Positron lifetime measurements have been carried out in two liquid-crystal-forming homologues of alkyl cyanobiphenyls, 7CB and 10CB. In each of these two compounds measurements were performed during the heating cycle of samples prepared either by quenching or by slow cooling from the respective liquid crystalline phase. In both compounds, the behavior of quenched and slow-cooled samples is found to be different. Unlike the slow-cooled sample, the material in the quenched sample seems to have transformed into a glassy solid. The o-Ps pick-off lifetime in the quenched sample exhibits a strong temperature dependence. In each case, its value exhibits six broad peaks at various characteristic temperatures which have been ascribed to various motions associated with the molecules of these compounds. The quenched samples of 7CB and 10CB exhibit glass transitions at -268 and -266 K, respectively. The present work demonstrates an interesting application of positron lifetime spectroscopy (PLS).