[en] We study the rare semileptonic decays of B mesons induced by $b\to <!--\; ???\; -->s\mathrm{\nu <!--\; ??\; -->}\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}$ as well as $b\to <!--\; ???\; -->{sl}^{+}{l}^{-<!--\; ???\; -->}$ transitions in the scalar leptoquark (LQ) model, where the LQs have the representation (3, 2, 7/6) and (3, 2, 1/6) under the standard model gauge group. The LQ parameter space is constrained using the most recent experimental results on $\mathrm{B}\mathrm{r}(B_s\to <!--\; ???\; -->{\mathrm{\mu <!--\; ??\; -->}}^{+}{\mathrm{\mu <!--\; ??\; -->}}^{-<!--\; ???\; -->})$ and $\mathrm{B}\mathrm{r}(B_d\to <!--\; ???\; -->X_s{\mathrm{\mu <!--\; ??\; -->}}^{+}{\mathrm{\mu <!--\; ??\; -->}}^{-<!--\; ???\; -->})$ processes. Considering only the baryon number conserving LQ interactions, we estimate the branching ratios for the exclusive $\stackrel{¯<!--\; ??\; -->}{B}\to <!--\; ???\; -->{\stackrel{¯<!--\; ??\; -->}{K}}^{(\ast <!--\; ???\; -->)}\mathrm{\nu <!--\; ??\; -->}\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}$ and inclusive $B\to <!--\; ???\; -->X_s\mathrm{\nu <!--\; ??\; -->}\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}$ decay processes by using the constraint parameters. We also obtain the low recoil (large lepton invariant mass, i.e., $q^2\sim <!--\; ???\; -->m_b^2$) predictions for the angular distribution of $\stackrel{¯<!--\; ??\; -->}{B}\to <!--\; ???\; -->\stackrel{¯<!--\; ??\; -->}{K}{l}^{+}{l}^{-<!--\; ???\; -->}$ process and several other observables including the flat term and lepton flavour non-universality factor in this model. (paper)