The number of types of bonds between two carbon atoms in calcium carbide is

The correct option is "One sigma, two pi".

To understand the nature of bonding in calcium carbide (${\mathrm{CaC}}_2$), we first analyze its chemical composition and structure. Calcium carbide is an ionic compound consisting of calcium cations (${\mathrm{Ca}}^{2+}$) and carbide anions ($C_2^{2-}$).

The bonding of interest is within the carbide anion ($C_2^{2-}$), which contains the two carbon atoms. The structure of the carbide ion (${[C\equiv C]}^{2-}$) features a carbon-carbon triple bond.

According to covalent bonding and molecular orbital theories, a triple bond between two atoms is always composed of:
1. One strong $\sigma$ (sigma) bond, which is formed by the head-on (axial) overlap of hybrid orbitals.
2. Two weaker $\pi$ (pi) bonds, which are formed by the lateral (sideways) overlap of unhybridized p-orbitals.

Therefore, the triple bond between the two carbon atoms in the calcium carbide unit consists of exactly one sigma ($\sigma$) bond and two pi ($\pi$) bonds.