Petroleum Engineering - PE 2018 GATE Paper with solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Going by the _________ that many hands make light work, the school _______ involved 
all the students in the task .” 
 
The words that best fill the blanks in the above sentence are  
 
(A) principle, principal (B) principal, principle 
(C) principle, principle (D) principal, principal 
 
 
Q.2  “Her _______ should not be confused with miserliness; she is ever willing to assist those in 
need. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) cleanliness (B) punctuality (C) frugality (D) greatness 
 
 
Q.3  Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many 
minutes would it take for 100 machines to make 100 toys? 
 
(A) 1 (B) 7 (C) 100 (D) 700 
 
 
Q.4  A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, 
respectively. During this process, the rectangle loses 650 m
2
 of area. What is the area of the 
original rectangle in square meters? 
 
(A) 1125 (B) 2250 (C) 2924 (D) 4500 
 
 
Q.5  A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the 
number, its digits are interchanged. What is the number? 
 
(A) 63 (B) 72 (C) 81 (D) 90 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  For integers ?? , ?? and ?? , what would be the minimum and maximum values respectively of 
?? + ?? + ?? if log |?? | + log |?? | + log |?? | = 0? 
 
(A) -3 and 3 (B) -1 and 1 (C) -1 and 3 (D) 1 and 3 
 
 
Page 2


GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Going by the _________ that many hands make light work, the school _______ involved 
all the students in the task .” 
 
The words that best fill the blanks in the above sentence are  
 
(A) principle, principal (B) principal, principle 
(C) principle, principle (D) principal, principal 
 
 
Q.2  “Her _______ should not be confused with miserliness; she is ever willing to assist those in 
need. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) cleanliness (B) punctuality (C) frugality (D) greatness 
 
 
Q.3  Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many 
minutes would it take for 100 machines to make 100 toys? 
 
(A) 1 (B) 7 (C) 100 (D) 700 
 
 
Q.4  A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, 
respectively. During this process, the rectangle loses 650 m
2
 of area. What is the area of the 
original rectangle in square meters? 
 
(A) 1125 (B) 2250 (C) 2924 (D) 4500 
 
 
Q.5  A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the 
number, its digits are interchanged. What is the number? 
 
(A) 63 (B) 72 (C) 81 (D) 90 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  For integers ?? , ?? and ?? , what would be the minimum and maximum values respectively of 
?? + ?? + ?? if log |?? | + log |?? | + log |?? | = 0? 
 
(A) -3 and 3 (B) -1 and 1 (C) -1 and 3 (D) 1 and 3 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 2/2 
Q.7  Given that ?? and ?? are integers and ?? + ?? 2
 ?? 3
 is odd, which one of the following 
statements is correct? 
 
(A) ?? and ?? are both odd (B) ?? and ?? are both even 
(C) ?? is even and ?? is odd (D) ?? is odd and ?? is even 
 
 
Q.8  From the time the front of a train enters a platform, it takes 25 seconds for the back of the 
train to leave the platform, while travelling at a constant speed of 54 km/h. At the same 
speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the 
train. What is the length of the train and that of the platform in meters, respectively? 
 
(A) 210 and 140 (B) 162.5 and 187.5 
(C) 245 and 130 (D) 175 and 200 
 
 
Q.9  Which of the following functions describe the graph shown in the below figure? 
 
 
 
(A) ?? = ||?? | + 1| - 2 (B) ?? = ||?? | - 1| - 1 
(C) ?? = ||?? | + 1| - 1 (D) ?? = ||?? - 1| - 1| 
 
 
Q.10  Consider the following three statements: 
(i) Some roses are red. 
(ii) All red flowers fade quickly. 
(iii) Some roses fade quickly. 
 
Which of the following statements can be logically inferred from the above statements? 
 
(A) If (i) is true and (ii) is false, then (iii) is false. 
(B) If (i) is true and (ii) is false, then (iii) is true. 
(C) If (i) and (ii) are true, then (iii) is true.  
(D) If (i) and (ii) are false, then (iii) is false.  
 
 
END OF THE QUESTION PAPER 
 
Page 3


GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Going by the _________ that many hands make light work, the school _______ involved 
all the students in the task .” 
 
The words that best fill the blanks in the above sentence are  
 
(A) principle, principal (B) principal, principle 
(C) principle, principle (D) principal, principal 
 
 
Q.2  “Her _______ should not be confused with miserliness; she is ever willing to assist those in 
need. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) cleanliness (B) punctuality (C) frugality (D) greatness 
 
 
Q.3  Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many 
minutes would it take for 100 machines to make 100 toys? 
 
(A) 1 (B) 7 (C) 100 (D) 700 
 
 
Q.4  A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, 
respectively. During this process, the rectangle loses 650 m
2
 of area. What is the area of the 
original rectangle in square meters? 
 
(A) 1125 (B) 2250 (C) 2924 (D) 4500 
 
 
Q.5  A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the 
number, its digits are interchanged. What is the number? 
 
(A) 63 (B) 72 (C) 81 (D) 90 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  For integers ?? , ?? and ?? , what would be the minimum and maximum values respectively of 
?? + ?? + ?? if log |?? | + log |?? | + log |?? | = 0? 
 
(A) -3 and 3 (B) -1 and 1 (C) -1 and 3 (D) 1 and 3 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 2/2 
Q.7  Given that ?? and ?? are integers and ?? + ?? 2
 ?? 3
 is odd, which one of the following 
statements is correct? 
 
(A) ?? and ?? are both odd (B) ?? and ?? are both even 
(C) ?? is even and ?? is odd (D) ?? is odd and ?? is even 
 
 
Q.8  From the time the front of a train enters a platform, it takes 25 seconds for the back of the 
train to leave the platform, while travelling at a constant speed of 54 km/h. At the same 
speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the 
train. What is the length of the train and that of the platform in meters, respectively? 
 
(A) 210 and 140 (B) 162.5 and 187.5 
(C) 245 and 130 (D) 175 and 200 
 
 
Q.9  Which of the following functions describe the graph shown in the below figure? 
 
 
 
(A) ?? = ||?? | + 1| - 2 (B) ?? = ||?? | - 1| - 1 
(C) ?? = ||?? | + 1| - 1 (D) ?? = ||?? - 1| - 1| 
 
 
Q.10  Consider the following three statements: 
(i) Some roses are red. 
(ii) All red flowers fade quickly. 
(iii) Some roses fade quickly. 
 
Which of the following statements can be logically inferred from the above statements? 
 
(A) If (i) is true and (ii) is false, then (iii) is false. 
(B) If (i) is true and (ii) is false, then (iii) is true. 
(C) If (i) and (ii) are true, then (iii) is true.  
(D) If (i) and (ii) are false, then (iii) is false.  
 
 
END OF THE QUESTION PAPER 
 
GATE 2018    Petroleum Engineering  
PE 1/17 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The Taylor series expansion of the function, 
 
?? (?? ) =
-1
1+??  , 
 
around ?? = 0 (up to 4
th
 order term) is: 
(A) 1 + ?? + ?? 2
+ ?? 3
+ ?? 4
 
(B) -1 + ?? - ?? 2
+ ?? 3
- ?? 4
 
(C) -1 - ?? + ?? 2
- ?? 3
+ ?? 4
 
(D) -1 + ?? - 2?? 2
+ 3?? 3
- 4?? 4
 
 
 
Q.2  
The inverse of the matrix [
1 3
1 2
] is, 
 
(A) [
2 3
1 1
] (B) [
-2 1
3 -1
] (C)  [
-2 3
1 -1
] (D)  [
2 -3
-1 1
] 
 
 
Q.3  The line integral of a vector function ?? ¯
(?? ¯ ) over a curve C in a simply connected domain D 
in space, is defined by: 
 
? ?? ¯
(?? ¯ ). ?? ?? ¯
?? = ? (?? 1
???? + ?? 2
???? + ?? 3
???? )
?? 
 
The line integral is independent of path in D. ?? 1
, ?? 2
, and ?? 3
 are continuous, and have 
continuous first partial derivatives in D. ?? '
 is a closed curve in D.  
 
Which one of the following is NOT ALWAYS true in domain D?  
(A) ?
¯
× ?? ¯
= 0
¯
 (B) ?
¯
. ?? ¯
= 0 
(C) ? ?? ¯
(?? ¯ ). ?? ?? ¯
?? '
= 0 
(D) ?? ¯
× ?? ¯
= 0
¯
 
 
 
Q.4  Which one of the following is the integrating factor (IF) for the differential equation, 
 (cos
2
?? )
????
????
+ ?? = cos?? ? 
 
(A) ?? tan ?? (B) ?? cos ?? 
(C) ?? - tan ?? (D) ?? sin ?? 
 
  
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GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Going by the _________ that many hands make light work, the school _______ involved 
all the students in the task .” 
 
The words that best fill the blanks in the above sentence are  
 
(A) principle, principal (B) principal, principle 
(C) principle, principle (D) principal, principal 
 
 
Q.2  “Her _______ should not be confused with miserliness; she is ever willing to assist those in 
need. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) cleanliness (B) punctuality (C) frugality (D) greatness 
 
 
Q.3  Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many 
minutes would it take for 100 machines to make 100 toys? 
 
(A) 1 (B) 7 (C) 100 (D) 700 
 
 
Q.4  A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, 
respectively. During this process, the rectangle loses 650 m
2
 of area. What is the area of the 
original rectangle in square meters? 
 
(A) 1125 (B) 2250 (C) 2924 (D) 4500 
 
 
Q.5  A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the 
number, its digits are interchanged. What is the number? 
 
(A) 63 (B) 72 (C) 81 (D) 90 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  For integers ?? , ?? and ?? , what would be the minimum and maximum values respectively of 
?? + ?? + ?? if log |?? | + log |?? | + log |?? | = 0? 
 
(A) -3 and 3 (B) -1 and 1 (C) -1 and 3 (D) 1 and 3 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 2/2 
Q.7  Given that ?? and ?? are integers and ?? + ?? 2
 ?? 3
 is odd, which one of the following 
statements is correct? 
 
(A) ?? and ?? are both odd (B) ?? and ?? are both even 
(C) ?? is even and ?? is odd (D) ?? is odd and ?? is even 
 
 
Q.8  From the time the front of a train enters a platform, it takes 25 seconds for the back of the 
train to leave the platform, while travelling at a constant speed of 54 km/h. At the same 
speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the 
train. What is the length of the train and that of the platform in meters, respectively? 
 
(A) 210 and 140 (B) 162.5 and 187.5 
(C) 245 and 130 (D) 175 and 200 
 
 
Q.9  Which of the following functions describe the graph shown in the below figure? 
 
 
 
(A) ?? = ||?? | + 1| - 2 (B) ?? = ||?? | - 1| - 1 
(C) ?? = ||?? | + 1| - 1 (D) ?? = ||?? - 1| - 1| 
 
 
Q.10  Consider the following three statements: 
(i) Some roses are red. 
(ii) All red flowers fade quickly. 
(iii) Some roses fade quickly. 
 
Which of the following statements can be logically inferred from the above statements? 
 
(A) If (i) is true and (ii) is false, then (iii) is false. 
(B) If (i) is true and (ii) is false, then (iii) is true. 
(C) If (i) and (ii) are true, then (iii) is true.  
(D) If (i) and (ii) are false, then (iii) is false.  
 
 
END OF THE QUESTION PAPER 
 
GATE 2018    Petroleum Engineering  
PE 1/17 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The Taylor series expansion of the function, 
 
?? (?? ) =
-1
1+??  , 
 
around ?? = 0 (up to 4
th
 order term) is: 
(A) 1 + ?? + ?? 2
+ ?? 3
+ ?? 4
 
(B) -1 + ?? - ?? 2
+ ?? 3
- ?? 4
 
(C) -1 - ?? + ?? 2
- ?? 3
+ ?? 4
 
(D) -1 + ?? - 2?? 2
+ 3?? 3
- 4?? 4
 
 
 
Q.2  
The inverse of the matrix [
1 3
1 2
] is, 
 
(A) [
2 3
1 1
] (B) [
-2 1
3 -1
] (C)  [
-2 3
1 -1
] (D)  [
2 -3
-1 1
] 
 
 
Q.3  The line integral of a vector function ?? ¯
(?? ¯ ) over a curve C in a simply connected domain D 
in space, is defined by: 
 
? ?? ¯
(?? ¯ ). ?? ?? ¯
?? = ? (?? 1
???? + ?? 2
???? + ?? 3
???? )
?? 
 
The line integral is independent of path in D. ?? 1
, ?? 2
, and ?? 3
 are continuous, and have 
continuous first partial derivatives in D. ?? '
 is a closed curve in D.  
 
Which one of the following is NOT ALWAYS true in domain D?  
(A) ?
¯
× ?? ¯
= 0
¯
 (B) ?
¯
. ?? ¯
= 0 
(C) ? ?? ¯
(?? ¯ ). ?? ?? ¯
?? '
= 0 
(D) ?? ¯
× ?? ¯
= 0
¯
 
 
 
Q.4  Which one of the following is the integrating factor (IF) for the differential equation, 
 (cos
2
?? )
????
????
+ ?? = cos?? ? 
 
(A) ?? tan ?? (B) ?? cos ?? 
(C) ?? - tan ?? (D) ?? sin ?? 
 
  
GATE 2018    Petroleum Engineering  
PE 2/17 
 
Q.5  A phase diagram of a black oil is shown in the figure (Y is the critical point).  
 
 
 
Match the following: 
(P) Curve XY (I)  Dew point curve 
(Q) Curve YZ (II) Single phase liquid 
 (R) Phase I (III) Bubble point curve 
 (S) Phase II (IV) Single phase gas 
   
 (A) P-I, Q-III, R-II, S-IV (B) P-III, Q-I, R-II, S-IV 
 (C)  P-III, Q-I, R-IV, S-II (D)  P-I, Q-II, R-III, S-IV 
 
 
Q.6  Match the following chemicals to their respective oilfield applications: 
(P) Hydrate inhibitor (I)   Formaldehyde  
(Q) Well stimulation (II)  Xanthan gum 
(R) Drilling fluid biocide (III) Methanol 
(S) Viscosifier (IV) Hydrochloric acid 
  
(A) P-IV, Q-III, R-II, S-I (B) P-III, Q-I, R-IV, S-II 
(C) P-I, Q-III R-IV, S-II (D) P-III, Q-IV, R-I, S-II  
 
 
Page 5


GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 1/2 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “Going by the _________ that many hands make light work, the school _______ involved 
all the students in the task .” 
 
The words that best fill the blanks in the above sentence are  
 
(A) principle, principal (B) principal, principle 
(C) principle, principle (D) principal, principal 
 
 
Q.2  “Her _______ should not be confused with miserliness; she is ever willing to assist those in 
need. ” 
 
The word that best fills the blank in the above sentence is  
 
(A) cleanliness (B) punctuality (C) frugality (D) greatness 
 
 
Q.3  Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many 
minutes would it take for 100 machines to make 100 toys? 
 
(A) 1 (B) 7 (C) 100 (D) 700 
 
 
Q.4  A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, 
respectively. During this process, the rectangle loses 650 m
2
 of area. What is the area of the 
original rectangle in square meters? 
 
(A) 1125 (B) 2250 (C) 2924 (D) 4500 
 
 
Q.5  A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the 
number, its digits are interchanged. What is the number? 
 
(A) 63 (B) 72 (C) 81 (D) 90 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  For integers ?? , ?? and ?? , what would be the minimum and maximum values respectively of 
?? + ?? + ?? if log |?? | + log |?? | + log |?? | = 0? 
 
(A) -3 and 3 (B) -1 and 1 (C) -1 and 3 (D) 1 and 3 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-1  
GA 2/2 
Q.7  Given that ?? and ?? are integers and ?? + ?? 2
 ?? 3
 is odd, which one of the following 
statements is correct? 
 
(A) ?? and ?? are both odd (B) ?? and ?? are both even 
(C) ?? is even and ?? is odd (D) ?? is odd and ?? is even 
 
 
Q.8  From the time the front of a train enters a platform, it takes 25 seconds for the back of the 
train to leave the platform, while travelling at a constant speed of 54 km/h. At the same 
speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the 
train. What is the length of the train and that of the platform in meters, respectively? 
 
(A) 210 and 140 (B) 162.5 and 187.5 
(C) 245 and 130 (D) 175 and 200 
 
 
Q.9  Which of the following functions describe the graph shown in the below figure? 
 
 
 
(A) ?? = ||?? | + 1| - 2 (B) ?? = ||?? | - 1| - 1 
(C) ?? = ||?? | + 1| - 1 (D) ?? = ||?? - 1| - 1| 
 
 
Q.10  Consider the following three statements: 
(i) Some roses are red. 
(ii) All red flowers fade quickly. 
(iii) Some roses fade quickly. 
 
Which of the following statements can be logically inferred from the above statements? 
 
(A) If (i) is true and (ii) is false, then (iii) is false. 
(B) If (i) is true and (ii) is false, then (iii) is true. 
(C) If (i) and (ii) are true, then (iii) is true.  
(D) If (i) and (ii) are false, then (iii) is false.  
 
 
END OF THE QUESTION PAPER 
 
GATE 2018    Petroleum Engineering  
PE 1/17 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The Taylor series expansion of the function, 
 
?? (?? ) =
-1
1+??  , 
 
around ?? = 0 (up to 4
th
 order term) is: 
(A) 1 + ?? + ?? 2
+ ?? 3
+ ?? 4
 
(B) -1 + ?? - ?? 2
+ ?? 3
- ?? 4
 
(C) -1 - ?? + ?? 2
- ?? 3
+ ?? 4
 
(D) -1 + ?? - 2?? 2
+ 3?? 3
- 4?? 4
 
 
 
Q.2  
The inverse of the matrix [
1 3
1 2
] is, 
 
(A) [
2 3
1 1
] (B) [
-2 1
3 -1
] (C)  [
-2 3
1 -1
] (D)  [
2 -3
-1 1
] 
 
 
Q.3  The line integral of a vector function ?? ¯
(?? ¯ ) over a curve C in a simply connected domain D 
in space, is defined by: 
 
? ?? ¯
(?? ¯ ). ?? ?? ¯
?? = ? (?? 1
???? + ?? 2
???? + ?? 3
???? )
?? 
 
The line integral is independent of path in D. ?? 1
, ?? 2
, and ?? 3
 are continuous, and have 
continuous first partial derivatives in D. ?? '
 is a closed curve in D.  
 
Which one of the following is NOT ALWAYS true in domain D?  
(A) ?
¯
× ?? ¯
= 0
¯
 (B) ?
¯
. ?? ¯
= 0 
(C) ? ?? ¯
(?? ¯ ). ?? ?? ¯
?? '
= 0 
(D) ?? ¯
× ?? ¯
= 0
¯
 
 
 
Q.4  Which one of the following is the integrating factor (IF) for the differential equation, 
 (cos
2
?? )
????
????
+ ?? = cos?? ? 
 
(A) ?? tan ?? (B) ?? cos ?? 
(C) ?? - tan ?? (D) ?? sin ?? 
 
  
GATE 2018    Petroleum Engineering  
PE 2/17 
 
Q.5  A phase diagram of a black oil is shown in the figure (Y is the critical point).  
 
 
 
Match the following: 
(P) Curve XY (I)  Dew point curve 
(Q) Curve YZ (II) Single phase liquid 
 (R) Phase I (III) Bubble point curve 
 (S) Phase II (IV) Single phase gas 
   
 (A) P-I, Q-III, R-II, S-IV (B) P-III, Q-I, R-II, S-IV 
 (C)  P-III, Q-I, R-IV, S-II (D)  P-I, Q-II, R-III, S-IV 
 
 
Q.6  Match the following chemicals to their respective oilfield applications: 
(P) Hydrate inhibitor (I)   Formaldehyde  
(Q) Well stimulation (II)  Xanthan gum 
(R) Drilling fluid biocide (III) Methanol 
(S) Viscosifier (IV) Hydrochloric acid 
  
(A) P-IV, Q-III, R-II, S-I (B) P-III, Q-I, R-IV, S-II 
(C) P-I, Q-III R-IV, S-II (D) P-III, Q-IV, R-I, S-II  
 
 
GATE 2018    Petroleum Engineering  
PE 3/17 
Q.7  The CH4-hydrate equilibrium curve (dashed) and CO2-hydrate equilibrium curve (solid) on 
a pressure-temperature plane above 0°C are shown in the figure. The two curves divide the 
plane in four non-overlapping regions. In which region are CO2-hydrates stable and CH4-
hydrates unstable?  
 
 
(A) I (B) II (C)  III (D)  IV 
 
 
Q.8  Plot of ratio of pressure to gas compressibility factor (P/Z) vs. cumulative gas production 
(Gp) for a gas reservoir (represented by solid curve in the figure) was shown to a reservoir 
engineering student.  
 
 
 
 
 
 
 
 
The student made the following statements: 
(I) A water aquifer is attached to this gas reservoir. 
(II) P/Z vs. Gp curve must always be a straight line for water encroachment in a gas 
reservoir. 
(III) The ultimate gas recovery is diminished due to water encroachment. 
 
Which of the above statements are TRUE?  
(A) Only I and II (B) Only II and III (C) Only I and III (D) I, II, and III 
 
 
Q.9  Waste water from oil industry consists of oil in free and emulsified forms. The oil in the 
free form can be recovered by: 
(A) Aerated lagoons 
(B) Trickling filters 
(C) Gravity separators  
(D) Biological oxygen pond 
 
 
P/Z 
G p