Bi-magnetic core/shell nanoparticles are gaining increasing interest due to their foreseen applications. Inverse antiferromagnetic(AFM)/ferrimagnetic(FiM) core/shell nanoparticles are particularly appealing since they may overcome some of the limitations of conventional FiM/AFM systems. However, virtually no simulations exist on this type of morphology. Here we present systematic Metropolis Monte Carlo simulations of the exchange bias properties of such nanoparticles. The coercivity, HC, and loop shift, Hex, present a non-monotonic dependence with the core diameter and the shell thickness, in excellent agreement with the available experimental data. Additionally, we demonstrate novel unconventional behavior in FiM/AFM particles. Namely, while HC and Hex decrease upon increasing FiM thickness for small AFM cores (as expected), they show the opposite trend for large cores. This presents a counterintuitive FiM size dependence for large AFM cores that is attributed to the competition between core and shell contributions, which expands over a wider range of core diameters leading to non-vanishing Hex even for very large cores. Moreover, the results also hint different possible ways to enhance the experimental performance of inverse core/shell nanoparticles for diverse applications.