We present results for the invariant and helicity amplitudes in the transitions $\Lambda_b\to\Lambda^{(\ast)}(J^P)+J/\psi$ where the $\Lambda^{(\ast)}(J^P)$ are $\Lambda(sud)$-type ground and excited states with $J^P$ quantum numbers $J^P=\frac12^{\pm},\frac32^{\pm}$. The calculations are performed in the framework of a covariant confined quark model. This analysis is important for the identification of the hidden charm pentaquark states $P_c^+(4380)$ and $P_c^+(4450)$ which were discovered by the LHCb Coll. We also discuss the possible New Physics effects in the exclusive decays $\bar{B}^0 \to D^{(\ast)} \tau\bar{\nu}_{\tau}$. We extend the Standard Model by taking into account right-handed vector (axial), left- and right-handed (pseudo)scalar, and tensor current contributions. The $\bar{B}^0 \to D^{(\ast)}$ transition form factors are calculated in the full kinematic $q^2$ range by employing a covariant quark model.