Photometric and Kinematic study of the three intermediate age open
  clusters NGC 381, NGC 2360, and Berkeley 68
  We present UBVRcIc 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 are 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.
