Retrieval-augmented generation (RAG) has become integral to large language models (LLMs), particularly for conversational AI systems where user questions may reference knowledge beyond the LLMs' training cutoff. However, many natural user questions lack well-defined answers, either due to limited domain knowledge or because the retrieval system returns documents that are relevant in appearance but uninformative in content. In such cases, LLMs often produce hallucinated answers without flagging them. While recent work has largely focused on questions with false premises, we study out-of-scope questions, where the retrieved document appears semantically similar to the question but lacks the necessary information to answer it. In this paper, we propose a guided hallucination-based approach ELOQ to automatically generate a diverse set of out-of-scope questions from post-cutoff documents, followed by human verification to ensure quality. We use this dataset to evaluate several LLMs on their ability to detect out-of-scope questions and generate appropriate responses. Finally, we introduce an improved detection method that enhances the reliability of LLM-based question-answering systems in handling out-of-scope questions.