In this work, we study the magnetic properties of a spherical ferrimagnetic core/shell, formed with nanoparticles of a spin-1/2 in the core surrounded by spin-1 in the shell layer. An external magnetic field is applied on this system. In addition, we examined the magnetizations as well as the susceptibilities of this system, for specific values of the coupling constants between the spins of the shell-shell Js, the core-shell Jp and core-core Jc. The response of the magnetization to the field is illustrated in the hysteresis loops.