In CBM Experiment at FAIR, dimuons will be detected by a Muon Chamber (MUCH) consisting of segmented absorbers of varying widths and tracking chambers sandwiched between the absorber-pairs. In this fixed target heavy-ion collision experiment, operating at highest interaction rate of $10~MHz$ for $Au+Au$ collision, after the first MUCH detector station in its inner radial ring will face a particle rate of $1~MHz/cm^2$. To operate at such a high particle density, GEM technology based detectors have been selected for the first two stations of MUCH. We have reported earlier the performance of several small-size GEM detector prototypes built at VECC for use in MUCH. In this work, we report on a large GEM chamber prototype tested with proton beam of momentum $2.36~GeV/c$ at COSY-J{u}elich Germany. The detector was read out using nXYTER ASIC operated in self-triggering mode. An efficiency higher than $96%$ at $Delta V_{GEM}~=~375.2~V$ was achieved. The variation of efficiency with the rate of incoming protons has been found to vary within $2%$ when tested up to a maximum rate of $2.8~MHz/cm^2$. The gain was found to be stable at high particle rate with a maximum variation of $sim~9%$.
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