I would like to give an update. Cortana is working in India if we do the following changes in settings.
First you will have to change 'Region and Language' settings. For this go to desktop control panel and select Clock, Language, and Region from the right hand side
Click on Region and change the following:
In the Format tab, set format as English (United States)
Set Home Location in the Location tab as United States
Finally, in the Administrative tab, set Current System Local to English (United States)
Also, set English (United States) as your primary display language