State which of the two, the capacitor or an inductor, tends to become a SHORT when the frequency of the applied alternating voltage has a very high value.

Capacitor.
Capacitors act like a short at high frequencies and an open at low frequencies. At high frequencies, the capacitor only has time to get a very little charge on it i.e. it has very little counter voltage. At low frequencies, there is sufficient time for a considerable amount of charge to collect on the capacitor. It indicates that there is a large reverse voltage on the capacitor.  Therefore the sum of the voltage of capacitor and the voltage of the ac source is nearly zero. That means the current will be nearly zero.

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Capacitor
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