  We investigate the implications of one vanishing minor in neutrino mass
matrix using trimaximal mixing matrix. In this context, we analyse all six
patterns of one vanishing minor zero in neutrino mass matrix and present
correlations of the neutrino oscillation parameters. All the six patterns are
found to be phenomenologically viable with the present neutrino oscillation
data. We also predict the values of effective Majorana mass, the effective
electron anti-neutrino mass and the total neutrino mass for all the patterns.
The value obtained for the effective neutrino mass is within the reach future
neutrinoless double $\beta$ decay experiments. We also propose a flavor model
where such patterns can be generated within the seesaw model.
