Four statements are given below:

(P) ${\mathrm{B}}_2$ solid does not exist, boron have basic building ${\mathrm{B}}_{12}$ icosahedral units made up of polyhedron having 20 faces and 12 corners.

(Q) In alum each metal ion is surrounded by six water molecules.

(R) Graphite is used as dry lubricant in machine running at high temperature in place of oil.

(S) Fullerene contains twenty, six-membered rings and twelve, five-membered rings.

The correct statements are:

Six water molecules surround each metal ion in alums. They liquefy when heated, and if the heat is kept up, the water that would otherwise form crystals is forced away, the salt froths and expands, and eventually just an amorphous powder is left.
Twenty six membered rings and twelve five membered rings of carbon atoms make up fullerence, which resembles a soccer ball. Five membered rings are only connected to six membered rings while six membered rings are fused with both six membered and five membered rings.
Graphite is highly soft and slippery because it cleaves easily between the layers. It is therefore applied as a dry lubricant in machinery that operates at high temperatures.