  The quasi-elastic scattering of muon neutrino and electrons on a carbon
target are analyzed using the relativistic distorted-wave impulse approximation
(RDWIA). We also evaluate the contribution of the two-particle and two-hole
meson exchange current ($2p-2h$ MEC) to electroweak response functions. The
nuclear model dependence of the (anti)neutrino cross sections is studied within
the RDWIA+MEC approach and RDWIA model with the large nucleon axial mass. It is
shown that the results for the squared momentum transfer distribution
$d\sigma/dQ^2$ and for invariant mass of the final hadronic system distribution
$d\sigma/dW$ obtained within these models are substantially different.
