Analogous structures are those organs which are structurally different, but they perform the same set of functions. Of the given pairs of structures, the gills of prawns and lungs of man are analogous in nature. Both of these are respiratory structures, which are anatomically different from each others. The lungs of man are balloon-like sac organs which inflate and deflate on breathing, while gills of prawn are crescent-shaped organs which perform gas exchange for respiration.
Wings of bat and wings of pigeon have anatomically similar structures as well as they perform the same function of flying. Hence, it is difficult to strictly mark them as analogous or homologous.
The other two examples exhibit homology. That is, they are structurally the same, but they perform different functions.