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We present the first comprehensive study of the most massive globular cluster Omega Centauri in the far-ultraviolet (FUV) extending from the center to ~ 28% of the tidal radius using the Ultraviolet Imaging Telescope aboard AstroSat. A comparison of the FUV-optical color-magnitude diagrams with available canonical models reveals that the horizontal branch (HB) stars bluer than the knee (hHBs) and the white dwarfs (WDs) are fainter in the FUV by ~ 0.5 mag than model predictions. They are also fainter than their counterparts in M13, another massive cluster. We simulated HB with at least five subpopulations, including three He-rich populations with a substantial He enrichment of Y up to 0.43 dex, to reproduce the observed FUV distribution. We find the He-rich younger subpopulations to be radially more segregated than the He-normal older ones, suggesting an in-situ enrichment from older generations. The Omega Cen hHBs span the same effective temperature range as their M13 counterparts, but some have smaller radii and lower luminosities. This may suggest that a fraction of Omega Cen hHBs are less massive than those of M13, similar to the result derived from earlier spectroscopic studies of outer extreme HB stars. The WDs in Omega Cen and M13 have similar luminosity-radius-effective temperature parameters, and 0.44 - 0.46 M$_\odot$ He-core WD model tracks evolving from progenitors with Y = 0.4 dex are found to fit the majority of these. This study provides constraints on the formation models of Omega Cen based on the estimated range in age, [Fe/H] and Y (in particular), for the HB stars.