"jucheck" is nothing but a update checker for Sun Java Platform on which you run the many different applications. One more thing, it is not an unsolicitaed or non consentual installation. It comes with when you installed Java on your system.
Please check the details of what this does, for your benefit & understanding:
The jucheck.exe is the Java update verification process. This process will check on the internet for available updates for the Java software installed on your computer. If updates are available, it will notify you and/or manage the download and install of the updates. You should leave this process running in order to keep your Java up to date.