Twisted nematic liquid crystal displays (TN-LCDs), doped with the nanoparticles of metal, such as Pd, Ag, or Ag-Pd, which are protected with ligand molecules, such as nematic liquid crystal, exhibit a frequency modulation (FM) electro-optical (EO) response with short response time of milliseconds (ms) or sub-ms order together with the ordinary rms voltage response. These devices are called FM/AM-TN-LCDs; they are distinct from the ordinary LCDs featured by the amplitude modulation (AM) response. The phenomena of the FM/AM LCDs may be attributed to the dielectric dispersion of a heterogeneous dielectric medium known as the Maxwell-Wagner effect. It is experimentally shown that the frequency range spreads from several tens hertz to several tens kilohertz and the spectrum is more or less centered about the dielectric relaxation frequency. We formulated a theory based on an equivalent circuit model to evaluate the dielectric relaxation frequency and the dielectric strengths; and we succeeded in explaining the dependence of the dielectric relaxation frequency on the concentration of nanoparticles and the their dielectric and electrical properties, whereas conventional theories based on electromagnetic theory are unable to explain this concentration dependence. This paper reports on the experimental results of the EO effects and the dielectric spectroscopy including the dielectric relaxation times and the dielectric strengths of nematic liquid crystal, 5CB (4-pentyl-4'-cyanobiphenyl), doped with the metal nanoparticles of I'd alone and Ag-Pd composite; and discusses how the observed dielectric relaxation frequency or dielectric relaxation time depend on the concentration of the doped nanoparticles and also their electrical and dielectric properties