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Optical photometric and polarimetric investigation of NGC 1931

We present optical photometric and polarimetric observations of stars towards NGC 1931 with the aim to derive the cluster parameters such as distance, reddening, age and luminosity/mass function as well as to understand the dust properties and star formation in the region. The distance to the cluster is found to be 2.3$\pm$0.3 kpc and the reddening E(B-V) in the region is found to be variable. The stellar density contours reveal two clustering in the region. The observations suggest differing reddening law within the cluster region. Polarization efficiency of the dust grains towards the direction of the cluster is found to be less than that for the general diffuse interstellar medium (ISM). The slope of the mass function (-0.98$\pm$0.22) in the southern region in the mass range 0.8 \textless $M/M_{\sun}$ $\textless$ 9.8 is found to be shallower in comparison to that in the northern region (-1.26$\pm$0.23), which is comparable to the Salpeter value (-1.35). The K-band luminosity function (KLF) of the region is found to be comparable to the average value of slope (~0.4) for young clusters obtained by Lada & Lada (2003), however, the slope of the KLF is steeper in the northern region as compared to the southern region. The region is probably ionized by two B2 main-sequence type stars. The mean age of the young stellar objects (YSOs) is found to be 2$\pm$1 Myr which suggests that the identified YSOs could be younger than the ionizing sources of the region. The morphology of the region, the distribution of the YSOs as well as ages of the YSOs and ionizing sources indicate a triggered star formation in the region.