The far-field and near-field responses of Au/Ag nanoshell (NS) irradiated by a plane wave are studied theoretically using the Mie theory. The locally enhanced electric fields at the plasmon modes of NS are shown useful to excite a pair of nearby quantum dots (QDs) simultaneously. The dipole mode can be utilized for inducing an anti-symmetric radial bi-dipole and the quadrupole mode for the symmetric radial one. Moreover, the radiative and nonradiative powers of the anti-symmetric and symmetric emitting bi-dipoles in the presence of Au/Ag NS are analyzed using the dyadic Green's functions. The results show that the Purcell factors of NS on the emission of these bi-dipoles are increased dramatically at these plasmon modes. These results illustrate that NS possesses dual functions at these modes: a nanolens for focusing irradiating light locally to excite any nearby QD and an efficient nanoantenna for enhancing the emission of the excited emitter in the proximity of NS. According to the apparent quantum yield, the dipole mode is a bright mode, while the quadrupole mode is a dark one. In addition, these plasmon modes of Au/Ag NS, whose wavelengths are in between those of Au and Ag NSs, are tunable by adjusting the percentage of Au. This advantage allows us to tailor NS for matching these modes with the emission spectrum of specific QD.