The ability to identify and acquire missing information is a critical component of effective decision making and problem solving. With the rise of conversational artificial intelligence (AI) systems, strategically formulating information-seeking questions becomes crucial and demands efficient methods to guide the search process. We introduce a novel approach to adaptive question-asking through a combination of Large Language Models (LLM) for generating questions that maximize information gain, Monte Carlo Tree Search (MCTS) for constructing and leveraging a decision tree across multiple samples, and a hierarchical feedback mechanism to learn from past interactions. We present two key innovations: (1) an adaptive MCTS algorithm that balances exploration and exploitation for efficient search over potential questions; and (2) a clustering-based feedback algorithm that leverages prior experience to guide future interactions. Each incoming sample is assigned to a cluster based on its semantic similarity with previously observed samples. Our UCT (Upper Confidence bound for Trees) formulation selects optimal questions by combining expected rewards, a function of information gain, with a cluster-specific bonus that decays with depth, to emphasize the importance of early-stage questions that have proven effective for narrowing the solution space in similar samples. Experiments across three domains, including medical diagnosis and troubleshooting, demonstrate that our method leads to an average of 12% improvement in success rates and a 10x reduction in the average number of LLM calls made per conversation for the search process, in comparison to the state of the art.