  Results from experiments like LSND and MiniBooNE hint towards the possible
presence of an extra eV scale sterile neutrino. The addition of such a neutrino
will significantly impact the standard three flavour neutrino oscillations. In
particular, it can give rise to additional degeneracies due to additional
sterile parameters. For an eV scale sterile neutrino, the cosmological
constraints dictate that the sterile state is heavier than the three active
states. However, for lower masses of sterile neutrinos, it can be lighter than
one and/or more of the three states. In such cases, the mass ordering of the
sterile neutrinos also becomes unknown along with the mass ordering of the
active states. In this paper, we explore the mass ordering sensitivity in the
presence of a sterile neutrino assuming the mass squared difference
$|\Delta_{41}|$ to be in the range $10^{-4} - 1$ eV$^2$. We study (i) how the
ordering of the active states, i.e. the determination of the sign of
$\Delta_{31}$ gets affected by the presence of a sterile neutrino in the above
mass range, (ii) the possible determination of the sign of $\Delta_{41}$ for
$\Delta_{41}$ in the range $10^{-4} - 0.1$ eV$^2$. This analysis is done in the
context of a liquid argon detector using both beam neutrinos traveling a
distance of 1300 km and atmospheric neutrinos which propagates through a
distance ranging from 10 - 10000 km allowing resonant matter effects. Apart
from presenting separate results from these sources, we also do a combined
study and probe the synergy between these two in giving an enhanced
sensitivity.
