A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant $2 \mathrm{rad} /$ volt. If the carrier signal is $c(t)=2 \cos \left(2 \pi 10^6 t\right)$, the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is $\_\_\_\_$ Hz.

The complete Nyquist plot of the open-loop transfer function $G(s) H(s)$ of a feedback control system is shown in the figure.

If $G(s) H(s)$ has one zero in the right-half of the $s$-plane, the number of poles that the closed-loop system will have in the right-half of the $s$-plane is

A unity feedback system that uses proportional - integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters $K_p$ and $K_I$ The maximum value of $K_I$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally - stable (rounded off to three decimal places) is $\_\_\_\_$

The block diagram of a feedback control system is shown in the figure.$$ \text { The transfer function } \frac{Y(s)}{X(s)} \text { of the system is } $$