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Highly CPU intensive serial task when run on parallel architecture, OS does the Core switching of the given task. Mainly the task is executed by one core at a time, but both the cores are used for processing when core (currently executing) usage reaches 100%. In this scenario OS switches the task between cores. In this paper an attempt has been made to study the time taken to process a segment of serial code along with number of times the task is switched between two cores. Finally linear regression analysis is done on the data to find the influence of core switching on processing time. The study is made on a system having Intel Core 2 Duo with two cores having speed 2.20 GHz and Fedora Core 12.