Recent advancements in robot capabilities have enabled them to interact with people in various human-social environments (HSEs). In many of these environments, the perception of the robot often depends on its capabilities, e.g., task competency, language fluency, etc. To enable fluent human-robot interaction (HRI) in HSEs, it is crucial to understand the impact of these capabilities on the perception of the robot. Although many works have investigated the effects of various robot capabilities on the robot's perception separately, in this paper, we present a large-scale HRI study (n = 60) to investigate the combined impact of both language fluency and task competency on the perception of a robot. The results suggest that while language fluency may play a more significant role than task competency in the perception of the verbal competency of a robot, both language fluency and task competency contribute to the perception of the intelligence and reliability of the robot. The results also indicate that task competency may play a more significant role than language fluency in the perception of meeting expectations and being a good teammate. The findings of this study highlight the relationship between language fluency and task competency in the context of social HRI and will enable the development of more intelligent robots in the future.