Hello Niraj,
The only examples of dynamically generating a shapefile and offering it for download (or sending it by email) I have seen relied on custom geoprocessing tasks built with tools from the Data Extraction Toolset.
This use case is often called "Clip and Ship" and there are some examples for server side and for client side.
As far as I know, there is no simple option like saying "f=shp" in the REST API Query task. It could be very useful if it was possible to enable it as another capability of a service. At one point I though the GeoDataServer service would be able to offer easy data extraction interface, but I have no experience with the GeoDataServer type and I am not sure what the future plans around it are.
Filip.
