GATE-CS-2016 (Set 1)

Question 1

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.

• A. I will not leave the place until the minister does not meet me.
• B. I will not leave the place until the minister doesn’t meet me.
• C. I will not leave the place until the minister meet me.
• D. I will not leave the place until the minister meets me

Answer: (D)

GATE-CS-2016 (Set 1)
Discuss it

Not is already embedded in until. So, A and B are incorrect.   Also, the minister is a single person, and with a singular subject, singular verb follows(ending in 's'). Thus, C is incorrect and D is the right answer.

Question 2

A rewording of something written or spoken is a ______________.

• A. paraphrase
• B. paradox
• C. paradigm
• D. paraffin

Answer: (A)

GATE-CS-2016 (Set 1) English
Discuss it

Paraphrase - To express something in different words so that it becomes easy for the listener to understand.   Paradox - A statement which sounds logical, but proves to be illogical when investigated.   Paradigm - A way of looking or thinking (perception) about something.   Paraffin - A flammable substance used in candles, polishes, etc.   So, A is the correct choice.

Question 3

Archimedes said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world.” The sentence above is an example of a ___________ statement.

• A. figurative
• B. collateral
• C. literal
• D. figurine

Answer: (A)

GATE-CS-2016 (Set 1) English
Discuss it

Here, we are talking about figure of speech So, figurative is figure of speech meaning: Use of metamorphic meaning of words to explain your thoughts instead of literal use of them. This solution is contributed by Mohit Gupta.

Question 4

If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?

• A. zentaga
• B. tagafer
• C. tagazen
• D. relffer

Answer: (C)

GATE-CS-2016 (Set 1) General Aptitude
Discuss it

'taga' and 'care' are a matching pair in every combination. So, 'taga' surely represents 'care'.   Also, note here that the second half of the word in encoded value refers to the first half of the word in the decoded value. So, 'fer' represents 'less', 'relf' represents 'free' and 'o' represents 'full'.   Going by the same logic, the answer would be tagazen, i.e., C.

Question 5

A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is __________.

• A. 56
• B. 64
• C. 72
• D. 96

Answer: (D)

GATE-CS-2016 (Set 1) General Aptitude
Discuss it

The surface area of the body will remain unchanged as when a cube is removed, it exposes three faces, which makes the number of exposed faces same as before removal.   So, surface area of the body before removal = surface area of the body after removal = 6 * side * side = 6 * 4 * 4 = 96.   Thus, D is the correct choice.

Question 6

A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year.     Which product contributes the greatest fraction to the revenue of the company in that year?

• A. Elegance
• B. Executive
• C. Smooth
• D. Soft

Answer: (B)

GATE-CS-2016 (Set 1) General Aptitude
Discuss it

Revenue from Elegance = (27300+25222+28976+21012) * Rs. 48 = Rs. 4920480 Revenue from Smooth = (20009+19392+22429+18229) * Rs. 63 = Rs. 5043717 Revenue from Soft = (17602+18445+19544+16595) * Rs. 78 = Rs. 5630508 Revenue from Executive = (9999+8942+10234+10109) * Rs. 173 = Rs. 6796132 Total Revenue = Rs. 22390837   Fraction of Revenue for Elegance = 0.219 Fraction of Revenue for Smooth = 0.225 Fraction of Revenue for Soft = 0.251 Fraction of Revenue for Executive = 0.303   Thus, B (Executive) is the correct answer.

Question 7

Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is. Which of the following can be logically inferred from the above sentences?

• A. India is a country of exactly seventeen languages.
• B. Linguistic pluralism is the only indicator of a nation’s diversity.
• C. Indian currency notes have sufficient space for all the Indian languages.
• D. Linguistic pluralism is strong evidence of India’s diversity.

Answer: (D)

GATE-CS-2016 (Set 1) General Aptitude
Discuss it

A is incorrect as it cannot be inferred that exactly 17 languages are there, because the statement says that there are atleast 17 languages on the currency note.   B is incorrect because of the word 'only' in the option, which is too strong to be inferred.   C is incorrect as it says 'space for all Indian languages', but the number of languages in India is not mentioned in the question.   D is correct as it can be easily inferred from the statement.

Question 8

Consider the following statements relating to the level of poker play of four players P, Q, R, and S.

I    P always beats Q
II.  R always beats S
III. S loses to P only sometimes
IV.  R always loses to Q 

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set 

• A. (i) only
• B. (ii) only
• C. (i) and (ii)
• D. neither (i) nor (ii)

Answer: (D)

GATE-CS-2016 (Set 1) General Aptitude
Discuss it

All three can Beat S, but S loses to P only sometimes. So, (ii) can not be inferred from the given statements. Defeating in Poker is not transitive. P beats Q. Q beats R and R beats S. Yet S loses to P only sometimes, meaning that S mostly wins against P. So we can not logically infer that P is likely to beat R.

Question 9

If f(x) = 2x⁷ + 3x - 5 Which of the following is a factor of f(x)?

• A. (x³ + 8)
• B. (x - 1)
• C. (2x - 5)
• D. (x + 1)

Answer: (B)

GATE-CS-2016 (Set 1) General Aptitude
Discuss it

f(x) = 2x7 + 3x - 5
     = 2x7 - 2x + 5x - 5

Putting x = 1, we get f(x) = 0. So, x-1 is a factor of f(x).   Thus, B is the correct choice.

Question 10

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.

• A. 40.00
• B. 46.02
• C. 60.01
• D. 92.02

Answer: (B)

GATE-CS-2016 (Set 1) General Aptitude
Discuss it

For exponential dependence we must have functions of form
f(x) = a.(k power x) : a,k are constants and f(0)=a

Let us assume: C = cycles for failure ; L = Load; a, k = constants
according to question C is an exponential function of L
Hence we can say,

1) C = a x (k^L) ---- > in case C is increasing exponentially
2) C = a / (k^L) ---- > in case C is decreasing exponentially

we take 2nd equation and apply log to both side we get:

log C + L x (log k) = log a ...... by logarithmic property

given (C=100 for L=80) and (C=10000 for L=40)
apply these to values to above equation, this gives us 2 equations
and 2 variables:

log a = log 100 + (80 x log k)...............(1)
log a = log 10000 + (40 x log k)...........(2)

we have 2 variables and 2 equations hence we find
log a = 6
log k= 1/20

now find, [ L = (log a - log C) / (log k) ] for C=5000 cycles

=> L = (6 - log 5000)*20 = 46.0206 ~ 46.02 => [ANS]