DULCET : RAUCOUS

Dulcet refers to something which is very pleasing or pleasant; whereas, raucous means something thats very loud, harsh and unpleasing. The given words are antonymous.
Option (a) is right because sweet or pleasing cannot be antonymous to song. A song can, in fact, be very sweet or pleasing.
Option (b) is similar to the relationship in the given question as words in it are antonyms to each other: crazy means lacking sanity or showing madness whereas sanity refers to having a proper and logical state of mind.
Option (c) is wrong, because palliative is something which smoothens or reduces pain or sorrow, but isnt expected to cure or remove the trouble. For example: a heating pack is a palliative when it is implied to temporality reduce the pain due to strained muscles. Exacerbating refers to making things worse or making a situation more painful or difficult.
Option (d) is wrong because the words here are antonyms too.