Abstract
A search for the decays $B^+_c \to J/\psi D^{(*)0}K^+$ and $B^+_c \to J/\psi D^{(*)+}K^{*0}$ is performed with data collected at the LHCb experiment corresponding to an integrated luminosity of 3 fb$^{−1}$. The decays $B^+_c \to J/\psi D^0K^+$ and $B^+_c \to J/\psi D^{*0} K^+$ are observed for the first time, while first evidence is reported for the $B^+_c \to J/\psi D^{*+} K^{*0}$ and $B^+_c \to J/\psi D^+ K^{*0}$ decays. The branching fractions of these decays are determined relative to the $B^+_c \to J/\psi\pi^+$ decay. The $B^+_c$ mass is measured, using the $J/\psi D^0 K^+$ final state, to be $6274.28 \pm 1.40(stat) \pm 0.32(syst) MeV/c^2$. This is the most precise single measurement of the $B^+_c$ mass to date.