Q1: In an RC differentiator, responding to repetitive pulses, the average value of the output

ANS:A - is zero

Because it is differentiator RC circuit ( having output across the resistor).

In differentiator, while the signal (pulse, step) at peak, the capacitor charges (as per time constant RC) and a later positive (without sign change) voltage appear across the resistor.
However, when the signal goes to zero, the capacitor discharges sending negative voltage (opposite sign) across the resistor.

The average is the sum of one total cycle/2. As sum will be zero, the average value of the output is also Zero.