**2004**

1. The open loop transfer function of a unity feedback system is G(s) = K

**/**[s(s

^{2 }+ s + 2)(s + 3)]. The range of K for which the system is stable is

a) 21/44 > K > 0

b) 13 > K > 0

c) 21/4 < K < ∞

d) - 6 < K < ∞

**Solution :**https://www.youtube.com/watch?v=KmUOC_i7USs

2. for the polynomial R(s) = s

^{5}+ s

^{4}+ 2s

^{3}+ 2s

^{2}+ 3s + 15, the number of roots which lie in the Right Half of the S-plane is

a) 4

b) 2

c) 3

d) 1

**Solution :**https://www.youtube.com/watch?v=P_CSEbYpX0s

**2006**

3. The positive values of "K" and "a" so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

a) 1, 0.75

b) 2, 0.75

c) 1, 1

d) 2, 2

**Solution :**https://www.youtube.com/watch?v=VYWtxlytlC8

**2008**

4. The number of open right half plane poles of G(s) = 10 / (s

^{5}+ 2s

^{4}+ 3s

^{3}+ 6s

^{2}+ 5s + 3) is

a) 0

b) 1

c) 2

d) 3

**Solution :**https://www.youtube.com/watch?v=Seaj7dcM1yk

**2012**

5. The feedback system shown below oscillates at 2 rad/sec, when

a) K = 2 and a = 0.75

b) K = 3 and a = 0.75

c) K = 4 and a = 0.5

d) K = 2 and a = 0.5

**Solution :**https://www.youtube.com/watch?v=IBPC5lyX_X4

**2014**

6. Consider a transfer function

with p a positive real parameter. The maximum value of p until which G

_{p}remains stable is ______________

**Solution :**https://www.youtube.com/watch?v=2psgTIOta3M

**2015**

7. A plant transfer function is given as

When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is

a) K

_{P}> K

_{I}/2 > 0

b) 2K

_{I}> K

_{P}> 0

c) 2K

_{I}< K

_{P}

d) 2K

_{I}> K

_{P}

**Solution :**https://www.youtube.com/watch?v=1jJORFpuY5Y

8. The characteristic equation of an LTI system is given by F(s) = s

^{5}+ 2s

^{4}+ 3s

^{3}+ 6s

^{2 }– 4s – 8 = 0. The number of roots that lie strictly in the left half S – plane is __________.

**Solution :**https://www.youtube.com/watch?v=oz77HAXHwQU