Two of the pairings are unambiguous and they fix the code: (A)-(IV), (B)-(III), (C)-(I), (D)-(II), option 1.

(A) White noise and Johnson noise. Johnson-Nyquist noise is thermal noise in a resistor, and its power spectral density is flat — the same at every frequency up to terahertz:

\(S(f)=4kTR\ \text{V}^{2}/\text{Hz}\)

A flat spectrum is precisely what "white" means, by analogy with white light containing all colours equally. The two names describe the same thing from different angles: one names the mechanism, the other the spectrum.

(D) P_DSBSC and P_cm²/2. In double-sideband suppressed-carrier transmission the carrier is removed entirely, so the whole transmitted power is in the two sidebands. Each carries \(m^{2}P_{c}/4\), giving a total of

\(P_{DSBSC}=\dfrac{m^{2}P_{c}}{2}\)

which is exactly the sideband term of the full AM expression \(P_{t}=P_{c}\left(1+m^{2}/2\right)\) with the carrier's 1 dropped — the whole point of suppressing it.

(C) Modulation and reduced antenna height. An efficient antenna must be comparable with a wavelength, conventionally \(\lambda/4\). A 1 kHz baseband signal has \(\lambda=300\) km, needing a 75 km aerial — impossible. Modulating it onto a 1 MHz carrier shortens the wavelength to 300 m and the aerial to 75 m. Translating the signal upward in frequency is therefore the reason radio is possible at all, and it is the first justification given for modulation in every textbook.

(B) RMS noise voltage and the inverse square root. The thermal noise voltage itself is

\(V_{n}=\sqrt{4kTBR}\)

which rises as the square root of absolute temperature. The entry is therefore to be read with T as the observation time: measuring noise over a longer interval averages more independent samples, and the uncertainty of the resulting RMS estimate falls as \(1/\sqrt{T}\). This is why a noise measurement is integrated for as long as the experiment allows, and it is the only pairing left once the other three are placed.

Hence, the correct code is (A)-(IV), (B)-(III), (C)-(I), (D)-(II).