  We present detailed photometric observations of the Galactic globular cluster
NGC 7492 using the data obtained with two far-ultraviolet (FUV: 1300 - 1800
\AA) and three near-ultraviolet (NUV: 2000 - 3000 \AA) filters of Ultraviolet
Imaging Telescope (UVIT) on-board the \textit{AstroSat} satellite. We confirmed
the cluster membership of the extracted sources using GAIA data release 2 (Gaia
DR2) proper motion data. We have used color-magnitude diagrams (CMDs) using
UVIT and GAIA filters to separate out different evolutionary stages of the
stars present in the cluster. We have identified a new extreme horizontal
branch (EHB) star at the core of the cluster using UV and UV-optical CMDs. The
estimated distance-modulus of the cluster is $16.95\pm0.05$ obtained by fitting
BaSTI isochrones with cluster parameters, $[Fe/H] = -1.8$ dex and age $= 12.0$
Gyr on the V $-$ I vs V CMD. Interestingly, only the EHB star and blue
horizontal branch stars (BHBs) among the UV-bright hot sources are detected in
FUV filters of UVIT. We have derived the effective temperature of BHBs using
color-temperature relation and spectral energy distributions (SEDs) of
multi-band filters, which are in the range from 8,000 K to 10,500 K. We find a
variation of He abundance of BHBs by fitting the BaSTI ZAHB. The range in the
He abundance of the BHBs corresponding to the best fit isochrones is 0.247 to
0.350. We have estimated various physical parameters of the newly identified
EHB star in the cluster using SED fit and post-HB evolutionary tracks. We have
studied the radial distribution of all the sources of the cluster detected in
UVIT. The sources detected in FUV filters extend beyond the half light radius
(1.15$'$) of the cluster, whereas the sources detected in NUV filters extend
beyond the tidal radius (9.2$'$) of the cluster.
