Final answer:
The assumptions for deriving Bernoulli's equation are that the fluid flow is frictionless (I), steady (II), incompressible (V), and occurs along a streamline (VI), making option C the correct answer.
Step-by-step explanation:
The correct set of assumptions used in the derivation of Bernoulli's equation is I) Fluid flow is frictionless, II) Fluid flow is steady, V) Fluid is incompressible, and VI) Fluid flow occurs along a streamline. Therefore, the correct answer to the question is C. I, II, V, VI. Bernoulli's principle is based on the conservation of energy for a fluid in motion and states that the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume is constant along a streamline for an incompressible, non-viscous fluid.