No, but you are right in thinking that there is no single correct answer. Since the vegetables listed don't have much in common aside from being vegetables, I wouldn't use (A). But "and so on" simply means "and other vegetables", and "etc." means the same as "and so on"—so both answers (B) and (C) are correct.The sentence is: "I like to eat vegetables such as celery, cucumber, turnip, eggplant, __."
There are three choices:
A. and the like.
B. and so on.
In my view, all the choices are right. Am I right?