The correct statements among the following are-

a. Fullerenes have dangling bonds

b. Fullerenes are cage-like molecules

c. Graphite is thermodynamically most stable allotrope of carbon

d. Graphite is slippery and hard and therefore used as a dry lubricant in machines.

1. (a, b)
2. (b, c)
3. (c, d)
4. (a, d)


Hint: Fullerenes are cage-like molecules

Fullerene an allotrope of carbon with finite number of carbon atoms with closed cage structure has been identified. The C60 isotope is more dominants. The structure is nearly spherical, like football.
Sphere is formed by the combination of 20 hexagons and 12 pentagons. The structure of C60 is as follows:


Graphite is thermodynamically more stable than all allotropes of carbon.
Dangling bond is an unsatisfied valence on an immobilized atom. It is also known as immobilized free radical or an immobilized radical. 
Diamond(1 0 0) surfaces have two dangling bonds per surface carbon atom in the ideal unreconstructed (1×1) structure.

graphite is slippery but not HARD structure.