  New exact solutions of Einstein's field equations (EFEs) by assuming linear
equation of state, $ p_r = \alpha (\rho - \rho_R) $ where $ p_r $ is the radial
pressure and $ \rho_R $ is the surface density, are obtained on the background
of a paraboloidal spacetime. By assuming estimated mass and radius of strange
star candidate 4U 1820-30, various physical and energy conditions are used for
estimating the range of parameter $ \alpha $. The suitability of the model for
describing pulsars like PSR J1903+327, Vela X-1, Her X-1 and SAX J1804.3658 has
been explored and respective ranges of $ \alpha $, for which all physical and
energy conditions are satisfied throughout the distribution, are obtained.
