A detailed investigation of exchange bias properties of an inverted nanoparticle with an antiferromagnetic core and a ferromagnetic binary alloy shell of the type BxCi, is presented by benefiting from Monte Carlo simulations. Exchange bias displays a non-monotonic behavior with the varying value of the concentration the type-B magnetic components, x. Coercivity exhibits a monotonic or a non-monotonic variation with x depending on the relative strength between unlike magnetic components in the shell. Particular attention has also been given to determine the effects of the cooling field process on the magnetic properties of the nanoparticle. Numerical results obtained in this work present a different physical mechanism and an alternative way for tuning the exchange bias and coercivity of bimagnetic core/shell nanoparticles. (C) 2018 Elsevier B.V. All rights reserved.