GATE-CS-2017 (Set 1)

Question 1

Find the smallest number y such that y x 162 (y multiplied by 162) is a perfect cube.

• A. 24
• B. 27
• C. 32
• D. 36

Answer: (D)

GATE-CS-2017 (Set 1)
Discuss it

162 = 3 * 3 * 3 * 3 * 2 To make it a perfect cube, we need at least 2 * 2 * 3 * 3 which is 36.

Alternate Solution

Take the prime factor of 162: 162 = 2 * 81 = 2 * 9 * 9 = 2 * 3 * 3 * 3 * 3, now if we add minimum two 2 and two 3, then it will be perfect cube of a number. Therefore, the value of y will be = 2 * 2 * 3 * 3 = 4 * 9 = 36 Note that you can multiple 162 with values in given options, then take cube root with the help of calculator for each option, the answer should be an integer. This explanation has been contributed by Mithlesh Upadhyay

Question 2

Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other ?

• A. Rahul and Murali
• B. Srinivas and Arul
• C. Srinivas and Murali
• D. Srinivas and Rahul

Answer: (C)

GATE-CS-2017 (Set 1)
Discuss it

Assume, they are looking to the center of circular table, then the possible arrangement is:

Question 3

Research in the workplace reveals thatpeople work for many reasons _________.

• A. money beside
• B. beside money
• C. money besides
• D. besides money

Answer: (D)

GATE-CS-2017 (Set 1)
Discuss it

Grammatically, besides is an adverb or a preposition, and beside a preposition. Beside means next to. As a preposition, besides means in addition to or apart from. As an adverb, besides means as well or furthermore.
Here, we use "besides" as a preposition meaning "in addition to".
"besides money" is correct choice. This explanation is contributed by Mithlesh Upadhyay.

Question 4

The probability that a k-digit number does NOT contain the digits 0, 5 or 9 is

• A. 0.3^k
• B. 0.6^k
• C. 0.7^k
• D. 0.9^k

Answer: (C)

GATE-CS-2017 (Set 1)
Discuss it

For 10 digits(0 to 9) total possible cases = (10)^k
Excluding digits 0, 5, 9, total possible cases = (7)^k with numbers 1,2,3,4,6,7,8
Required probability = (7)^k/(10)^k= (0.7)^k
Therefore option C is correct

Alternate Solution
Case(1): When 0 can not be as left most digit:
Then sample space = 9 * 10^{k-1}
Favorable event = 7^{k}
Required probability = ( 7^{k} ) / ( 9 * 10^{k-1}).
None option matches.
Case(2): When 0 can be as left most digit:
Then sample space = 10^{k}
Favorable event = 7^{k}
Required probability = ( 7^{k} ) / ( 10^{k} ) = (7/10)^{k} = (0.7)^{k}.
Option (c) matches.

This solution is contributed by Mithlesh Upadhyay

Question 5

After Rajendra Chola returned from his voyage to Indonesia, he ______ to visit the temple in Tanjavur.

• A. was wishing
• B. is wishing
• C. wished
• D. had wished

Answer: (C)

GATE-CS-2017 (Set 1)
Discuss it

According to the rule : when the main clause is in the past or past perfect tense, the subordinate clause must be in the past or past perfect tense.

Question 6

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

• A. 2
• B. 3
• C. 4
• D. Can not be determined

Answer: (A)

GATE-CS-2017 (Set 1)
Discuss it

Let's draw what these statements say:

• There are atleast Two Men and Two Women.
• There are atleast 3 Right Handed People
• No women are Right Handed - infers there are three right handed men
• Every woman has a left-handed person to her immediate right - Means women circled in red needs to have a left handed person on her right and that too a man as on right side of ?? there is a right handed man.
• So,  ?? - will be a left handed man

  Therefore, option A (only 2 women) is correct

Question 7

"The hold of the nationalist imagination on our colonial past is such that 
anything inadequately or improperly natinalist is just not history"

Which of the following statements best reflects the author's opinion?

• A. Nationalists are highly imaginative
• B. History is viewed through the filter of nationalism
• C. Our colonial past never happened
• D. Nationalism has to be both adequately and properly imagined

Answer: (B)

GATE-CS-2017 (Set 1)
Discuss it

The author is trying to say that everything related to colonial past has a hold of nationalism in people’s imagination. It is not necessary that anything which is represented inadequately is the history. History and nationalism has a strong connection, but sometimes history is viewed with nationalism in mind. This is the author’s opinion. This explanation has been provided by Sonal Kukreja.

Question 8

The expression [ (x + y) - |x - y| ] / 2 is equal to

• A. the maximum of x and y
• B. the minimum of x and y
• C. 1
• D. none of the above

Answer: (B)

GATE-CS-2017 (Set 1)
Discuss it

As we know that, if x > y, then |x - y| = x - y and
if x < y then |x - y| = y - x , because value of |x - y| is always non-negative.
Therefore,

• Case 1: If x > y : (x + y) - |x - y| ] / 2 =  (x + y) - (x - y) ] / 2 = 2y / 2 = y (Minimum of x , y)
• Case 2: If x < y : (x + y) - |x - y| ] / 2 = (x + y) - (y - x) ] / 2 = 2x / 2 = x (Minimum of x , y)

Therefore in both the case we get minimum of (x,y). So, option B
Note that you can take some random values of x and y, then verify given options.

Question 9

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot. If in a flood, the water level rises to 525 m, which of the villages P, Q, R, S, T get submerged?

• A. P,Q
• B. P,Q,T
• C. R,S,T
• D. Q,R,S

Answer: (C)

GATE-CS-2017 (Set 1)
Discuss it

Given data - height of all villages

• P = 575
• Q = 525
• R = 475
• S = 425
• T = 500

Villages  below the flood level - 525m are

1. R <500m
2. 425m<= S<=450m
3. 500m <=T<= 525m

Therefore option C is correct.

Question 10

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

• A. 21
• B. 18
• C. 16
• D. 14

Answer: (D)

GATE-CS-2017 (Set 1)
Discuss it

Total number of Shirts = 4 , Total candidates =4

• So total combination of possibilities = 4 X 4 = 16
• No.of ways  'Arun chooses red' + No.of ways Shwetha chooses white '=  2

Therefore, Answer is 16-2 = 14. Alternative approach - We can solve using inclusion-exclusion: Total possibilities = 4! = 24 Number of ways 'Arun chooses red' or 'Shwetha chooses white' = (Number of ways 'Arun chooses red) + (Number of ways 'Shwetha chooses white) - (Number of ways 'Arun chooses red' and 'Shwetha chooses white) = 6 + 6 − 2 = 10 Required answer = 24 − 10 = 14.