Read the following sentences and choose the ones belonging to the domain of compound sentences.
(A) Her fear is that she may fall ill.
(B) Sheela is clever, still she does not do well in her studies.
(C) Noel was caught stealing, therefore he was punished.
(D) That animal is either a fish or a serpant.
Choose the correct answer from the options given below :

A compound sentence is one that contains two or more independent clauses joined by a coordinating conjunction (and, or, for, but, etc). Let's analyse the sentences one by one:

(A) Her fear is that she may fall ill.
This is a complex sentence with one independent clause ("She may fall ill") and a dependent noun clause ("Her fear is that"). It is not compound.

(B) Sheela is clever, still she does not do well in her studies.
This contains two independent clauses ("Sheela is clever" and "she does not do well in her studies") joined by the conjunctive adverb "still," functioning like a coordinating conjunction. It is compound.

(C) Noel was caught stealing, therefore he was punished. 
This has two independent clauses ("Noel was caught stealing" and "he was punished") linked by "therefore." It is compound.

(D) That animal is either a fish or a serpent.
This is a Compound Sentence because it connects two independent clauses ("That animal is  a fish" and "[that animal is] a serpent") using the coordinating conjunction "either...or".

The correct answer is option b) (B), (C) and (D) only.