Decays of the form $B^{0}_{(s)}rightarrow J/psi K_{{rm S}}^{0} h^+ h^{left(primeright) -}$ ($h^{(prime)} = K, pi$) are searched for in proton-proton collision data corresponding to an integrated luminosity of $1.0 , {rm fb}^{-1}$ recorded with the LHCb detector. The first observation of the $B^{0}_{s}rightarrow J/psi K_{{rm S}}^{0} K^{pm} pi^{mp}$ decay is reported, with significance in excess of 10 standard deviations. The $B^{0}rightarrow J/psi K_{{rm S}}^{0} K^{+} K^{-}$ decay is also observed for the first time. The branching fraction of $B^{0}rightarrow J/psi K_{{rm S}}^{0} pi^{+} pi^{-}$ is determined, to significantly better precision than previous measurements, using $B^0 rightarrow J/psi K_{{rm S}}^{0}$ as a normalisation channel. Branching fractions and upper limits of the other $B^{0}_{(s)}rightarrow J/psi K_{{rm S}}^{0} h^+ h^{left(primeright) -}$ modes are determined relative to that of the $B^{0}rightarrow J/psi K_{{rm S}}^{0} pi^{+} pi^{-}$ decay.
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