The case study will be something with respect to a client issue with various problems, it's pretty much up to you to determine what's most important and justify why, you'll have to prepare some slides on it. Written exercise is about preparing a synopsis to a board of why Deloitte should be involved as a partner in their project, basically it's a case of including stuff that strengthens your case and glossing over anything that will detract from it. As for the partner interview, in my one they talked about a client they were working with and how you could go about addressing their issues, plus standard questions about demonstrating teamwork, leadership, why Deloitte etc. HTH, but please don't create multiple posts in future, it really is unnecessary.