Consider a real, narrowband signal $x(t)=A(t) \cos \left[2 \pi f_c t+\theta(t)\right]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_M$ and $f_C\left(=1000 f_M\right)$, respectively. Which of the following statements is/are correct for $-\infty

The average bit error rate at the input of a $(7,4,1)$ Hamming decoder is 0.10 . The probability that the decoder will fail to decode a received word correctly is $\_\_\_\_$ . (rounded off to two decimal places)

A control system is shown in the Figure.

Which option represents the correct transfer function of the system?

For the control system shown in the Figure, the transfer function of a plant, $G(s)=\frac{1}{(s+1)(s+2)}$ is connected in cascade with a compensator $C(s)=K(s+\alpha)$, where $K$ and $\alpha$ are positive real valued constants.

Which of the following pairs ( $K, \alpha$ ) represent the correct values for the closed loop system to have poles at $(-3 \pm j \sqrt{5})$ ?