The defining property of frequency modulation is that its total power never changes — option 3.

Why the power is fixed. An FM wave is

\(s(t)=A_{c}\cos\left(\omega_{c}t+m_{f}\sin\omega_{m}t\right)\)

The amplitude \(A_{c}\) is constant — only the argument of the cosine varies — so the transmitted power is

\(P=\dfrac{A_{c}^{2}}{2R}\)

whatever the modulation index. Modulation redistributes power from the carrier into the sidebands but never adds or removes any, which is expressed by the Bessel identity

\(J_{0}^{2}(m_{f})+2\sum_{n=1}^{\infty}J_{n}^{2}(m_{f})=1\)

Contrast with AM, where total power does depend on the index, \(P_{t}=P_{c}\left(1+m^{2}/2\right)\), because there the amplitude itself is being varied. This difference is the reason an FM transmitter's output stage can be driven into saturation for efficiency, and the reason a limiter at the receiver can strip amplitude noise without harming the signal.

Option 1 is plainly false, and instructively so: the carrier amplitude is \(A_{c}J_{0}(m_{f})\), and \(J_{0}\) has zeros at 2.405, 5.52, 8.65 and so on. At those indices the carrier disappears completely while all the power sits in the sidebands — the eigenvalue or carrier-null method, used in the laboratory to set a known deviation precisely.

Why option 2 is flagged rather than dismissed. Bessel functions of the first kind do take negative values, so the statement is literally true. But a negative \(J_{n}\) merely indicates a 180° phase reversal of that sideband pair; the power depends on \(J_{n}^{2}\) and is unaffected. It is an incidental detail of the mathematics, whereas option 3 states the property that characterises FM — which is why option 3 is the intended answer.

Hence, in FM the total power remains constant with respect to the modulation index.