There's a high chance my exam will fall on Ashura this year and I really dont want to give it, as I've read narrations that state we should avoid engaging in worldly stuff such as work etc.. But if I dont take it this year, I'd have to retake the module and give the exam after a year. What can I do in such case? I hope you can give me some advice.

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You can go a head with your exams.You do not need to delay your exams.