Quantum-Dot Cellular Automata (QCA) is a radical technology, which works at Nanoscale. Due to its numerous advantages over the conventional CMOS-based digital circuits, researchers are now concentrating more on designing digital circuits using this technology. Researchers have reported various findings in this field till now. In this paper, a modular 2:1 Multiplexer has been designed followed by its application in the designing of 1-bit parallel memory. A 4:1 MUX is designed using cascading of two 2:1 multiplexers. This paper also incorporates a comparative analysis of the proposed circuits with some previous designs. This comparison indicates that the designed Multiplexer is showing a considerable reduction in cell count as well as in the area. Here the design and simulation of the circuits are done using QCA Designer Ver. 1.40. Power dissipation simulation analysis of the designed 4:1 multiplexer is also done using QCA Pro tool.