Java standardlib functions in exam

Are we allowed to use standardlib functions like the string.tohashcode() functions in the exam if not stated otherwise?

Yes.
That being said, you will not need to remember all of the Java API for the exam (frankly, that’s not really possible). If you need something from it, it will be provided in the exam, and if it’s forbidden to use it that will also be stated.
If it is neither forbidden nor explicitly stated, then you may use it – but it’s probably not helpful anyway.

Note that there is no method tohashcode in the String class. You probably mean str.hashCode().

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