In general it has been stated that we select the project with highest NPV. However at the time of Mutually exclusive projects selection, do we still use NPV as criteria or do we use LCM and EAA approaches.
As long as they are mutual exclusive projects you can choose only one
LCM and EAA do also decide on basis of NPV, because they assume you can repeat the projects indefinitely. If you can repeat the projects over and over again then you simply need to find the highest NPV per unit of time, which is what EAA and LCM methods do.