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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?

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    Please edit the question to detail what steps you have taken to implement your task. GIS SE is not a tutoring service; we'll help you when you get tangled, but you need to document the steps you have taken before we can make effective suggestions. Note that ArcGIS 10.2.0/.1/.2 moves to retired status Tuesday, so you're working with an elderly build of ArcGIS, and most folks here using the Esri tools have moved on to modern releases, so it may be difficult to reproduce any errors you encounter or for you to implement modern solutions. – Vince Dec 28 '18 at 18:40
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As long as your data layers are already defined as WGS 1984, you should be fine with the following steps:

  1. Open data frame properties (right-click Layers in the table of contents).

  2. Select the coordinate system tab.

  3. 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.

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