In this paper a scenario with the participation of the exotic scalar S, tensor T and pseudoscalar couplings of the right-handed neutrinos in addition to the standard vector V, axial A couplings of the left-handed neutrinos in the low-energy (ν_μe^-) and (ν_ee^-) scattering processes is considered. Neutrinos are assumed to be massive Dirac fermions and to be polarized. Both reactions are studied at the level of the four-fermion point interaction. The main goal is to show that the physical

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... ence of the presence of the right-handed neutrinos is an appearance of the azimuthal asymmetry in the angular distribution of the recoil electrons caused by the non-vanishing interference terms between the standard and exotic couplings, proportional to the transverse neutrino polarization vector. The upper limits on the expected effect of this asymmetry for the low-energy neutrinos (E_ν < 1 MeV) are found. We also show that if the neutrino helicity rotation (ν_eL→ν_eR) in the solar magnetic field takes place, the similar effect of the azimuthal asymmetry of the recoil electrons scattered by the solar neutrinos should be observed. This effect would also come from the interference terms between the standard (V, A)_L and exotic (S, T, P)_R couplings. New-type neutrino detectors with good angular resolution could search for the azimuthal asymmetry in event number.