Unfit & Beginner

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I don't have access to a gym and my time for working out is limited. My fitness is terrible, especially stamina and arm strength. I can't even do a single push-up properly.
I am going to take up weekly karate (1 hour), but what exercises can I do at home which won't kill me in the first few weeks and won't eat into my time? I'm sure this is a very common question, but I am finding it difficult to know where to start, especially as I hate exercising due to my lack of fitness.

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