Roots on LHS& RHS

Q. The forward transfer function of a unity feedback system is
$G\left(s\right)=\frac{K(s^2+1)}{(s+1)(s+2)}.$

The system is stable for

1. K < - 1
2. K > - 1
3. K < - 2
4. K > - 1

Q. The close loop transfer function of a system is, $T\left(s\right)=\frac{s^3+4s^2+8s+16}{s^5+3s^4+5s^2+4s+3}$
The number of poles in the right half plane and in left half plane are

1. 3, 2
2. 1, 4
3. 2, 3
4. 4, 1

Q. The number of roots of $s^3+5s^2+7s+3=0$ in the left half of the s-plane is

1. zero
2. one
3. two
4. three

Q. If $s^3+3s^2+4s+A=0$ , then all the roots of this equation are in the left half plane provided that

1. $A>12$
2. $-3<A<4$
3. $0<A<12$
4. $5<A<12$

Q. The value of $a_0$ which will ensure that the polynomial $s^3+3s^2+2s+a_0$ has roots on the left half of the s-plane is

1. 11
2. 9
3. 7
4. 5

Q. The range of K for which all the roots of the equation $s^3+3s^2+2s+K=0$ are in the left half of the complex s-plane is

1. 0 < K < 6
2. 0 < K < 16
3. 6 < K < 36
4. 6 < K < 16

Q. A closed loop system has the characteristic equation given by $s^3+K{s}^2+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be satisfied?

1. 0 < K < 0.5
2. 0.5 < K < 1
3. 0 < K < 1
4. K > 1

Q. The the feedback system given below, the transfer function $G\left(s\right)=\frac{1}{(s+1{)}^2}$. The system CANNOT be stabilized with

1. $C\left(s\right)=1+\frac{3}{s}$
2. $C\left(s\right)=3+\frac{7}{s}$
3. $C\left(s\right)=3+\frac{9}{s}$
4. $C\left(s\right)=\frac{1}{s}$

Q. The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $(2-j3)$. List all the poles and zeros.

1. Poles at $(2\pm j3)$, no zeros.
2. Poles at $(\pm 2-j3)$, one zero at orgin.
3. Poles at $(2-j3),(-2+j3),$ zeros at $(-2-j3),(2+j3)$.
4. Poles at $(2\pm j3)$, zeros at $(-2\pm j3).$