A nuclear track emulsion was exposed to a mixed beam of relativistic $^{12}$N, $^{10}$C, and $^7$Be nuclei having a momentum of 2 GeV/$c$ per nucleon. The beam was formed upon charge exchange processes involving $^{12}$C primary nuclei and their fragmentation. An analysis indicates that $^{10}$C nuclei are dominant in the beam and that $^{12}$N nuclei are present in it. The charge topology of relativistic fragments in the coherent dissociation of these nuclei is presented.