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We present UBVR_cI_c photometric study of three intermediate age open star clusters NGC 381, NGC 2360, and Berkeley 68 (Be 68). We examine the cluster membership of stars using recently released Gaia DR2 proper motions and obtain a total of 116, 332, and 264 member stars in these three clusters. The mean reddening of E(B - V) = 0.36 ± 0.04, 0.08 ± 0.03, and 0.52 ± 0.04 mag is found in the direction of these clusters where we observe an anomalous reddening towards NGC 381. We fitted the solar metallicity isochrones to determine age and distance of the clusters which are found to be log(Age) = 8.65 ± 0.05, 8.95 ± 0.05, and 9.25 ± 0.05 yr with the respective distance of 957 ± 152, 982 ± 132, and 2554 ± 387 pc for the clusters NGC 381, NGC 2360, and Be 68. A two-stage power law in the mass function (MF) slope is observed in the cluster NGC 381, however, we observe only a single MF slope in the clusters NGC 2360 and Be68. To study a possible spatial variation in the slope of MF, we estimate slopes separately in the inner and the outer regions of these clusters and notice a steeper slope in outer region. The dynamic study of these clusters reveals deficiency of low-mass stars in their inner regions suggesting the mass segregation process in all these clusters. The relaxation times of 48.5, 78.9, and 87.6 Myr are obtained for the clusters NGC 381, NGC 2360, and Be 68, respectively, which are well below to their respective ages. This suggests that all the clusters are dynamically relaxed.