GATE 2018 Engineering Mathematics (XE-A) Question Paper with Answer

GATE 2018 General Aptitude (GA) Set-1

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 m2 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 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of
𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3 (B) -1 and 1 (C) -1 and 3 (D) 1 and 3

GA 1/2

GATE 2018 General Aptitude (GA) Set-1
Q.7 Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏 3 is odd, which one of the following
statements is correct?

(A) 𝑎 and 𝑏 are both odd (B) 𝑎 and 𝑏 are both even
(C) 𝑎 is even and 𝑏 is odd (D) 𝑎 is odd and 𝑏 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) 𝑦 = ||𝑥| + 1| − 2 (B) 𝑦 = ||𝑥| − 1| − 1
(C) 𝑦 = ||𝑥| + 1| − 1 (D) 𝑦 = ||𝑥 − 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

GA 2/2

GATE 2018 Engineering Mathematics (XE-A)

XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each.

Q.1 The largest interval in which the initial value problem

ex
d2y
dx 2

1 dy
 x  5 dx
  x  y  ln  x  , y (1) = 0 and
dy
dx
1  1,

has a unique solution is

(A) ( ,  ) (B) ( 5, 5) (C) (0, ) (D) (0, 5)

Q.2 The sum of the roots of the indicial equation at x  0 of the differential equation

d2y dy
x3 2
  x sin x   (tan x) y  0, x  0,
dx dx
is
(A) 0 (B) 1 (C) 2 (D) 2

Q.3 Let f be a three times continuously differentiable real valued function on (0, 5) such that
1
its third derivative f ( x)  for all x  (0, 5). If P ( x ) is a polynomial of degree  2
100
such that P(1)  f (1), P(2)  f (2) and P(3)  f (3) then | f (4)  P(4) |
equals _______________

Q.4 1
For real numbers  1 and  2 , if the formula 1 f ( x) dx  1 f  21   2 f  12  is exact for
all polynomials of degree  1 then 21  3 2 equals _______________

Q.5 Raju has four fair coins and one fair dice. At first Raju tosses a coin. If the coin shows head
then he rolls the dice and the number that dice shows is taken as his score. If the coin
shows tail then he tosses three more coins and the total number of tails shown (including
the first one) is taken as his score. If Raju tells that his score is 2 then the probability that
he rolled the dice is (up to two decimal places) _______________

Q.6 Let f be a continuously differentiable real valued function defined by
bx  a if x  1,
f ( x)   2
 5x if x  1.
Then the value of a 2 b is _______________

XE-A 1/2

GATE 2018 Engineering Mathematics (XE-A)

Q.7 A rectangular box without top cover having a square base is to be made from a sheet of
108 square meters. Then the largest possible volume of the box in cubic meters
is ______________

Q.8  5 3 
Let A   1000
 . Then the trace of A equals
 6 4 
(A) 21000  1 (B) 21000  1 (C) 1 (D) 21000

Q.9 Let denote the set of complex numbers and i 2  1. Let  be the simple positively
oriented circle | z |  1 and S   z  0  | z |  2 . If f : S  is analytic in S and is
given by

1 7
f ( z)     an z n , z  S
8 z 2 2 z n 0

then the value of the contour integral
 ez 

1
  f ( z )  dz
i
 
cos z
is
1 7
(A) 0 (B) (C) 7 (D)
8 2

Q.10 Let 3
denote the three dimensional Euclidean space and F( x, y, z )   y iˆ  x ˆj  z kˆ for all
( x, y, z )  3 . If C is the curve described by the parametric equation
r (t )  cos t iˆ  sin t ˆj  2t 2 kˆ, 0  t  1, then the value of the line integral F  dr 
C
is_______________

Q.11 Let u ( x, t ) satisfy the initial and boundary value problem
u  2u
2 2, 0  x   , t  0,
t x
u (0, t )  0  u ( , t ), t  0,
u ( x, 0)  sin x  2sin 4 x, 0  x  .

 
Then the value of u  , ln(5)  is_______________
2 

END OF THE QUESTION PAPER
XE-A 2/2

Q.No. Type Section Key/Range Marks

1 MCQ GA A 1

2 MCQ GA C 1

3 MCQ GA B 1

4 MCQ GA B 1

5 MCQ GA B 1

6 MCQ GA A 2

7 MCQ GA D 2

8 MCQ GA D 2

9 MCQ GA B 2

10 MCQ GA C 2

1 MCQ XE‐A D 1

2 MCQ XE‐A A 1

3 NAT XE‐A 0.01 to 0.01 1

4 NAT XE‐A 5 to 5 1

5 NAT XE‐A 0.29 to 0.32 1

6 NAT XE‐A 250 to 250 1

7 NAT XE‐A 108 to 108 1

8 MCQ XE‐A B 2

9 MCQ XE‐A C 2

10 NAT XE‐A 3 to 3 2

11 NAT XE‐A 0.04 to 0.04 2

1 MCQ XE‐B B 1

2 MCQ XE‐B A 1

Q.No. Type Section Key/Range Marks

3 MCQ XE‐B D 1

4 MCQ XE‐B A 1

5 MCQ XE‐B C 1

6 MCQ XE‐B B 1

7 MCQ XE‐B A 1

8 NAT XE‐B 4 to 4 1

9 NAT XE‐B 39 to 42 1

10 MCQ XE‐B B 2

11 MCQ XE‐B C 2

12 MCQ XE‐B C 2

13 MCQ XE‐B A 2

14 NAT XE‐B 900 to 990 2

15 NAT XE‐B 40 to 42 2

16 NAT XE‐B 2.9 to 3.1 2

17 NAT XE‐B 107 to 127 2

18 NAT XE‐B 440000 to 442000 2

19 NAT XE‐B 0.001 to 0.002 2

20 NAT XE‐B 30 to 45 2

21 NAT XE‐B 4800 to 4800 2

22 NAT XE‐B 1200 to 1350 2

1 MCQ XE‐C C 1

2 MCQ XE‐C A 1

3 MCQ XE‐C B 1

Q.No. Type Section Key/Range Marks

4 MCQ XE‐C C 1

5 MCQ XE‐C A 1

6 MCQ XE‐C D 1

7 MCQ XE‐C C 1

8 NAT XE‐C 2 to 2 1

9 NAT XE‐C 6 to 6 1

10 MCQ XE‐C B 2

11 MCQ XE‐C A 2

12 MCQ XE‐C B 2

13 NAT XE‐C 430 to 500 2

14 NAT XE‐C 124 to 124 2

15 NAT XE‐C 2.60 to 2.70 2

16 NAT XE‐C 59.00 to 60.00 2

17 NAT XE‐C 1.85 to 2.00 2

18 NAT XE‐C 132 to 132 2

19 NAT XE‐C 5.01 to 5.17 2

20 NAT XE‐C 5 to 5 2

21 NAT XE‐C 15.5 to 18.5 2

22 NAT XE‐C 1420 to 1480 2

1 MCQ XE‐D D 1

2 MCQ XE‐D A 1

3 MCQ XE‐D D 1

4 MCQ XE‐D B 1

Q.No. Type Section Key/Range Marks

5 MCQ XE‐D B 1

6 NAT XE‐D 52.50 to 53.50 1

7 NAT XE‐D 27.00 to 28.00 1

8 NAT XE‐D 80 to 80 1

9 NAT XE‐D 220.00 to 222.00 1

10 MCQ XE‐D B 2

11 MCQ XE‐D B 2

12 MCQ XE‐D D 2

13 MCQ XE‐D C 2

14 MCQ XE‐D C 2

15 MCQ XE‐D A 2

16 MCQ XE‐D D 2

17 NAT XE‐D 195.00 to 197.00 2

18 NAT XE‐D 0.01 to 0.02 2

19 NAT XE‐D 14.5 to 15.5 2

20 NAT XE‐D 26.00 to 27.00 2

21 NAT XE‐D 3.10 to 3.20 2

22 NAT XE‐D 13.5 to 14.5 2

1 MCQ XE‐E B 1

2 MCQ XE‐E A 1

3 MCQ XE‐E C 1

4 MCQ XE‐E A 1

5 MCQ XE‐E C 1

Q.No. Type Section Key/Range Marks

6 MCQ XE‐E D 1

7 NAT XE‐E 160.0 to 161.0 1

8 NAT XE‐E 14.5 to 15.0 1

9 NAT XE‐E 0.30 to 0.32 1

10 MCQ XE‐E C 2

11 MCQ XE‐E C 2

12 MCQ XE‐E D 2

13 MCQ XE‐E B 2

14 MCQ XE‐E A 2

15 MCQ XE‐E D 2

16 NAT XE‐E 332.5 to 336.5 2

17 NAT XE‐E 3.01 to 3.07 2

18 NAT XE‐E 838.0 to 844.0 2

19 NAT XE‐E 961.0 to 962.0 2

20 NAT XE‐E 5.7 to 6.1 2

21 NAT XE‐E 12950.0 to 13000.0 2

22 NAT XE‐E 513.0 to 517.0 2

1 MCQ XE‐F C 1

2 MCQ XE‐F A 1

3 MCQ XE‐F D 1

4 MCQ XE‐F B 1

5 MCQ XE‐F D 1

6 MCQ XE‐F B 1

Q.No. Type Section Key/Range Marks

7 MCQ XE‐F A 1

8 NAT XE‐F 1500.00 to 1500.00 1

9 NAT XE‐F 48.52 to 48.72 1

10 MCQ XE‐F D 2

11 MCQ XE‐F A 2

12 MCQ XE‐F B 2

13 MCQ XE‐F D 2

14 MCQ XE‐F B 2

15 MCQ XE‐F D 2

16 MCQ XE‐F C 2

17 MCQ XE‐F C 2

18 NAT XE‐F ‐25.00 to ‐24.50 2

19 NAT XE‐F 98.80 to 99.10 2

20 NAT XE‐F 0.90 to 0.93 2

21 NAT XE‐F 17.91 to 18.00 2

22 NAT XE‐F 2600 to 2600 2

1 MCQ XE‐G B 1

2 MCQ XE‐G A 1

3 MCQ XE‐G C 1

4 MCQ XE‐G D 1

5 MCQ XE‐G D 1

6 NAT XE‐G 1.55 to 1.65 1

7 NAT XE‐G 103.0 to 103.2 1

Q.No. Type Section Key/Range Marks

8 NAT XE‐G 54 to 56 1

9 NAT XE‐G 0 to 0 1

10 MCQ XE‐G B 2

11 MCQ XE‐G C 2

12 MCQ XE‐G C 2

13 MCQ XE‐G A 2

14 MCQ XE‐G D 2

15 MCQ XE‐G A 2

16 MCQ XE‐G C 2

17 MCQ XE‐G B 2

18 NAT XE‐G 9.8 to 10.2 2

19 NAT XE‐G 1.1 to 1.8 2

20 NAT XE‐G 14.5 to 15.5 2

21 NAT XE‐G 6.0 to 6.4 2

22 NAT XE‐G 10 to 10 2

1 MCQ XE‐H B 1

2 MCQ XE‐H C 1

3 MCQ XE‐H A 1

4 MCQ XE‐H B 1

5 MCQ XE‐H B 1

6 MCQ XE‐H C 1

7 MCQ XE‐H D 1

8 MCQ XE‐H D 1

Q.No. Type Section Key/Range Marks

9 MCQ XE‐H B 1

10 MCQ XE‐H A 2

11 MCQ XE‐H B 2

12 MCQ XE‐H A 2

13 MCQ XE‐H B 2

14 NAT XE‐H 1254 to 1256 2

15 NAT XE‐H 19.42 to 19.44 2

16 NAT XE‐H 734.8 to 735.0 2

17 NAT XE‐H 9.16 to 9.18 2

18 NAT XE‐H 12.8 to 13.2 2

19 NAT XE‐H 92.4 to 92.8 2

20 NAT XE‐H 1.3 to 1.4 2

21 NAT XE‐H 0.11 to 0.12 2

22 NAT XE‐H 9.99 to 10.01 2