In an information retrieval system user cannot accurately give their queries for retrieving a particular context. So, it can lead to the mismatch problem. To rectify existing system in our proposed system we use mathematical framework and query expansion techniques. Query expansion adds terms to the original query, which provides more information about the user needs. The proposed query representation model is applicable for Vector space model (VSM), Okapi best matching 25 and Language model (LM).the proposed model used to rectify all the previous issues and extends the accuracy in global query expansion.