Graphite is thermodynamically more stable than diamond, diamond is kinetically stable thus statement c is incorrect. 

Graphite is an allotrope of carbon. It is an electrical conductor due to vast electron delocalisation within the layers. These are mobile electrons hence responsible for electrical conduction.

The bonds between carbon atoms in diamond are covalent because covalent bonding is the only option when only nonmetals are present.

Catenation is a self-linking property which is maximum present in carbon, because of this property large number of carbon atoms joined together to form molecule.

Buckyballs, diamond and graphite are allotrops of carbon while carbon dioxide is a compound of carbon.

Fullerene, graphite and diamond all are different allotrops of carbon.

Carbon shares electrons while making compounds. It do not transfers electrons to other ions.

Carbon atoms form 4 covalent bonds. Carbon (atomic number 6) has electronic configuration $\displaystyle 1s^2 2s^22p^4$ It has $4$ valence electrons which are shared with other atoms to form $4$ covalent bonds.

Graphite is one of three forms of crystalline, or crystal-forming, carbon. Carbon also exists in an amorphous, or “shapeless,” form in substances such as coal and coke. Different forms of the same element are called allotropes. Besides graphite, the other allotropes of crystalline carbon are diamond and fullerenes

Allotropy is a phenomenon wherein an element especially from group $13$ to group $16$ exists in more than one form. These forms differ in arrangement of atoms in their crystalline form. Few list of various elements showing allotropy -

Forms | | --- | --- | | Carbon : | Graphite, Diamond, Fullerenes | | Sulphur $(S _{8})$: | Rhombic, Monocline, Triclinic sulphur | | Phosphorous $(P _{4})$:  | Red, Black, Yellow | | Tin $(Sn)$: | White, Grey |

$C(graphite)+O _2(g)\longrightarrow CO _2(g)$

Carbon shows the property of catenation as it is small in size and has the ability to form stable covalent bonds with other carbon atoms to form a chain-like structure. The bond energy between the C-C bond is very high which enables them to form a long chain of C-C stable bonds.

Carbon can form huge number of carbon compounds due to following properties: 

Catenation is  a self linkage property, present in carbon. Because of catenation, carbon can form long chains, branched chains and closed chains.

Tetravalence: It is the state of an atom with four electrons available for covalent chemical bonding in its valence 

Carbon is capable of forming many allotropes due to its valency.  
Sixty carbon atoms form the shape of a ball like a football with a carbon atom at each corner of the 20 hexagons and 12 pentagons. The buckminsterfullerenes, is also called fullerenes, Fullerenes are molecules of varying sizes composed entirely of carbon, which take the form of a hollow sphere, ellipsoid, or tube.
Option "C" is correct.

In diamond, each carbon atom is covalently bonded to four other carbon atoms. A lot of energy is needed to separate the atoms in diamond. 

Diamond is transparent, hard and poor conductor of electricity. In-fact, diamond is hardest known substance on earth. The hardness is due to the presence of strong covalent bonds between C atoms. Hence, the option (B) is the correct answer.

Graphite is an allotrope of carbon. Each carbon is covalently bobded to other three carbon atoms, it contains layers of carbon. The layers slid over each other easily because of the weak Van der Walls' forces between them.

Fullerene is an allotrope of carbon in the form of hollow sphere and called as buckyballs. $C-60$ is the crystalline form and is used as semiconductor.

Crystal density of graphite is $2.266 g/cm^3$ as compared with $3.53 g/cm^3$ for diamond.
In the graphite structure, only three of the four valence electrons of carbon form regular covalent bonds with adjacent carbon atoms.

C-60 is the most stable form and it led the scientists to the conclusion that the cluster must be a spheroidal closed cage in the form of icosahedron.

The first fullerene was discovered in 1985 by Sir Harold W.Kroto, Smalley and Robert F.Curl. They obtained a cage like molecules composed of 60 carbon atoms.

60 carbon atoms are joined together by single and double bonds to form a hollow sphere with 12 pentagonal and 20 hexagonal faces, a design that resembles a football.

Diamond is an allotrope of carbon and it is present in pure form since it contains carbon atoms tetrahedrally bonded to each other.

The  statement C is  true for graphite.
(a) In graphite, each carbon atom is bonded to three other carbon atoms.
(b) Graphite is soft.
(c) It is a good conductor of electricity as delocalised electrons are free to move in delocalised molecular orbitals.

Diamond is the purest form of carbon while glass is composed of silica, sodium carbonate. Marble is calcium carbonate and sand is silicon dioxide.

Graphite is an allotrope of carbon other than diamond. 

Graphite is the most stable form of carbon under standard conditions. Special grades of synthetic graphite also used as neutron moderator within nuclear reactor. Its low neutron cross-section also recommends its use in proposed fusion reactors.

Allotropes of carbon have a different physical form but chemically they are similar, e.g., diamond and graphite are allotropes of carbon which are chemically carbon compounds but physically diamond is the hardest material known while graphite is soft material.

The dominant industrial use of diamond is in cutting, drilling (drill bits), grinding. It is used for these purposes due to its hardness.

Carbon has a valency of 4. In graphite, each carbon atoms 3 electrons are strongly bonded to other carbon atoms forming a hexagonal structure while one of the electrons of graphite is loosely bound and can thus conduct electricity. 

The term allotrope refers to one or more forms of a chemical element that occur in the physical state. Graphite and diamond are both allotropes of carbon that occur in the solid state. Allotropism only refers to different forms of chemical elements.

Because the layers are only weakly held together they can easily slip over one another, hence, show lubricating property.

The substance with the following applications is graphite. It is an allotrope of carbon.
(i) It is used in making leads of pencils.
(ii) It is used as a dry lubricant.
(iii) It is used in making black paint and printers ink.
(iv) It is used in nuclear reactors as a moderator.

Graphite, C(s) can conduct electricity in the solid state.
Ferric chloride and sodium hydroxide are ionic solids which do not conduct electricity in solid state.
They conduct electricity in molten state or in aqueous solution.
Iodine and sucrose are molecular solids which do not conduct electricity.
Graphite is a network solid and conducts electricity as it has delocalised molecular orbitals in which delocalised electrons are free to move.

Carbon has an allotrophic form that is a good electrical conductor at standard conditions.
This allotrope is graphite.

Ozone, an allotrope of oxygen is the primary absorber of UV solar radiation in Earth's atmosphere.

Diamond and graphite are allotropes of each other.
They are are allotropes of carbon. Allotropes are different forms of same element. Another allotrope of carbon is fullerene.

The number of free electrons in the outermost shell of carbon in graphite is one. Each $\displaystyle C$ atom is $\displaystyle sp^2$ hybridised. Each $\displaystyle C$ atom forms 3 covalent bonds with 3 other $\displaystyle C$ atoms. Thus, each $\displaystyle C$ atom has one electron in unhybridized $\displaystyle 2p$ orbital which it uses for $\displaystyle \pi $ bonding.

Hybridization of carbon is $sp^2$ in graphite as $1$ carbon atom is joined to $3$ other carbon atoms. In diamond, the hybridization is $sp^3$ as $1$ carbon atom is joined to $4$ other carbon atoms.

Allotropy or allotropism is the property of some chemical elements to exist in two or more different forms, known as allotropes of these elements.