Hi again Agrajag
We might need to see the SVG file, which is set up to show the problem. But here are a few things you can try first, if you like.
First, you can double-check what's selected, and you didn't accidentally select and/or copy something unintentionally. I know it sounds silly, but it's a common problem with beginners.
If there's anything with any amount of transparency in the new object being pasted in, you'll see things through it, from what was already in the file It will make the partially transparent object appear darker.
If the objects are all opaque, then I would think the problem could be with a layer. Could you have made any layers either partially transparent (Opacity slider in the layers dialog) or maybe you experimented with, or just accidentally set a Blend mode for a layer (it's a dropdown menu just above the Opacity slider).
Or if you haven't been using the Layers dialog, then a Blend mode is probably not likely. But you can check the Opacity setting for each layer, in the status bar.
Note that if you paste anything into, or copy anything out of a partially transparent layer, that object will be partially transparent. It sort of picks it up from the layer. I've always found it confusing to use layers for anything more than organization. (Edit -- If you need a partially transparent layer, you could lock it, to prevent accidentally pasting things into it.)
Also note that if you group something with partial transparency, the group will not indicate that. (It used to, and I wish it still did - kind of drives me crazy, to be honest.) So if you have a group, you need to either enter the group (double-click on it), or ungroup it, to check the individual objects in the group.
If none of that helps, please share the SVG file with us, which is showing the problem. Also explain how to produce the problem, if it's not exactly showing yet.
Just out of curiosity (I'm always interested in how people are using Inkscape) are you going to have these cards actually printed up, into an actual deck of cards?