Am I obliged to answer student queries that can readily be answered by reading the syllabus?
Whether or not you're obliged is debatable, but here is what you can do to reduce the time that's consumed by answering redundant emails:

Have your students write all questions into an online forum that's accessible for every participant of your course.* Post your answers there as well.

You can "pin" answers that are of a general nature. Your first pinned message should be a FAQ, entitled "Frequently asked questions. Read first before posting" and with the first line reading something like:


  Before posting a question, please make sure that it has not already
  been answered. In particular, check the pinned messages first. Chances
  are, your question has been answered and you can save yourself and me some work.


If you get a duplicate question, just refer the student to the relevant message. This should work as a gentle nudge that deters other students form asking redundant questions in the future (remember that the answer can be read by the whole course).

* and only them.