The increasing demand for the web-based digital assistants has given a rapid rise in the interest of the Information Retrieval (IR) community towards the field of conversational question answering (ConvQA). However, one of the critical aspects of ConvQA is the effective selection of conversational history turns to answer the question at hand. The dependency between relevant history selection and correct answer prediction is an intriguing but under-explored area. The selected relevant context can better guide the system so as to where exactly in the passage to look for an answer. Irrelevant context, on the other hand, brings noise to the system, thereby resulting in a decline in the model's performance. In this paper, we propose a framework, DHS-ConvQA (Dynamic History Selection in Conversational Question Answering), that first generates the context and question entities for all the history turns, which are then pruned on the basis of similarity they share in common with the question at hand. We also propose an attention-based mechanism to re-rank the pruned terms based on their calculated weights of how useful they are in answering the question. In the end, we further aid the model by highlighting the terms in the re-ranked conversational history using a binary classification task and keeping the useful terms (predicted as 1) and ignoring the irrelevant terms (predicted as 0). We demonstrate the efficacy of our proposed framework with extensive experimental results on CANARD and QuAC -- the two popularly utilized datasets in ConvQA. We demonstrate that selecting relevant turns works better than rewriting the original question. We also investigate how adding the irrelevant history turns negatively impacts the model's performance and discuss the research challenges that demand more attention from the IR community.