The electrocatalytic activity of core-shell Au$_{100-x}$Ag$_x$ ($x = 15$, 27, 46, and 60) bimetallic nanoparticles embedded in methyl functionalized silicate MTMOS network towards the reduction of hydrogen peroxide was investigated by using cyclic voltammetry and chronoamperometric techniques. Core-shell Au/Ag bimetallic nanoparticles were characterized by absorption spectra and HRTEM. The MTMOS silicate sol-gel embedded Au₇₃Ag₂₇ core-shell nanoparticles modified electrode showed better synergistic electrocatalytic effect towards the reduction of hydrogen peroxide when compared to monometal MTMOS-Au_nps and MTMOS-Ag_nps modified electrodes. These modified electrodes were studied without immobilizing any enzyme in the MTMOS sol-gel matrix. The present study highlights the influence of molar composition of Ag nanoparticles in the Au/Ag bimetallic composition towards the electrocatalytic reduction and sensing of hydrogen peroxide in comparison to monometal Au and Ag nanoparticles.