What are analogous organs? 

Concept: The organs which have diverse life structures but perform comparative capacities are called as practically equivalent to organs. They have distinctive root. Example: wings of creepy crawlies and feathered creatures. Sweet potatoes and potatoes both have the same work of nourishment capacity but have diverse beginning. The organs with similar functions but different structures are regarded as the analogous organs. An example of an analogous organ is the wings of the insects and birds that perform the same flying process.

Therefore, a lobster's tailfin and a whale's flukes are analogous organs.

Hence,the correct answer is option A.