  In this paper, we investigate the noval possibilities of hybrid textures
comprising a vanishing minor (or element) and two equal elements (or cofactors)
in light neutrino mass matrix $M_{\nu}$. Such type of texture structures lead
to sixty phenomenological cases each, out of which only fifty six are viable
with texture containing a vanishing minor and an equality between the elements
in $M_{\nu}$, while fifty are found to be viable with texture containing a
vanishing element and an equality of cofactors in $M_{\nu}$ under the current
experimental test at 3$\sigma$ confidence level. Detailed numerical analysis of
all the possible cases have been presented.
