1. Consider the following statements with respect to Routh-Hurwitz criterion:

- It can be used to determine relative stability.
- It is valid only for real coefficients of the characteristic equation.
- It is applicable only for non-linear systems.
- It does not provide the exact location of closed-loop poles in left or right-half of s-plane.

Which of the above statements are correct?

- i, ii and iii only
- iii and iv only
- i, ii and iv only
- i, ii, iii and iv

2. The first element of each of the rows of a Routh-Hurwitz stability test showed the signs as follows:

Row |
I |
II |
III |
IV |
V |

Sign |
+ | + | – | + | – |

Consider the following statements:

- The system has three roots in the right-half of s-plane
- The system has three roots in the left-half of s-plane.
- The system is stable.
- The system is unstable.

Which of the above statements about the system are correct?

- i and iv
- i and iii
- ii and iv
- ii and iii

3. Consider the following statements about Routh-Hurwitz criterion:

If all the elements in one row of Routh array are zero, then there are

- Pairs of conjugate roots on imaginary axis.
- Pairs of equal real roots with opposite sign
- Conjugate roots forming a quadrate in the s-plane.

Which of these statements are correct?

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

4. Using Routh’s criterion, the number of roots in the right half s-plane for the characteristic equation:

s^{4} + 2s^{3} + 2s^{2} + 3s + 6 = 0 is

- two
- one
- four
- three

5. Consider the following statements regarding Routh-Hurwitz criterion for stability:

- Routh-Hurwitz criterion is a necessary and sufficient condition for stability.
- The relative stability is dictated by the location of the roots of the characteristic equation.
- A stable system is a dynamic system with a bounded response to a bounded input.

Which of the statements given above are correct?

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

6. The characteristic equation for a third-order system is

q(s) = a_{0}s^{3} + a_{1}s^{2} + a_{2}s + a_{3} = 0

For the third-order system to be stable, besides that all the coefficients have to be positive, which one of the following has to be satisfied as a necessary and sufficient condition?

- a
_{0}a_{1}≥ a_{2}a_{3} - a
_{1}a_{2}≥ a_{0}a_{3} - a
_{2}a_{3}≥ a_{1}a_{0} - a
_{0}a_{3}≥ a_{1}a_{2}

7. Consider the following statements:

When all the elements in one row of the Routh’s tabulation are zero then this condition indicates:

- one pair of real roots with opposite sign in s-plane
- one pair of conjugate roots on the imaginary axis in s-plane
- conjugate roots forming a quadrate in s-plane

Which of the statements given below is/are correct?

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

8. While forming a Routh array, the situation of a row of zeros indicates that the system

- has asymmetrically located roots
- is insensitive to variation in gain
- is stable
- has symmetrically located roots