In the commutative geometrical background, one finds the total charge $\mathcal{(Q)}$ and/or the total angular momentum $\mathcal{(J)}$ of a generalized black hole of mass $M$ to be bounded by the condition $\mathcal{Q^{2} + (J/M)^{2} \leq M^{2}}$, whereas the inclusion of the concept of non-commutativity in geometry leads to a much more richer result. It predicts that the upper limit to $\mathcal{Q}$ and/or $\mathcal{J}$ is not fixed but depends on the mass/length scale of black holes; it (the upper limit to $\mathcal{Q}$ and/or $\mathcal{J}$ ) goes towards a ‘commutative limit’ when $M \gg \sqrt{\vartheta} (\sqrt{\vartheta}$ characterizes the minimal length scale) and rapidly diminishes towards zero with $M$ decreasing in the strongly non-commutative regime, until approaching a perfect zero value for $M \simeq 1.904\sqrt{\vartheta}$. We have performed separate calculations for a pure Kerr or a pure Reissner–Nordström black hole, and briefly done it for a generalized black hole.