The UK Maths Challenges provide a wonderful library of multiple choice problems; you can practice for the UK Maths Challenges with past papers for the Junior, Intermediate, or Senior Challenges. Questions and full solutions are provided.
As well as a full solution that does not use the multiple-choice answers further ideas are given for investigation.
Maths Challenge questions are an excellent resource at any time – not just for preparation for the competitions, particularly with the increased requirement for problem-solving skills at all levels. On the outstanding Diagnostic Questions site you can choose Junior Maths Challenge questions by topic by choosing the Themed Quizzes option. These quizzes consist of sets of four or five questions grouped by topic. (Log in to Diagnostic Questions to use the link.)
Further outstanding resources from UKMT include the Team Challenge resources.
For more sources of multiple-choice questions see this post.