The antonym for well is bad. Therefore, “student sang well” is connected with connecting word, “but”. This is followed by connecting with a “sentence” with “she danced badly (badly –adverb)”.
The correct word formation is as described above. The other sentences are not become meaningful if we fill with poor or poorer in the above sentence.
Thus, the options (d), (c) and (a) are incorrect.
The antonym for well is bad. Therefore, “student sang well” is connected with connecting word, “but”. This is followed by connecting with a “sentence” with “she danced badly”.
Therefore, the correct option is – b. badly.