Step 1: Understanding the Concept
Honey bees show haplodiploid sex determination.
Step 2: Origin of each caste
Fertilised diploid eggs become females, that is workers, or queens when fed royal jelly. Unfertilised haploid eggs develop into males called drones.
Step 3: Conclusion
Development of an egg without fertilisation is parthenogenesis. So a drone forms by parthenogenesis.
Final Answer:
A drone develops from an unfertilised egg by parthenogenesis.
\[ \boxed{\text{(C) }\text{parthenogenesis of unfertilized egg}} \]