A multimeter effectively acts as a small battery-and-ammeter combination that forces a bias across the diode and reads the resulting resistance, so checking a diode really means checking how the depletion region responds in each direction. Let's evaluate each option against that behaviour.
- High resistance in reverse bias and low resistance in forward bias: In forward bias, the applied voltage pushes the p-side and n-side charge carriers toward the junction, narrowing the depletion region until current flows freely, which the meter reads as low resistance. In reverse bias, the same carriers get pulled away from the junction, widening the depletion region until only a tiny leakage current remains, which the meter reads as high resistance. This is exactly the behaviour expected of a healthy diode.
- High resistance in both forward bias and reverse bias: If the diode showed high resistance even in forward bias, it would mean the junction never allows current through in either direction, this describes an open (broken) diode, not a working one.
- Low resistance in both reverse bias and forward bias: If the diode conducted freely in both directions, it would mean the depletion region never forms a barrier at all, this describes a shorted (failed) diode, again not a working one.
- High resistance in forward bias and low resistance in reverse bias: This is the reverse of how a p-n junction actually behaves, forward bias is supposed to narrow the barrier and reverse bias is supposed to widen it, so a diode showing the opposite pattern would indicate it is either connected backwards or damaged.
Only the first option correctly reflects how the depletion region responds to each bias direction in a properly functioning diode.
Therefore, the correct answer is high resistance in reverse bias and a low resistance in forward bias.