Complementing our Washington photometric studies on Galactic open clusters (OCs), we now focus on four poorly studied OCs located in the first and fourth Galactic quadrants, namely BH 84, NGC 5381, BH 211 and Czernik 37. We have obtained CCD photometry in the Washington system $C$ and $T_1$ passbands down to $T_1$ $sim$ 18.5 magnitudes for these four clusters. Their positions and sizes were determined using the stellar density radial profiles. We derived reddening, distance, age and metallicity of the clusters from extracted $(C-T_1,T_1)$ color-magnitude diagrams (CMDs), using theoretical isochrones computed for the Washington system. There are no previous photometric data in the optical band for BH 84, NGC 5381 and BH 211. The CMDs of the observed clusters show relatively well defined main sequences, except for Czernik 37, wherein significant differential reddening seems to be present. The red giant clump is clearly seen only in BH 211. For this cluster, we estimated the age in (1000$^{+260}_{-200}$) Myr, assuming a metallicity of $Z$ = 0.019. BH 84 was found to be much older than it was previously believed, while NGC 5381 happened to be much younger than previously reported. The heliocentric distances to these clusters are found to range between 1.4 and 3.4 kpc. BH 84 appears to be located at the solar galactocentric distance, while NGC 5381, BH 211 and Czernik 37 are situated inside the solar ring.
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