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In this paper we report on the Markarian 501 results obtained during our TeV$\gamma$-ray observations from March 11 to May 12, 2005 and February 28 to May7, 2006 for 112.5 hours with the TACTIC $\gamma$-ray telescope. During 2005observations for 45.7 hours, the source was found to be in a low state and wehave placed an upper limit of 4.62 $\times$ 10$^{-12}$ photons cm$^{-2}$s$^{-1}$ at 3$\sigma$ level on the integrated TeV $\gamma$-ray flux above 1 TeVfrom the source direction. However, during the 2006 observations for 66.8h,detailed data analysis revealed the presence of a TeV $\gamma$-ray signal fromthe source with a statistical significance of 7.5$\sigma$ above$E_{\gamma}\geq$ 1 TeV. The time averaged differential energy spectrum of thesource in the energy range 1-11 TeV is found to match well with the power lawfunction of the form ($d\Phi/dE=f_0 E^{-\Gamma}$) with $f_0=(1.66\pm0.52)\times10^{-11}cm^{-2}s^{-1}TeV^{-1}$ and $\Gamma=2.80\pm0.27$.

Very High Energy gamma-ray observations of Mrk 501 using TACTIC imaging gamma-ray telescope during 2005-06