matrix $M^D_\nu$ are obtained by scanning over the allowed parameter space. We have varied the elements of $\l^{\prime}_R$ matrix between 0.5 to 1 keeping them very close to each other by allowing a spread of only 10%. To generate $M^{R}_{\nu}$, we set the charged Higgs masses and mixings as given in Appendix A. Fig. \[fig:nyuk\] gives a scatter plot of the allowed neutrino Dirac masses (directly proportional to the Dirac Yukawa coupling $Y_l$) satisfying the experimental 3$\sigma$ ranges for the light neutrino parameters given in Tab. \[tab:neut\]. Here we plot the neutrino Dirac masses along the Y-axis with $M^D_{\nu_{11}}$ along the X-axis. This gives us an clear indication of the allowed values of the various terms in the $M^D_\nu$ matrix relative to each other. Note that the hierarchy between $(M^D_{\nu})_{11}, (M^D_{\nu})_{12},$ and $(M^D_{\nu})_{13}$ is clearly visible from the figure, with $(13)$ element of the Dirac mass matrix allowed to take highest values. The hierarchy between $(13)$ and $(12)$ element is largest for lower $(M^D_{\nu})_{11}$ mass $(M^D_{\nu})_{11} \sim 0.1 $ eV.

As it is clear from the preceding discussion, in the present model we have an eV scale right-handed neutrino. Hence it may give the contribution to the relativistic degree of 