# GATE CS Mock 2018

• Last Updated : 14 Sep, 2021

 Question 1
Which of the following statement(s) is/are correct?
1. 1 is the remainder when 7^700 is divided by 100.
2. 1 is the remainder when 7^26 is divided by 100.
3. 2 is the remainder when 7^35 is divided by 13.
 A Only (1) B Only (2) C Only (1) and (3) D All (1), (2), and (3)
General Aptitude    Number Divisibility    GATE CS Mock 2018
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Question 1 Explanation:
1. (7^700) mod 100 = 7^(700 mod 100) = 7^0 = 1.
2. Last two digits of 7^1 are 07 Last two digits of 7^2 are 49 Last two digits of 7^3 are 43 Last two digits of 7^4 are 01. This cycle is 7, 9, 3, 1, 7, 9, … And, 26 mod 4 = 2. Therefore, 7^26 = 7^(4n+2) will end in 49. → 7^26 mod 100 = 7^2 mod 100 = 49.
3. (7^35) mod 13 = ((7^12)*(7^12)*(7^11)) mod 13 A^(P-1)/P (where A is any natural number, and P is any prime number which is not a factor of A) will give remainder 1. Therefore, (7^12) mod 13 = 1 So, → (1*1*(7^11)) mod 13 → (7^11) mod 13 → ((7)*(7^10)) mod 13 → ((7)*((7^2)^5)) mod 13 → ((7)*(49^5)) mod 13 → ((7)*((39+10)^5)) mod 13 → ((7)*(10^5)) mod 13 → ((7)*(100*100*10)) mod 13 → ((7)*(9*9*10)) mod 13 → 2
Therefore, only statements (1) and (3) are correct. Option (C) is true.
 Question 2
I haven't worked as a mechanic before, ________ I've been fixing cars since I was a child.
 A always B yet C no longer D already
English    General Aptitude    GATE CS Mock 2018
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Question 2 Explanation:
Always is an adverb of frequency, like never, often, frequently, and usually. Yet is a conjunction meaning nevertheless or however. Yet usually carries a sense of negation, so and yet means the same thing as but still. No longer means not now as formerly; not any more. We use already to show that something has happened sooner than it was expected to happen. Therefore, "yet" is most appropriate choice here. Option (B) is correct.
 Question 3
A dice is thrown. Let A be the event that the number obtained is greater than 5. Let B be the event that the number obtained is less than 5. Then P (AUB) is
 A 5/6 B 2/6 C 3/6 D None of these
Combinatorics    General Aptitude    GATE CS Mock 2018
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Question 3 Explanation:
Since, A{6}, and B{1, 2, 3, 4}. Therefore, A∩B = {∅}. So, P(A∪B) = P(A)+P(B)-P(A∩B) = 1/6 + 4/6 - 0 = 5/6 So, option (A) is correct.
 Question 4
____________ is usually used for something that was done in the past and still applies (multiple events).
 A Had/has/have been B Was/were C Had/was/were D All of the above
English    General Aptitude    GATE CS Mock 2018
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Question 4 Explanation:
Had/has/have been is usually used for something that was done in the past and still applies (multiple events). Was/were usually applies to something done in the past that no longer applies (single event). So, option (A) is correct.
 Question 5
Ram is smarter than Mohan. Rakesh is smarter than Ramu and Mohini is smarter than Rakesh. Which of the following is a set(s) of additional information that can determine the smartest person?
```(I) Mohini is smarter than Ram and Mohan is smarter than Rakesh.
(II) Mohan is smarter than Mohini.
(III) Ram is smarter than Mohini.
```
 A Only (II) B Only (III) C Either (I) or (II) D None of these
English    General Aptitude    GATE CS Mock 2018
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Question 5 Explanation:
It is given that : Ram is smarter than Mohan, (i.e., Ram > Mohan). Rakesh is smarter than Ramu and Mohini is smarter than Rakesh (Mohni > Rakesh > Ramu). Our purpose is to add more possible set(s) of additional information that can determine smartest person. With the help of set (I), we can get Mohini as smartest person. With the help of set (II), we can get Ram as smartest person. But we can not conclude smartest person with set (III), because we have ambiguity (can be either Ram or Mohni). So, only set (I) or (II) can decide smartest person. Option (C) is correct.
 Question 6
The long, anxious, and frustrating wait by people outside banks and ATMs across the country over the last five days is an inevitable consequence of the decision to demonetize notes of Rs.500 and Rs.1,000. When 86 per cent of the value of notes in circulation turns suddenly invalid, as it did with Prime Minister Modi’s ‘surgical strike’ last week, a certain degree of disruption and pain is unavoidable. But the question is whether this chaos could have been anticipated and managed better than it has been. Replacement of the demonetized notes is a time-consuming exercise that requires planning of the highest order. The experience of the last few days shows that preparation was lacking and the transition could have been handled much better. Thankfully, the Centre has woken up to ease the pressure on the system by increasing withdrawal limits, allowing for petroleum outlets and hospitals to accept the old series of notes until November 24 and pushing more cash through post offices. Why do you think that the replacement of the demonetized notes is a time-consuming exercise?
 A It takes more than 50 days to replace demonized notes. B Demonetization is a ‘futile exercise’ to target black money and fake currency C The government was lazy enough to issue the decision of demonetization before. D Replacement process requires planning of the highest order and careful implementation.
English    General Aptitude    GATE CS Mock 2018
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Question 6 Explanation:
According to the passage, the demonetization process requires careful thought process, well-chalked out implementation strategies and above all planning of the highest order from the policy makers as well as government. So, option (D) is most appropriate choice.
 Question 7
The long, anxious, and frustrating wait by people outside banks and ATMs across the country over the last five days is an inevitable consequence of the decision to demonetize notes of Rs.500 and Rs.1,000. When 86 per cent of the value of notes in circulation turns suddenly invalid, as it did with Prime Minister Modi’s ‘surgical strike’ last week, a certain degree of disruption and pain is unavoidable. But the question is whether this chaos could have been anticipated and managed better than it has been. Replacement of the demonetized notes is a time-consuming exercise that requires planning of the highest order. The experience of the last few days shows that preparation was lacking and the transition could have been handled much better. Thankfully, the Centre has woken up to ease the pressure on the system by increasing withdrawal limits, allowing for petroleum outlets and hospitals to accept the old series of notes until November 24 and pushing more cash through post offices. Which of the following option is false ?
 A ‘Unconcerned’ is similar in meaning to the word ‘anxious’ as used in the passage. B 'Disorder' is similar in meaning to the word ‘chaos’ as used in the passage. C 'Hardship' is opposite in meaning to the word ‘ease’ as used in the passage. D ‘Shift’ is opposite in meaning to the word ‘transition’as used in the passage.
English    General Aptitude    GATE CS Mock 2018
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Question 7 Explanation:
(A) ‘Unconcerned’ is opposite in meaning to the word ‘anxious’ as used in the passage. (B) ‘Disorder’ word implies that due to the demonetization, citizens all over the country were facing issues with the currency exchange. (C) ‘Hardship’ is the right choice.  (D) ‘shift’ is the right choice. Only option (A) is false.
 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
Numerical Methods and Calculus    General Aptitude    GATE CS Mock 2018
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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, Case 1: If x > y : (x + y) + |x – y| ] / 2 = (x + y) + (x – y) ] / 2 = 2x / 2 = x (Maximum of x , y) Case 2: If x < y : (x + y) + |x – y| ] / 2 = (x + y) + (y – x) ] / 2 = 2y / 2 = y (Maximum of x , y) Therefore, in both the cases we get maximum of (x, y). So, option (A) is correct. Note that you can take some random values of x and y and verify given options.
 Question 9
Study the given graphs to answer these questions. The total production of wheat is 50 lakh tonnes. Production of wheat in different states of India is given : Abbreviations : U.P. = Uttar Pradesh, M.P. = Madhya Pradesh, A.P. = Andhra Pradesh, C.G. = ChhattisGarh.  What is the ratio of production by conventional method in A.P. to that by scientific method in U.P.?
 A 484/949 B 99/260 C 51/260 D 48/77
General Aptitude    Ratio and Proportion    GATE CS Mock 2018
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Question 9 Explanation:
The production by conventional method in A.P. = 50*0.22*0.22 = 2.420 lakh tonne The production by scientific method in U.P. = 50*0.13*0.73 = 4.74500 lakh tonne Hence, the required ratio = 2.420 / 4.74500 = 484/949 So, option (A) is correct.
 Question 10
There are 100 students. 85 choose Math, 80 choose Physics, 75 choose Chemistry, 70 choose Biology. What is the minimum number of students choosing all 4 subjects? Assume each student chosen at least one subject.
 A 15 B 10 C 5 D Data is insufficient
Combinatorics    General Aptitude    GATE CS Mock 2018
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Question 10 Explanation:
Let A,B,C,D ⊂ {1,2,…,100} be the four sets, with |A| = 85, |B| = 80, |C| = 75, |D| = 70. Then we want the minimum size of (A∩B∩C∩D). Combining the fact that |A∩B∩C∩D| = 100 − |A'∪B'∪C'∪D'| where A' refers to A complement, along with the fact that for any sets |X∪Y|≤|Y|+|X| we see that |A∩B∩C∩D| ≥ 100 − |A'|−|B'|−|C'|−|D'| = 10. So, option (B) is correct.l
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