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Text classification in low-resource languages has become increasingly important due to the rapid growth of user-generated digital content. While multitask learning has long been studied in NLP, the use of LLMs for multitask text classification in low-resource languages such as Bengali remains underexplored. Although LLMs are inherently multilingual and multitasking, their effectiveness in structured multitask classification settings for Bengali has not been systematically evaluated. In this work, we investigate how LLMs can be leveraged for multitask Bengali text classification across five domains: sentiment analysis, aggressive text detection, fake news detection, news categorization, and emotion analysis. We compare in-context learning strategies—including zero-shot, one-shot, and chain-of-thought prompting—with parameter-efficient fine-tuning approaches. Our findings show that CoT prompting does not consistently improve performance and often degrades performance, highlighting the instability of prompt-based adaptation in low-resource settings with limited pretraining exposure. Moreover, reasoning-optimized models such as DeepSeek-R1 exhibit substantial performance drops, indicating that enhanced reasoning capabilities alone cannot overcome the challenges posed by low-resource settings. Among the evaluated mLLMs, Gemma-3-4B demonstrates the most stable and balanced cross-task performance under both in-context learning and parameter-efficient fine-tuning, making it a strong backbone candidate for multitask Bengali text classification. These results provide empirical evidence on the limitations of prompting and the advantages of lightweight fine-tuning for low-resource multilingual NLP.