The ground state molecular frame dipole moments of alkaline earth metal monofluorides and Group ІІB-monohydrides have been computed using two analytic methods, namely the Z-vector technique and the linear expectation value method within the four-component relativistic coupled cluster singles and doubles framework. We have compared our results with the experimentally measured permanent dipole moments wherever available. It is found that the Z-vector method, which is an energy-derivative approach predicts the molecular permanent dipole moment more accurately than the linear expectation value approach in DZ and TZ quality basis set.Further, our study shows that the high-energy virtual spinors seem to have almost no influence on the permanent dipole moment whereas the core electron correlation slightly affects this molecular property.