  The study has been carried out on the prospects of probing the sterile
neutrino mixing with the magnetized Iron CALorimeter (ICAL) at the India-based
Neutrino Observatory (INO), using atmospheric neutrinos as a source. The
so-called 3~$+$~1 scenario is considered for active-sterile neutrino mixing and
lead to projected exclusion curves in the sterile neutrino mass and mixing
angle plane. The analysis is performed using the neutrino event generator
NUANCE, modified for ICAL, and folded with the detector resolutions obtained by
the INO collaboration from a full GEANT4 based detector simulation. A
comparison has been made between the results obtained from the analysis
considering only the energy and zenith angle of the muon and combined with the
hadron energy due to the neutrino induced event. A small improvement has been
observed with the addition of the hadron information to the muon. In the
analysis we consider neutrinos coming from all zenith angles and the Earth
matter effects are also included. The inclusion of events from all zenith
angles improves the sensitivity to sterile neutrino mixing by about 35$\%$ over
the result obtained using only down-going events. The improvement mainly stems
from the impact of Earth matter effects on active-sterile mixing. The expected
precision of ICAL on the active-sterile mixing is explored and allowed
confidence level (C.L.) contours presented. At the assumed true value of
$10^\circ$ for the sterile mixing angles and marginalization over $\Delta
m^2_{41}$ and the sterile mixing angles, the upper bound at 90\% C.L. (from 2
parameter plots) is around $20^\circ$ for $\theta_{14}$ and $\theta_{34}$, and
about $12^\circ$ for $\theta_{24}$.
