The reality of red-shifts in the emission and absorption spectra of QSOs is questioned. Investigations in the spirit of the paper by Russel and Bowen (1929, Astrophys.J., 69, 196) are carried out to examine the question of whether the numerical coincidences found between the ratios of wavelengths of lines observed in the QSOs and those of the wavelengths of lines in the search list are significantly more than would be expected from chance coincidences. QSOs having z > = 0.2 are considered. Computer experiments to simulate the spectra of two-emission-line QSOs is described; about 85 percent of these nonsense spectra can be assigned reasonable redshifts. The redshift distribution of QSOs is calculated on the chance coincidence hypothesis and is found to be in broad accord with the observed one. Large discrepancies between the observed and calculated emission line wavelengths (on the redshift hypothesis) for a number of QSOs are pointed out. Distribution of absorption-line red-shifts of 4C 05.34 is shown to be nearly the same as that expected from the chance coincidence hypothesis and the plasma-laser star (PLS) model of Varshni (1974) in explaining the following points are compared: