Statements (A), (C) and (E) are correct — option 4 — and each names one of the three roles the same network plays.

(A) — an AC bridge that measures frequency. Unlike a Wheatstone bridge, whose balance depends only on resistances, the Wien bridge balances only at one frequency:

\(f=\dfrac{1}{2\pi\sqrt{R_{1}R_{2}C_{1}C_{2}}}=\dfrac{1}{2\pi RC}\ \text{for equal components}\)

With R and C known, the balance point measures the applied frequency. It must be an AC bridge, since capacitors are involved and a DC excitation would settle to nothing — which disposes of (B) at once.

(C) — the frequency-determining element. Turn the bridge round and use its frequency selectivity to set a frequency rather than measure one. In the Wien-bridge oscillator the series-parallel RC arm feeds positive feedback to the non-inverting input, and since it is the only frequency at which that path has zero phase shift, the circuit oscillates there and nowhere else.

(E) — the notch filter, and why it rather than (D). This is the discriminating pair, and the distinction lies in what is taken as the output.

The RC arm alone is indeed a band-pass network: its transfer function peaks at \(f=1/2\pi RC\), where the attenuation is a maximum of \(1/3\).

The complete bridge takes the output as the difference between the two arms. At balance that difference is zero, so the output nulls at the very frequency the arm passes best — a band-reject, that is a notch. Since the question says "Wien bridge" rather than "Wien network", (E) is the correct member of the pair.

Where the notch is used : removing 50 Hz mains hum from an instrumentation signal, and measuring distortion — null the fundamental with the bridge and whatever remains is harmonic content, which is exactly how a distortion analyser works.

The historical footnote ties the three uses together: Hewlett's 1939 Wien-bridge audio oscillator, stabilised by a small lamp in the negative-feedback arm, was Hewlett-Packard's first product.

Hence, the correct statements are (A), (C) and (E).