(Abridged) This paper presents integrated magnitude and colours for synthetic clusters. The integrated parameters have been obtained for the whole cluster population as well as for the main-sequence (MS) population of star clusters. We have also esti
mated observed integrated magnitudes and colours of MS population of galactic open clusters, LMC and SMC star clusters. It is found that the colour evolution of MS population of star clusters is not affected by the stochastic fluctuations, however these fluctuations significantly affect the colour evolution of the whole cluster population. The fluctuations are maximum in $(V-I)$ colour in the age range 6.7 $<$ log (age) $<$ 7.5. Evolution of integrated colours of MS population of the clusters in the Milky Way, LMC and SMC, obtained in the present study are well explained by the present synthetic cluster model. The observed integrated $(B-V)$ colours of MS population of LMC star clusters having age $geq$ 500 Myr seem to be distributed around $Z=$ 0.004 model, whereas $(V-I)$ colours are found to be more bluer than those predicted by the $Z=$ 0.004 model. $(V-I)$ vs $(B-V)$ two-colour diagram for the MS population of the Milky Way star clusters shows a fair agreement between the observations and present model, however the diagrams for LMC and SMC clusters indicate that observed $(V-I)$ colours are relatively bluer. Possible reasons for this anomaly have been discussed.
The discovery of large number of Cepheid variables in far-off galaxies offers a unique opportunity to determine the accurate distance of the host galaxy through their period-luminosity relation. The main aim of the present study is to identify short-
period and relatively faint Cepheids in the crowded field of M31 disk which was observed as part of the Nainital Microlensing Survey. The Cousins R and I-band photometric observations were obtained with a 1-m telescope on more than 150 nights over the period between November 1998 to January 2002. The data was analysed using the pixel technique and the mean magnitudes of the Cepheids were determined by correlating their pixel fluxes with the corresponding PSF-fitted photometric magnitudes. Here, we report identification of 39 short-period Cepheid variables in the M31 disk. Most of the Cepheids are found with R (mean) ~ 20-21 mag and the dense phase coverage of our observations enabled us to identify Cepheids with periods as short as 3.4 days The frequency-period distribution of these Cepheids peaks at logP ~ 0.9 and 1.1 days.
