# GATE-CS-2017 (Set 1)

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Question 1 |

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

24 | |

27 | |

32 | |

36 |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 1 Explanation:

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

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

**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 ?

Rahul and Murali | |

Srinivas and Arul | |

Srinivas and Murali | |

Srinivas and Rahul |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 3 |

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

money beside | |

beside money
| |

money besides | |

besides money |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 3 Explanation:

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

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

0.3 ^{k} | |

0.6 ^{k} | |

0.7 ^{k} | |

0.9 ^{k} |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 4 Explanation:

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.

was wishing | |

is wishing | |

wished | |

had wished |

**GATE-CS-2017 (Set 1)**

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Question 5 Explanation:

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

2 | |

3 | |

4 | |

Can not be determined |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 6 Explanation:

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**

**option A**(only 2 women) is correctQuestion 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?

Nationalists are highly imaginative | |

History is viewed through the filter of nationalism | |

Our colonial past never happened | |

Nationalism has to be both adequately and properly imagined |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 7 Explanation:

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

the maximum of x and y | |

the minimum of x and y | |

1 | |

none of the above |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 8 Explanation:

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,

Note that you can take some random values of x and y, then verify given options.

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)

**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?

P,Q | |

P,Q,T | |

R,S,T | |

Q,R,S |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 9 Explanation:

Given data - height of all villages

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

- R <500m
- 425m<= S<=450m
- 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?

21 | |

18 | |

16 | |

14 |

**GATE-CS-2017 (Set 1)**

**Discuss it**

Question 10 Explanation:

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

**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.
There are 65 questions to complete.