Neutrino Mass Matrices with Two Vanishing Elements/Cofactors

We study the phenomenological implications of the recent neutrino data for class B of two texture zeros and two vanishing cofactors for Majorana neutrinos in the flavor basis. We find that classes $B_{1}$($B_2$) of two texture zeros and classes $B_5$($B_6$) of two vanishing cofactors have similar predictions for neutrino oscillation parameters for the same mass hierarchy. Similar predictions for classes $B_3$($B_4$) of two texture zeros and classes $B_3$($B_4$) of two vanishing cofactors are expected. However, a preference for a shift in the quadrant of the Dirac-type CP violating phase($\delta$) in contrast to the earlier analysis has been predicted for a relatively large value of the reactor neutrino mixing angle($\theta_{13}$) for class B of two texture zeros and two vanishing cofactors for an inverted mass spectrum. No such shift in the quadrant of $\delta$ has been found for the normal mass spectrum.