  We have computed the branching ratios of the exclusive pseudoscalar (vector)
+ tensor modes that are allowed in the decays of the B_c meson. The dominant
spectator and annihilation contributions in those decays are evaluated using
the factorization hypothesis. We find that some of these decay channels, such
as B_c --> (\rho^-, D_s^{*-}, D_s^{-})\chi_{c2} and B_c^ -->\pi^-
\bar{B_{s2}^{*0}}, have branching ratios of the order of 10^{-4}, which seems
to be at the reach of forthcoming experiments at the LHC. The inclusive
branching fraction of the two-body B_c decays involving tensor particles is
approximately 1.28 x10^{-3}. At the dynamical level, it is interesting to
observe that the exclusive decays B_c --> K^-(\pi^-)\bar{D_2^{*0}}, \pi^0
D_2^{*-}, \eta^{'} D_{s2}^{*-} are dominated by the annihilation contributions.
