Dear Candidate,
Since you are from a non psychology background, you may have to clear the basic concepts first. This can take time as you may have lots of doubts as well. So if you want to pursue masters and give entrance, to save the time, you can enroll in a coaching, they will prepare you within 6 to 7 months, along with some MCQ practice.
It depends on the number of hours you are willing to dedicate for preparation. Ideally MA Psychology entrance examination covers Bachelor level syllabus. And you haven't mentioned the entrance exam for which University you are preparing and so it makes it difficult to help you with the syllabus per se. But do prepare in Psychology at Bachelor's level and you can do better. But if you can also help us with the entrance exam you are preparing for, we can also help you with syllabus.
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