Option 1 states that fullerenes have only six-membered carbon rings. Fullerenes are actually composed of carbon atoms arranged in a spherical or cylindrical shape, forming a cage-like structure. These carbon cages can contain a varying number of carbon atoms, such as C60 or C70, and are not limited to having only six-membered carbon rings. Therefore, option 1 is incorrect.

Option 2 correctly states that fullerenes are cage-like molecules. Fullerenes, such as Buckminsterfullerene or C60, are composed of carbon atoms arranged in a three-dimensional structure that resembles a soccer ball or a geodesic dome. This unique structure makes fullerenes useful in various applications, including in the field of nanotechnology.

Option 3 states that diamond is thermodynamically the most stable allotrope of carbon. This statement is correct. Diamond, with its tightly bonded carbon atoms in a three-dimensional lattice, is highly stable and has the highest hardness among all known natural materials.

Option 4 states that graphite is slippery and hard, and is therefore used as a dry lubricant in machines. Although graphite is slippery, it is not hard. In fact, graphite is a soft material due to its layered structure, which allows the layers