Number and type of bonds between two carbon atoms in ${\mathrm{CaC}}_2$ are ;

Number and type of bonds between two carbon atoms in ${\mathrm{CaC}}_2$ are one $\mathrm{\sigma }$ and two $\mathrm{\pi }$ bonds.

A single bond between two atoms is always considered as sigma bond.
A double bond between two atoms is always considered as one sigma and one pi bond
A triple bond between two atoms is always considered as one sigma bond and two pi bonds.
So according to the given structure ${\mathrm{CaC}}_2$ (Calcium carbide) ha 1 sigma and 2 pi bonds.

Hence, the option B is correct.