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GATE2019-22

The baseband signal $m(t)$ shown in the figure is phase-modulated to generate the $PM$ signal $\varphi(t)=cos(2\pi f_{c}t+ k m(t)).$ The time $t$ on the $x-$ axis in the figure is in milliseconds. If the carrier frequency is $f_{c}=50kHz$ and $k=10 \pi,$ then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is ___________________ (rounded off to $2$ decimal places).

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