A lot of Nexus 10 owners lost the ability to hear any audio after receiving the Lollipop update. This includes all sources, whether it be apps, or even music stored on the device.
The good news is that there appears to be a fix at the user level. Some people found that just rebooting the device several times in a row (5 or 6 times) did the trick.
If that doesn’t work, others are reporting that sound comes back while running in Safe Mode. If that’s the case, then it has to be a running app that is conflicting with Lollipop. One such app is the Nexus Media Importer, but there could be others. You might want to try uninstalling some of your most recent apps, or even ones that you no longer use.
Let us know if you’re experiencing the same problem and/or if you were able to fix it.