**GATE 2008**

1.
The pole-zero plot given below corresponds to a

a)
Low pass filter

b)
High pass filter

c)
band pass filter

d)
Notch filter

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

2.
Step response of a set of three second order under damped systems all
have the same percentage overshoot. Which of the following diagrams
represents the poles of the three systems?

**Solution :**https://www.youtube.com/watch?v=X0RUYGCL8P4

3.
Group – I lists a set of four transfer functions. Group – II
gives a list of possible step responses y(t). Match the step
responses with the corresponding transfer functions.

a)
P - 3, Q - 1, R - 4, S - 2

b)
P - 3, Q - 2, R - 4, S - 1

c)
P - 2, Q - 1, R - 4, S - 3

d)
P - 3, Q - 4, R - 1, S – 2

**Solution :**https://www.youtube.com/watch?v=jXGZriqlb1c

4.
A certain system has transfer function G(s) = (s + 8)/(s

^{2}+ αs – 4 ), where α is a parameter. Consider the standard negative unity feedback configuration shown below.
Which
of the following statements is true?

a)
The closed loop system is never stable for any value of α

b)
For some positive values of α, the closed loop system is stable,
but not for all positive values

c)
For all positive values of α, the closed loop system is stable

d)
The closed loop system is stable for all values of α, both
positive and negative

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

5.
A signal flow graph of a system is given below.

The
set of equations that correspond to this signal flow graph is

**Solution :**https://www.youtube.com/watch?v=cxlX8Rpj9cs

6.
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

7.
The magnitude of frequency response of an under damped second order
system is 5 at 0 rad/sec and peaks to 10/√3 at 5√2 rad/sec. The
transfer function of the system is

**Solution :**https://www.youtube.com/watch?v=3a4n-8XUFCg

8.
Group – I gives two possible choices for the impedance Z in the
diagram. The circuit elements in Z satisfy the condition R

_{2}C_{2}>R_{1}C_{1}. The transfer function V_{o}/V_{1}represents a kind of controller. Match the impedance's in Group – I with the types of controllers in Group – II.
a)
Q – 1, R – 2

b)
Q – 1, R – 3

c)
Q – 2, R – 3

d)
Q – 3, R – 2

**Solution :**https://www.youtube.com/watch?v=Q3O1G2CU5Xw