  We study the "mixed spin" isotropic ladder system having S=1 spins on one leg
and S=1/2 spins on the other, with general-type exchange interactions between
spins on neighboring rungs. A set of model Hamiltonians with exact ground
states in the form of a certain matrix product wave function is obtained. We
show that sufficiently strong frustration can lead to exotic singlet ground
states with infinite (exponential) degeneracy. We also list a couple of rather
simple models with nontrivial ground states, including a model with only
bilinear exchange.
