Do we mention the work that we did ourselves while giving a research proposal? A university has asked for a research proposal of around 200-250 words in length.

I have done some work on it myself and hence I want to propose that same project for research. Should I mention about the work that I did or should I just present an abstract?
Including preliminary results that indicates the strength of the proposed research is never wrong. If your work has just started and your results are just inconclusive then you may consider not including them, simply because they do not contribute much to indicate the potential success of the proposed project. Mentioning that you have started work could still be useful to mention since it indicates you have thought through the process very carefully but then you should probably also consider adding something that makes it clear you cannot complete the research without additional resources. Otherwise, someone might get the idea you do not need any support and that you will complete the work anyway.