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The hypothesis of a default mode network (DMN) of brain function is based on observations of task-independent decreases of brain activity during effort as participants are engaged in tasks in contrast to resting. On the other hand, studies also showed that DMN regions activate rather than deactivate in response to task-related events. Thus, does DMN deactivate during effort as compared to resting? We addressed this question with two approaches. First, we examined DMN activities during resting, task residuals, and task conditions in the stop signal task using independent component analysis (ICA). Second, we compared the fractional amplitude of low frequency fluctuation (fALFF) signals of DMN in resting, task residuals, and task data. We hypothesized that, with high-frequency event-related signals removed, the task-residual activities of the DMN would decrease as compared to resting. In the results of ICA of 76 subjects, the precuneus and posterior cingulate cortex (PCC) showed increased activation during task as compared to resting and task residuals, indicating DMN responses to task events. Precuneus but not the PCC showed decreased activity during task residual as compared to resting. The latter finding was mirrored by fALFF, which is decreased in the precuneus during task residuals, as compared to resting and task. These results suggested that the low frequency BOLD signals of the precuneus may represent a useful index of effort during cognitive performance.