Mechanical Engineering - ME 2018 GATE Paper with solution - Set - 2 Mechanical Engineering Notes | EduRev

Mock Test Series - Mechanical Engineering (ME) for GATE 2020

Mechanical Engineering : Mechanical Engineering - ME 2018 GATE Paper with solution - Set - 2 Mechanical Engineering Notes | EduRev

 Page 1


GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 1/3 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “The dress _________ her so well that they all immediately _________ her on her 
appearance.” 
 
The words that best fill the blanks in the above sentence are 
 
(A) complemented, complemented (B) complimented, complemented 
(C) complimented, complimented (D) complemented, complimented 
 
 
Q.2  “The judge’s standing in the legal community, though shaken by false allegations of 
wrongdoing, remained _________.” 
 
The word that best fills the blank in the above sentence is  
 
(A) undiminished (B) damaged (C) illegal (D) uncertain 
 
 
Q.3  Find the missing group of letters in the following series: 
BC, FGH, LMNO, _____ 
 
(A) UVWXY (B) TUVWX (C) STUVW (D) RSTUV 
 
 
Q.4  The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the 
following statements is true? 
 
(A) The circle has the largest area. 
(B) The square has the largest area. 
(C) The equilateral triangle has the largest area. 
(D) All the three shapes have the same area. 
 
 
Q.5  
The value of the expression 
1
1 + log
?? ????
+
1
1 + log
?? ????
+
1
1 + log
?? ????
 is _________. 
 
(A) -1 (B) 0 (C) 1 (D) 3 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  Forty students watched films A, B and C over a week. Each student watched either only 
one film or all three. Thirteen students watched film A, sixteen students watched film B 
and nineteen students watched film C. How many students watched all three films? 
 
(A) 0 (B) 2 (C) 4 (D) 8 
 
 
Page 2


GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 1/3 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “The dress _________ her so well that they all immediately _________ her on her 
appearance.” 
 
The words that best fill the blanks in the above sentence are 
 
(A) complemented, complemented (B) complimented, complemented 
(C) complimented, complimented (D) complemented, complimented 
 
 
Q.2  “The judge’s standing in the legal community, though shaken by false allegations of 
wrongdoing, remained _________.” 
 
The word that best fills the blank in the above sentence is  
 
(A) undiminished (B) damaged (C) illegal (D) uncertain 
 
 
Q.3  Find the missing group of letters in the following series: 
BC, FGH, LMNO, _____ 
 
(A) UVWXY (B) TUVWX (C) STUVW (D) RSTUV 
 
 
Q.4  The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the 
following statements is true? 
 
(A) The circle has the largest area. 
(B) The square has the largest area. 
(C) The equilateral triangle has the largest area. 
(D) All the three shapes have the same area. 
 
 
Q.5  
The value of the expression 
1
1 + log
?? ????
+
1
1 + log
?? ????
+
1
1 + log
?? ????
 is _________. 
 
(A) -1 (B) 0 (C) 1 (D) 3 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  Forty students watched films A, B and C over a week. Each student watched either only 
one film or all three. Thirteen students watched film A, sixteen students watched film B 
and nineteen students watched film C. How many students watched all three films? 
 
(A) 0 (B) 2 (C) 4 (D) 8 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 2/3 
Q.7  A wire would enclose an area of 1936 m
2
, if it is bent into a square. The wire is cut into 
two pieces. The longer piece is thrice as long as the shorter piece. The long and the short 
pieces are bent into a square and a circle, respectively. Which of the following choices is 
closest to the sum of the areas enclosed by the two pieces in square meters? 
 
(A) 1096 (B) 1111 (C) 1243 (D) 2486 
 
 
Q.8  A contract is to be completed in 52 days and 125 identical robots were employed, each 
operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How 
many additional robots would be required to complete the work on time, if each robot is 
now operational for 8 hours a day? 
 
(A) 50 (B) 89 (C) 146 (D) 175 
 
 
Q.9  A house has a number which needs to be identified. The following three statements are 
given that can help in identifying the house number. 
i. If the house number is a multiple of 3, then it is a number from 50 to 59. 
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. 
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79. 
 
What is the house number? 
 
(A) 54 (B) 65 (C) 66 (D) 76 
 
  
Page 3


GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 1/3 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “The dress _________ her so well that they all immediately _________ her on her 
appearance.” 
 
The words that best fill the blanks in the above sentence are 
 
(A) complemented, complemented (B) complimented, complemented 
(C) complimented, complimented (D) complemented, complimented 
 
 
Q.2  “The judge’s standing in the legal community, though shaken by false allegations of 
wrongdoing, remained _________.” 
 
The word that best fills the blank in the above sentence is  
 
(A) undiminished (B) damaged (C) illegal (D) uncertain 
 
 
Q.3  Find the missing group of letters in the following series: 
BC, FGH, LMNO, _____ 
 
(A) UVWXY (B) TUVWX (C) STUVW (D) RSTUV 
 
 
Q.4  The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the 
following statements is true? 
 
(A) The circle has the largest area. 
(B) The square has the largest area. 
(C) The equilateral triangle has the largest area. 
(D) All the three shapes have the same area. 
 
 
Q.5  
The value of the expression 
1
1 + log
?? ????
+
1
1 + log
?? ????
+
1
1 + log
?? ????
 is _________. 
 
(A) -1 (B) 0 (C) 1 (D) 3 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  Forty students watched films A, B and C over a week. Each student watched either only 
one film or all three. Thirteen students watched film A, sixteen students watched film B 
and nineteen students watched film C. How many students watched all three films? 
 
(A) 0 (B) 2 (C) 4 (D) 8 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 2/3 
Q.7  A wire would enclose an area of 1936 m
2
, if it is bent into a square. The wire is cut into 
two pieces. The longer piece is thrice as long as the shorter piece. The long and the short 
pieces are bent into a square and a circle, respectively. Which of the following choices is 
closest to the sum of the areas enclosed by the two pieces in square meters? 
 
(A) 1096 (B) 1111 (C) 1243 (D) 2486 
 
 
Q.8  A contract is to be completed in 52 days and 125 identical robots were employed, each 
operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How 
many additional robots would be required to complete the work on time, if each robot is 
now operational for 8 hours a day? 
 
(A) 50 (B) 89 (C) 146 (D) 175 
 
 
Q.9  A house has a number which needs to be identified. The following three statements are 
given that can help in identifying the house number. 
i. If the house number is a multiple of 3, then it is a number from 50 to 59. 
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. 
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79. 
 
What is the house number? 
 
(A) 54 (B) 65 (C) 66 (D) 76 
 
  
GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 3/3 
 
Q.10  An unbiased coin is tossed six times in a row and four different such trials are conducted. 
One trial implies six tosses of the coin. If H stands for head and T stands for tail, the 
following are the observations from the four trials: 
(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __. 
 
Which statement describing the last two coin tosses of the fourth trial has the highest 
probability of being correct? 
 
(A) Two T will occur. 
(B) One H and one T will occur. 
(C) Two H will occur. 
(D) One H will be followed by one T. 
 
 
END OF THE QUESTION PAPER 
 
Page 4


GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 1/3 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “The dress _________ her so well that they all immediately _________ her on her 
appearance.” 
 
The words that best fill the blanks in the above sentence are 
 
(A) complemented, complemented (B) complimented, complemented 
(C) complimented, complimented (D) complemented, complimented 
 
 
Q.2  “The judge’s standing in the legal community, though shaken by false allegations of 
wrongdoing, remained _________.” 
 
The word that best fills the blank in the above sentence is  
 
(A) undiminished (B) damaged (C) illegal (D) uncertain 
 
 
Q.3  Find the missing group of letters in the following series: 
BC, FGH, LMNO, _____ 
 
(A) UVWXY (B) TUVWX (C) STUVW (D) RSTUV 
 
 
Q.4  The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the 
following statements is true? 
 
(A) The circle has the largest area. 
(B) The square has the largest area. 
(C) The equilateral triangle has the largest area. 
(D) All the three shapes have the same area. 
 
 
Q.5  
The value of the expression 
1
1 + log
?? ????
+
1
1 + log
?? ????
+
1
1 + log
?? ????
 is _________. 
 
(A) -1 (B) 0 (C) 1 (D) 3 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  Forty students watched films A, B and C over a week. Each student watched either only 
one film or all three. Thirteen students watched film A, sixteen students watched film B 
and nineteen students watched film C. How many students watched all three films? 
 
(A) 0 (B) 2 (C) 4 (D) 8 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 2/3 
Q.7  A wire would enclose an area of 1936 m
2
, if it is bent into a square. The wire is cut into 
two pieces. The longer piece is thrice as long as the shorter piece. The long and the short 
pieces are bent into a square and a circle, respectively. Which of the following choices is 
closest to the sum of the areas enclosed by the two pieces in square meters? 
 
(A) 1096 (B) 1111 (C) 1243 (D) 2486 
 
 
Q.8  A contract is to be completed in 52 days and 125 identical robots were employed, each 
operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How 
many additional robots would be required to complete the work on time, if each robot is 
now operational for 8 hours a day? 
 
(A) 50 (B) 89 (C) 146 (D) 175 
 
 
Q.9  A house has a number which needs to be identified. The following three statements are 
given that can help in identifying the house number. 
i. If the house number is a multiple of 3, then it is a number from 50 to 59. 
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. 
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79. 
 
What is the house number? 
 
(A) 54 (B) 65 (C) 66 (D) 76 
 
  
GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 3/3 
 
Q.10  An unbiased coin is tossed six times in a row and four different such trials are conducted. 
One trial implies six tosses of the coin. If H stands for head and T stands for tail, the 
following are the observations from the four trials: 
(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __. 
 
Which statement describing the last two coin tosses of the fourth trial has the highest 
probability of being correct? 
 
(A) Two T will occur. 
(B) One H and one T will occur. 
(C) Two H will occur. 
(D) One H will be followed by one T. 
 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                                         Mechanical Engineering (Set 2) 
ME 1/15 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The Fourier cosine series for an even function () fx is given by 
0
    1
( ) cos( )
n
n
f x a a nx
?
?
??
?
. 
 The value of the coefficient 
 2
a for the function 
2
( ) cos ( ) f x x ? in [0, ?] is 
(A) 0.5 ? (B) 0.0 (C)  0.5 (D)  1.0 
 
 
Q.2  
The divergence of the vector field ? ? j y i y e u
x
ˆ
sin
ˆ
cos ? ?
?
 is 
(A) 0 
(B) y e y e
x x
sin cos ? 
(C) y e
x
cos 2 (D) y e
x
sin 2 
 
 
Q.3  Consider a function u which depends on position x and time t. The partial differential 
equation 
2
2
uu
tx
??
?
??
 
is known as the    
(A) Wave equation 
(B) Heat equation 
(C) Laplace’s equation 
(D) Elasticity equation 
 
 
Q.4  
If y is the solution of the differential equation 0
3 3
? ? x
dx
dy
y , ? ? 1 0 ? y , the value of ? ? 1 ? y 
is 
(A) -2 (B) -1 (C) 0 (D) 1 
 
 
 
 
Q.5  The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned 
slender column with bending stiffness EI and length L is 
(A) 
2
2
4
EI
P
L
?
? (B) 
2
2
EI
P
L
?
? (C)  
2
2
3
4
EI
P
L
?
? (D)  
2
2
4 EI
P
L
?
? 
 
 
Page 5


GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 1/3 
Q. 1 – Q. 5 carry one mark each. 
Q.1  “The dress _________ her so well that they all immediately _________ her on her 
appearance.” 
 
The words that best fill the blanks in the above sentence are 
 
(A) complemented, complemented (B) complimented, complemented 
(C) complimented, complimented (D) complemented, complimented 
 
 
Q.2  “The judge’s standing in the legal community, though shaken by false allegations of 
wrongdoing, remained _________.” 
 
The word that best fills the blank in the above sentence is  
 
(A) undiminished (B) damaged (C) illegal (D) uncertain 
 
 
Q.3  Find the missing group of letters in the following series: 
BC, FGH, LMNO, _____ 
 
(A) UVWXY (B) TUVWX (C) STUVW (D) RSTUV 
 
 
Q.4  The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the 
following statements is true? 
 
(A) The circle has the largest area. 
(B) The square has the largest area. 
(C) The equilateral triangle has the largest area. 
(D) All the three shapes have the same area. 
 
 
Q.5  
The value of the expression 
1
1 + log
?? ????
+
1
1 + log
?? ????
+
1
1 + log
?? ????
 is _________. 
 
(A) -1 (B) 0 (C) 1 (D) 3 
 
 
Q. 6 – Q. 10 carry two marks each. 
 
Q.6  Forty students watched films A, B and C over a week. Each student watched either only 
one film or all three. Thirteen students watched film A, sixteen students watched film B 
and nineteen students watched film C. How many students watched all three films? 
 
(A) 0 (B) 2 (C) 4 (D) 8 
 
 
GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 2/3 
Q.7  A wire would enclose an area of 1936 m
2
, if it is bent into a square. The wire is cut into 
two pieces. The longer piece is thrice as long as the shorter piece. The long and the short 
pieces are bent into a square and a circle, respectively. Which of the following choices is 
closest to the sum of the areas enclosed by the two pieces in square meters? 
 
(A) 1096 (B) 1111 (C) 1243 (D) 2486 
 
 
Q.8  A contract is to be completed in 52 days and 125 identical robots were employed, each 
operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How 
many additional robots would be required to complete the work on time, if each robot is 
now operational for 8 hours a day? 
 
(A) 50 (B) 89 (C) 146 (D) 175 
 
 
Q.9  A house has a number which needs to be identified. The following three statements are 
given that can help in identifying the house number. 
i. If the house number is a multiple of 3, then it is a number from 50 to 59. 
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. 
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79. 
 
What is the house number? 
 
(A) 54 (B) 65 (C) 66 (D) 76 
 
  
GATE 2018                                                                                            General Aptitude (GA) Set-2  
GA 3/3 
 
Q.10  An unbiased coin is tossed six times in a row and four different such trials are conducted. 
One trial implies six tosses of the coin. If H stands for head and T stands for tail, the 
following are the observations from the four trials: 
(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __. 
 
Which statement describing the last two coin tosses of the fourth trial has the highest 
probability of being correct? 
 
(A) Two T will occur. 
(B) One H and one T will occur. 
(C) Two H will occur. 
(D) One H will be followed by one T. 
 
 
END OF THE QUESTION PAPER 
 
GATE 2018                                                                                                                                                                         Mechanical Engineering (Set 2) 
ME 1/15 
Q. 1 – Q. 25 carry one mark each. 
Q.1  The Fourier cosine series for an even function () fx is given by 
0
    1
( ) cos( )
n
n
f x a a nx
?
?
??
?
. 
 The value of the coefficient 
 2
a for the function 
2
( ) cos ( ) f x x ? in [0, ?] is 
(A) 0.5 ? (B) 0.0 (C)  0.5 (D)  1.0 
 
 
Q.2  
The divergence of the vector field ? ? j y i y e u
x
ˆ
sin
ˆ
cos ? ?
?
 is 
(A) 0 
(B) y e y e
x x
sin cos ? 
(C) y e
x
cos 2 (D) y e
x
sin 2 
 
 
Q.3  Consider a function u which depends on position x and time t. The partial differential 
equation 
2
2
uu
tx
??
?
??
 
is known as the    
(A) Wave equation 
(B) Heat equation 
(C) Laplace’s equation 
(D) Elasticity equation 
 
 
Q.4  
If y is the solution of the differential equation 0
3 3
? ? x
dx
dy
y , ? ? 1 0 ? y , the value of ? ? 1 ? y 
is 
(A) -2 (B) -1 (C) 0 (D) 1 
 
 
 
 
Q.5  The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned 
slender column with bending stiffness EI and length L is 
(A) 
2
2
4
EI
P
L
?
? (B) 
2
2
EI
P
L
?
? (C)  
2
2
3
4
EI
P
L
?
? (D)  
2
2
4 EI
P
L
?
? 
 
 
GATE 2018                                                                                                                                                                         Mechanical Engineering (Set 2) 
ME 2/15 
Q.6  A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque 
of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is 
 
 
(A) 5 (B) 20 (C)  500 (D)  2000 
 
 
 
 
 
 
Q.8  Pre-tensioning of a bolted joint is used to 
(A) strain harden the bolt head (B) decrease stiffness of the bolted joint 
(C) increase stiffness of the bolted joint (D) prevent yielding of the thread root 
 
 
Q.9  The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 
1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 µm, then the 
temperature (in K) of the black body is 
(A) 500 (B) 1000 (C)  4000 (D)  8000 
 
 
 
 
 
 
 
 
Q.7  In a single degree of freedom underdamped spring-mass-damper system as shown in the 
figure, an additional damper is added in parallel such that the system still remains 
underdamped. Which one of the following statements is ALWAYS true? 
    
 
 
 
 
 
 
 
         
(A) Transmissibility will increase. 
(B) Transmissibility will decrease. 
(C) Time period of free oscillations will increase. 
(D) Time period of free oscillations will decrease.  
12 Teeth  
T =100 N-m 
48 Teeth  
12 Teeth  
60 Teeth  
 
C 
K 
M 
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