<p>A theoretical investigation of dust acoustic shock waves (DAShWs) in a magnetized dusty plasma containing Cairns distributed electrons, inertial negatively and positively charged dust grains, and Maxwellian ions has been carried out. The Burgers equation is derived by employing the reductive perturbation method to examine the propagation of small but finite amplitude DAShWs. The effect of intrinsic parameters (viz. nonthermal parameter, the kinematic viscosity of the dust grains, number density of positive-to-negative dust, ion-to-negative dust number density, electron-to-ion temperature ratio, oblique angle) on the basic characteristics of DAShWs has been examined. The coexistence of shock structures with positive and negative potential is found. It has been found that the polarity of DAShWs depends on the ratio of electron-to-ion temperature as well as the number density of ion-to-negative dust. The results of this study could aid in understanding wave propagation in both laboratory and space plasmas.</p>