Nd_0.5 Ca_0.5 MnO_3 (NCMO) nanoparticles (average diameter ~ 20 and 40 nm) are synthesized by polymeric precursor sol-gel method and characterized by X- ray diffraction, transmission electron microscopy (TEM), selective area electron diffraction (SAED), superconducting quantum interference device (SQUID) magnetometery and resistivity measurements. Both single crystalline and polycrystalline particles are present in the samples and they are found to retain the orthorhombic structure of the bulk NCMO. However, most strikingly, in the 20 nm particles, the charge ordered (CO) and the antiferromagnetic phases observed in the bulk at 250 K and 160 K respectively are completely absent. Instead, a ferromagnetic (FM) transition is observed at 95 K followed by an insulator to metal transition at 75 K. In the 40 nm particles, though a weak, residual CO phase is observed, transition to FM state also occurs, but at a slightly higher temperature of 110 K. The magnetization is found to increase with the decrease of particle size.