  Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an
antiferromagnetic leg are considered where the spins on the legs interact
through antiferromagnetic rung couplings $J_1$. These ladders can have two
geometrical arrangements either zigzag or normal ladder and these systems are
frustrated irrespective of their geometry. This frustration gives rise to
incommensurate spin density wave, dimer and spin fluid phases in the ground
state. The magnetization in the systems decreases linearly with $J^2_1$, and
the systems show an incommensurate phase for $0.0<J_1<1.0$. The spin-spin
correlation functions in the incommensurate phase follow power law decay which
is very similar to Heisenberg antiferromagnetic chain in external magnetic
field. In large $J_1$ limit, the normal ladder behaves like a collection of
singlet dimers, whereas the zigzag ladder behaves as a one dimensional spin-1/2
antiferromagnetic chain.
