The storage oscilloscope's pairing is beyond doubt and selects the code: a-iii, b-ii, c-i, d-iv — option 2.

a — why storage means memory. An ordinary oscilloscope's trace is redrawn many times a second and persists only as long as the phosphor glows. A single, non-repetitive event flashes once and is gone. A storage oscilloscope retains it — originally on a bistable storage mesh inside the CRT, now by digitising into memory — and holds it indefinitely for examination. "Long term memories" is a direct description of that capability, and no other instrument in the list has it.

c — why pulse testing needs bandwidth. A pulse's edges contain its high-frequency content: for a Gaussian response,

\(t_{r}\approx\dfrac{0.35}{BW}\)

so an instrument of 100 MHz cannot display an edge faster than 3.5 ns, and the measured rise time combines signal and instrument in quadrature. Examining overshoot, ringing and settling on fast pulses is therefore squarely the high-frequency oscilloscope's work.

d — why servo work is low-frequency. A servo's mechanical loop responds over hundreds of milliseconds to seconds, so its step response, overshoot and settling time occur at fractions of a hertz to a few hertz. Displaying that needs a very slow timebase and DC coupling — the opposite requirement from pulse work.

b — the sampling oscilloscope. It builds a picture of a repetitive waveform by taking one sample per cycle, each slightly later than the last, and assembling them into a complete trace — equivalent-time sampling. This reaches far beyond the bandwidth of any real-time instrument, into tens of gigahertz, because only the sampling gate need be fast. It reconstructs the waveform against time, so "time domain" fits, though the phrase is the loosest in the list — which is why the answer is flagged.

The pairing is nevertheless secure, since a is certain and the remaining three sort themselves by frequency range.

Hence, the correct code is a-iii, b-ii, c-i, d-iv.