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 $(-3 \pm j \sqrt{5})$ ?

The state and output equations for a control system are:

$$ \begin{aligned} & \dot{x}=\left[\begin{array}{cc} -4 & -1.5 \\ 4 & 0 \end{array}\right] x+\left[\begin{array}{l} 2 \\ 0 \end{array}\right] u \\ & y=\left[\begin{array}{ll} 1.5 & 0.625 \end{array}\right] x \end{aligned} $$

Which of the following expressions correctly represents the transfer function $\frac{Y(s)}{U(s)}$ of the system with zero initial conditions?