Quantum mechanically accurate calculations are carried out for the following reactions involving muonium atom (Mu) using the hyperspherical coordinate approach : Mu+H-2-->MuH+H, Mu+D-2-->MuD+D, Mu+HD-->MuH(MuD)+D(H), H+MuH-->MuH+H, and H+MuD <->MuH+D. The initial vibrational state is restricted to the ground state(v(i)=0) and the collision energies considered are up to similar to 1.2 eV. The various aspects of the dynamics, such as the isotope effects, the initial rotational state (j(i)) dependence, and the final rotational state (j(f)) distribution are analyzed for a wide range of j(i) and j(f). Some of the isotope effects can be interpreted in terms of the variations in reaction barrier and endothermicity. The following two intriguing features are also found : (1) strong enhancement of reaction by initial rotational excitation, and (2) oscillation of integral cross section as a function of collision energy in the case of the Mu-transfer reactions.