GATE Electronics and Communications (EC) 2020 Solved Papers

SPM(t) and SFM(t) as defined below, are the phase modulated and frequency modulated waveforms, respectively, corresponding to the message signal $\mathit{m}\left(\mathit{t}\right)$ shown in the figure.
${\mathit{S}}_{\mathit{P}\mathit{M}}\left(\mathit{t}\right)=\cos (1000\mathit{\pi }\mathit{t}+{\mathit{K}}_{\mathit{p}}\mathit{m}\left(\mathit{t}\right)$ and Where ${\mathit{K}}_{\mathit{p}}$ is the phase deviation constant in radians\/volt and $\mathit{K}\mathit{f}$ is the frequency deviation constant in radians\/second\/volt. If the highest instantaneous frequencies of $\mathit{S}\mathit{P}\mathit{M}\left(\mathit{t}\right)$ and
$\mathit{S}\mathit{F}\mathit{M}\left(\mathit{t}\right)$ are same, then the value of the ratio $\frac{{\mathit{K}}_{\mathit{p}}}{{\mathit{K}}_{\mathit{f}}}$ is ____________ seconds.