Instrumentation Engineering - IN 2018 GATE Paper with solution GATE Notes | EduRev

 Page 1


GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “When she fell down the _______, she received many _______ but little help. ” 
 
The words that best fill the blanks in the above sentence are  
 
(A) stairs, stares (B) stairs, stairs 
(C) stares, stairs (D) stares, stares 
 
 
Q.2  “In spite of being warned repeatedly, he failed to correct his _________ behaviour. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) rational (B) reasonable (C) errant (D) good 
 
 
Q.3  For 0 = ?? = 2 ?? , sin ?? and cos ?? are both decreasing functions in the interval ________. 
 
(A) ( 0 ,
?? 2
) (B) (
?? 2
, ?? ) (C) (?? ,
3 ?? 2
) (D) (
3 ?? 2
, 2 ?? ) 
 
 
Q.4  
The area of an equilateral triangle is v 3. What is the perimeter of the triangle? 
 
(A) 2 (B) 4 (C) 6 (D) 8 
 
 
Q.5  Arrange the following three-dimensional objects in the descending order of their volumes: 
(i)  A cuboid with dimensions 10 cm, 8 cm and 6 cm
 
 
(ii)  A cube of side 8 cm 
(iii)  A cylinder with base radius 7 cm and height 7 cm 
(iv)  A sphere of radius 7 cm 
 
(A) (i), (ii), (iii), (iv) 
(B) (ii), (i), (iv), (iii) 
(C) (iii), (ii), (i), (iv) 
(D) (iv), (iii), (ii), (i) 
 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An automobile travels from city A to city B and returns to city A by the same route. The 
speed of the vehicle during the onward and return journeys were constant at 60 km/h and 
90 km/h, respectively. What is the average speed in km/h for the entire journey? 
 
(A) 72 (B) 73 (C) 74 (D) 75 
 
Page 2


GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “When she fell down the _______, she received many _______ but little help. ” 
 
The words that best fill the blanks in the above sentence are  
 
(A) stairs, stares (B) stairs, stairs 
(C) stares, stairs (D) stares, stares 
 
 
Q.2  “In spite of being warned repeatedly, he failed to correct his _________ behaviour. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) rational (B) reasonable (C) errant (D) good 
 
 
Q.3  For 0 = ?? = 2 ?? , sin ?? and cos ?? are both decreasing functions in the interval ________. 
 
(A) ( 0 ,
?? 2
) (B) (
?? 2
, ?? ) (C) (?? ,
3 ?? 2
) (D) (
3 ?? 2
, 2 ?? ) 
 
 
Q.4  
The area of an equilateral triangle is v 3. What is the perimeter of the triangle? 
 
(A) 2 (B) 4 (C) 6 (D) 8 
 
 
Q.5  Arrange the following three-dimensional objects in the descending order of their volumes: 
(i)  A cuboid with dimensions 10 cm, 8 cm and 6 cm
 
 
(ii)  A cube of side 8 cm 
(iii)  A cylinder with base radius 7 cm and height 7 cm 
(iv)  A sphere of radius 7 cm 
 
(A) (i), (ii), (iii), (iv) 
(B) (ii), (i), (iv), (iii) 
(C) (iii), (ii), (i), (iv) 
(D) (iv), (iii), (ii), (i) 
 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An automobile travels from city A to city B and returns to city A by the same route. The 
speed of the vehicle during the onward and return journeys were constant at 60 km/h and 
90 km/h, respectively. What is the average speed in km/h for the entire journey? 
 
(A) 72 (B) 73 (C) 74 (D) 75 
 
GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 2/2 
Q.7  A set of 4 parallel lines intersect with another set of 5 parallel lines. How many 
parallelograms are formed? 
 
(A) 20 (B) 48 (C) 60 (D) 72 
 
 
Q.8  To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 
6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 
candidates. Question B was answered correctly by 2,50,000 candidates. Question C was 
answered correctly by 2,60,000 candidates. Both questions A and B were answered 
correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 
90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. 
If the number of students answering all questions correctly is the same as the number 
answering none, how many candidates failed to clear the test? 
 
(A) 30,000 (B) 2,70,000 (C) 3,90,000 (D) 4,20,000 
 
 
Q.9  
If ?? 2
+ ?? - 1 = 0 what is the value of ?? 4
+
1
?? 4
? 
 
(A) 1 (B) 5 (C) 7 (D) 9 
 
 
Q.10  In a detailed study of annual crow births in India, it was found that there was relatively no 
growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another 
unrelated study, it was found that the revenue from cracker sales in India which remained 
fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. 
The solid line in the graph below refers to annual sale of crackers and the dashed line refers 
to the annual crow births in India. Choose the most appropriate inference from the above 
data. 
 
 
(A) There is a strong correlation between crow birth and cracker sales. 
(B) Cracker usage increases crow birth rate. 
(C) If cracker sale declines, crow birth will decline. 
(D) Increased birth rate of crows will cause an increase in the sale of crackers. 
 
END OF THE QUESTION PAPER 
 
Page 3


GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “When she fell down the _______, she received many _______ but little help. ” 
 
The words that best fill the blanks in the above sentence are  
 
(A) stairs, stares (B) stairs, stairs 
(C) stares, stairs (D) stares, stares 
 
 
Q.2  “In spite of being warned repeatedly, he failed to correct his _________ behaviour. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) rational (B) reasonable (C) errant (D) good 
 
 
Q.3  For 0 = ?? = 2 ?? , sin ?? and cos ?? are both decreasing functions in the interval ________. 
 
(A) ( 0 ,
?? 2
) (B) (
?? 2
, ?? ) (C) (?? ,
3 ?? 2
) (D) (
3 ?? 2
, 2 ?? ) 
 
 
Q.4  
The area of an equilateral triangle is v 3. What is the perimeter of the triangle? 
 
(A) 2 (B) 4 (C) 6 (D) 8 
 
 
Q.5  Arrange the following three-dimensional objects in the descending order of their volumes: 
(i)  A cuboid with dimensions 10 cm, 8 cm and 6 cm
 
 
(ii)  A cube of side 8 cm 
(iii)  A cylinder with base radius 7 cm and height 7 cm 
(iv)  A sphere of radius 7 cm 
 
(A) (i), (ii), (iii), (iv) 
(B) (ii), (i), (iv), (iii) 
(C) (iii), (ii), (i), (iv) 
(D) (iv), (iii), (ii), (i) 
 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An automobile travels from city A to city B and returns to city A by the same route. The 
speed of the vehicle during the onward and return journeys were constant at 60 km/h and 
90 km/h, respectively. What is the average speed in km/h for the entire journey? 
 
(A) 72 (B) 73 (C) 74 (D) 75 
 
GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 2/2 
Q.7  A set of 4 parallel lines intersect with another set of 5 parallel lines. How many 
parallelograms are formed? 
 
(A) 20 (B) 48 (C) 60 (D) 72 
 
 
Q.8  To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 
6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 
candidates. Question B was answered correctly by 2,50,000 candidates. Question C was 
answered correctly by 2,60,000 candidates. Both questions A and B were answered 
correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 
90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. 
If the number of students answering all questions correctly is the same as the number 
answering none, how many candidates failed to clear the test? 
 
(A) 30,000 (B) 2,70,000 (C) 3,90,000 (D) 4,20,000 
 
 
Q.9  
If ?? 2
+ ?? - 1 = 0 what is the value of ?? 4
+
1
?? 4
? 
 
(A) 1 (B) 5 (C) 7 (D) 9 
 
 
Q.10  In a detailed study of annual crow births in India, it was found that there was relatively no 
growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another 
unrelated study, it was found that the revenue from cracker sales in India which remained 
fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. 
The solid line in the graph below refers to annual sale of crackers and the dashed line refers 
to the annual crow births in India. Choose the most appropriate inference from the above 
data. 
 
 
(A) There is a strong correlation between crow birth and cracker sales. 
(B) Cracker usage increases crow birth rate. 
(C) If cracker sale declines, crow birth will decline. 
(D) Increased birth rate of crows will cause an increase in the sale of crackers. 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                                         Instrumentation Engineering  
IN 1/14 
Q. 1 – Q. 25 carry one mark each. 
Q.1  Let ?? be a 3 by 3 matrix with real number entries. The matrix  ?? is such that ?? 2
= 0. The eigen 
values of N are  
(A) 0, 0, 0 (B) 0,0,1 (C)  0,1,1 (D)  1,1,1 
 
 
Q.2  Let 
 
?? 1
(?? ) = ?? 2   
 and  ?? 2
(?? ) = ?? ¯ be two complex variable functions. Here ?? ¯  is the complex 
conjugate of z.  Choose the correct answer. 
(A) Both ?? 1
(?? ) and ?? 2
(?? ) are analytic  
(B) Only ?? 1
(?? ) is analytic 
(C) Only ?? 2
(?? ) is analytic 
(D) Both ?? 1
(?? ) and ?? 2
(?? ) are not analytic 
 
 
Q.3  ?? and ?? are two independent random variables with variances 1 and 2, respectively.  
Let ?? = ?? - ?? . The variance of ?? is  
(A) 0 (B) 1 (C)  2 (D)  3 
 
 
Q.4  Consider two functions ?? (?? ) = (?? - 2)
2
 and ?? (?? ) = 2?? - 1, where ?? is real. The smallest 
value of ?? for which ?? (?? ) = ?? (?? ) ???? _______. 
 
Q.5  Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. 
The probability of getting the head for the third time in the fifth toss is   
 
 (A)     
5
16
  (B)    
3
16
  (C)   
3
5
  (D)  
9
16
 
 
 
Q.6  A series R-C circuit is excited by a 1 ?0 V sinusoidal ac voltage source. The locus diagram 
of the phasor current ?? = (x + jy) A, when C is varied, while keeping R fixed, is 
(A)   
 
(B)   
 
(C)  
 
(D) 
 
 
 
+jy 
x 
+jy 
+jy 
x 
+jy 
x 
x 
Page 4


GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “When she fell down the _______, she received many _______ but little help. ” 
 
The words that best fill the blanks in the above sentence are  
 
(A) stairs, stares (B) stairs, stairs 
(C) stares, stairs (D) stares, stares 
 
 
Q.2  “In spite of being warned repeatedly, he failed to correct his _________ behaviour. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) rational (B) reasonable (C) errant (D) good 
 
 
Q.3  For 0 = ?? = 2 ?? , sin ?? and cos ?? are both decreasing functions in the interval ________. 
 
(A) ( 0 ,
?? 2
) (B) (
?? 2
, ?? ) (C) (?? ,
3 ?? 2
) (D) (
3 ?? 2
, 2 ?? ) 
 
 
Q.4  
The area of an equilateral triangle is v 3. What is the perimeter of the triangle? 
 
(A) 2 (B) 4 (C) 6 (D) 8 
 
 
Q.5  Arrange the following three-dimensional objects in the descending order of their volumes: 
(i)  A cuboid with dimensions 10 cm, 8 cm and 6 cm
 
 
(ii)  A cube of side 8 cm 
(iii)  A cylinder with base radius 7 cm and height 7 cm 
(iv)  A sphere of radius 7 cm 
 
(A) (i), (ii), (iii), (iv) 
(B) (ii), (i), (iv), (iii) 
(C) (iii), (ii), (i), (iv) 
(D) (iv), (iii), (ii), (i) 
 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An automobile travels from city A to city B and returns to city A by the same route. The 
speed of the vehicle during the onward and return journeys were constant at 60 km/h and 
90 km/h, respectively. What is the average speed in km/h for the entire journey? 
 
(A) 72 (B) 73 (C) 74 (D) 75 
 
GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 2/2 
Q.7  A set of 4 parallel lines intersect with another set of 5 parallel lines. How many 
parallelograms are formed? 
 
(A) 20 (B) 48 (C) 60 (D) 72 
 
 
Q.8  To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 
6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 
candidates. Question B was answered correctly by 2,50,000 candidates. Question C was 
answered correctly by 2,60,000 candidates. Both questions A and B were answered 
correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 
90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. 
If the number of students answering all questions correctly is the same as the number 
answering none, how many candidates failed to clear the test? 
 
(A) 30,000 (B) 2,70,000 (C) 3,90,000 (D) 4,20,000 
 
 
Q.9  
If ?? 2
+ ?? - 1 = 0 what is the value of ?? 4
+
1
?? 4
? 
 
(A) 1 (B) 5 (C) 7 (D) 9 
 
 
Q.10  In a detailed study of annual crow births in India, it was found that there was relatively no 
growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another 
unrelated study, it was found that the revenue from cracker sales in India which remained 
fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. 
The solid line in the graph below refers to annual sale of crackers and the dashed line refers 
to the annual crow births in India. Choose the most appropriate inference from the above 
data. 
 
 
(A) There is a strong correlation between crow birth and cracker sales. 
(B) Cracker usage increases crow birth rate. 
(C) If cracker sale declines, crow birth will decline. 
(D) Increased birth rate of crows will cause an increase in the sale of crackers. 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                                         Instrumentation Engineering  
IN 1/14 
Q. 1 – Q. 25 carry one mark each. 
Q.1  Let ?? be a 3 by 3 matrix with real number entries. The matrix  ?? is such that ?? 2
= 0. The eigen 
values of N are  
(A) 0, 0, 0 (B) 0,0,1 (C)  0,1,1 (D)  1,1,1 
 
 
Q.2  Let 
 
?? 1
(?? ) = ?? 2   
 and  ?? 2
(?? ) = ?? ¯ be two complex variable functions. Here ?? ¯  is the complex 
conjugate of z.  Choose the correct answer. 
(A) Both ?? 1
(?? ) and ?? 2
(?? ) are analytic  
(B) Only ?? 1
(?? ) is analytic 
(C) Only ?? 2
(?? ) is analytic 
(D) Both ?? 1
(?? ) and ?? 2
(?? ) are not analytic 
 
 
Q.3  ?? and ?? are two independent random variables with variances 1 and 2, respectively.  
Let ?? = ?? - ?? . The variance of ?? is  
(A) 0 (B) 1 (C)  2 (D)  3 
 
 
Q.4  Consider two functions ?? (?? ) = (?? - 2)
2
 and ?? (?? ) = 2?? - 1, where ?? is real. The smallest 
value of ?? for which ?? (?? ) = ?? (?? ) ???? _______. 
 
Q.5  Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. 
The probability of getting the head for the third time in the fifth toss is   
 
 (A)     
5
16
  (B)    
3
16
  (C)   
3
5
  (D)  
9
16
 
 
 
Q.6  A series R-C circuit is excited by a 1 ?0 V sinusoidal ac voltage source. The locus diagram 
of the phasor current ?? = (x + jy) A, when C is varied, while keeping R fixed, is 
(A)   
 
(B)   
 
(C)  
 
(D) 
 
 
 
+jy 
x 
+jy 
+jy 
x 
+jy 
x 
x 
GATE 2018                                                                                                                                                                         Instrumentation Engineering  
IN 2/14 
Q.7  The Thevenin equivalent circuit representation across terminals p-q of the circuit shown in 
the figure is a  
 
(A) 1 V source in series with 150 k?  (B)  1 V source in parallel with 100 k? 
(C) 2 V source in series with 150 k? (D)  2 V source in parallel with 200 k?  
 
 
Q.8  A coil having an impedance of (10 + j100) ? is connected in parallel to a variable capacitor 
as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor 
is changed so that parallel resonance occurs. The impedance across terminals p-q at 
resonance (in ?) is ______. 
 
 
 
Q.9  Two periodic signals ?? (?? ) and ?? (?? ) have the same fundamental period of 3 seconds. Consider 
the signal ?? (?? ) = ?? (-?? ) + ?? (2?? + 1). The fundamental period of ?? (?? ) in seconds is   
(A) 1 (B) 1.5 (C)  2 (D)  3 
 
 
 
Q.10  Consider signal ?? (?? ) = {
1, |?? | = 2
0 |?? | > 2
. Let ?? (?? ) denote the unit impulse (Dirac-delta) 
function. The value of the integral  ? 2?? (?? - 3)?? (?? - 4)???? 5
0
 is  
(A) 2 (B) 1 (C)  0 (D)  3 
 
 
100 k? 
100 k? 
p 
q 
4 V  
+ 
- 
100 k? 
p 
q 
Page 5


GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “When she fell down the _______, she received many _______ but little help. ” 
 
The words that best fill the blanks in the above sentence are  
 
(A) stairs, stares (B) stairs, stairs 
(C) stares, stairs (D) stares, stares 
 
 
Q.2  “In spite of being warned repeatedly, he failed to correct his _________ behaviour. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) rational (B) reasonable (C) errant (D) good 
 
 
Q.3  For 0 = ?? = 2 ?? , sin ?? and cos ?? are both decreasing functions in the interval ________. 
 
(A) ( 0 ,
?? 2
) (B) (
?? 2
, ?? ) (C) (?? ,
3 ?? 2
) (D) (
3 ?? 2
, 2 ?? ) 
 
 
Q.4  
The area of an equilateral triangle is v 3. What is the perimeter of the triangle? 
 
(A) 2 (B) 4 (C) 6 (D) 8 
 
 
Q.5  Arrange the following three-dimensional objects in the descending order of their volumes: 
(i)  A cuboid with dimensions 10 cm, 8 cm and 6 cm
 
 
(ii)  A cube of side 8 cm 
(iii)  A cylinder with base radius 7 cm and height 7 cm 
(iv)  A sphere of radius 7 cm 
 
(A) (i), (ii), (iii), (iv) 
(B) (ii), (i), (iv), (iii) 
(C) (iii), (ii), (i), (iv) 
(D) (iv), (iii), (ii), (i) 
 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  An automobile travels from city A to city B and returns to city A by the same route. The 
speed of the vehicle during the onward and return journeys were constant at 60 km/h and 
90 km/h, respectively. What is the average speed in km/h for the entire journey? 
 
(A) 72 (B) 73 (C) 74 (D) 75 
 
GATE 2018                                                                                            General Aptitude (GA) Set-4  
GA 2/2 
Q.7  A set of 4 parallel lines intersect with another set of 5 parallel lines. How many 
parallelograms are formed? 
 
(A) 20 (B) 48 (C) 60 (D) 72 
 
 
Q.8  To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 
6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 
candidates. Question B was answered correctly by 2,50,000 candidates. Question C was 
answered correctly by 2,60,000 candidates. Both questions A and B were answered 
correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 
90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. 
If the number of students answering all questions correctly is the same as the number 
answering none, how many candidates failed to clear the test? 
 
(A) 30,000 (B) 2,70,000 (C) 3,90,000 (D) 4,20,000 
 
 
Q.9  
If ?? 2
+ ?? - 1 = 0 what is the value of ?? 4
+
1
?? 4
? 
 
(A) 1 (B) 5 (C) 7 (D) 9 
 
 
Q.10  In a detailed study of annual crow births in India, it was found that there was relatively no 
growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another 
unrelated study, it was found that the revenue from cracker sales in India which remained 
fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. 
The solid line in the graph below refers to annual sale of crackers and the dashed line refers 
to the annual crow births in India. Choose the most appropriate inference from the above 
data. 
 
 
(A) There is a strong correlation between crow birth and cracker sales. 
(B) Cracker usage increases crow birth rate. 
(C) If cracker sale declines, crow birth will decline. 
(D) Increased birth rate of crows will cause an increase in the sale of crackers. 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                                         Instrumentation Engineering  
IN 1/14 
Q. 1 – Q. 25 carry one mark each. 
Q.1  Let ?? be a 3 by 3 matrix with real number entries. The matrix  ?? is such that ?? 2
= 0. The eigen 
values of N are  
(A) 0, 0, 0 (B) 0,0,1 (C)  0,1,1 (D)  1,1,1 
 
 
Q.2  Let 
 
?? 1
(?? ) = ?? 2   
 and  ?? 2
(?? ) = ?? ¯ be two complex variable functions. Here ?? ¯  is the complex 
conjugate of z.  Choose the correct answer. 
(A) Both ?? 1
(?? ) and ?? 2
(?? ) are analytic  
(B) Only ?? 1
(?? ) is analytic 
(C) Only ?? 2
(?? ) is analytic 
(D) Both ?? 1
(?? ) and ?? 2
(?? ) are not analytic 
 
 
Q.3  ?? and ?? are two independent random variables with variances 1 and 2, respectively.  
Let ?? = ?? - ?? . The variance of ?? is  
(A) 0 (B) 1 (C)  2 (D)  3 
 
 
Q.4  Consider two functions ?? (?? ) = (?? - 2)
2
 and ?? (?? ) = 2?? - 1, where ?? is real. The smallest 
value of ?? for which ?? (?? ) = ?? (?? ) ???? _______. 
 
Q.5  Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. 
The probability of getting the head for the third time in the fifth toss is   
 
 (A)     
5
16
  (B)    
3
16
  (C)   
3
5
  (D)  
9
16
 
 
 
Q.6  A series R-C circuit is excited by a 1 ?0 V sinusoidal ac voltage source. The locus diagram 
of the phasor current ?? = (x + jy) A, when C is varied, while keeping R fixed, is 
(A)   
 
(B)   
 
(C)  
 
(D) 
 
 
 
+jy 
x 
+jy 
+jy 
x 
+jy 
x 
x 
GATE 2018                                                                                                                                                                         Instrumentation Engineering  
IN 2/14 
Q.7  The Thevenin equivalent circuit representation across terminals p-q of the circuit shown in 
the figure is a  
 
(A) 1 V source in series with 150 k?  (B)  1 V source in parallel with 100 k? 
(C) 2 V source in series with 150 k? (D)  2 V source in parallel with 200 k?  
 
 
Q.8  A coil having an impedance of (10 + j100) ? is connected in parallel to a variable capacitor 
as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor 
is changed so that parallel resonance occurs. The impedance across terminals p-q at 
resonance (in ?) is ______. 
 
 
 
Q.9  Two periodic signals ?? (?? ) and ?? (?? ) have the same fundamental period of 3 seconds. Consider 
the signal ?? (?? ) = ?? (-?? ) + ?? (2?? + 1). The fundamental period of ?? (?? ) in seconds is   
(A) 1 (B) 1.5 (C)  2 (D)  3 
 
 
 
Q.10  Consider signal ?? (?? ) = {
1, |?? | = 2
0 |?? | > 2
. Let ?? (?? ) denote the unit impulse (Dirac-delta) 
function. The value of the integral  ? 2?? (?? - 3)?? (?? - 4)???? 5
0
 is  
(A) 2 (B) 1 (C)  0 (D)  3 
 
 
100 k? 
100 k? 
p 
q 
4 V  
+ 
- 
100 k? 
p 
q 
GATE 2018                                                                                                                                                                         Instrumentation Engineering  
IN 3/14 
Q.11  An ideal square wave with period of 20 ms shown in the figure, is passed through an ideal 
low pass filter with cut-off frequency 120 Hz. Which of the following is an accurate 
description of the output? 
 
(A)  Output is zero. 
(B)  Output consists of both 50 Hz and 100 Hz frequency components. 
(C)  Output is a pure sinusoid of frequency 50 Hz. 
(D)  Output is a square wave of fundamental frequency 50 Hz.  
  
 
 
Q.12  
An input ?? (?? ) = sin(?? )  is applied to the system ?? (?? ) = 
?? -1
?? +1
.  The corresponding steady 
state output is ?? (?? ) = sin(?? + ?? ), where the phase ?? (in degrees), when restricted to  
 0 ? = ?? = 360 ?, is ______ . 
 
 
 
Q.13  
The approximate phase response of 
100
2
 ?? -0.01 ?? ?? 2
+0.2 ?? + 100
2
 is  
 
(A) 
 
(B) 
 
(C) 
 
(D)