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Students collaborated with generative AI (GAI) across varied tasks, but imbalanced collaboration can hinder learning. This study examines how student-GAI collaboration (measured through acceptance, cognitive trust, curiosity, and dependence on GAI) varies across task complexity (remember/understand, apply/analyze, evaluate/create) and goal orientation (mastery vs. performance). From our survey of 368 students, part of an explanatory sequential design, we found: (1) apply/analyze tasks elicited the highest acceptance and cognitive trust, followed by remember/understand and evaluate/create tasks; (2) curiosity or dependence peaked during apply/analyze tasks; (3) mastery-oriented tasks showed universally higher levels across all measured constructs compared to performance-oriented tasks. Meanwhile, undergraduate and postgraduate students showed differing collaborative patterns with GAI. We concluded with theoretical and practical insights.