Is there any book containing exercises about quantum mechanics?With answers?
Depends entirely on what you're looking for, what topics, what level, etc. But a good book along those lines to recommend is "Practical Quantum Mechanics" by S Flugge. It's composed entirely of 219 worked problems, covering the entire range from basic 1-D potentials to the Dirac Equation and radiation theory.
Zettili's book has a lot of examples. It's at sort of an intermediate/advanced undergraduate level, and starts with Dirac notation pretty much right from the get go (chapter 2 is a pretty heavy introduction to the math you need. Don't get discouraged if you have trouble getting through that chapter in one pass).
https://www.amazon.com/Selected-problems-quantum-mechanics-Haar/dp/B0007IKXQG (A superset of the Dover book, with 71 more problems.)
Separate names with a comma.