We propose AnveshanaAI, an application-based learning platform for artificial intelligence. With AnveshanaAI, learners are presented with a personalized dashboard featuring streaks, levels, badges, and structured navigation across domains such as data science, machine learning, deep learning, transformers, generative AI, large language models, and multimodal AI, with scope to include more in the future. The platform incorporates gamified tracking with points and achievements to enhance engagement and learning, while switching between Playground, Challenges, Simulator, Dashboard, and Community supports exploration and collaboration. Unlike static question repositories used in existing platforms, AnveshanaAI ensures balanced learning progression through a dataset grounded in Bloom's taxonomy, with semantic similarity checks and explainable AI techniques improving transparency and reliability. Adaptive, automated, and domain-aware assessment methods are also employed. Experiments demonstrate broad dataset coverage, stable fine-tuning with reduced perplexity, and measurable gains in learner engagement. Together, these features illustrate how AnveshanaAI integrates adaptivity, gamification, interactivity, and explainability to support next-generation AI education.