Recently our company purchased Cartosat-2 Image from NRSC. Our Mining Lease area Boundary is not aligning with Image.It is around 100 meter offset.We are using QGIS 3.4.Spatial reference of Cartosat-2 UTM Zone-45 and WGS-84 datum.Project spatial reference is GCS WGS-84.On the fly projection is there. It aligned properly with LISS-4 Image.
Cartosat-2 scenes can have a misalignment of up to 100m. So your observation of the image not aligning with your shapefile is common. To solve your problem you need to georeference the Cartosat-2 image onto your shapefile or onto your LISS-4 image, which will be much easier and 'failure proof' depending on the size of your area. The process basically involves searching for common points in both images and calculating a transformation function. There are tools in QGIS for that.