Answer:
D : lagging by 1/4 of a cycle (ideal inductor)
Step-by-step explanation:
The rate of change of current in an inductor is proportional to the voltage across the inductor. Hence voltage must increase before current can. That means current in an inductor lags the voltage across it.
For an ideal inductor (with no effective series resistance), the lag will be 1/4 cycle of a sinusoidal waveform.
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If the inductor has internal losses (resistance), then the lag will be less than 1/4 cycle.
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Comment on the problem
No circuit image or other description of the inductor is provided here, so we don't know that the inductor is ideal.