  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.
