In the wake of the recent measurements of the decays Bc→J/ψπ(K) and Bc→J/ψℓνℓ reported by the LHCb Collaboration we calculate the form factors for the Bc→J/ψ and Bc→ηc transitions in full kinematical region within covariant confined quark model. Then we use the calculated form factors to evaluate the partial decay widths of the above-mentioned semileptonic and nonleptonic decays of the Bc meson. We find that the theoretical predictions on the ratios of RK+/π+ and Rπ+/μ+ν are in good agreement with last LHCb-data. However, the prediction for the RJ/ψ is found to be underestimated.