My study area i.e North Eastern Arabian Sea belongs UTM Q42 and Q43.
How can I re-project the maps from GCS-WGS1984 to UTM in ArcGIS Desktop 10.1?
As long as your data layers are already defined as WGS 1984, you should be fine with the following steps:
Open data frame properties (right-click Layers in the table of contents).
Select the coordinate system tab.
Under projected coordinate systems, select UTM, then WGS 1984. I honestly can't remember if we had divided the zones into northern and southern hemisphere folders. You're looking for 42N (North) and 42N (North).
Select one and okay all dialogs.
Note: You'll need to pick one or the other. You can 'label' a layout with a grid in using either UTM zone, but the map itself has to be in either 42N or 43N.