Observations of $B^0_s \rightarrowψ(2S)η$ and $B^0_{(s)}\rightarrowψ(2S)π^+π^-$ decays
First observations of the $B^0_s \rightarrow ψ(2S) η$, $B^0 \rightarrow ψ(2S) π^+ π^-$ and $B^0_s \rightarrow ψ(2S) π^+ π^-$ decays are made using a dataset corresponding to an integrated luminosity of 1.0~$fb^{-1}$ collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=7$ TeV. The ratios of the branching fractions of each of the $ψ(2S)$ modes with respect to the corresponding $J/ψ$ decays are \[ \frac{\mathcal{B}(B^0_s \rightarrow ψ(2S) η) }{\mathcal{B}(B^0_s \rightarrow J/ψη)} =0.83\pm0.14\,(stat)\pm0.12\,(syst)\pm0.02\,(\mathcalB}), \] \[ \frac{\mathcal{B}(B^0 \rightarrow ψ(2S) π^+ π^-)}{\mathcal{B}(B^0 \rightarrow J/ψπ^+ π^-)} =0.56\pm0.07\,(stat)\pm0.05\,(syst)\pm0.01\,(\mathcal{B}), \] \[ \frac{\mathcal{B}(B^0_s \rightarrow ψ(2S) π^+ π^-)}{\mathcal{B}(B^0_s \rightarrow J/ψπ^+ π^-)} =0.34\pm0.04\,(stat)\pm0.03\,(syst)\pm0.01\,(\mathcal{B}), \] where the third uncertainty corresponds to the uncertainties of the dilepton branching fractions of the $J/ψ$ and $ψ(2S)$ meson decays.