Mathematics - MA 2018 GATE Paper with solution - GATE Past Year Papers for Practice (All Branches)

 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 MATHEMATICS
Q.1Q.25carryonemarkeach
Q.1 The principal value of (1)
(2i=)
is
(A) e
2
(B) e
2i
(C) e
2i
(D) e
2
Q.2 Letf :C!C be an entire function withf(0) = 1,f(1) = 2 andf
0
(0) = 0. If there exists
M > 0 such thatjf
00
(z)jM for allz2C, thenf(2) =
(A) 2 (B) 5 (C) 2 + 5i (D) 5 + 2i
Q.3 In the Laurent series expansion of f(z) =
1
z(z 1)
valid forjz 1j> 1; the coef?cient of
1
z 1
is
(A) 2 (B) 1 (C) 0 (D) 1
Q.4 LetX andY be metric spaces, and letf :X!Y be a continuous map. For any subsetS of
X; which one of the following statements is true?
(A) IfS is open, thenf(S) is open
(B) IfS is connected, thenf(S) is connected
(C) IfS is closed, thenf(S) is closed
(D) IfS is bounded, thenf(S) is bounded
Q.5 The general solution of the differential equation
xy
0
=y +
p
x
2
+y
2
forx> 0
is given by (with an arbitrary positive constantk)
(A) ky
2
=x +
p
x
2
+y
2
(B) kx
2
=x +
p
x
2
+y
2
(C) kx
2
=y +
p
x
2
+y
2
(D) ky
2
=y +
p
x
2
+y
2
MA 1/10
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 MATHEMATICS
Q.1Q.25carryonemarkeach
Q.1 The principal value of (1)
(2i=)
is
(A) e
2
(B) e
2i
(C) e
2i
(D) e
2
Q.2 Letf :C!C be an entire function withf(0) = 1,f(1) = 2 andf
0
(0) = 0. If there exists
M > 0 such thatjf
00
(z)jM for allz2C, thenf(2) =
(A) 2 (B) 5 (C) 2 + 5i (D) 5 + 2i
Q.3 In the Laurent series expansion of f(z) =
1
z(z 1)
valid forjz 1j> 1; the coef?cient of
1
z 1
is
(A) 2 (B) 1 (C) 0 (D) 1
Q.4 LetX andY be metric spaces, and letf :X!Y be a continuous map. For any subsetS of
X; which one of the following statements is true?
(A) IfS is open, thenf(S) is open
(B) IfS is connected, thenf(S) is connected
(C) IfS is closed, thenf(S) is closed
(D) IfS is bounded, thenf(S) is bounded
Q.5 The general solution of the differential equation
xy
0
=y +
p
x
2
+y
2
forx> 0
is given by (with an arbitrary positive constantk)
(A) ky
2
=x +
p
x
2
+y
2
(B) kx
2
=x +
p
x
2
+y
2
(C) kx
2
=y +
p
x
2
+y
2
(D) ky
2
=y +
p
x
2
+y
2
MA 1/10
GATE 2018 MATHEMATICS
Q.6 Letp
n
(x) be the polynomial solution of the differential equation
d
dx
[(1x
2
)y
0
] +n(n + 1)y = 0
withp
n
(1) = 1 forn = 1; 2; 3;:::: If
d
dx
[p
n+2
(x)p
n
(x)] =
n
p
n+1
(x);
then 
n
is
(A) 2n (B) 2n + 1 (C) 2n + 2 (D) 2n + 3
Q.7 In the permutation groupS
6
; the number of elements of order 8 is
(A) 0 (B) 1 (C) 2 (D) 4
Q.8 LetR be a commutative ring with 1 (unity) which is not a ?eld. Let I R be a proper ideal
such that every element ofR not inI is invertible inR: Then the number of maximal ideals of
R is
(A) 1 (B) 2 (C) 3 (D) in?nite
Q.9 Letf :R!R be a twice continuously differentiable function. The order of convergence of
the secant method for ?nding root of the equationf(x) = 0 is
(A)
1 +
p
5
2
(B)
2
1 +
p
5
(C)
1 +
p
5
3
(D)
3
1 +
p
5
Q.10 The Cauchy problem uu
x
+yu
y
=x withu(x; 1) = 2x; when solved using its characteristic
equations with an independent variablet; is found to admit of a solution in the form
x =
3
2
se
t

1
2
se
t
; y =e
t
; u =f(s;t):
Thenf(s;t) =
(A)
3
2
se
t
+
1
2
se
t
(B)
1
2
se
t
+
3
2
se
t
(C)
1
2
se
t

3
2
se
t
(D)
3
2
se
t

1
2
se
t
Q.11 An urn contains four balls, each ball having equal probability of being white or black. Three
black balls are added to the urn. The probability that ?ve balls in the urn are black is
(A) 2=7 (B) 3=8 (C) 1=2 (D) 5=7
MA 2/10