The number of $\mathrm{p\pi }\cdot \mathrm{d\pi }$bonds in ${\mathrm{SO}}_3$ molecule is :

$\mathrm{S}$ in ${\mathrm{SO}}_3$ is ${\mathrm{sp}}^2$ hybridised. Between the three ${\mathrm{sp}}^2$, three bonds are created. Sulfur's hybridised orbital and the three oxygen atoms' pure p orbitals. In sulphur, there is one pure  orbital and two pure d -orbitals. Two $\mathrm{p}\pi -\mathrm{p}\pi$ bonds and one $\mathrm{p}\pi -\mathrm{p}\pi$  bond each contain these three orbitals.