b
Given : Resistance \(\mathrm{R}=100\,\,kilo\,ohm\) \(=100 \times 10^{3} \Omega\)

Capacitance \(\mathrm{C}=250\) picofarad \(=250 \times 10^{-12} \mathrm{F}\)

\(\tau=\mathrm{RC}=100 \times 10^{3} \times 250 \times 10^{-12} \mathrm{sec}\)

\(=2.5 \times 10^{7} \times 10^{-12} \mathrm{sec}\)

\(=2.5 \times 10^{-5} \mathrm{sec}\)

The higher frequency wheih can be detected with tolerable distortion is

\(f=\frac{1}{2 \pi m_{a} R C}=\frac{1}{2 \pi \times 0.6 \times 2.5 \times 10^{-5}} \mathrm{Hz}\)

\(=\frac{100 \times 10^{4}}{25 \times 1.2 \pi} H z=10.61 \mathrm{KHz}\)

This condition is obtained by applying the condition that rate of decay of capacitor voltage must be equal or less than the rate of decay modulated singnal voltage for proper detection of mdoulated signal.