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Despite Bengali being the sixth most spoken language in the world, no prior work has systematically evaluated hallucination in large language models (LLMs) for Bengali. We introduce BenHalluEval, a fine-grained hallucination evaluation framework for Bengali covering four tasks: Generative Question Answering (GQA), Bangla-English Code-Mixed QA, Summarization, and Reasoning. We construct 12,000 hallucinated candidates using GPT-5.4 across twelve task-specific hallucination types, drawn from three existing Bengali datasets, and evaluate seven LLMs spanning reasoning-oriented, multilingual, and Bengali-centric categories under a dual-track protocol that independently measures false-positive rate on ground-truth instances (Track A) and hallucination detection rate on hallucinated candidates (Track B). To jointly penalise both failure modes and prevent inflated scores from uniform response bias, we propose BenHalluScore, a dual-track calibration metric that ranges from 7.72% to 55.42% across models and tasks, revealing substantial variation in hallucination calibration. Chain-of-thought prompting, applied as a mitigation strategy, shifts response distributions without consistently improving hallucination discrimination. BenHalluEval establishes the first dedicated hallucination benchmark for Bengali and highlights the inadequacy of single-track and prompting-only evaluation approaches for low-resource language settings. The dataset and code are available at this https URL.