We consider the standard three-generation framework augmented by an extra sterile neutrino in
2 = 10 4 : 1 eV 2 ). In this picture, four mass spectrums are possible due to
the mass range (Δ𝑚 41
2 ) and sterile(Δ𝑚 2 ) mass-squared differences. We study
unknown signs of the atmospheric(Δ𝑚 31
21
how the sensitivity to the ordering of the active states and the octant of mixing angle 𝜃 23 get
2 . This
affected in this scenario. We also discuss the possible determination of the sign of Δ𝑚 41
analysis is done in the context of a liquid argon detector using beam neutrinos traveling a distance
of 1300 km and atmospheric neutrinos propagating through a distance (10 : 10 4 ) km, allowing
resonant matter effects. We present separate results from these sources, do a combined study,
and probe the synergy between these two to give an enhanced sensitivity. We also discuss the
implications for cosmology, beta decay, and neutrinoless double beta decay in presence of a sterile
neutrino.