If in the expansion of (1 + x )^p (1 – x)^q, the coefficients of x and x² are 1 and –2, respectively, then p² + q² is equal to :  

$(1+\mathrm{x}{)}^{\mathrm{p}}(1-\mathrm{x}{)}^{\mathrm{q}}=\left({ }^{\mathrm{p}}{\mathrm{C}}_0{+}^{\mathrm{p}}{\mathrm{C}}_1\mathrm{x}{+}^{\mathrm{p}}{\mathrm{C}}_2{\mathrm{x}}^2+\dots \right)\left({ }^{\mathrm{q}}{\mathrm{C}}_0{-}^{\mathrm{q}}{\mathrm{C}}_1\mathrm{x}{+}^{\mathrm{q}}{\mathrm{C}}_2{\mathrm{x}}^2+\dots \right)$
coff of $\mathrm{x}{\equiv }^{\mathrm{p}}{{\mathrm{C}}_0}^{\mathrm{q}}{\mathrm{C}}_1{+}^{\mathrm{p}}{{\mathrm{C}}_1}^{\mathrm{q}}{\mathrm{C}}_0=1$
$\mathrm{p}-\mathrm{q}=1$
coff of ${\mathrm{X}}^2{\equiv }^{\mathrm{p}}{{\mathrm{C}}_0}^{\mathrm{q}}{\mathrm{C}}_2{-}^{\mathrm{p}}{{\mathrm{C}}_1}^{\mathrm{q}}{\mathrm{C}}_1{+}^{\mathrm{p}}{{\mathrm{C}}_2}^{\mathrm{q}}{\mathrm{C}}_0=-2$
$\begin{array}{l}\frac{\mathrm{q}(\mathrm{q}-1)}{2}-\mathrm{pq}+\frac{\mathrm{p}(\mathrm{p}-1)}{2}=-2\\ {\mathrm{q}}^2-\mathrm{q}-2\mathrm{pq}+{\mathrm{p}}^2-\mathrm{p}=-4\\ 1-(\mathrm{p}+\mathrm{q})=-4\\ \mathrm{p}+\mathrm{q}=5\\ \mathrm{p}=3\\ \mathrm{q}=2\\ \text{ so }{\mathrm{p}}^2+{\mathrm{q}}^2=13\end{array}$