Hi Sahil,
When looking at the above link, do you see the following ifnormation?
Error: The administrator has disabled the Services Directory.
Code: 403
If os, this is the expected behavior of the services. While we are not allowed to browse the REST directory of the services, we can still send requests to the API through the URL. Here is an example pulled from the documentation:
https://route.arcgis.com/arcgis/rest/services/World/Route/NAServer/Route_World/solve? stops={"features":[{"geometry":{"x":-122.473948,"y":37.7436}, "attributes":{"Name":"Office","Attr_TravelTime":0}},{"geometry":{"x":-122.439613,"y":37.746144}, "attributes":{"Name":"Store 1","Attr_TravelTime":25}},{"geometry":{"x":-122.488254,"y":37.754092}, "attributes":{"Name":"Store 2","Attr_TravelTime":20}},{"geometry":{"x":-122.44915,"y":37.731837}, "attributes":{"Name":"Store 3","Attr_TravelTime":30}},{"geometry":{"x":-122.46441,"y":37.774756}, "attributes":{"Name":"Store 4","Attr_TravelTime":25}},{"geometry":{"x":-122.426896,"y":37.769352}, "attributes":{"Name":"Store 5","Attr_TravelTime":20}},{"geometry":{"x":-122.473948,"y":37.7436}, "attributes":{"Name":"Office","Attr_TravelTime":0}}]}&findBestSequence=true&preserverFirstStop=true& preserveLastStop=true&returnStops=true&returnDirections=true&returnRoutes=true&f=json&token=<yourToken>
This will return a response, provided you provide a valid ArcGIS Online token as a URL parameter.
Does this address the situation you are encountering?
Thanks,
Calvin