The processes of neutrino production of electron-positron pairs, νν̅→ e^- e^+ and ν→ν e^- e^+, in a magnetic field of arbitrary strength, where electrons and positrons can be created in the states corresponding to excited Landau levels, are analysed. The results can be applied for calculating the efficiency of the electron-positron plasma production by neutrinos in the conditions of the Kerr black hole accretion disc considered by experts as the most possible source of a short cosmological gamma burst.