Electrical Engineering (EE) 1998 GATE Paper without solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


GATE EE - 1998
SECTION – A 
1. In each of sub question (1.1 to 1.25) four alternatives A, B, C and D are provided
of which one is correct. Indicate in your book, at the space provided, the correct
answer by writing the alphabet corresponding to the answer.
1.1 A sinusoidal source of voltage V and frequency f is connected to a series circuit of 
variable resistance, R and a fixed reactance, X. The locus of the tip of the 
current-phasor, I, as R is varied from 0 to 8 is:  
(a) a semicircle with a diameter of .
V
X
 
(b) a straight line with a slop of 
R
X
(c) an ellipse with 
V
R
as major axis. 
(d) a circle of radius 
R
X
and origin at 0,
2
V ? ?
? ?
? ?
. 
1.2 A circuit with a resistor, inductor and capacitor in series is resonant of .
o
f Hz If all 
the component values are now doubled, the new resonant frequency is:
(a) 2
o
f (b) still 
o
f (c) 
4
o
f
(d) 
2
o
f
1.3 In the circuit shown in Fig.1.3, it is desired to have a constant direct current i(t) 
through the ideal inductor L. the nature of the voltage source v(t) must be: 
(a) constant voltage  
(b) linearly increasing voltage 
(c) an ideal impulse  
(d) exponentially increasing voltage 
1.4 The reflection coefficient for the transmission line shown in Fig.1.4 at P is: 
(a) +1 
(b) -1 
(c) 0   
(d) 0.5 
i(t)
v(t) 
L
P Transmission line 
Load 300O 
Z o = 300O
Z o = Sugar impedance 
Page 2


GATE EE - 1998
SECTION – A 
1. In each of sub question (1.1 to 1.25) four alternatives A, B, C and D are provided
of which one is correct. Indicate in your book, at the space provided, the correct
answer by writing the alphabet corresponding to the answer.
1.1 A sinusoidal source of voltage V and frequency f is connected to a series circuit of 
variable resistance, R and a fixed reactance, X. The locus of the tip of the 
current-phasor, I, as R is varied from 0 to 8 is:  
(a) a semicircle with a diameter of .
V
X
 
(b) a straight line with a slop of 
R
X
(c) an ellipse with 
V
R
as major axis. 
(d) a circle of radius 
R
X
and origin at 0,
2
V ? ?
? ?
? ?
. 
1.2 A circuit with a resistor, inductor and capacitor in series is resonant of .
o
f Hz If all 
the component values are now doubled, the new resonant frequency is:
(a) 2
o
f (b) still 
o
f (c) 
4
o
f
(d) 
2
o
f
1.3 In the circuit shown in Fig.1.3, it is desired to have a constant direct current i(t) 
through the ideal inductor L. the nature of the voltage source v(t) must be: 
(a) constant voltage  
(b) linearly increasing voltage 
(c) an ideal impulse  
(d) exponentially increasing voltage 
1.4 The reflection coefficient for the transmission line shown in Fig.1.4 at P is: 
(a) +1 
(b) -1 
(c) 0   
(d) 0.5 
i(t)
v(t) 
L
P Transmission line 
Load 300O 
Z o = 300O
Z o = Sugar impedance 
GATE EE - 1998
1.5 The laws of electromagnetic induction (Faraday’s and Lenz’s law) are summarized 
in the following equation: 
(a) e = iR (b) 
di
e L
dt
=
(c) 
d
e
dt
?
= - (d) None of the above 
1.6 A synchronous generator connected to an infinite bus is overexcited. Considering 
only the reactive power, from the point of view of the system, the machine acts 
as 
(a) a capacitor (b) an inductor 
(c) a resistor (d) None of the above 
1.7 A 3 phase squirrel cage induction motor has a full load efficiency of 0.8 and a 
maximum efficiency of 0.9. It is operated at a slip of 0.6 by applying a reduced 
voltage. The efficiency of the motor at this operating point is: 
(a) less than 0.4 (b) greater than 0.6 
(c) in the range of 0.8 ±0.1 (d) None of the above 
1.8 The efficiency of a 100 KVA transform is 0.98 at full as well as at half load. For 
this transformer at full load the copper loss. 
(a) is less than core loss  (b) is equal to core loss 
(c) is more than core loss  (d) None of the above 
1.9 The magnetizing current in a transformer is rich in 
(a) 3
rd
 harmonic (b) 5
th
 harmonic (c) 7
th
 harmonic (d) 13
th
 harmonic 
1.10 Series capacitive compensation in EHV transmission lines is used to 
(a) reduce the line loading 
(b) improve the stability of the system 
(c) reduce the voltage profile (d) improve the protection of the line 
1.11 Bulk power transmission over long HVDC lines are preferred, on account of 
(a) low cost of HVDC terminals (b) no harmonic problems 
(c) minimum line power losses (d) simple protection 
Page 3


GATE EE - 1998
SECTION – A 
1. In each of sub question (1.1 to 1.25) four alternatives A, B, C and D are provided
of which one is correct. Indicate in your book, at the space provided, the correct
answer by writing the alphabet corresponding to the answer.
1.1 A sinusoidal source of voltage V and frequency f is connected to a series circuit of 
variable resistance, R and a fixed reactance, X. The locus of the tip of the 
current-phasor, I, as R is varied from 0 to 8 is:  
(a) a semicircle with a diameter of .
V
X
 
(b) a straight line with a slop of 
R
X
(c) an ellipse with 
V
R
as major axis. 
(d) a circle of radius 
R
X
and origin at 0,
2
V ? ?
? ?
? ?
. 
1.2 A circuit with a resistor, inductor and capacitor in series is resonant of .
o
f Hz If all 
the component values are now doubled, the new resonant frequency is:
(a) 2
o
f (b) still 
o
f (c) 
4
o
f
(d) 
2
o
f
1.3 In the circuit shown in Fig.1.3, it is desired to have a constant direct current i(t) 
through the ideal inductor L. the nature of the voltage source v(t) must be: 
(a) constant voltage  
(b) linearly increasing voltage 
(c) an ideal impulse  
(d) exponentially increasing voltage 
1.4 The reflection coefficient for the transmission line shown in Fig.1.4 at P is: 
(a) +1 
(b) -1 
(c) 0   
(d) 0.5 
i(t)
v(t) 
L
P Transmission line 
Load 300O 
Z o = 300O
Z o = Sugar impedance 
GATE EE - 1998
1.5 The laws of electromagnetic induction (Faraday’s and Lenz’s law) are summarized 
in the following equation: 
(a) e = iR (b) 
di
e L
dt
=
(c) 
d
e
dt
?
= - (d) None of the above 
1.6 A synchronous generator connected to an infinite bus is overexcited. Considering 
only the reactive power, from the point of view of the system, the machine acts 
as 
(a) a capacitor (b) an inductor 
(c) a resistor (d) None of the above 
1.7 A 3 phase squirrel cage induction motor has a full load efficiency of 0.8 and a 
maximum efficiency of 0.9. It is operated at a slip of 0.6 by applying a reduced 
voltage. The efficiency of the motor at this operating point is: 
(a) less than 0.4 (b) greater than 0.6 
(c) in the range of 0.8 ±0.1 (d) None of the above 
1.8 The efficiency of a 100 KVA transform is 0.98 at full as well as at half load. For 
this transformer at full load the copper loss. 
(a) is less than core loss  (b) is equal to core loss 
(c) is more than core loss  (d) None of the above 
1.9 The magnetizing current in a transformer is rich in 
(a) 3
rd
 harmonic (b) 5
th
 harmonic (c) 7
th
 harmonic (d) 13
th
 harmonic 
1.10 Series capacitive compensation in EHV transmission lines is used to 
(a) reduce the line loading 
(b) improve the stability of the system 
(c) reduce the voltage profile (d) improve the protection of the line 
1.11 Bulk power transmission over long HVDC lines are preferred, on account of 
(a) low cost of HVDC terminals (b) no harmonic problems 
(c) minimum line power losses (d) simple protection 
GATE EE - 1998
1.12  The output of a linear time invariant control system is c(t) for a certain input 
r(t). If r(t) is modified by passing it through a block whose transfer function is 
s
e
-
and then applied to the system, the modified output of the system would be 
(a) 
( )
1
t
c t
e +
(b) 
( )
1
t
c t
e
-
+
(c) ( ) ( ) 1 1 c t u t - - (d) ( ) ( ) 1 c t u t -
1.13 None of the poles of a linear control system lie in the right half of s-plane. For a 
bounded input, the output of this system 
(a) is always bounded  (b) could be unbounded 
(c) always tends to zero  (d) None of the above 
1.14 The phase lead compensation is used to 
(a) increase rise time and decrease overshoot 
(b) decrease both rise time and overshoot  
(c) increase both rise time and overshoot  
(d) decrease rise time and increase overshoot 
1.15 A set of linear equations is represented by the matrix equation Ax=b. the 
necessary condition for the existence of a solution for this system is: 
(a) A must be invertible  
(b) b must be linearly depended on the columns of A 
(c) b must be linearly independent of the columns of A 
(d) None of the above 
1.16 The vector 
1
2
1
? ?
? ?
? ?
? ?
-
? ?
is an eigen vector of 
2 2 3
2 1 6 .
1 2 0
A
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
 One of the given values of 
A is: 
(a) 1 (b) 2 (c) 5 (d) -1 
1.17 
2 0 0 1
0 1 0 0
.
0 0 3 0
1 0 0 4
A
- ? ?
? ?
? ?
=
? ?
? ?
- ? ?
? ?
 The sum of the eigen values of the matrix A is: 
(a) 10 (b) -10 (c) 24 (d) 22 
1.18 A d.c. voltmeter has a sensitivity of 1000 O/volt. When it measures half full scale 
in 100V range, the current through the voltmeter is 
(a) 100 mA (b) 1 mA (c) 0.5 mA (d) 50 mA 
Page 4


GATE EE - 1998
SECTION – A 
1. In each of sub question (1.1 to 1.25) four alternatives A, B, C and D are provided
of which one is correct. Indicate in your book, at the space provided, the correct
answer by writing the alphabet corresponding to the answer.
1.1 A sinusoidal source of voltage V and frequency f is connected to a series circuit of 
variable resistance, R and a fixed reactance, X. The locus of the tip of the 
current-phasor, I, as R is varied from 0 to 8 is:  
(a) a semicircle with a diameter of .
V
X
 
(b) a straight line with a slop of 
R
X
(c) an ellipse with 
V
R
as major axis. 
(d) a circle of radius 
R
X
and origin at 0,
2
V ? ?
? ?
? ?
. 
1.2 A circuit with a resistor, inductor and capacitor in series is resonant of .
o
f Hz If all 
the component values are now doubled, the new resonant frequency is:
(a) 2
o
f (b) still 
o
f (c) 
4
o
f
(d) 
2
o
f
1.3 In the circuit shown in Fig.1.3, it is desired to have a constant direct current i(t) 
through the ideal inductor L. the nature of the voltage source v(t) must be: 
(a) constant voltage  
(b) linearly increasing voltage 
(c) an ideal impulse  
(d) exponentially increasing voltage 
1.4 The reflection coefficient for the transmission line shown in Fig.1.4 at P is: 
(a) +1 
(b) -1 
(c) 0   
(d) 0.5 
i(t)
v(t) 
L
P Transmission line 
Load 300O 
Z o = 300O
Z o = Sugar impedance 
GATE EE - 1998
1.5 The laws of electromagnetic induction (Faraday’s and Lenz’s law) are summarized 
in the following equation: 
(a) e = iR (b) 
di
e L
dt
=
(c) 
d
e
dt
?
= - (d) None of the above 
1.6 A synchronous generator connected to an infinite bus is overexcited. Considering 
only the reactive power, from the point of view of the system, the machine acts 
as 
(a) a capacitor (b) an inductor 
(c) a resistor (d) None of the above 
1.7 A 3 phase squirrel cage induction motor has a full load efficiency of 0.8 and a 
maximum efficiency of 0.9. It is operated at a slip of 0.6 by applying a reduced 
voltage. The efficiency of the motor at this operating point is: 
(a) less than 0.4 (b) greater than 0.6 
(c) in the range of 0.8 ±0.1 (d) None of the above 
1.8 The efficiency of a 100 KVA transform is 0.98 at full as well as at half load. For 
this transformer at full load the copper loss. 
(a) is less than core loss  (b) is equal to core loss 
(c) is more than core loss  (d) None of the above 
1.9 The magnetizing current in a transformer is rich in 
(a) 3
rd
 harmonic (b) 5
th
 harmonic (c) 7
th
 harmonic (d) 13
th
 harmonic 
1.10 Series capacitive compensation in EHV transmission lines is used to 
(a) reduce the line loading 
(b) improve the stability of the system 
(c) reduce the voltage profile (d) improve the protection of the line 
1.11 Bulk power transmission over long HVDC lines are preferred, on account of 
(a) low cost of HVDC terminals (b) no harmonic problems 
(c) minimum line power losses (d) simple protection 
GATE EE - 1998
1.12  The output of a linear time invariant control system is c(t) for a certain input 
r(t). If r(t) is modified by passing it through a block whose transfer function is 
s
e
-
and then applied to the system, the modified output of the system would be 
(a) 
( )
1
t
c t
e +
(b) 
( )
1
t
c t
e
-
+
(c) ( ) ( ) 1 1 c t u t - - (d) ( ) ( ) 1 c t u t -
1.13 None of the poles of a linear control system lie in the right half of s-plane. For a 
bounded input, the output of this system 
(a) is always bounded  (b) could be unbounded 
(c) always tends to zero  (d) None of the above 
1.14 The phase lead compensation is used to 
(a) increase rise time and decrease overshoot 
(b) decrease both rise time and overshoot  
(c) increase both rise time and overshoot  
(d) decrease rise time and increase overshoot 
1.15 A set of linear equations is represented by the matrix equation Ax=b. the 
necessary condition for the existence of a solution for this system is: 
(a) A must be invertible  
(b) b must be linearly depended on the columns of A 
(c) b must be linearly independent of the columns of A 
(d) None of the above 
1.16 The vector 
1
2
1
? ?
? ?
? ?
? ?
-
? ?
is an eigen vector of 
2 2 3
2 1 6 .
1 2 0
A
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
 One of the given values of 
A is: 
(a) 1 (b) 2 (c) 5 (d) -1 
1.17 
2 0 0 1
0 1 0 0
.
0 0 3 0
1 0 0 4
A
- ? ?
? ?
? ?
=
? ?
? ?
- ? ?
? ?
 The sum of the eigen values of the matrix A is: 
(a) 10 (b) -10 (c) 24 (d) 22 
1.18 A d.c. voltmeter has a sensitivity of 1000 O/volt. When it measures half full scale 
in 100V range, the current through the voltmeter is 
(a) 100 mA (b) 1 mA (c) 0.5 mA (d) 50 mA 
GATE EE - 1998
1.19. A moving coil galvanometer is made into a d.c. ammeter by connecting 
(a) a low resistance across the meter 
(b) a high resistance in series with the meter 
(c) a pure inductance across the meter 
(d) a capacitor in series with the meter 
1.20. The open collector outputs of two 2-inputs NAND gates are connected to a 
common pull up resistor. If the input to the gates are P, Q and R, S respectively, 
the output is equal to 
(a) . . . . PQRS (b) PQ RS + (c) . . PQ RS + (d) . . . PQ RS
1.21. In standard TTL gates, the totem pole output stage is primarily used to 
(a) increase the noise margin of the gate 
(b) decrease the output switching delay 
(c) facilitate a wired OR logic connection 
(d) increase the output impedance of the circuit 
1.22. One of the applications of current mirror is: 
(a) output current limiting 
(b) obtaining a very high current gain 
(c) current feedback 
(d) temperature stabilized biasing 
1.23. The uncontrolled electronic switch employed in power electronic converters is: 
(a) thyristor   (b) bipolar junction transistor 
(c) diode   (d) MOSFET 
1.24. The MOSFET switch in its on-state may be considered equivalent to: 
(a) resistor (b) inductor (c) capacitor (d) battery 
1.25 In a commutation circuit employed to turn off an SCR, satisfactory turn-off is 
obtained when 
(a) circuit turn-off time < device turn-off time 
(b) circuit turn-off time > device turn-off time 
(c) circuit time constant > device turn-off time 
(d) circuit time constant < device turn-off time 
Page 5


GATE EE - 1998
SECTION – A 
1. In each of sub question (1.1 to 1.25) four alternatives A, B, C and D are provided
of which one is correct. Indicate in your book, at the space provided, the correct
answer by writing the alphabet corresponding to the answer.
1.1 A sinusoidal source of voltage V and frequency f is connected to a series circuit of 
variable resistance, R and a fixed reactance, X. The locus of the tip of the 
current-phasor, I, as R is varied from 0 to 8 is:  
(a) a semicircle with a diameter of .
V
X
 
(b) a straight line with a slop of 
R
X
(c) an ellipse with 
V
R
as major axis. 
(d) a circle of radius 
R
X
and origin at 0,
2
V ? ?
? ?
? ?
. 
1.2 A circuit with a resistor, inductor and capacitor in series is resonant of .
o
f Hz If all 
the component values are now doubled, the new resonant frequency is:
(a) 2
o
f (b) still 
o
f (c) 
4
o
f
(d) 
2
o
f
1.3 In the circuit shown in Fig.1.3, it is desired to have a constant direct current i(t) 
through the ideal inductor L. the nature of the voltage source v(t) must be: 
(a) constant voltage  
(b) linearly increasing voltage 
(c) an ideal impulse  
(d) exponentially increasing voltage 
1.4 The reflection coefficient for the transmission line shown in Fig.1.4 at P is: 
(a) +1 
(b) -1 
(c) 0   
(d) 0.5 
i(t)
v(t) 
L
P Transmission line 
Load 300O 
Z o = 300O
Z o = Sugar impedance 
GATE EE - 1998
1.5 The laws of electromagnetic induction (Faraday’s and Lenz’s law) are summarized 
in the following equation: 
(a) e = iR (b) 
di
e L
dt
=
(c) 
d
e
dt
?
= - (d) None of the above 
1.6 A synchronous generator connected to an infinite bus is overexcited. Considering 
only the reactive power, from the point of view of the system, the machine acts 
as 
(a) a capacitor (b) an inductor 
(c) a resistor (d) None of the above 
1.7 A 3 phase squirrel cage induction motor has a full load efficiency of 0.8 and a 
maximum efficiency of 0.9. It is operated at a slip of 0.6 by applying a reduced 
voltage. The efficiency of the motor at this operating point is: 
(a) less than 0.4 (b) greater than 0.6 
(c) in the range of 0.8 ±0.1 (d) None of the above 
1.8 The efficiency of a 100 KVA transform is 0.98 at full as well as at half load. For 
this transformer at full load the copper loss. 
(a) is less than core loss  (b) is equal to core loss 
(c) is more than core loss  (d) None of the above 
1.9 The magnetizing current in a transformer is rich in 
(a) 3
rd
 harmonic (b) 5
th
 harmonic (c) 7
th
 harmonic (d) 13
th
 harmonic 
1.10 Series capacitive compensation in EHV transmission lines is used to 
(a) reduce the line loading 
(b) improve the stability of the system 
(c) reduce the voltage profile (d) improve the protection of the line 
1.11 Bulk power transmission over long HVDC lines are preferred, on account of 
(a) low cost of HVDC terminals (b) no harmonic problems 
(c) minimum line power losses (d) simple protection 
GATE EE - 1998
1.12  The output of a linear time invariant control system is c(t) for a certain input 
r(t). If r(t) is modified by passing it through a block whose transfer function is 
s
e
-
and then applied to the system, the modified output of the system would be 
(a) 
( )
1
t
c t
e +
(b) 
( )
1
t
c t
e
-
+
(c) ( ) ( ) 1 1 c t u t - - (d) ( ) ( ) 1 c t u t -
1.13 None of the poles of a linear control system lie in the right half of s-plane. For a 
bounded input, the output of this system 
(a) is always bounded  (b) could be unbounded 
(c) always tends to zero  (d) None of the above 
1.14 The phase lead compensation is used to 
(a) increase rise time and decrease overshoot 
(b) decrease both rise time and overshoot  
(c) increase both rise time and overshoot  
(d) decrease rise time and increase overshoot 
1.15 A set of linear equations is represented by the matrix equation Ax=b. the 
necessary condition for the existence of a solution for this system is: 
(a) A must be invertible  
(b) b must be linearly depended on the columns of A 
(c) b must be linearly independent of the columns of A 
(d) None of the above 
1.16 The vector 
1
2
1
? ?
? ?
? ?
? ?
-
? ?
is an eigen vector of 
2 2 3
2 1 6 .
1 2 0
A
- - ? ?
? ?
= -
? ?
? ?
- -
? ?
 One of the given values of 
A is: 
(a) 1 (b) 2 (c) 5 (d) -1 
1.17 
2 0 0 1
0 1 0 0
.
0 0 3 0
1 0 0 4
A
- ? ?
? ?
? ?
=
? ?
? ?
- ? ?
? ?
 The sum of the eigen values of the matrix A is: 
(a) 10 (b) -10 (c) 24 (d) 22 
1.18 A d.c. voltmeter has a sensitivity of 1000 O/volt. When it measures half full scale 
in 100V range, the current through the voltmeter is 
(a) 100 mA (b) 1 mA (c) 0.5 mA (d) 50 mA 
GATE EE - 1998
1.19. A moving coil galvanometer is made into a d.c. ammeter by connecting 
(a) a low resistance across the meter 
(b) a high resistance in series with the meter 
(c) a pure inductance across the meter 
(d) a capacitor in series with the meter 
1.20. The open collector outputs of two 2-inputs NAND gates are connected to a 
common pull up resistor. If the input to the gates are P, Q and R, S respectively, 
the output is equal to 
(a) . . . . PQRS (b) PQ RS + (c) . . PQ RS + (d) . . . PQ RS
1.21. In standard TTL gates, the totem pole output stage is primarily used to 
(a) increase the noise margin of the gate 
(b) decrease the output switching delay 
(c) facilitate a wired OR logic connection 
(d) increase the output impedance of the circuit 
1.22. One of the applications of current mirror is: 
(a) output current limiting 
(b) obtaining a very high current gain 
(c) current feedback 
(d) temperature stabilized biasing 
1.23. The uncontrolled electronic switch employed in power electronic converters is: 
(a) thyristor   (b) bipolar junction transistor 
(c) diode   (d) MOSFET 
1.24. The MOSFET switch in its on-state may be considered equivalent to: 
(a) resistor (b) inductor (c) capacitor (d) battery 
1.25 In a commutation circuit employed to turn off an SCR, satisfactory turn-off is 
obtained when 
(a) circuit turn-off time < device turn-off time 
(b) circuit turn-off time > device turn-off time 
(c) circuit time constant > device turn-off time 
(d) circuit time constant < device turn-off time 
GATE EE - 1998
2. Questions 2.1 to 2.20 are accompanied by four answers of which one is correct.
Indicate the correct answer, in the space provided in the answer book, by writing
the alphabet A, B, C or D.
For each of questions 2.21 to 2.25, three items are given on the left side and
more than three on the right. For each item on the left, match a suitable answer
from the items on the right (e.g.A-Q, B-S, C-T). Write your answer in the space
provided in the answer book.
2.1 Viewed from the terminals A, B the following circuit shown in Fig.2.1 can be 
reduced to an equivalent circuit of a single voltage source in series with a single 
resistor with the following parameters: 
(a) 5 volt source in series with 10O resistor  
(b) 1 volt source in series with 2.4O resistor 
(c) 15 volt source in series with 2.4O resistor 
(d) 1 volt source in series with 10O resistor 
2.2. 
The effective inductance of the circuit across the terminals A, B in the Fig.2.2 
shown below is: 
(a) 9 H 
(b) 21 H 
(c) 11 H 
(d) 6 H 
2.3. The neutral of 10 MVA, 11 KV alternator is earthed through a resistance of 5 
ohms. The earth fault relay is set to operate at 0.75A. The CT’s have a ratio of 
1000 :5.What percentage of the alternator winding is protected? 
(a) 85% (b) 88.2% (c) 15% (d) 11.8% 
2.4. If the length of a wire of resistance R is uniformly stretched to n times its original 
value, its new resistance is: 
(a) nR (b) 
R
n
(c) 
2
n R (d) 
R
n
2
2.5. A cable has the following characteristics. L =0.201 µH/m and C = 196.2 p/F/m. 
The velocity of wave propagation through the cable is: 
(a) 32 m/s (b) 159.24 µ/ms (c) 0.0312 m/s (d) 159.24 m/s 
+ 
- 
4O 
5V 
+ 
- 
A
B 
10V 
6O 
1H
2H 
3H 
6H 
4H
5H 
A
B