1. Consider a second order system whose state space representation is of the form

$\dot x = Ax + Bu$. If x_{1}(t) = x_{2}(t), then system is

- unstable
- observable
- uncontrollable
- controllable

2. For a feedback control system all the roots of the characteristic equation can be placed at the desired location in the s-plane if and only if the system is

- observable
- controllable

Which of the above statements are correct?

- i only
- ii only
- both i and ii
- neither i nor ii

3. A transfer function of a control system does not have pole-zero cancellation. Which one of the following statement is true?

- system is controllable but unobservable
- system is observable but uncontrollable
- system is completely controllable and observable
- system is neither controllable nor observable

4. For the system $\dot x = \begin{bmatrix} 2 & 3\\ 0 & 5 \end{bmatrix}x + \begin{bmatrix} 1\\ 0 \end{bmatrix}u$, which of the following statement is true?

- The system is uncontrollable and stable.
- The system is controllable and stable.
- The system is uncontrollable and unstable.
- The system is controllable but unstable.