Answer
$F_{x}\left( 1\right) =F_{x}\left( 3\right) > F_{x}\left( 2\right) =0$
Work Step by Step
Magnitude of horizontal force acting on rod by the hinge is equal to the magnitude of horizontal component tension on the rope (because there is no other horizontal force).
Vertical components of tensions in all 3 situations are the same because the net torque is zero ( and the distances are same).
So in situations (1) and (3), the magnitudes of horizontal components of tension on the rope are the same (because of same vertical components and same angle relative to vertical line) and in situation (2), the horizontal component of tension on the rope is zero (because rope is vertical).
Therefore, the comparison will be :
$F_{x}\left( 1\right) =F_{x}\left( 3\right) > F_{x}\left( 2\right) =0$
