21. Which of the following transfer functions is/are minimum phase transfer function(s)?

- $\frac{1}{(s-1)}$
- $\frac{s-1}{(s+3)(s+4)}$
- $\frac{(s+2)}{(s+3)(s-4)}$

Select the correct answer using the code given below:

- i and iii
- i only
- ii and iii
- None of these

22. If the poles of a system lie on the imaginary axis, the system will be

- Stable
- Conditionally stable
- Marginally stable
- Unstable

23. Which one of the following is the correct statement?

A non-minimum phase network is one whose transfer function has

- zeros in the left-hand plane and poles in the right-hand plane.
- zeros and poles in the left-hand plane.
- zeros in the right-hand plane and poles in the left-hand plane.
- arbitrary distribution of zeros and poles in the s-plane.

24. The open-loop transfer function of a unity feedback control system is given by G(s) = Ke^{-Ts}, where K and T are constants and these are greater than zero. The stability of closed-loop system depends on which of the following?

- Both K and T
- K only
- Neither on K nor on T
- T only

25. The characteristic equation of a system is given as

s^{3} + 25s^{2} + 10s + 50 = 0.

What is the number of roots in the right half of s-plane and on the jω axis, respectively?

- 1, 1
- 0, 0
- 1, 2
- 2, 1

26. The transfer function of a system is $\frac{(1-s)}{(1+s)}$.

The system is then which one of the following?

- Non-minimum phase system
- Minimum phase system
- Low-pass system
- Second-order system

27. Which one of the following is the correct statement?

A minimum phase transfer function has

- poles in the right half of s-plane
- zeros in the right half of s-plane
- poles in the left half of s-plane and zeros the right half of s-plane
- no poles or zeros in the right half of s-plane or on the jω-axis excluding the origin

28. An electromechanical closed-loop control system has the transfer function

$\frac{C(s)}{R(s)}=\frac{k}{s(s^2+s+1)(s+4)+k}$

Which one of the following is correct?

- The system is stable for all positive values of k.
- The system is unstable for all values of k.
- The system is stable for values of k between 0 and 3.36.
- The system is stable for values of k between 1.6 and 2.45.

29. Consider the following equation:

2s^{4} + s^{3} + 3s^{2} + 5s + 10 = 0

How many roots does this equation have in the right half of s-plane?

- Two
- One
- Four
- Three

30. A control system is defined in s-domain. Following points regarding the poles of the transfer function obtained from the characteristic equation were noted:

- Poles with positive real part denote stable system
- Complex poles always occur in pairs
- A pole s = -σ (σ > 0) means that the transient response contains exponential decay.

Which of the above are correct?

- i and iii
- i and ii
- i, ii and iii
- ii and iii

31. The characteristic equation of a system is given by

3s^{4} + 10s^{3} + 5s^{2} +2 = 0.

This system is

- marginally stable
- stable
- unstable
- neither (a), (b) nor (c)