  We present a detailed analysis and phenomenological consequences of neutrino
mass matrix, $M_{\nu}$, with one-zero texture in the flavor basis where the
active neutrino sector is extended by one sterile neutrino (3+1 case). In
particular, our aim is to explore behaviour of the sterile mixing parameters in
detail when one of the elements of the neutrino mass matrix goes to zero. To
study this, we consider two distinct mass spectrum of the active neutrinos: (i)
completely hierarchical mass spectrum with a vanishing neutrino mass and (ii)
completely quasidegenerate mass spectrum. In 3+1 scenario, the low energy
neutrino mass matrix, $M_{\nu}$, is a $4 \times 4$ matrix and has 10
independent elements. Thus it can have 10 possible one-zero textures. From the
earlier studies it can be inferred that, if one assumes one vanishing neutrino
mass, then only seven of these $M_{\nu}$ are phenomenologically allowed by the
current neutrino oscillation data. On the other hand, if the neutrinos are
quasidegenerate then there are eight phenomenologically viable one-zero
textures. In this present work, we study the correlations between the sterile
mixing parameters for each of these allowed textures for both mass spectrum and
also their implications on the effective Majorana mass.
