  Intense experimental and theoretical efforts have recently been brought to
bear on the determination of the symmetry of superconducting order parameter in
high T$_c$ Cuprates as this would shed light on the nature of microscopic
interactions that are responsible for superconductivity in these unusual
systems. We use a two band model that reproduces the Fermi surface seen in
ARPES experiments of Shen et al., and study the symmetry of order parameter in
the YBCO system. The model incorporates the effects of tunnelling in the
c-direction between the planes and chains of these Cuprates. It is observed
that a suitable choice of the phase of the pair wave-function in the planes and
chains lead to both s- and d-wave like features. We calculate the detailed
phase diagram of this system, observe the shift in the position of the node(s)
of the order parameter(s) on the Fermi surface with doping and explain the
seemingly contradictory experimental observations about the presence of both s-
and/or d-wave symmetry in these systems.
