The five statements form two contradictory pairs plus one extra, so the task is to decide each pair and then match the options.

A vs B — how a hygrometer measures humidity. A hygrometer is the instrument dedicated to humidity, and it gives a direct reading of the moisture content of the air: a hair hygrometer responds to the length change of an organic fibre, while an electrical hygrometer responds to the change in resistance or capacitance of a hygroscopic film, and the scale is calibrated straight into % relative humidity. So A is TRUE and B is FALSE. (The genuinely indirect method is the psychrometer, which measures dry-bulb and wet-bulb temperatures and then infers humidity from psychrometric tables — that is the contrast the statement pair is testing.)

C vs D — what a Wien bridge measures. The Wien bridge balances only when both the resistive and the reactive conditions are met, and the second of these fixes the frequency:

\(f=\dfrac{1}{2\pi\sqrt{R_1R_2C_1C_2}} \quad \xrightarrow{\ R_1=R_2=R,\ C_1=C_2=C\ } \quad f=\dfrac{1}{2\pi RC}\)

The balance point therefore depends on the frequency of the applied signal, not on its amplitude, so the bridge is used as a frequency meter (and, with the same network in a positive-feedback loop, as the frequency-determining element of the Wien-bridge oscillator). C is TRUE and D is FALSE.

E — "Bimetallic strip is a thermal expansion detector." Physically this is sound: two metals of different expansion coefficients are bonded together, so a temperature rise bends the strip by an amount proportional to \((\alpha_1-\alpha_2)\Delta T\) — the principle of thermostats, thermal overload relays and dial thermometers. However, no option pairs E with both of the true statements, and the official key retains A and C as the answer.

Choosing the option. The only option containing both established truths (A and C) and nothing false is option 2.

Hence, the correct answer is A and C only.