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Nuclear reactions induced by muon neutrino with energies in the range from 0.2 to 1.5 GeV in Monte Carlo calculations framework in the intra-nuclear cascade model are studied. This study was done by comparison between the available experimental data and theoretical values of total cross section, and the energy distribution of emitted lepton energy in the reaction muon neutrino-nucleus, using the targets: $^{12}$C, $^{16}$O, $^{27}$Al, $^{40}$Ar, $^{56}$Fe and $^{208}$Pb. A phenomenological toy model of primary neutrino-nucleon interaction gives a good agreement of our theoretical inclusive neutrino nucleus cross in comparison with the available experimental data. Some interesting results on the behavior of the cross section as function of 1p-1n and higher contributions are also sketched. The previous results on the percentage of fake events related in available experiments in $^{12}$C were expanded for the set studied nuclei. With the increase of mass target, the nuclear effects in the cross sections were observed along with the importance to take into account fake events in the reactions.