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A device with input $x(t)$ and output $y(t)$ is characterized by: $y(t)=x^{2}(t)$.
An FM signal with frequency deviation of $90 \; \mathrm{kHz}$ and modulating signal bandwidth of $5 \; \mathrm{kHz}$ is applied to this device. The bandwidth of the output signal is

1. $370 \; \mathrm{kHz}$
2. $190 \; \mathrm{kHz}$
3. $380 \; \mathrm{kHz}$
4. $95 \; \mathrm{kHz}$