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In this paper we introduce a LTB-Bianchi I (plane symmetric) model of Universe. We study and solve Einstein field equations. We investigate the effects of such model of Universe in particular these results are important in understanding the effect of the combined presence of an inhomogeneous and anisotropic Universe. The observational magnitude-redshift data deviated from UNION 2 catalog has been analyzed in the framework of this LTB-anisotropic Universe and the fit has been achieved without the inclusion of any dark energy.

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