Step 1: Separate the behavior into a shear rate dependence and a time dependence:
Rheological behavior of a fluid can be split into how apparent viscosity changes with shear rate at a given instant, and how it changes with time at a fixed shear rate. Drilling fluid design has requirements on both counts.
Step 2: Consider the shear rate dependence, options (A) and (B):
In terms of shear rate, a fluid is either dilatant, viscosity rises as shear rate rises, or pseudoplastic, viscosity falls as shear rate rises. A drilling fluid needs low resistance to flow at the very high shear rates through the bit jets, but must still carry cuttings at the lower shear rates in the annulus, which is the classic pseudoplastic (shear thinning) signature. A dilatant response would work against efficient hydraulics, so it is not the behavior of a conventional drilling fluid. This confirms option (B) as correct and rules out option (A).
Step 3: Consider the time dependence, options (C) and (D):
In terms of time dependence at constant shear, a fluid is either thixotropic, viscosity or gel strength falls with time under shear and rebuilds at rest, or rheopectic, viscosity rises with continued shearing. Drilling fluids must gel when circulation is stopped so that cuttings and barite do not settle in the annulus or the hole, and this gel must break down quickly once pumping resumes, which is thixotropic behavior. Rheopectic behavior would mean the fluid keeps thickening while being pumped, which is not how drilling fluids behave. This confirms option (C) as correct and rules out option (D).
Step 4: Combine both dependencies:
Since the drilling fluid must be shear thinning with shear rate and gel forming with time at rest, both pseudoplastic and thixotropic describe the same fluid at different levels, one in the shear rate domain and one in the time domain.
Final Answer:
\[ \boxed{\text{(B) Pseudoplastic and (C) Thixotropic}} \]