or effect of.
Hence, option B is the correct answer.