$$\begin{aligned} \text { Given, carrier wave frequency } f_C & =20 \mathrm{MHz} \\ & =20 \times 10^6 \mathrm{~Hz} \end{aligned}$$

Bandwidth required for modulation is

$$\begin{aligned} 2 f_m & =3 \mathrm{kHz}=3 \times 10^3 \mathrm{~Hz} \\ f_m & =\frac{3 \times 10^3}{2}=1.5 \times 10^3 \mathrm{~Hz} \end{aligned}$$

Demodulation by a diode is possible if the condition $\frac{1}{f_c}<< R C<\frac{1}{f_m}$ is satisfied

$$\begin{aligned} \text{Thus,}\quad & \frac{1}{t_c}=\frac{1}{20 \times 10^6}=0.5 \times 10^{-7} \quad\text{.... (i)}\\ \text{and}\quad & \frac{1}{f_m}=\frac{1}{1.5 \times 10^3} \mathrm{~Hz}=0.7 \times 10^{-3} \mathrm{~s}\quad\text{.... (ii)} \end{aligned}$$

Now, gain through all the options of $R$ and $C$ one by one, we get

(i) $R C=1 \mathrm{k} \Omega \times 0.01 \propto \mathrm{~F}=10^3 \Omega \times\left(0.01 \times 10^{-6} \mathrm{~F}\right)=10^{-5} \mathrm{~S}$

Here, condition $\frac{1}{f_c} \ll R C<\frac{1}{f_m}$ is satisfied.

Hence it can be demodulated.

(ii) $R C=10 \mathrm{k} \Omega \times 0.01 \propto \mathrm{~F}=10^4 \Omega \times 10^{-8} \mathrm{~F}=10^{-4} \mathrm{~s}$

Here condition $\frac{1}{f_c} \ll R C<\frac{1}{f_m}$ is satisfied.

Hence, it can be demodulated.

(iii) $R C=10 \mathrm{k} \Omega \times 1 \propto \propto \mathrm{~F}=10^4 \Omega \times 10^{-12} \mathrm{~F}=10^{-8} \mathrm{~S}$

Here, condition $\frac{1}{f_c}>R C$, so this cannot be demodulated.