We report experimental studies on optical (birefringence, \(\Delta n\)), dielectric \((\Delta \varepsilon)\) and bend-splay elastic anisotropies (\(\Delta K=K_{33}-K_{11})\) of a few mixtures of two nematic liquid crystals, namely CCH-7 and CCN-47, made of highly polar molecules with identical cores and antagonistic orientation of permanent dipoles. In particular, the polar group (-CN) attached to the bicyclohexane core of CCH-7 is oriented along the longitudinal direction whereas, in CCN-47, it is oriented along the transverse direction. We show that apart from the significant contribution to the optical and dielectric anisotropies, the antagonistic orientation of strongly polar groups plays a crucial role in determining the bend-splay elastic anisotropy. The elastic properties are explained based on a model proposed by Priest, considering the effect of intermolecular association and the resulting length-to-width ratio of the molecules.