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# Electrical Engineering (EE) 2013 GATE Paper (Set D) with solution Electrical Engineering (EE) Notes | EduRev

## GATE : Electrical Engineering (EE) 2013 GATE Paper (Set D) with solution Electrical Engineering (EE) Notes | EduRev

``` Page 1

|EE-GATE-2013 PAPER|

1
Q. No. 1 – 25 Carry One Mark Each
1. Given a vector field
2 2
x y z
F y xa yza x a , = - = the line integral F.dl
?
evaluated along
a segment on the x-axis from x=1 to x=2 is
(A) -2.33 (B) 0 (C) 2.33 (D) 7
2. The equation
1
2
x 2 2 0
x 1 1 0
- ? ? ? ? ? ?
=
? ? ? ? ? ?
-
? ? ? ? ? ?
has
(A) no solution (B) only one solution
1
2
x 0
x 0
? ? ? ?
=
? ? ? ?
? ? ? ?
(C) non-zero unique solution (D) multiple solutions
3. Square roots of i, where i 1, are - = -
(A) i, i -
(B)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
- + - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(C)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(D)
3 3 3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ - - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
4. Three moving iron type voltmeters are connected as shown below.  Voltmeter
1 2
V, V and V as indicated.  The correct relation among the voltmeter
(A)
1 2
V V
V
2 2
= + (B)
1 2
V V V = + (C)
1 2
V V V = (D)
2 1
V V V = -
5. Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
j1 - O
j2O
V
1
V
2
V
I
Page 2

|EE-GATE-2013 PAPER|

1
Q. No. 1 – 25 Carry One Mark Each
1. Given a vector field
2 2
x y z
F y xa yza x a , = - = the line integral F.dl
?
evaluated along
a segment on the x-axis from x=1 to x=2 is
(A) -2.33 (B) 0 (C) 2.33 (D) 7
2. The equation
1
2
x 2 2 0
x 1 1 0
- ? ? ? ? ? ?
=
? ? ? ? ? ?
-
? ? ? ? ? ?
has
(A) no solution (B) only one solution
1
2
x 0
x 0
? ? ? ?
=
? ? ? ?
? ? ? ?
(C) non-zero unique solution (D) multiple solutions
3. Square roots of i, where i 1, are - = -
(A) i, i -
(B)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
- + - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(C)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(D)
3 3 3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ - - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
4. Three moving iron type voltmeters are connected as shown below.  Voltmeter
1 2
V, V and V as indicated.  The correct relation among the voltmeter
(A)
1 2
V V
V
2 2
= + (B)
1 2
V V V = + (C)
1 2
V V V = (D)
2 1
V V V = -
5. Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
j1 - O
j2O
V
1
V
2
V
I
|EE-GATE-2013 PAPER|

2
6. The angle d in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current
(B) angular displacement of the rotor with respect to the stator
(C) angular displacement of the stator mmf with respect to a synchronously
rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a
synchronously rotating axis.
7. Consider a delta connection of resistors and its equivalent star connection as
shown below.  If all elements of the delta connection are scaled by a factor k,
k>0, the elements of the corresponding star equivalent will be scaled by a factor
of
(A)
2
k (B) k (C)
1
k
(D) k
8. A band-limited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the sampling frequency in kHz which is not
valid is
(A) 5 (B) 12 (C) 15 (D) 20
9. For a periodic signal v(t) 30 sin 100 t 10 cos300 t 6 sin(500 t ),
4
p
= + + + the
(A) 100 (B) 300 (C) 500 (D) 1500
10. A bulb in a staircase has two switches, one switch being at the ground floor and
the other one at the first floor.  The bulb can be turned ON and also can be
turned OFF by any one of the switches irrespective of the state of the other
switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D)a NAND gate
b
R
a
R
c
R
B
R
A
R
C
R
Page 3

|EE-GATE-2013 PAPER|

1
Q. No. 1 – 25 Carry One Mark Each
1. Given a vector field
2 2
x y z
F y xa yza x a , = - = the line integral F.dl
?
evaluated along
a segment on the x-axis from x=1 to x=2 is
(A) -2.33 (B) 0 (C) 2.33 (D) 7
2. The equation
1
2
x 2 2 0
x 1 1 0
- ? ? ? ? ? ?
=
? ? ? ? ? ?
-
? ? ? ? ? ?
has
(A) no solution (B) only one solution
1
2
x 0
x 0
? ? ? ?
=
? ? ? ?
? ? ? ?
(C) non-zero unique solution (D) multiple solutions
3. Square roots of i, where i 1, are - = -
(A) i, i -
(B)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
- + - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(C)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(D)
3 3 3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ - - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
4. Three moving iron type voltmeters are connected as shown below.  Voltmeter
1 2
V, V and V as indicated.  The correct relation among the voltmeter
(A)
1 2
V V
V
2 2
= + (B)
1 2
V V V = + (C)
1 2
V V V = (D)
2 1
V V V = -
5. Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
j1 - O
j2O
V
1
V
2
V
I
|EE-GATE-2013 PAPER|

2
6. The angle d in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current
(B) angular displacement of the rotor with respect to the stator
(C) angular displacement of the stator mmf with respect to a synchronously
rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a
synchronously rotating axis.
7. Consider a delta connection of resistors and its equivalent star connection as
shown below.  If all elements of the delta connection are scaled by a factor k,
k>0, the elements of the corresponding star equivalent will be scaled by a factor
of
(A)
2
k (B) k (C)
1
k
(D) k
8. A band-limited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the sampling frequency in kHz which is not
valid is
(A) 5 (B) 12 (C) 15 (D) 20
9. For a periodic signal v(t) 30 sin 100 t 10 cos300 t 6 sin(500 t ),
4
p
= + + + the
(A) 100 (B) 300 (C) 500 (D) 1500
10. A bulb in a staircase has two switches, one switch being at the ground floor and
the other one at the first floor.  The bulb can be turned ON and also can be
turned OFF by any one of the switches irrespective of the state of the other
switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D)a NAND gate
b
R
a
R
c
R
B
R
A
R
C
R
|EE-GATE-2013 PAPER|

3
11. The Bode plot of a transfer function G(s) is shown in the figure below.
The gain (20log G(s)) is 32 dB and -8 dB at 1 radians/s and 10 radians/s
respectively.  The phase is negative for all . ? Then G(s) is
(A)
39.8
s
(B)
2
39.8
s
(C)
32
s
(D)
2
32
s
12. In the feedback network shown below, if the feedback factor k is increased, then
the
(A) input impedance increases and other output impedance decreases
(B) input impedance increases and output impedance also increases.
(C) input impedance decreases and output impedance also decreases.
(D) input impedance decreases and output impedance increases.
13. The input impedance of the permanent magnet moving coil (PMMC) voltmeter is
infinite.  Assuming that the diode shown in the figure below is ideal, the reading
of the voltmeter in Volts is
(A) 4.46 (B) 3.15 (C) 2.23 (D) 0
Gain(dB)
0
1
10 100
40
32
20
8 -
0
A
k
1
V
f out
V kv =
out
V in
V
+
-
+
-
+
-
+
-
+
-
1 kO
Voltmeter
-
+
100 kO
14.14sin(314t)V
Page 4

|EE-GATE-2013 PAPER|

1
Q. No. 1 – 25 Carry One Mark Each
1. Given a vector field
2 2
x y z
F y xa yza x a , = - = the line integral F.dl
?
evaluated along
a segment on the x-axis from x=1 to x=2 is
(A) -2.33 (B) 0 (C) 2.33 (D) 7
2. The equation
1
2
x 2 2 0
x 1 1 0
- ? ? ? ? ? ?
=
? ? ? ? ? ?
-
? ? ? ? ? ?
has
(A) no solution (B) only one solution
1
2
x 0
x 0
? ? ? ?
=
? ? ? ?
? ? ? ?
(C) non-zero unique solution (D) multiple solutions
3. Square roots of i, where i 1, are - = -
(A) i, i -
(B)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
- + - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(C)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(D)
3 3 3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ - - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
4. Three moving iron type voltmeters are connected as shown below.  Voltmeter
1 2
V, V and V as indicated.  The correct relation among the voltmeter
(A)
1 2
V V
V
2 2
= + (B)
1 2
V V V = + (C)
1 2
V V V = (D)
2 1
V V V = -
5. Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
j1 - O
j2O
V
1
V
2
V
I
|EE-GATE-2013 PAPER|

2
6. The angle d in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current
(B) angular displacement of the rotor with respect to the stator
(C) angular displacement of the stator mmf with respect to a synchronously
rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a
synchronously rotating axis.
7. Consider a delta connection of resistors and its equivalent star connection as
shown below.  If all elements of the delta connection are scaled by a factor k,
k>0, the elements of the corresponding star equivalent will be scaled by a factor
of
(A)
2
k (B) k (C)
1
k
(D) k
8. A band-limited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the sampling frequency in kHz which is not
valid is
(A) 5 (B) 12 (C) 15 (D) 20
9. For a periodic signal v(t) 30 sin 100 t 10 cos300 t 6 sin(500 t ),
4
p
= + + + the
(A) 100 (B) 300 (C) 500 (D) 1500
10. A bulb in a staircase has two switches, one switch being at the ground floor and
the other one at the first floor.  The bulb can be turned ON and also can be
turned OFF by any one of the switches irrespective of the state of the other
switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D)a NAND gate
b
R
a
R
c
R
B
R
A
R
C
R
|EE-GATE-2013 PAPER|

3
11. The Bode plot of a transfer function G(s) is shown in the figure below.
The gain (20log G(s)) is 32 dB and -8 dB at 1 radians/s and 10 radians/s
respectively.  The phase is negative for all . ? Then G(s) is
(A)
39.8
s
(B)
2
39.8
s
(C)
32
s
(D)
2
32
s
12. In the feedback network shown below, if the feedback factor k is increased, then
the
(A) input impedance increases and other output impedance decreases
(B) input impedance increases and output impedance also increases.
(C) input impedance decreases and output impedance also decreases.
(D) input impedance decreases and output impedance increases.
13. The input impedance of the permanent magnet moving coil (PMMC) voltmeter is
infinite.  Assuming that the diode shown in the figure below is ideal, the reading
of the voltmeter in Volts is
(A) 4.46 (B) 3.15 (C) 2.23 (D) 0
Gain(dB)
0
1
10 100
40
32
20
8 -
0
A
k
1
V
f out
V kv =
out
V in
V
+
-
+
-
+
-
+
-
+
-
1 kO
Voltmeter
-
+
100 kO
14.14sin(314t)V
|EE-GATE-2013 PAPER|

4
14. The curl of the gradient of the scalar field defined by
2 2 2
V 2x y 3y z 4z x is = + +
(A)
x y z
4xya 6yza 8zxa + +
(B)
x y z
4a 6a 8a + +
(C)
( ) ( ) ( )
2 2 2
x y z
4xy 4z a 2x 6yz a 3y 8zx a + + + + +
(D) 0
15. A continuous random variable X has a probability density function
x
f(x) e ,0 x .
-
= < < 8 Then P{X 1} is >
(A) 0.368 (B) 0.5 (C) 0.632 (D) 1.0
16. The flux density at a point in space is given by
2
x y z
B 4xa 2kya 8a Wb / m . = + +
The value of constant k must be equal to
(A) -2 (B) -0.5 (C) +0.5 (D) +2
17. A single-phase transformer has no-load loss of 64 W, as obtained from an open-
circuit test.  When a short-circuit test is performed on it with 90% of the rated
currents flowing in its both LV and HV windings, he measured loss is 81 W.  The
transformer has maximum efficiency when operated at
(A) 50.0% of the rated current. (B) 64.0% of the rated current.
(C) 80.0% of the rated current. (D) 88.8% of the rated current.
18. A single-phase load is supplied by a single-phase voltage source.  If the current
flowing from the load to the source is 10 150 A ? - ° and if the voltage at the load
terminals is 100 60 V ? ° , then the
(A) load absorbs real power and delivers reactive power.
(B) load absorbs real power and absorbs reactive power.
(C) load delivers real power and delivers reactive power.
(D) load delivers real power and absorbs reactive power.
19. A source
s
v (t) V cos 100 t = p has an internal impedance of ( ) 4 j3 . + O If a purely
resistive load connected to this source has to extract the maximum power out of
the source, its value in O should be
(A) 3 (B) 4 (C) 5 (D) 7
Page 5

|EE-GATE-2013 PAPER|

1
Q. No. 1 – 25 Carry One Mark Each
1. Given a vector field
2 2
x y z
F y xa yza x a , = - = the line integral F.dl
?
evaluated along
a segment on the x-axis from x=1 to x=2 is
(A) -2.33 (B) 0 (C) 2.33 (D) 7
2. The equation
1
2
x 2 2 0
x 1 1 0
- ? ? ? ? ? ?
=
? ? ? ? ? ?
-
? ? ? ? ? ?
has
(A) no solution (B) only one solution
1
2
x 0
x 0
? ? ? ?
=
? ? ? ?
? ? ? ?
(C) non-zero unique solution (D) multiple solutions
3. Square roots of i, where i 1, are - = -
(A) i, i -
(B)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
- + - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(C)
3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
(D)
3 3 3 3
cos isin , cos isin
4 4 4 4
p p p p ? ? ? ? ? ? ? ?
+ - - +
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
4. Three moving iron type voltmeters are connected as shown below.  Voltmeter
1 2
V, V and V as indicated.  The correct relation among the voltmeter
(A)
1 2
V V
V
2 2
= + (B)
1 2
V V V = + (C)
1 2
V V V = (D)
2 1
V V V = -
5. Leakage flux in an induction motor is
(A) flux that leaks through the machine
(B) flux that links both stator and rotor windings
(C) flux that links none of the windings
(D) flux that links the stator winding or the rotor winding but not both
j1 - O
j2O
V
1
V
2
V
I
|EE-GATE-2013 PAPER|

2
6. The angle d in the swing equation of a synchronous generator is the
(A) angle between stator voltage and current
(B) angular displacement of the rotor with respect to the stator
(C) angular displacement of the stator mmf with respect to a synchronously
rotating axis.
(D) angular displacement of an axis fixed to the rotor with respect to a
synchronously rotating axis.
7. Consider a delta connection of resistors and its equivalent star connection as
shown below.  If all elements of the delta connection are scaled by a factor k,
k>0, the elements of the corresponding star equivalent will be scaled by a factor
of
(A)
2
k (B) k (C)
1
k
(D) k
8. A band-limited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the sampling frequency in kHz which is not
valid is
(A) 5 (B) 12 (C) 15 (D) 20
9. For a periodic signal v(t) 30 sin 100 t 10 cos300 t 6 sin(500 t ),
4
p
= + + + the
(A) 100 (B) 300 (C) 500 (D) 1500
10. A bulb in a staircase has two switches, one switch being at the ground floor and
the other one at the first floor.  The bulb can be turned ON and also can be
turned OFF by any one of the switches irrespective of the state of the other
switch. The logic of switching of the bulb resembles
(A) an AND gate (B) an OR gate (C) an XOR gate (D)a NAND gate
b
R
a
R
c
R
B
R
A
R
C
R
|EE-GATE-2013 PAPER|

3
11. The Bode plot of a transfer function G(s) is shown in the figure below.
The gain (20log G(s)) is 32 dB and -8 dB at 1 radians/s and 10 radians/s
respectively.  The phase is negative for all . ? Then G(s) is
(A)
39.8
s
(B)
2
39.8
s
(C)
32
s
(D)
2
32
s
12. In the feedback network shown below, if the feedback factor k is increased, then
the
(A) input impedance increases and other output impedance decreases
(B) input impedance increases and output impedance also increases.
(C) input impedance decreases and output impedance also decreases.
(D) input impedance decreases and output impedance increases.
13. The input impedance of the permanent magnet moving coil (PMMC) voltmeter is
infinite.  Assuming that the diode shown in the figure below is ideal, the reading
of the voltmeter in Volts is
(A) 4.46 (B) 3.15 (C) 2.23 (D) 0
Gain(dB)
0
1
10 100
40
32
20
8 -
0
A
k
1
V
f out
V kv =
out
V in
V
+
-
+
-
+
-
+
-
+
-
1 kO
Voltmeter
-
+
100 kO
14.14sin(314t)V
|EE-GATE-2013 PAPER|

4
14. The curl of the gradient of the scalar field defined by
2 2 2
V 2x y 3y z 4z x is = + +
(A)
x y z
4xya 6yza 8zxa + +
(B)
x y z
4a 6a 8a + +
(C)
( ) ( ) ( )
2 2 2
x y z
4xy 4z a 2x 6yz a 3y 8zx a + + + + +
(D) 0
15. A continuous random variable X has a probability density function
x
f(x) e ,0 x .
-
= < < 8 Then P{X 1} is >
(A) 0.368 (B) 0.5 (C) 0.632 (D) 1.0
16. The flux density at a point in space is given by
2
x y z
B 4xa 2kya 8a Wb / m . = + +
The value of constant k must be equal to
(A) -2 (B) -0.5 (C) +0.5 (D) +2
17. A single-phase transformer has no-load loss of 64 W, as obtained from an open-
circuit test.  When a short-circuit test is performed on it with 90% of the rated
currents flowing in its both LV and HV windings, he measured loss is 81 W.  The
transformer has maximum efficiency when operated at
(A) 50.0% of the rated current. (B) 64.0% of the rated current.
(C) 80.0% of the rated current. (D) 88.8% of the rated current.
18. A single-phase load is supplied by a single-phase voltage source.  If the current
flowing from the load to the source is 10 150 A ? - ° and if the voltage at the load
terminals is 100 60 V ? ° , then the
(A) load absorbs real power and delivers reactive power.
(B) load absorbs real power and absorbs reactive power.
(C) load delivers real power and delivers reactive power.
(D) load delivers real power and absorbs reactive power.
19. A source
s
v (t) V cos 100 t = p has an internal impedance of ( ) 4 j3 . + O If a purely
resistive load connected to this source has to extract the maximum power out of
the source, its value in O should be
(A) 3 (B) 4 (C) 5 (D) 7
|EE-GATE-2013 PAPER|

5
20. Two systems with impulse responses
1 2
h (t) and h (t) are connected in cascade.
Then the overall impulse response of the cascaded system is given by
(A) product of
1 2
h (t) and h (t)
(B) Sum of
1 2
h (t) and h (t)
(C) Convolution of
1 2
h (t) and h (t)
(D) subtraction of
2 1
h (t) and h (t)
21. Which one of the following statements is NOT TRUE for a continuous time causal
and stable LTI system?
(A) All the poles of the system must lie on the left side of the j? axis
(B) Zeros of the system can lie anywhere in the s-plane
(C) All the poles must lie within s 1 =
(D) All the roots of the characteristic equation must be located on the left side of
the j? axis
22. The impulse response of a system is h(t) tu(t). = For an input u(t 1), - the output
is
(A)
2
t
u(t)
2
(B)
t(t 1)
u(t 1)
2
-
-
(C)
2
(t 1)
u(t 1)
2
-
- (D)
2
(t 1)
u(t 1)
2
-
-
23. Assuming zero initial condition, the response y(t) of the system given below to a
unit step input u(t) is
(A) u(t) (B) tu(t) (C)
2
t
u(t)
2
(D)
t
e u(t)
-

24. The transfer function
2
1
V (s)
V (s)
of the circuit shown below is
U(s)
Y(s)
1
s
1
V (s)
+ +
- -
10kO
100 F µ
2
V (s)
100 F µ
```
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## GATE Past Year Papers for Practice (All Branches)

380 docs|127 tests

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