Quantum phase transitions (QPT's) are phase transitions that are driven by zero-temperature quantum fluctuations, and are accessed by varying a non-thermal control parameter. Matter near a QPT shows unconventional features, like a non-Fermi-liquid behaviour. The magnetic QPT occurring in the metallic NixPd1-x alloy system across the quantum critical point (xc = 0.026) is one such example, wherein signatures of quantum criticality have been observed in bulk macroscopically, and microscopically using 54Fe time-differential perturbed angular distribution technique. Further, matter in reduced dimensions shows many quantum-physical properties dissimilar to bulk. It would, therefore, be quite intriguing to explore QPT in NixPd1-x nanoparticles. In the present proposal, we would like to perform such studies of quantum criticality and NFL behavior locally using muSR.