The number of $\pi$ bonds present in C₂ molecule is

 The configuration of ${\mathrm{C}}_2\left(12\right):{\mathrm{\sigma }}_{1\mathrm{s}}^2{\mathrm{\sigma }}_{1\mathrm{s}}^{2^{\ast }}{\mathrm{\sigma }}_{2\mathrm{s}}^2{\mathrm{\sigma }}_{2\mathrm{s}}^{2^{\ast }}\left({\mathrm{\pi }}_{\mathrm{x}}^2={\mathrm{\pi }}_{\mathrm{y}}^2\right)$ The bonds formed by $\pi$ orbitals.

C2​ molecules have been found in vapour state. Their double bonds are made of two pi bonds because four electrons need to be accomodated in each bond. So this is against the rule that there must be a sigma bond before a pi bond is formed in the double bond.