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In the wake of recent measurements of ratios of semileptonic branchingfractions: ${\cal R}_{J/\psi}, {\cal R}_D$ and ${\cal R}_{D^*}$ reported by theLHCb, BELLE and HFLAV Collaborations, we calculate invariant form factors forthe exclusive semileptonic $B_c$-meson decays to radially excited charmoniumand charm meson states in the full kinematical region within the framework ofrelativistic independent quark (RIQ)model. We evaluate the lepton mass effectin the decay processes induced by $b\to c,u$ transition at the quark level. Ourpredictions on branching fractions for $B_c\to \eta_c/\psi(nS)$ are found$\sim10^{-2}-10^{-4}$ and that for $B_c\to D^*(nS)$ are $\sim 10^{-4}$ in their$e^-$ decay modes, which lie within the detection accuracy of currentexperiment. Our predictions on branching fractions, forward backward asymmetryand asymmetry parameter are found in reasonable agreement with other modelpredictions; which can hopefully be tested in future experiments at LHC andTevatron. Our predicted observable ${\cal R}$ in this sector are foundcomparable to other standard model (SM) predictions that violate the leptonflavor universality hinting at new physics beyond SM.

Exclusive semileptonic $B_c$-meson decays to radially excited charmonium and charm meson states