An effective medium approach together with a multiple scattering formalism is considered to study the steady-state dynamics of suspensions of spheres and rigid stiff polymer chains (Gaussian) without excluded volume interactions. The translational diffusion coefficients of the moving probe sphere and of the probe polymer chain, and the shear viscosity of the suspensions have been derived for finite volume fractions of spheres FSP and of polymers FPOL. The role of the geometrical parameter

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... a ("a" is the radius of any sphere and R_g the radius of gyration of a polymer chain) is discussed. Dynamics of the probe objects is frozen when FPOL approaches 0.31. An optimum range of FSP that maximizes the difference in the diffusion coefficients of polymer chains characterized by distinct "t" values has been noticed.