Which one of the following characteristics of the transition metal is associated with their catalytic activity?

Variable oxidation states

The answer is (1) variable oxidation states.

Transition metals are able to exist in multiple oxidation states, which means that they can change their valence electrons. This ability to change oxidation states is important for their catalytic activity because it allows them to form bonds with different reactants.

The other options are not directly associated with the catalytic activity of transition metals.

Color of hydrated ions:  The color of hydrated ions is due to the d-electrons in the transition metal ion. This property is not directly related to catalytic activity.

Paramagnetic behavior:  Paramagnetic behavior is due to the presence of unpaired electrons in the transition metal ion. This property is not directly related to catalytic activity.

High enthalpy of atomization:  High enthalpy of atomization is due to the strong metallic bonding in transition metals. This property is not directly related to catalytic activity.

So the answer is (1), variable oxidation states.