GATE-CS-2017 (Set 2)

Question 1
A test has questions worth 100 marks totals. There are two types of questions, multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?
A
12
B
15
C
18
D
19
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Question 1 Explanation: 
Let us consider all choices :

Choice A : 12 [Wrong] 
There is no integer x that satisfies below equation
12 * 3  + x * 11 = 100
x = 64/11 [Which is not an integer]

Choice B : 15 [Right] 
15 * 3  + x * 11 = 100
x = 55/11  = 5

Choice C : 18 [Wrong] 
There is no integer x that satisfies below equation
18 * 3  + x * 11 = 100
x = 46/11 [Which is not an integer]

Choice C : 19 [Wrong] 
There is no integer x that satisfies below equation
19 * 3  + x * 11 = 100
x = 43/11 [Which is not an integer] 
Question 2
There are 5 buildings called V, W, X, Y, Z in a row (not necessarily in order). V is to the West of W, Z is to the East of X and the West of V. W is to West of Y. Which building is in the middle?
A
V
B
W
C
X
D
Y
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Question 2 Explanation: 
V is to the West of W,
V

W
Z is to the East of X and the West of V.
X

Z

V

W
W is to West of Y.
X

Z

V

W

Y
Therefore, V is in middle. So option A is correct.
Question 3
Saturn is __________ to be seen on a clear night with the naked eye?
A
enough bright
B
bright enough
C
as enough bright
D
bright as enough
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Question 3 Explanation: 
With adjectives and adverbs, enough comes after adjectives and adverbs.
With nouns, enough comes before noun.
In the given question, enough is used with bright which is an adjective, so enough will come after the adjective.
So bright enough is the correct option.
This explanation has been contributed by Parul Sharma.
Question 4
There are 3 red socks, 5 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same color is
A
1/5
B
7/30
C
1/4
D
4/15
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Question 4 Explanation: 
Ways to collect both Red = 3C2
Ways to collect both Green = 3C2
Ways to collect both Blue = 5C2

Total Ways = 10C2

P(Socks of Same Colour) = (3C2 + 5C2+ 3C2 ) /  10C2

= 4/15 
Therefore, Option D is correct
Question 5
Chose the option with words that are not synonyms.
A
aversion, dislike
B
luminous, radiant
C
plunder, loot
D
yielding, resistant
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Question 5 Explanation: 
  • Yield - produce or provide
  • Resistance - the refusal to accept or comply with something. Rest are all synonyms. Hence, (D) is correct.
Question 6
The numbers of the roots of ex + 0.5x2 -2 = 0 in the range [-5, 5] are
A
0
B
1
C
2
D
3
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Question 6 Explanation: 
The given function is a continuous function in range [-5, 5]. The Intermediate Value Theorem states if a continuous function has values of opposite sign inside an interval, then it has a root in that interval. The function changes sign twice in range [-5, 5].
  1. It becomes positive to negative in range [-5, 0] when ex + 0.5x2 becomes less than 2.
  2. It becomes positive to negative in range [0, 5] when ex + 0.5x2 becomes more than 2.
Question 7
There are three boxes, one contains apples, another contains oranges and last one contains both apples and oranges. All three are known to be incorrectly labelled. You are permitted to open just one box and then pull out and inspect only one fruit. Which box would you open to determine the contents of all three boxes?
A
The box labelled apples
B
The box labelled both apples and oranges
C
The box labelled oranges
D
can't be determined
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Question 7 Explanation: 
In given question there are three boxes incorrectly labeled:
  • Box 3 labeled as Apples and Oranges - Original Content can be Apple or Orangle (This box will have only one fruit, so whichever we pick would  be the correct label). Let's say the picked item was Apple, therefore the box labeled Orange will have Apples and Oranges.)
  • Box 2 - Oranges - This box will definitely not have orange (as its mislabeled) and it can not contain only apple (As it is in box 3) - So this will have Original Content- both oranges and Apples
  • Box 1 - Apples - This is the leftover box and it can now have Original Content - Orange
Therefore option B is correct
Question 8
X is 30 digit number starting with 4 followed 7. Then number X3 will have
A
90 digits
B
91 digits
C
92 digits
D
93 digits
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Question 8 Explanation: 
X = 4777....(till 30 digits)

or X = 4.7777⋯ ∗ 1029

X29 = (4.777⋯∗1029 )
  = (4.777…)∗ 10 87

So, (X3 ) requires 3 + 87 = 90 digits. 
Therefore, option A
Question 9
"We lived in culture and denied any merit to literally works, Considering them important only when they were handmaidens to something seemingly more urgent - namely ideology. This was a country where all gestures even the most private , interpreted as political terms." The author's believes that ideology is not as important as literature is revealed by the word :
A
culture
B
seemingly
C
urgent
D
political
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Question 10
An air pressure contour line join the locations in the region having the same atmospheric pressure. The following is the air pressure contour of a geographical region. The contour line are shown as 0.05 bar intervals in this plot. aptitute_1 If the probability of thunderstorm is given by how fast air pressure rises or drops over a region. Which of the following region is most likely to have thunderstorm.
A
P
B
Q
C
R
D
S
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Question 10 Explanation: 
Region R has maximum air pressure variation as it  which has maximum number of lines crossing the area. Therefore option C is correct

Alternate Solution
We have to see for the region which has maximum change in air pressure for thunderstorm.
In region P – the air pressure changes only once by 0.05 as only 2 lines are crossing the region. The first line with the air pressure 0.95 and the next one is with pressure 0.9.
In region Q – No line crosses the region which implies that the air pressure doesn’t change.
In region R – the air pressure changes at 4 places resulting in maximum change in air pressure in the whole region. The minimum pressure in R is 0.65 and the maximum is 0.8.
In region S – the air pressure in the region in 0.95 and other contouring line is outside the region thus no change in air pressure within the region.
Thus the probability of thunderstorm is maximum in region R. This solution is contributed by Parul Sharma.
There are 65 questions to complete.

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