Direction of induced current in all the situations shown above can be decided in the light of Lenz’s law.
Fig. (a) : South pole is moving closer, so the current is clockwise in the end of solenoid closest to magnet. Fig. (b) : Following Lenz’s law, the current flow anticlockwise in the loop at the left and clockwise in the loop at the right. Fig. (c) : Induced current in the right loop will be along xyz. Fig. (d) : Current is decreasing with increase in rheostat, so North pole is getting weaker, the current in inner part of loop-1 will flow clockwise. Fig. (e) : Induced current in the right coil is from X to Y. Fig. (f) : No induced current since magnetic lines of force are in the plane of the loop.