  The behavior of collective oscillations of a trapped boson-fermion mixed
condensate is studied in the sum rule approach. Mixing angle of bosonic and
fermionic multipole operators is introduced so that the mixing characters of
the low-lying collective modes are studied as functions of the boson-fermion
interaction strength. For an attractive boson-fermion interaction, the
low-lying monopole mode becomes a coherent oscillation of bosons and fermions
and shows a rapid decrease in the excitation energy towards the instability
point of the ground state. In contrast, the low-lying quadrupole mode keeps a
bosonic character over a wide range of the interaction strengths. For the
dipole mode the boson-fermion in-phase oscillation remains to be the eigenmode
under the external oscillator potential. For weak repulsive values of the
boson-fermion interaction strengths we found that an average energy of the
out-of-phase dipole mode stays lower than the in-phase oscillation.
  Physical origin of the behavior of the multipole modes against boson-fermion
interaction strength is discussed in some detail.
