Concept:
In rheology, fluids are classified by how their viscosity (resistance to flow) behaves when you stir or push them harder (i.e., change the shear rate). Newtonian fluids are the simplest case.
Step 1: For a Newtonian fluid, the shear stress is directly proportional to the shear rate, and the proportionality constant is the viscosity.
Step 2: Because that ratio stays fixed, the viscosity remains constant no matter how fast you shear the fluid. Water and simple oils behave this way.
Why the others are wrong: Viscosity rising with shear rate describes dilatant (shear-thickening) fluids; viscosity falling with shear rate describes pseudoplastic (shear-thinning) fluids; a yield value (a minimum stress needed before flow begins) is the hallmark of plastic/Bingham systems. None of these are Newtonian. A Newtonian fluid simply keeps a constant viscosity.
Answer: Option (3) — Constant viscosity irrespective of shear rate.