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 Mν. 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 Mν, while fifty are found to be viable with texture containing a
vanishing element and an equality of cofactors in Mν under the current
experimental test at 3σ confidence level. Detailed numerical analysis of
all the possible cases have been presented