The present work aims to discriminate among the theoretically predicted different forms of Majorana neutrino mass matrix including texture zeros. The neutrino oscillation parameters are numerically extracted by diagonalizing a general charge-parity (CP)-conserving Majorana neutrino mass matrix whose elements are randomly generated within a certain range of allowed values using adaptive Monte Carlo method. The latest neutrino oscillation experimental data within 3 \(\sigma \) determines allowed values of the elements of the neutrino mass matrix. The latest Planck upper bound on the sum of three absolute masses \(\sum \vert m_i\vert <0.12\) eV is imposed in the numerical analysis. Both normal hierarchy (NH) and inverted hierarchy (IH) mass models are allowed, thus showing the possibility of both mass hierarchies within \(3\sigma \) . Further, the detailed numerical analysis confirms that the normal hierarchical mass model is valid up to mass bound, \(\sum \vert m_i\vert \ge 0.06\) eV while the inverted hierarchical mass model is valid up to mass bound, \(\sum \vert m_i\vert \ge 0.1 \) eV. In both models, the value of \(\theta _{23}\) is allowed in both below and above \(45^0\) . However, \(\theta _{23}>45^0\) is found to be more favourable for NH whereas \(\theta _{23}<45^0\) is more favourable for IH.