This paper reports the systematic investigation performed to bring out the effects of combustion-flow coupling with variable density and the presence of inherent shear layer in altering the response of non-premixed ducted flame to acoustic like external perturbations imposed at the inlet plane. Due to expansion brought in because of density variation with temperature, the flame responds poorly when compared to its constant-density counterpart at higher frequencies whose time scales are smaller than the convective time scales. The difference in the response between the constant and variable density cases diminishes as the acoustic time scales approaches the diffusive time scales. The flame response is further decreased in the presence of inherent shear layer, as in the case of a flame stabilized at a backward-facing step. The response of the cold-flow shear layer to inlet acoustic like perturbations is shown to play a role in determining the response of the flame. The shear layer amplifies or attenuates the inlet flow fluctuations, which in turn affects the flame depending upon its stabilization location in the shear layer in the various conditions considered.