**GATE 2003**

1.
The Laplace transform of i(t) is given by I(s) = 2 / [s(1 + s)]. As t
→ ∞, the value of i(t) tends to

a)
0

b)
1

c)
2

d)
∞

**
**

**Solution : https://www.youtube.com/watch?v=DK3hqukI4co**

2.
Figure shows the Nyquist plot of the open loop transfer function
G(s)H(s) of a system. If G(s)H(s) has one right hand pole, the closed
loop system is

a)
always stable

b)
unstable with one closed loop right hand pole

c)
unstable with two closed loop right hand poles

d)
unstable with three closed loop right hand poles

**
**

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

3.
A PD controller is used to compensate a system. Compared to the
uncompensated system, the compensated system has

a)
a higher type number

b)
reduced damping

c)
higher noise amplification

d)
larger transient overshoot

**
**

**Solution : https://www.youtube.com/watch?v=flVQh4IItX4**

4.
The driving point impedance Z(s) of a network has the pole-zero
locations as shown in figure. If Z(0) = 3, then Z(s) is

**
**

**Solution : https://www.youtube.com/watch?v=VkjfxpWTPj4**

5.
The signal flow graph of a system is shown in figure. The transfer
function C(s)/R(s) of the system is

**
**

**Solution : https://www.youtube.com/watch?v=UiYZch03Bsg**

6.
The root locus of the system G(s)H(s) = K / [s(s + 2)(s + 3)] has the
break away point located at

a)
(-0.5, 0)

b)
(-2.548, 0)

c)
(-4, 0)

d)
(-0.748, 0)

**
**

**Solution : https://www.youtube.com/watch?v=f_IljSih2eU**

7.
The approximate Bode magnitude plot of a minimum phase system is
shown in figure. The transfer function of the system is

**
**

**Solution : https://www.youtube.com/watch?v=BXoIP2em_cc**

8.
A second order system has the transfer function C(s)/R(s) = 4 / [s

^{2}+ 4s + 4] with r(t) as the unit step function, the response c(t) of the system is represented by**
**

**Solution : https://www.youtube.com/watch?v=-G7mdzB-60I**

9.
The gain margin and the phase margin of a feedback system with
G(s)H(s) = s/(s + 100)

^{3 }are
a)
0 dB, 0

^{o}
b)
∞, ∞

c)
∞, 0

^{o}
d)
88.5 dB, ∞

**
**

**Solution : https://www.youtube.com/watch?v=n44i9T5koz4**

10.
The zero input response of a system given by the state space
equation

**
**

**Solution : https://www.youtube.com/watch?v=BzTXlRJ5M9k**