  It is believed that quark stars or neutron stars with mixed phase in the core
have smaller radii compared to ordinary compact stars. With the recent
observation of several low radius objects, typically a radius of $<10 Km.$ for
star of mass $< 1M_0$ in low mass X-ray binaries (LMXB), it has become very
important to understand the nature of these objects. An accurate determination
of mass-radius relationship of these objects provide us with a physical
laboratory to study the composition of high density matter and the nature of
phase transition. We study the effect of quark and nuclear matter mixed phase
on mass radius relationship and radial oscillations of neutron stars. We find
that the effect of the mixed phase is to decrease the maximum mass of a stable
neutron star and to decrease the radial frequencies .
