  The nature of the highly dense matter inside the supernova remnant compact
star is not constrained by terrestrial experiments and hence modeled
phenomenologically to accommodate the astrophysical observations from compact
stars. The observable properties of the compact stars are highly sensitive to
the microscopic model of highly dense matter. However, some universal relations
exist between some macroscopic properties of compact stars independent of the
matter model. We study the universal relation including the stars containing
exotic degrees of freedom such as heavier strange and non-strange baryons,
strange quark matter in normal and superconducting phases, etc. We examine the
universal relations for quantities moment of inertia - tidal love number -
quadrupole moment. We also study the correlation of non-radial f-mode and
p-mode frequencies with stellar properties. We find the f-mode frequency
observes the universal relation with dimensionless tidal deformability but the
p-mode frequency does not show a good correlation with stellar properties. The
p-mode frequency is sensitive to the composition of the matter. We find that
universal relation is also applicable for stars with exotic matter in the core
of the star with several models of exotic matter.
