Stability on PM & GM

Q. The phase margin of a system with the open loop transfer function$G\left(s\right)H\left(s\right)=\frac{(1-s)}{(1+s)(3+s)}$, is

1. $\infty$
2. ${90}^o$
3. ${68.3}^o$
4. 0

Q. If $G\left(s\right)H\left(s\right)=\frac{10}{(s+1)(s+20)}$ then the gain margin and phase margin of the system are respectively.

1. $\frac{1}{2},\infty$

2. 0, 180
3. $\infty ,\infty$
4. $\infty ,180{}^{\circ }$

Q. Consider the unity feedback control system shown. The value of K that results in phase margin of the system to be ${30}^{\circ }$ is
(Give the answer up to two decimal places.)

1. 1.047

Q. If the gain margin of the system is 10 dB and phase margin of the system is zero then the system is

1. stable
2. unstable
3. marginally stable
4. Such type of system does not exist