Question: I have a single select drop down and need to enable the user to clear his selection too.

Is it elegant to do this:

[![enter image description here](https://i.stack.imgur.com/UgB2z.png)](https://i.stack.imgur.com/UgB2z.png)

Or, on selection of an option should the drop down be hidden, showing the selected items text along with the `X` mark beside it clicking on which the drop down would be shown again?

Answer: 
Your proposal looks fine to me as it is. 

I would say that you should not mess about with the interface. Do not have it morphing unless it is absolutely warranted... because that makes for a confusing user experience.

Also in this particular case: no, do not force the user to click the [x] in order to make a new selection. It will be particularly annoying in case of mis-clicks.
One option would be to use the phrase 'Please select a thing' as a label above the field, and to include a 'blank' (as in empty) option in the dropdown or a "none".

That way a user could select an option, and if they change their mind they can select the 'blank'/"none" option again.

I would say one possible advantage of using a blank option, is that when the user scans over their entered information, it is easier for them to see that they have not entered a selection for this dropdown. It quickly and easily visible as an empty field, as there is no placeholder text in the field.

This of course depends on implementation, and whether you want a label above the field.

As for the 'X', I would lose it (certainly in my above suggestion), and if you really want it, change it to a small text link that says 'clear selection' or something similar.