  We present results from multi-wavelength study of intense flaring activity
from a high frequency peaked BL Lac object Mrk 421. The source was observed in
its flaring state on February 16, 2010 with the $TACTIC$ at energies above 1.5
TeV. Near simultaneous multi-wavelength data were obtained from high energy
(MeV-GeV) $\gamma$--ray observations with \emph{Fermi}--LAT, X--ray
observations by the \emph{Swift} and \emph{MAXI} satellites, optical V-band
observation by SPOL at \emph{Steward Observatory} and radio 15 GHz observation
at OVRO 40 meter-telescope. We have performed a detailed spectral and temporal
analysis of $TACTIC$, \emph{Fermi}--LAT and \emph{Swift}--XRT observations of
Mrk 421 during February 10--23, 2010 (MJD 55237-55250). The flaring activity of
the source is studied by investigating the properties of daily light curves
from radio to $TeV$ energy range and we present the correlation and variability
analysis in each energy band. The $TeV$ flare detected by $TACTIC$ on February
16, 2010 is well correlated with the activity in lower energy bands. The
differential energy spectrum of the source, in the energy range 1.5-11 TeV, as
measured by $TACTIC$ on this night is described by a power law ($dN/dE \propto
E^{-\Gamma}$) with spectral index $\Gamma = 2.6\pm0.3$. After accounting for
absorption of $TeV$ photons by low energy extragalactic background light
photons via pair production, the intrinsic $TeV$ spectrum reveals a power law
index of $2.3\pm0.3$. Finally the broad band spectral energy distribution of
the source in flaring state is reproduced using a simple emission model
involving synchrotron and synchrotron self Compton processes. The obtained
parameters are then used to understand the energetics of the source during the
flaring episode.
