Electrical Engineering - EE 2018 GATE Paper with solution - GATE Electrical Engineering (EE) 2024 Mock Test Series

 Page 1


GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Since you have gone off the ________, the _________ sand is likely to damage the car. ” 
 
The words that best fill the blanks in the above sentence are 
 
(A) course, coarse (B) course, course 
(C) coarse, course (D) coarse, coarse 
 
 
Q.2  “A common misconception among writers is that sentence structure mirrors thought; the 
more _________ the structure, the more complicated the ideas. ” 
 
The word that best fills the blank in the above sentence is 
 
(A) detailed (B) simple (C) clear (D) convoluted 
 
 
Q.3  The three roots of the equation ?? ( ?? ) = 0 are ?? = { - 2 , 0 , 3 }. What are the three values of ?? 
for which ?? ( ?? - 3 ) = 0? 
 
(A) - 5 , - 3 , 0 (B) - 2 , 0 , 3 
(C) 0 , 6 , 8 (D) 1 , 3 , 6 
 
 
Q.4  
For what values of ?? given below is 
( ?? + 2 )
2
?? - 3
 an integer? 
 
(A) 4, 8, 18 (B) 4, 10, 16 
(C) 4, 8, 28 (D) 8, 26, 28 
 
 
Q.5  Functions ?? ( ?? , ?? ) and ?? ( ?? , ?? ) are defined as follows: 
?? ( ?? , ?? ) = ( ?? - ?? )
2
 and ?? ( ?? , ?? ) = | ?? - ?? |, where | ?? | represents the absolute value of ?? . 
What would be the value of ?? ( ?? ( 1 , 3 ) , ?? ( 1 , 3 ) )? 
 
(A) 2 (B) 4 (C) 6 (D) 36 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An e-mail password must contain three characters. The password has to contain one 
numeral from 0 to 9, one upper case and one lower case character from the English 
alphabet. How many distinct passwords are possible? 
 
(A) 6,760 (B) 13,520 (C) 40,560 (D) 1,05,456 
 
 
Page 2


GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Since you have gone off the ________, the _________ sand is likely to damage the car. ” 
 
The words that best fill the blanks in the above sentence are 
 
(A) course, coarse (B) course, course 
(C) coarse, course (D) coarse, coarse 
 
 
Q.2  “A common misconception among writers is that sentence structure mirrors thought; the 
more _________ the structure, the more complicated the ideas. ” 
 
The word that best fills the blank in the above sentence is 
 
(A) detailed (B) simple (C) clear (D) convoluted 
 
 
Q.3  The three roots of the equation ?? ( ?? ) = 0 are ?? = { - 2 , 0 , 3 }. What are the three values of ?? 
for which ?? ( ?? - 3 ) = 0? 
 
(A) - 5 , - 3 , 0 (B) - 2 , 0 , 3 
(C) 0 , 6 , 8 (D) 1 , 3 , 6 
 
 
Q.4  
For what values of ?? given below is 
( ?? + 2 )
2
?? - 3
 an integer? 
 
(A) 4, 8, 18 (B) 4, 10, 16 
(C) 4, 8, 28 (D) 8, 26, 28 
 
 
Q.5  Functions ?? ( ?? , ?? ) and ?? ( ?? , ?? ) are defined as follows: 
?? ( ?? , ?? ) = ( ?? - ?? )
2
 and ?? ( ?? , ?? ) = | ?? - ?? |, where | ?? | represents the absolute value of ?? . 
What would be the value of ?? ( ?? ( 1 , 3 ) , ?? ( 1 , 3 ) )? 
 
(A) 2 (B) 4 (C) 6 (D) 36 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An e-mail password must contain three characters. The password has to contain one 
numeral from 0 to 9, one upper case and one lower case character from the English 
alphabet. How many distinct passwords are possible? 
 
(A) 6,760 (B) 13,520 (C) 40,560 (D) 1,05,456 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 2/2 
Q.7  In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will 
DHLP be written in that code? 
 
(A) RSTN (B) TLPH (C) HLPT (D) XSVR 
 
 
Q.8  A class of twelve children has two more boys than girls. A group of three children are 
randomly picked from this class to accompany the teacher on a field trip. What is the 
probability that the group accompanying the teacher contains more girls than boys? 
 
(A) 0 
(B) 
325
864
 (C)  
525
864
 (D) 
5
12
 
 
 
Q.9  A designer uses marbles of four different colours for his designs. The cost of each marble 
is the same, irrespective of the colour. The table below shows the percentage of marbles of 
each colour used in the current design. The cost of each marble increased by 25%. 
Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep 
the total cost unchanged. What is the percentage of blue marbles in the new design? 
 
Blue Black Red Yellow 
40% 25% 20% 15% 
 
 
(A) 35.75 (B) 40.25 (C) 43.75 (D) 46.25 
 
 
Q.10  P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only 
one set of oars. The following additional facts are available. 
(i) The boat held two persons on each of the three forward trips across the lake and one 
person on each of the two return trips. 
(ii) P is unable to row when someone else is in the boat. 
(iii) Q is unable to row with anyone else except R. 
(iv) Each person rowed for at least one trip. 
(v) Only one person can row during a trip. 
 
Who rowed twice? 
 
(A) P (B) Q (C) R (D) S 
 
 
END OF THE QUESTION PAPER 
 
Page 3


GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Since you have gone off the ________, the _________ sand is likely to damage the car. ” 
 
The words that best fill the blanks in the above sentence are 
 
(A) course, coarse (B) course, course 
(C) coarse, course (D) coarse, coarse 
 
 
Q.2  “A common misconception among writers is that sentence structure mirrors thought; the 
more _________ the structure, the more complicated the ideas. ” 
 
The word that best fills the blank in the above sentence is 
 
(A) detailed (B) simple (C) clear (D) convoluted 
 
 
Q.3  The three roots of the equation ?? ( ?? ) = 0 are ?? = { - 2 , 0 , 3 }. What are the three values of ?? 
for which ?? ( ?? - 3 ) = 0? 
 
(A) - 5 , - 3 , 0 (B) - 2 , 0 , 3 
(C) 0 , 6 , 8 (D) 1 , 3 , 6 
 
 
Q.4  
For what values of ?? given below is 
( ?? + 2 )
2
?? - 3
 an integer? 
 
(A) 4, 8, 18 (B) 4, 10, 16 
(C) 4, 8, 28 (D) 8, 26, 28 
 
 
Q.5  Functions ?? ( ?? , ?? ) and ?? ( ?? , ?? ) are defined as follows: 
?? ( ?? , ?? ) = ( ?? - ?? )
2
 and ?? ( ?? , ?? ) = | ?? - ?? |, where | ?? | represents the absolute value of ?? . 
What would be the value of ?? ( ?? ( 1 , 3 ) , ?? ( 1 , 3 ) )? 
 
(A) 2 (B) 4 (C) 6 (D) 36 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An e-mail password must contain three characters. The password has to contain one 
numeral from 0 to 9, one upper case and one lower case character from the English 
alphabet. How many distinct passwords are possible? 
 
(A) 6,760 (B) 13,520 (C) 40,560 (D) 1,05,456 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 2/2 
Q.7  In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will 
DHLP be written in that code? 
 
(A) RSTN (B) TLPH (C) HLPT (D) XSVR 
 
 
Q.8  A class of twelve children has two more boys than girls. A group of three children are 
randomly picked from this class to accompany the teacher on a field trip. What is the 
probability that the group accompanying the teacher contains more girls than boys? 
 
(A) 0 
(B) 
325
864
 (C)  
525
864
 (D) 
5
12
 
 
 
Q.9  A designer uses marbles of four different colours for his designs. The cost of each marble 
is the same, irrespective of the colour. The table below shows the percentage of marbles of 
each colour used in the current design. The cost of each marble increased by 25%. 
Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep 
the total cost unchanged. What is the percentage of blue marbles in the new design? 
 
Blue Black Red Yellow 
40% 25% 20% 15% 
 
 
(A) 35.75 (B) 40.25 (C) 43.75 (D) 46.25 
 
 
Q.10  P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only 
one set of oars. The following additional facts are available. 
(i) The boat held two persons on each of the three forward trips across the lake and one 
person on each of the two return trips. 
(ii) P is unable to row when someone else is in the boat. 
(iii) Q is unable to row with anyone else except R. 
(iv) Each person rowed for at least one trip. 
(v) Only one person can row during a trip. 
 
Who rowed twice? 
 
(A) P (B) Q (C) R (D) S 
 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                         ELECTRICAL ENGINEERING 
EE 1/15 
Q. 1 – Q. 25 carry one mark each. 
Q.1  A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% 
across its series impedance at full load. Of this, 3% is due to resistance. The percentage 
regulation of the transformer at full load with 0.8 lagging power factor is 
(A)  4.8 (B)  6.8 (C)  8.8 (D)  10.8 
 
 
Q.2  In a salient pole synchronous motor, the developed reluctance torque attains the maximum 
value when the load angle in electrical degrees is 
(A) 0 (B) 45 (C)  60 (D) 90 
 
 
Q.3  A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as 
shown in the figure. All switches and diodes are ideal. Which one of the following is true 
for instantaneous load voltage and current? 
 
o
v
o
i
L
O
A
D
 
(A)  0 & 0
oo
vi ?? (B)  0 & 0
oo
vi ?? 
(C)  0 & 0
oo
vi ?? (D)  0 & 0
oo
vi ?? 
 
 
Q.4  Four power semiconductor devices are shown in the figure along with their relevant 
terminals. The device(s) that can carry dc current continuously in the direction shown when 
gated appropriately is (are) 
I I
G
MT
1
MT
2
A
K G
Thyristor Triac
G
D
S
I
MOSFET
A
K G
GTO
I
 
(A) Triac only 
(B) Triac and MOSFET 
(C) Triac and GTO 
(D) Thyristor and Triac 
 
Page 4


GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Since you have gone off the ________, the _________ sand is likely to damage the car. ” 
 
The words that best fill the blanks in the above sentence are 
 
(A) course, coarse (B) course, course 
(C) coarse, course (D) coarse, coarse 
 
 
Q.2  “A common misconception among writers is that sentence structure mirrors thought; the 
more _________ the structure, the more complicated the ideas. ” 
 
The word that best fills the blank in the above sentence is 
 
(A) detailed (B) simple (C) clear (D) convoluted 
 
 
Q.3  The three roots of the equation ?? ( ?? ) = 0 are ?? = { - 2 , 0 , 3 }. What are the three values of ?? 
for which ?? ( ?? - 3 ) = 0? 
 
(A) - 5 , - 3 , 0 (B) - 2 , 0 , 3 
(C) 0 , 6 , 8 (D) 1 , 3 , 6 
 
 
Q.4  
For what values of ?? given below is 
( ?? + 2 )
2
?? - 3
 an integer? 
 
(A) 4, 8, 18 (B) 4, 10, 16 
(C) 4, 8, 28 (D) 8, 26, 28 
 
 
Q.5  Functions ?? ( ?? , ?? ) and ?? ( ?? , ?? ) are defined as follows: 
?? ( ?? , ?? ) = ( ?? - ?? )
2
 and ?? ( ?? , ?? ) = | ?? - ?? |, where | ?? | represents the absolute value of ?? . 
What would be the value of ?? ( ?? ( 1 , 3 ) , ?? ( 1 , 3 ) )? 
 
(A) 2 (B) 4 (C) 6 (D) 36 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An e-mail password must contain three characters. The password has to contain one 
numeral from 0 to 9, one upper case and one lower case character from the English 
alphabet. How many distinct passwords are possible? 
 
(A) 6,760 (B) 13,520 (C) 40,560 (D) 1,05,456 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 2/2 
Q.7  In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will 
DHLP be written in that code? 
 
(A) RSTN (B) TLPH (C) HLPT (D) XSVR 
 
 
Q.8  A class of twelve children has two more boys than girls. A group of three children are 
randomly picked from this class to accompany the teacher on a field trip. What is the 
probability that the group accompanying the teacher contains more girls than boys? 
 
(A) 0 
(B) 
325
864
 (C)  
525
864
 (D) 
5
12
 
 
 
Q.9  A designer uses marbles of four different colours for his designs. The cost of each marble 
is the same, irrespective of the colour. The table below shows the percentage of marbles of 
each colour used in the current design. The cost of each marble increased by 25%. 
Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep 
the total cost unchanged. What is the percentage of blue marbles in the new design? 
 
Blue Black Red Yellow 
40% 25% 20% 15% 
 
 
(A) 35.75 (B) 40.25 (C) 43.75 (D) 46.25 
 
 
Q.10  P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only 
one set of oars. The following additional facts are available. 
(i) The boat held two persons on each of the three forward trips across the lake and one 
person on each of the two return trips. 
(ii) P is unable to row when someone else is in the boat. 
(iii) Q is unable to row with anyone else except R. 
(iv) Each person rowed for at least one trip. 
(v) Only one person can row during a trip. 
 
Who rowed twice? 
 
(A) P (B) Q (C) R (D) S 
 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                         ELECTRICAL ENGINEERING 
EE 1/15 
Q. 1 – Q. 25 carry one mark each. 
Q.1  A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% 
across its series impedance at full load. Of this, 3% is due to resistance. The percentage 
regulation of the transformer at full load with 0.8 lagging power factor is 
(A)  4.8 (B)  6.8 (C)  8.8 (D)  10.8 
 
 
Q.2  In a salient pole synchronous motor, the developed reluctance torque attains the maximum 
value when the load angle in electrical degrees is 
(A) 0 (B) 45 (C)  60 (D) 90 
 
 
Q.3  A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as 
shown in the figure. All switches and diodes are ideal. Which one of the following is true 
for instantaneous load voltage and current? 
 
o
v
o
i
L
O
A
D
 
(A)  0 & 0
oo
vi ?? (B)  0 & 0
oo
vi ?? 
(C)  0 & 0
oo
vi ?? (D)  0 & 0
oo
vi ?? 
 
 
Q.4  Four power semiconductor devices are shown in the figure along with their relevant 
terminals. The device(s) that can carry dc current continuously in the direction shown when 
gated appropriately is (are) 
I I
G
MT
1
MT
2
A
K G
Thyristor Triac
G
D
S
I
MOSFET
A
K G
GTO
I
 
(A) Triac only 
(B) Triac and MOSFET 
(C) Triac and GTO 
(D) Thyristor and Triac 
 
GATE 2018                                                                                                                                                         ELECTRICAL ENGINEERING 
EE 2/15 
 
Q.5  Two wattmeter method is used for measurement of power in a balanced three-phase load 
supplied from a balanced three-phase system. If one of the wattmeters reads half of the 
other (both positive), then the power factor of the load is 
(A) 0.532 (B) 0.632 (C)  0.707 (D)  0.866 
 
 
Q.6  
Consider a lossy transmission line with 
1
V and 
2
V as the sending and receiving end 
voltages, respectively. Z and X are the series impedance and reactance of the line, 
respectively.  The steady-state stability limit for the transmission line will be 
(A) greater than 
12
VV
X
 (B) less than 
12
VV
X
 
(C) equal to 
12
VV
X
 (D) equal to 
12
VV
Z
 
 
 
Q.7  The graph of a network has 8 nodes and 5 independent loops. The number of branches of 
the graph is 
(A) 11 (B) 12 (C)  13 (D)  14 
 
Q.8  In the figure, the voltages are ?? 1
( ?? ) = 100 cos ? ( ???? ), ?? 2
( ?? ) = 100 cos ? ( ???? + ?? /18 ) and 
?? 3
( ?? ) = 100 cos ? ( ???? + ?? /36 ). The circuit is in sinusoidal steady state, and ?? < < ???? . ?? 1
, 
?? 2
 and ?? 3
 are the average power outputs. Which one of the following statements is true? 
+
-
+
-
+
-
P
1
P
2
P
3
R R L L
1
v  (t)
2
v  (t)
3
v  (t)
 
 
(A) ? ?? 1
= ?? 2
= ?? 3
= 0 (B) ? ?? 1
< 0 , ?? 2
> 0 , ?? 3
> 0 
(C) ? ?? 1
< 0 , ?? 2
> 0 , ?? 3
< 0 (D) ? ?? 1
> 0 , ?? 2
< 0 , ?? 3
> 0 
 
Page 5


GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Since you have gone off the ________, the _________ sand is likely to damage the car. ” 
 
The words that best fill the blanks in the above sentence are 
 
(A) course, coarse (B) course, course 
(C) coarse, course (D) coarse, coarse 
 
 
Q.2  “A common misconception among writers is that sentence structure mirrors thought; the 
more _________ the structure, the more complicated the ideas. ” 
 
The word that best fills the blank in the above sentence is 
 
(A) detailed (B) simple (C) clear (D) convoluted 
 
 
Q.3  The three roots of the equation ?? ( ?? ) = 0 are ?? = { - 2 , 0 , 3 }. What are the three values of ?? 
for which ?? ( ?? - 3 ) = 0? 
 
(A) - 5 , - 3 , 0 (B) - 2 , 0 , 3 
(C) 0 , 6 , 8 (D) 1 , 3 , 6 
 
 
Q.4  
For what values of ?? given below is 
( ?? + 2 )
2
?? - 3
 an integer? 
 
(A) 4, 8, 18 (B) 4, 10, 16 
(C) 4, 8, 28 (D) 8, 26, 28 
 
 
Q.5  Functions ?? ( ?? , ?? ) and ?? ( ?? , ?? ) are defined as follows: 
?? ( ?? , ?? ) = ( ?? - ?? )
2
 and ?? ( ?? , ?? ) = | ?? - ?? |, where | ?? | represents the absolute value of ?? . 
What would be the value of ?? ( ?? ( 1 , 3 ) , ?? ( 1 , 3 ) )? 
 
(A) 2 (B) 4 (C) 6 (D) 36 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An e-mail password must contain three characters. The password has to contain one 
numeral from 0 to 9, one upper case and one lower case character from the English 
alphabet. How many distinct passwords are possible? 
 
(A) 6,760 (B) 13,520 (C) 40,560 (D) 1,05,456 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-6  
GA 2/2 
Q.7  In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will 
DHLP be written in that code? 
 
(A) RSTN (B) TLPH (C) HLPT (D) XSVR 
 
 
Q.8  A class of twelve children has two more boys than girls. A group of three children are 
randomly picked from this class to accompany the teacher on a field trip. What is the 
probability that the group accompanying the teacher contains more girls than boys? 
 
(A) 0 
(B) 
325
864
 (C)  
525
864
 (D) 
5
12
 
 
 
Q.9  A designer uses marbles of four different colours for his designs. The cost of each marble 
is the same, irrespective of the colour. The table below shows the percentage of marbles of 
each colour used in the current design. The cost of each marble increased by 25%. 
Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep 
the total cost unchanged. What is the percentage of blue marbles in the new design? 
 
Blue Black Red Yellow 
40% 25% 20% 15% 
 
 
(A) 35.75 (B) 40.25 (C) 43.75 (D) 46.25 
 
 
Q.10  P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only 
one set of oars. The following additional facts are available. 
(i) The boat held two persons on each of the three forward trips across the lake and one 
person on each of the two return trips. 
(ii) P is unable to row when someone else is in the boat. 
(iii) Q is unable to row with anyone else except R. 
(iv) Each person rowed for at least one trip. 
(v) Only one person can row during a trip. 
 
Who rowed twice? 
 
(A) P (B) Q (C) R (D) S 
 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                         ELECTRICAL ENGINEERING 
EE 1/15 
Q. 1 – Q. 25 carry one mark each. 
Q.1  A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% 
across its series impedance at full load. Of this, 3% is due to resistance. The percentage 
regulation of the transformer at full load with 0.8 lagging power factor is 
(A)  4.8 (B)  6.8 (C)  8.8 (D)  10.8 
 
 
Q.2  In a salient pole synchronous motor, the developed reluctance torque attains the maximum 
value when the load angle in electrical degrees is 
(A) 0 (B) 45 (C)  60 (D) 90 
 
 
Q.3  A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as 
shown in the figure. All switches and diodes are ideal. Which one of the following is true 
for instantaneous load voltage and current? 
 
o
v
o
i
L
O
A
D
 
(A)  0 & 0
oo
vi ?? (B)  0 & 0
oo
vi ?? 
(C)  0 & 0
oo
vi ?? (D)  0 & 0
oo
vi ?? 
 
 
Q.4  Four power semiconductor devices are shown in the figure along with their relevant 
terminals. The device(s) that can carry dc current continuously in the direction shown when 
gated appropriately is (are) 
I I
G
MT
1
MT
2
A
K G
Thyristor Triac
G
D
S
I
MOSFET
A
K G
GTO
I
 
(A) Triac only 
(B) Triac and MOSFET 
(C) Triac and GTO 
(D) Thyristor and Triac 
 
GATE 2018                                                                                                                                                         ELECTRICAL ENGINEERING 
EE 2/15 
 
Q.5  Two wattmeter method is used for measurement of power in a balanced three-phase load 
supplied from a balanced three-phase system. If one of the wattmeters reads half of the 
other (both positive), then the power factor of the load is 
(A) 0.532 (B) 0.632 (C)  0.707 (D)  0.866 
 
 
Q.6  
Consider a lossy transmission line with 
1
V and 
2
V as the sending and receiving end 
voltages, respectively. Z and X are the series impedance and reactance of the line, 
respectively.  The steady-state stability limit for the transmission line will be 
(A) greater than 
12
VV
X
 (B) less than 
12
VV
X
 
(C) equal to 
12
VV
X
 (D) equal to 
12
VV
Z
 
 
 
Q.7  The graph of a network has 8 nodes and 5 independent loops. The number of branches of 
the graph is 
(A) 11 (B) 12 (C)  13 (D)  14 
 
Q.8  In the figure, the voltages are ?? 1
( ?? ) = 100 cos ? ( ???? ), ?? 2
( ?? ) = 100 cos ? ( ???? + ?? /18 ) and 
?? 3
( ?? ) = 100 cos ? ( ???? + ?? /36 ). The circuit is in sinusoidal steady state, and ?? < < ???? . ?? 1
, 
?? 2
 and ?? 3
 are the average power outputs. Which one of the following statements is true? 
+
-
+
-
+
-
P
1
P
2
P
3
R R L L
1
v  (t)
2
v  (t)
3
v  (t)
 
 
(A) ? ?? 1
= ?? 2
= ?? 3
= 0 (B) ? ?? 1
< 0 , ?? 2
> 0 , ?? 3
> 0 
(C) ? ?? 1
< 0 , ?? 2
> 0 , ?? 3
< 0 (D) ? ?? 1
> 0 , ?? 2
< 0 , ?? 3
> 0 
 
GATE 2018                                                                                                                                                         ELECTRICAL ENGINEERING 
EE 3/15 
Q.9  Match the transfer functions of the second-order systems with the nature of the systems 
given below. 
 
  Transfer functions                                          Nature of system 
 
P:  
2
15
5 15 ss ??
                                                I:  Overdamped  
 
Q:  
2
25
10 25 ss ??
                                            II: Critically damped 
 
R:  
2
35
18 35 ss ??
                                           III: Underdamped 
 
(A) P-I,   Q-II,  R-III 
(B) P-II,  Q-I,   R-III 
(C) P-III, Q-II, R-I  
(D) P-III, Q-I,  R-II 
 
Q.10  A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. 
Consider the x - y plane to be a conducting ground plane. Take 
12
0
8.85 10
?
?? F/m. The 
z component of the E field at (0, 0, 0.1) is closest to 
(A) 899.18 V/m (B) 899.18 ? V/m 
 
(C)  999.09 V/m 
 
(D)  999.09 ? V/m 
 
Q.11  
Let f be a real-valued function of a real variable defined as 
2
() f x x ? for 0 x ? , and 
2
() f x x ?? for 0 x ? . Which one of the following statements is true? 
(A) () fx is discontinuous at 0 x ? . 
(B) () fx is continuous but not differentiable at 0 x ? . 
(C) () fx is differentiable but its first derivative is not continuous at 0 x ? . 
(D) () fx is differentiable but its first derivative is not differentiable at 0 x ? . 
 
 
Q.12  The value of the directional derivative of the function ?? ( ?? , ?? , ?? ) = ????
2
+ ???? 2
+ ????
2
 at the 
point (2, -1, 1) in the direction of the vector ?? = ?? + 2 ?? + 2 ?? is 
(A) 1 (B) 0.95 (C) 0.93  (D) 0.9  
 
 
Q.13  
The value of the integral ?
?? + 1
?? 2
- 4
???? ?? in counter clockwise direction around a circle ?? of 
radius 1 with center at the point ?? = - 2 is 
(A) 
????
2
 
(B) 2 ???? 
(C)  -
????
2
 
(D)  - 2 ????