Mass function and dynamical study of the open clusters Berkeley 24 and
  Czernik 27
  We present a $UBVI$ photometric study of the open clusters Berkeley 24 (Be
24) and Czernik 27 (Cz 27). The radii of the clusters are determined as
2\farcm7 and 2\farcm3 for Be 24 and Cz 27, respectively. We use the Gaia Data
Release 2 (GDR2) catalogue to estimate the mean proper motions for the
clusters. We found the mean proper motion of Be 24 as $0.35\pm0.06$ mas
yr$^{-1}$ and $1.20\pm0.08$ mas yr$^{-1}$ in right ascension and declination
for Be 24 and $-0.52\pm0.05$ mas yr$^{-1}$ and $-1.30\pm0.05$ mas yr$^{-1}$ for
Cz 27. We used probable cluster members selected from proper motion data for
the estimation of fundamental parameters. We infer reddenings $E(B-V)$ =
$0.45\pm0.05$ mag and $0.15\pm0.05$ mag for the two clusters. Analysis of
extinction curves towards the two clusters show that both have normal
interstellar extinction laws in the optical as well as in the near-IR band.
From the ultraviolet excess measurement, we derive metallicities of [Fe/H]=
$-0.025\pm0.01$ dex and $-0.042\pm0.01$ dex for the clusters Be 24 and Cz 27,
respectively. The distances, as determined from main sequence fitting, are
$4.4\pm0.5$ kpc and $5.6\pm0.2$ kpc. The comparison of observed CMDs with
$Z=0.01$ isochrones, leads to an age of $2.0\pm0.2$ Gyr and $0.6\pm0.1$ Gyr for
Be 24 and Cz 27, respectively.
  In addition to this, we have also studied the mass function and dynamical
state of these two clusters for the first time using probable cluster members.
The mass function is derived after including the corrections for data
incompleteness and field star contamination. Our analysis shows that both
clusters are now dynamically relaxed
