Haha some interesting advice on here. The answer is for the purposes of the test neither of these things matter. Use the handbrake when at a standstill or don't, we're looking at wether you keep control of the vehicle or not. So you can not use the handbrake at all if you had no loss of control without using it. You might want to use it when stopping on a hill, to make it easier to move off as others have said.
Emergency stop: handbrake or clutch first? What kind of question is this, we'd expect people to use the footbrake first and foremost. You don't even need to use the clutch, you can stall the car! As long as the vehicle stops!! Handbrake is not needed whatsoever and should not be used during this exercise. When you have come to a complete stop we say "thank you, I won't ask you to do that again, drive on when you're ready", then you can take your foot off the brake and drive on. No handbrake necessary.
Definitely do not listen to Aiden above about the risk of sliding into an obstruction ahead if you don't use the handbrake! Handbrake will make no difference to stopping distance and in a situation where you're stopping in an emergency to avoid anything you are DEFINITELY going to want both hands on the wheel.