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Context. At least four high-frequency quasiperiodic oscillations (QPOs) at frequencies 41Hz, 67 Hz, 113 Hz, and 167 Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin a > 0.98. Aims. We attempt to explain all four observed frequencies by an extension of the standard resonant model of epicyclic oscillations. Methods. We use the idea of oscillations induced by the hump of the orbital velocity profile ( related to locally non-rotating frames-LNRF) in discs orbiting near-extreme Kerr black holes, which are characterized by a " humpy frequency" v(h), that could excite the radial and vertical epicyclic oscillations with frequencies v(r), v(v). Due to non-linear resonant phenomena, the combinational frequencies are allowed as well. Results. Assuming mass M = 14.8 M-circle dot and spin a = 0.9998 for the GRS 1915+105 Kerr black hole, the model predicts frequencies v(h) = 41Hz, r = 67Hz, v(h) +v(r) = 108 Hz, and v(v) - v(r) = 170 Hz corresponding quite well to the observed ones. Conclusions. For black-hole parameters being in good agreement with those given observationally, the forced resonant phenomena in non-linear oscillations, excited by the " hump-induced" oscillations in a Keplerian disc, can explain high-frequency QPOs in near-extreme Kerr black-hole binary system GRS 1915+105 within the range of observational errors.