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# Electrical Engineering (EE) 2015 GATE Paper (Set 1) without solution (unsolved) GATE Notes | EduRev

## GATE : Electrical Engineering (EE) 2015 GATE Paper (Set 1) without solution (unsolved) GATE Notes | EduRev

``` Page 1

GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q. 1 – Q. 25 carry one mark each.
Q.1  A random variable ???? has probability density function ???? ( ???? ) as given below:

???? ( ???? ) = ?
???? + ????????  ????????????  0 < ???? < 1
0 otherwise

If the expected value ???? [ ???? ] = 2/3, then ???????? [ ???? < 0.5] is  _____________.

Q.2  If a continuous function ???? ( ???? ) does not have a root in the interval [ ???? , ???? ], then which one of the
following statements is TRUE?
(A) ???? ( ???? ) · ???? ( ???? ) = 0
(B) ???? ( ???? ) · ???? ( ???? ) < 0
(C) ???? ( ???? ) · ???? ( ???? ) > 0
(D) ???? ( ???? )/ ???? ( ???? ) = 0

Q.3  If the sum of the diagonal elements of a 2 × 2 matrix is -6, then the maximum possible value of
determinant of the matrix is ________.

Q.4
Consider a function r
r
f ˆ
1
2
=
?

, where r is the distance from the origin and r ˆ is the unit vector in
the radial direction. The divergence of this function over a sphere of radius R, which includes the
origin, is
(A) 0 (B) 2p (C)  4p (D)  Rp

Q.5  When the Wheatstone bridge shown in the figure is used to find the value of resistor ???? ???? , the
galvanometer G indicates zero current when ???? 1
= 50 O, ???? 2
= 65 O and ???? 3
= 100 O. If ???? 3
is
known with  ±5% tolerance on its nominal value of 100 O , what is the range of ???? ???? in Ohms?

R1 R2
R3 RX
V
G

(A) [123.50, 136.50]
(B) [125.89, 134.12]
(C) [117.00, 143.00]
(D) [120.25, 139.75]

Q.6  A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale
deflection. The external shunt resistance (in milliohms) needed to extend its range to (0 – 500 A) is
_______.

EE 1/14
Page 2

GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q. 1 – Q. 25 carry one mark each.
Q.1  A random variable ???? has probability density function ???? ( ???? ) as given below:

???? ( ???? ) = ?
???? + ????????  ????????????  0 < ???? < 1
0 otherwise

If the expected value ???? [ ???? ] = 2/3, then ???????? [ ???? < 0.5] is  _____________.

Q.2  If a continuous function ???? ( ???? ) does not have a root in the interval [ ???? , ???? ], then which one of the
following statements is TRUE?
(A) ???? ( ???? ) · ???? ( ???? ) = 0
(B) ???? ( ???? ) · ???? ( ???? ) < 0
(C) ???? ( ???? ) · ???? ( ???? ) > 0
(D) ???? ( ???? )/ ???? ( ???? ) = 0

Q.3  If the sum of the diagonal elements of a 2 × 2 matrix is -6, then the maximum possible value of
determinant of the matrix is ________.

Q.4
Consider a function r
r
f ˆ
1
2
=
?

, where r is the distance from the origin and r ˆ is the unit vector in
the radial direction. The divergence of this function over a sphere of radius R, which includes the
origin, is
(A) 0 (B) 2p (C)  4p (D)  Rp

Q.5  When the Wheatstone bridge shown in the figure is used to find the value of resistor ???? ???? , the
galvanometer G indicates zero current when ???? 1
= 50 O, ???? 2
= 65 O and ???? 3
= 100 O. If ???? 3
is
known with  ±5% tolerance on its nominal value of 100 O , what is the range of ???? ???? in Ohms?

R1 R2
R3 RX
V
G

(A) [123.50, 136.50]
(B) [125.89, 134.12]
(C) [117.00, 143.00]
(D) [120.25, 139.75]

Q.6  A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale
deflection. The external shunt resistance (in milliohms) needed to extend its range to (0 – 500 A) is
_______.

EE 1/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.7  Of the four characteristics given below, which  are the major requirements for an instrumentation
amplifier?

P. High common mode rejection ratio
Q. High input impedance
R. High linearity
S. High output impedance
(A) P, Q and R only (B) P and R only
(C) P, Q and S only (D) Q, R and S only

Q.8  In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are
sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the
charging current (in Ampere) of the 5 V battery, under steady-state, is_____.
C
20 V
3 ?
5 V
S
L

Q.9
A moving average function is given by  ???? ( ???? ) =
1
???? ? ???? ( ???? ) ???????? ???? ???? - ???? . If the input ????  is a sinusoidal signal
of frequency
1
2 ???? Hz, then in steady state, the output  ???? will lag ???? (in degree) by  ______ .

Q.10  The impulse response g(t) of a system, ???? , is as shown in Figure (a). What is the maximum value
attained by the impulse response of two cascaded blocks of ???? as shown in Figure (b)?
t
G G
1
1
g(t)
(a) (b)
0

(A)
2
3
(B)
3
4
(C)
4
5

(D)  1
EE 2/14
Page 3

GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q. 1 – Q. 25 carry one mark each.
Q.1  A random variable ???? has probability density function ???? ( ???? ) as given below:

???? ( ???? ) = ?
???? + ????????  ????????????  0 < ???? < 1
0 otherwise

If the expected value ???? [ ???? ] = 2/3, then ???????? [ ???? < 0.5] is  _____________.

Q.2  If a continuous function ???? ( ???? ) does not have a root in the interval [ ???? , ???? ], then which one of the
following statements is TRUE?
(A) ???? ( ???? ) · ???? ( ???? ) = 0
(B) ???? ( ???? ) · ???? ( ???? ) < 0
(C) ???? ( ???? ) · ???? ( ???? ) > 0
(D) ???? ( ???? )/ ???? ( ???? ) = 0

Q.3  If the sum of the diagonal elements of a 2 × 2 matrix is -6, then the maximum possible value of
determinant of the matrix is ________.

Q.4
Consider a function r
r
f ˆ
1
2
=
?

, where r is the distance from the origin and r ˆ is the unit vector in
the radial direction. The divergence of this function over a sphere of radius R, which includes the
origin, is
(A) 0 (B) 2p (C)  4p (D)  Rp

Q.5  When the Wheatstone bridge shown in the figure is used to find the value of resistor ???? ???? , the
galvanometer G indicates zero current when ???? 1
= 50 O, ???? 2
= 65 O and ???? 3
= 100 O. If ???? 3
is
known with  ±5% tolerance on its nominal value of 100 O , what is the range of ???? ???? in Ohms?

R1 R2
R3 RX
V
G

(A) [123.50, 136.50]
(B) [125.89, 134.12]
(C) [117.00, 143.00]
(D) [120.25, 139.75]

Q.6  A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale
deflection. The external shunt resistance (in milliohms) needed to extend its range to (0 – 500 A) is
_______.

EE 1/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.7  Of the four characteristics given below, which  are the major requirements for an instrumentation
amplifier?

P. High common mode rejection ratio
Q. High input impedance
R. High linearity
S. High output impedance
(A) P, Q and R only (B) P and R only
(C) P, Q and S only (D) Q, R and S only

Q.8  In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are
sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the
charging current (in Ampere) of the 5 V battery, under steady-state, is_____.
C
20 V
3 ?
5 V
S
L

Q.9
A moving average function is given by  ???? ( ???? ) =
1
???? ? ???? ( ???? ) ???????? ???? ???? - ???? . If the input ????  is a sinusoidal signal
of frequency
1
2 ???? Hz, then in steady state, the output  ???? will lag ???? (in degree) by  ______ .

Q.10  The impulse response g(t) of a system, ???? , is as shown in Figure (a). What is the maximum value
attained by the impulse response of two cascaded blocks of ???? as shown in Figure (b)?
t
G G
1
1
g(t)
(a) (b)
0

(A)
2
3
(B)
3
4
(C)
4
5

(D)  1
EE 2/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.11  Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the
figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4 ???? ,
and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is
given by ???? ( ???? ) = 0.25 sin ???????? , where ???? = 2???? × 50 radian/second. The power absorbed (in Watt) by
the loop from the magnetic field is ________.

10 cm
5 cm

Q.12  A steady current ???? is flowing in the - ???? direction through each of two infinitely long wires at
???? = ±
???? 2
as shown in the figure. The permeability of the medium is ???? 0
. The ???? ? ?
-field at (0,L,0) is
y
z
y=-L/2 y=L/2
x
Current=I Current=I
0

(A) -
4 ???? 0
???? 3 ???????? ???? ^ (B) +
4 ???? 0
???? 3 ???????? ???? ^
(C)  0
(D)  -
3 ???? 0
???? 4 ???????? ???? ^

Q.13  Consider the circuit shown in the figure. In this circuit R=1 k?, and C=1 µF. The input voltage is
sinusoidal with a frequency of 50 Hz, represented as a phasor with magnitude ???? ???? and phase angle 0
radian as shown in the figure. The output voltage is represented as a phasor with magnitude ???? ???? and
phase angle ???? radian. What is the value of the output phase angle ???? (in radian) relative to the phase
angle of the input voltage?
+
-
R
R
C
C
v
o
= V
o
d
i
v = V
i
0

(A) 0 (B) ???? (C)
???? 2
?
(D)  -
???? 2
?

EE 3/14
Page 4

GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q. 1 – Q. 25 carry one mark each.
Q.1  A random variable ???? has probability density function ???? ( ???? ) as given below:

???? ( ???? ) = ?
???? + ????????  ????????????  0 < ???? < 1
0 otherwise

If the expected value ???? [ ???? ] = 2/3, then ???????? [ ???? < 0.5] is  _____________.

Q.2  If a continuous function ???? ( ???? ) does not have a root in the interval [ ???? , ???? ], then which one of the
following statements is TRUE?
(A) ???? ( ???? ) · ???? ( ???? ) = 0
(B) ???? ( ???? ) · ???? ( ???? ) < 0
(C) ???? ( ???? ) · ???? ( ???? ) > 0
(D) ???? ( ???? )/ ???? ( ???? ) = 0

Q.3  If the sum of the diagonal elements of a 2 × 2 matrix is -6, then the maximum possible value of
determinant of the matrix is ________.

Q.4
Consider a function r
r
f ˆ
1
2
=
?

, where r is the distance from the origin and r ˆ is the unit vector in
the radial direction. The divergence of this function over a sphere of radius R, which includes the
origin, is
(A) 0 (B) 2p (C)  4p (D)  Rp

Q.5  When the Wheatstone bridge shown in the figure is used to find the value of resistor ???? ???? , the
galvanometer G indicates zero current when ???? 1
= 50 O, ???? 2
= 65 O and ???? 3
= 100 O. If ???? 3
is
known with  ±5% tolerance on its nominal value of 100 O , what is the range of ???? ???? in Ohms?

R1 R2
R3 RX
V
G

(A) [123.50, 136.50]
(B) [125.89, 134.12]
(C) [117.00, 143.00]
(D) [120.25, 139.75]

Q.6  A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale
deflection. The external shunt resistance (in milliohms) needed to extend its range to (0 – 500 A) is
_______.

EE 1/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.7  Of the four characteristics given below, which  are the major requirements for an instrumentation
amplifier?

P. High common mode rejection ratio
Q. High input impedance
R. High linearity
S. High output impedance
(A) P, Q and R only (B) P and R only
(C) P, Q and S only (D) Q, R and S only

Q.8  In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are
sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the
charging current (in Ampere) of the 5 V battery, under steady-state, is_____.
C
20 V
3 ?
5 V
S
L

Q.9
A moving average function is given by  ???? ( ???? ) =
1
???? ? ???? ( ???? ) ???????? ???? ???? - ???? . If the input ????  is a sinusoidal signal
of frequency
1
2 ???? Hz, then in steady state, the output  ???? will lag ???? (in degree) by  ______ .

Q.10  The impulse response g(t) of a system, ???? , is as shown in Figure (a). What is the maximum value
attained by the impulse response of two cascaded blocks of ???? as shown in Figure (b)?
t
G G
1
1
g(t)
(a) (b)
0

(A)
2
3
(B)
3
4
(C)
4
5

(D)  1
EE 2/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.11  Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the
figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4 ???? ,
and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is
given by ???? ( ???? ) = 0.25 sin ???????? , where ???? = 2???? × 50 radian/second. The power absorbed (in Watt) by
the loop from the magnetic field is ________.

10 cm
5 cm

Q.12  A steady current ???? is flowing in the - ???? direction through each of two infinitely long wires at
???? = ±
???? 2
as shown in the figure. The permeability of the medium is ???? 0
. The ???? ? ?
-field at (0,L,0) is
y
z
y=-L/2 y=L/2
x
Current=I Current=I
0

(A) -
4 ???? 0
???? 3 ???????? ???? ^ (B) +
4 ???? 0
???? 3 ???????? ???? ^
(C)  0
(D)  -
3 ???? 0
???? 4 ???????? ???? ^

Q.13  Consider the circuit shown in the figure. In this circuit R=1 k?, and C=1 µF. The input voltage is
sinusoidal with a frequency of 50 Hz, represented as a phasor with magnitude ???? ???? and phase angle 0
radian as shown in the figure. The output voltage is represented as a phasor with magnitude ???? ???? and
phase angle ???? radian. What is the value of the output phase angle ???? (in radian) relative to the phase
angle of the input voltage?
+
-
R
R
C
C
v
o
= V
o
d
i
v = V
i
0

(A) 0 (B) ???? (C)
???? 2
?
(D)  -
???? 2
?

EE 3/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.14  In the given circuit, the silicon transistor has ???? = 75 and a collector voltage ???? ???? = 9 V. Then the
ratio of ???? ???? and ???? ???? is  ________.
R
C
R
B
15 V
V
C

Q.15  In the 4  × 1 multiplexer, the output F is given by F = A ? B. Find the required input ‘ ???? 3
???? 2
???? 1
???? 0
’.

I
0
s
0
I
1
I
2
I
3
s
1
A B
F
4  ×  1
MUX

(A) 1010 (B) 0110 (C)  1000 (D)  1110

Q.16  Consider a HVDC link which uses thyristor based line-commutated converters as shown in the
figure.  For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and
the current, are given by: ???? 1
= 500 kV, ???? 2
= 485 kV  and ???? = 1.5 kA.  If the direction of power
flow is to be reversed (that is, from System 2 to System 1) without changing the electrical
connections, then which one of the following combinations is feasible?

System 1
System 2
I
V1 V2
+
-
+
-

(A) ???? 1
= -500 kV, ???? 2
= -485 kV  and ???? = 1.5 kA
(B) ???? 1
= -485 kV, ???? 2
= -500 kV  and ???? = 1.5 kA
(C) ???? 1
= 500 kV, ???? 2
= 485 kV  and ???? = -1.5 kA
(D) ???? 1
= -500 kV, ???? 2
= -485 kV  and ???? = -1.5 kA

EE 4/14
Page 5

GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q. 1 – Q. 25 carry one mark each.
Q.1  A random variable ???? has probability density function ???? ( ???? ) as given below:

???? ( ???? ) = ?
???? + ????????  ????????????  0 < ???? < 1
0 otherwise

If the expected value ???? [ ???? ] = 2/3, then ???????? [ ???? < 0.5] is  _____________.

Q.2  If a continuous function ???? ( ???? ) does not have a root in the interval [ ???? , ???? ], then which one of the
following statements is TRUE?
(A) ???? ( ???? ) · ???? ( ???? ) = 0
(B) ???? ( ???? ) · ???? ( ???? ) < 0
(C) ???? ( ???? ) · ???? ( ???? ) > 0
(D) ???? ( ???? )/ ???? ( ???? ) = 0

Q.3  If the sum of the diagonal elements of a 2 × 2 matrix is -6, then the maximum possible value of
determinant of the matrix is ________.

Q.4
Consider a function r
r
f ˆ
1
2
=
?

, where r is the distance from the origin and r ˆ is the unit vector in
the radial direction. The divergence of this function over a sphere of radius R, which includes the
origin, is
(A) 0 (B) 2p (C)  4p (D)  Rp

Q.5  When the Wheatstone bridge shown in the figure is used to find the value of resistor ???? ???? , the
galvanometer G indicates zero current when ???? 1
= 50 O, ???? 2
= 65 O and ???? 3
= 100 O. If ???? 3
is
known with  ±5% tolerance on its nominal value of 100 O , what is the range of ???? ???? in Ohms?

R1 R2
R3 RX
V
G

(A) [123.50, 136.50]
(B) [125.89, 134.12]
(C) [117.00, 143.00]
(D) [120.25, 139.75]

Q.6  A (0-50 A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale
deflection. The external shunt resistance (in milliohms) needed to extend its range to (0 – 500 A) is
_______.

EE 1/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.7  Of the four characteristics given below, which  are the major requirements for an instrumentation
amplifier?

P. High common mode rejection ratio
Q. High input impedance
R. High linearity
S. High output impedance
(A) P, Q and R only (B) P and R only
(C) P, Q and S only (D) Q, R and S only

Q.8  In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are
sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the
charging current (in Ampere) of the 5 V battery, under steady-state, is_____.
C
20 V
3 ?
5 V
S
L

Q.9
A moving average function is given by  ???? ( ???? ) =
1
???? ? ???? ( ???? ) ???????? ???? ???? - ???? . If the input ????  is a sinusoidal signal
of frequency
1
2 ???? Hz, then in steady state, the output  ???? will lag ???? (in degree) by  ______ .

Q.10  The impulse response g(t) of a system, ???? , is as shown in Figure (a). What is the maximum value
attained by the impulse response of two cascaded blocks of ???? as shown in Figure (b)?
t
G G
1
1
g(t)
(a) (b)
0

(A)
2
3
(B)
3
4
(C)
4
5

(D)  1
EE 2/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.11  Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the
figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4 ???? ,
and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is
given by ???? ( ???? ) = 0.25 sin ???????? , where ???? = 2???? × 50 radian/second. The power absorbed (in Watt) by
the loop from the magnetic field is ________.

10 cm
5 cm

Q.12  A steady current ???? is flowing in the - ???? direction through each of two infinitely long wires at
???? = ±
???? 2
as shown in the figure. The permeability of the medium is ???? 0
. The ???? ? ?
-field at (0,L,0) is
y
z
y=-L/2 y=L/2
x
Current=I Current=I
0

(A) -
4 ???? 0
???? 3 ???????? ???? ^ (B) +
4 ???? 0
???? 3 ???????? ???? ^
(C)  0
(D)  -
3 ???? 0
???? 4 ???????? ???? ^

Q.13  Consider the circuit shown in the figure. In this circuit R=1 k?, and C=1 µF. The input voltage is
sinusoidal with a frequency of 50 Hz, represented as a phasor with magnitude ???? ???? and phase angle 0
radian as shown in the figure. The output voltage is represented as a phasor with magnitude ???? ???? and
phase angle ???? radian. What is the value of the output phase angle ???? (in radian) relative to the phase
angle of the input voltage?
+
-
R
R
C
C
v
o
= V
o
d
i
v = V
i
0

(A) 0 (B) ???? (C)
???? 2
?
(D)  -
???? 2
?

EE 3/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.14  In the given circuit, the silicon transistor has ???? = 75 and a collector voltage ???? ???? = 9 V. Then the
ratio of ???? ???? and ???? ???? is  ________.
R
C
R
B
15 V
V
C

Q.15  In the 4  × 1 multiplexer, the output F is given by F = A ? B. Find the required input ‘ ???? 3
???? 2
???? 1
???? 0
’.

I
0
s
0
I
1
I
2
I
3
s
1
A B
F
4  ×  1
MUX

(A) 1010 (B) 0110 (C)  1000 (D)  1110

Q.16  Consider a HVDC link which uses thyristor based line-commutated converters as shown in the
figure.  For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and
the current, are given by: ???? 1
= 500 kV, ???? 2
= 485 kV  and ???? = 1.5 kA.  If the direction of power
flow is to be reversed (that is, from System 2 to System 1) without changing the electrical
connections, then which one of the following combinations is feasible?

System 1
System 2
I
V1 V2
+
-
+
-

(A) ???? 1
= -500 kV, ???? 2
= -485 kV  and ???? = 1.5 kA
(B) ???? 1
= -485 kV, ???? 2
= -500 kV  and ???? = 1.5 kA
(C) ???? 1
= 500 kV, ???? 2
= 485 kV  and ???? = -1.5 kA
(D) ???? 1
= -500 kV, ???? 2
= -485 kV  and ???? = -1.5 kA

EE 4/14
GATE 2015                                               SET1                                            ELECTRICAL  –  EE
Q.17  Base load power plants are

P:  wind farms.
Q:  run-of-river plants.
R:  nuclear power plants.
S:  diesel power plants.

(A) P, Q and S  only (B) P, R and S only
(C) P, Q and R only (D) Q and R only

Q.18  The voltages developed across the 3 O and 2 O resistors shown in the figure are 6 ???? and 2 ????
respectively, with the polarity as marked. What is the power (in Watt) delivered by the 5 ???? voltage
source?
Network N1
Network N2
3 ?
5 V
2 ?
6 V
2 V
+
+
+
_
_
_

(A) 5 (B) 7 (C)  10 (D)  14

Q.19  For the given circuit, the Thevenin equivalent is to be determined. The Thevenin voltage, ???? Th
(in
Volt), seen from terminal AB is  __________.

EE 5/14
```
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