Mineral Nutrition

Frankia is a filamentous actinomycete that forms nitrogen-fixing root nodules (actinorhizae) on certain non-leguminous plants such as Alnus and Casuarina.
It forms specialised thick-walled vesicles at the tips of its hyphae; the walls contain hopanoid lipids that limit the entry of oxygen and so protect the nitrogenase. This statement is correct.
In hosts such as Alnus it enters through deformed root hairs and stimulates cell division in the cortex, much as Rhizobium does. This statement is correct.
According to the answer key of this paper, the statement that Frankia can induce root nodules on many plant species is the incorrect one, because its host range is restricted to the actinorhizal plants (a limited number of genera such as Alnus, Casuarina and Myrica), unlike the wide range implied.
Note: Frankia can in fact fix nitrogen in the free-living state as well, inside its vesicles, so the statement that it cannot fix nitrogen in the free-living state is also inaccurate; this question is disputed.