For which of the following fluids, the apparent viscosity can be considered to be independent of the rate of shear strain and equal to the fluid's viscosity?

Option 2 : Water

Thixotropic: 

Apparent viscosity for Newtonian fluid can be considered to be independent of the rate of shear strain and equal to the fluid's viscosity. Hence the correct answer is water.

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Examples of other fluids:

Rheopectic fluids:

Apparent viscosity for Rheopectic fluids increases with time under constant applied shear stress.

Very rare liquid-solid suspensions, gypsum suspension in water and bentonite solutions, Printer’s ink

Newtonian Fluids:

Air, water, mercury, glycerine, kerosene, and other engineering fluids under normal circumstances.

Pseudoplastic or shear-thinning fluid:

Fine particle suspension, gelatine, blood, milk, paper pulp, polymeric solutions such as rubbers, paints.

Dilatant fluids or shear thickening fluid:

Ultra-fine irregular particle suspension, sugar in water, aqueous suspension of rice starch, quicksand, butter printing ink.

Ideal plastics or Bingham fluids:

Sewage sludge, drilling muds.

Viscoelastic fluids:

Liquids are solid combinations in pipe flow, bitumen, tar, asphalt, and polymerized fluids with drag reduction features.