Recent advances in QA pair generation (QAG) have raised interest in applying this technique to the educational field. However, the diversity of QA types remains a challenge despite its contributions to comprehensive learning and assessment of children. In this paper, we propose a QAG framework that enhances QA type diversity by producing different interrogative sentences and implicit/explicit answers. Our framework comprises a QFS-based answer generator, an iterative QA generator, and a relevancy-aware ranker. The two generators aim to expand the number of candidates while covering various types. The ranker trained on the in-context negative samples clarifies the top-N outputs based on the ranking score. Extensive evaluations and detailed analyses demonstrate that our approach outperforms previous state-of-the-art results by significant margins, achieving improved diversity and quality. Our task-oriented processes are consistent with real-world demand, which highlights our system’s high applicability.