A lamp is connected in series with a capacitor

A) When a dc source is connected to the combination, the lamp will not glow in steady state

B) When ac source is connected to the combination, the brightness of glow of lamp increases with increases of frequency of ac.

Capacitive reactance offered by a capacitor is ${\mathrm{X}}_{\mathrm{c}}=\frac{1}{\mathrm{\omega C}}$

for steady dc source frequency being zero, capacitor offers infinite opposition. so current will pass through the capacitor and the circuit acts as an open circuit. so the bulb in series with the capacitor does not glow.

For ac with increase in frequency capacitive reactance will decrease, which in turn increases the brightness of the bulb.

So both A and B are true.