GATE General Aptitude questions with solutions

Q1. If ‘→’ denotes increasing order of intensity, then the meaning of the words [simmer → seethe → smolder] is analogous to [break → raze → ________]. Which one of the given options is appropriate to fill the blank?

1. obfuscate
2. obliterate
3. fracture
4. fissure

Answer: obliterate

The correct option 'obliterate' fits the analogy because it represents a more intense or complete form of destruction, similar to how 'seethe' is a more intense state than 'simmer' and 'smolder' represents a lingering state. Each pair reflects a progression in intensity.

Q2. Which one of the given options is a possible value of x in the following sequence? 3, 7, 15, x, 63, 127, 255

1. 35
2. 40
3. 45
4. 31

Answer: 31

The sequence follows a pattern where each term is one less than a power of 2: 3 (2² - 1), 7 (2³ - 1), 15 (2⁴ - 1), 31 (2⁵ - 1), 63 (2⁶ - 1), 127 (2⁷ - 1), and 255 (2⁸ - 1). Thus, 31 is the only option that fits this pattern.

Q3. On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?

1. 51
2. 49
3. 50
4. 55

Answer: 49

The second-hand and minute-hand of a clock cross each other 49 times in an hour because they align approximately every 1 minute and 5.45 seconds, resulting in 49 crossings within the 50-minute span from 12:05 to 12:55.

Q4. In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. From the ancient Athenian arena to the modern Olympic stadiums, athletics (i) the potential for a spectacle. The crowd (ii) with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to cross-step. Six cross-steps (iii) in an abrupt stop on his left foot. As his body (iv) like a door turning on a hinge, the javelin is launched skyward at a precise angle.

1. (i) hold (ii) waits (iii) culminates (iv) pivot
2. (i) holds (ii) wait (iii) culminates (iv) pivot
3. (i) hold (ii) wait (iii) culminate (iv) pivots
4. (i) holds (ii) waits (iii) culminate (iv) pivots

Answer: (i) holds (ii) waits (iii) culminate (iv) pivots

The correct option uses the singular verb "holds" to agree with the singular subject "athletics," while "waits" matches the singular subject "the crowd." The plural form "culminate" fits with the plural subject "six cross-steps," and "pivots" correctly aligns with the singular subject "body."

Q5. Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin?

1. 12
2. 14
3. 10
4. 28

Answer: 12

To find the unique seating arrangements, we can treat each pair of twins as a single unit or block. With three pairs, we have three blocks to arrange around the circular table, which can be done in (3-1)! = 2! = 2 ways. Each pair can be arranged internally in 2 ways, leading to a total of 2 * 2 * 2 = 8 arrangements. Thus, the total unique arrangements are 2 * 8 = 16, but since we need to account for indistinguishable twins, we divide by 2 for the pairs, resulting in 12 unique arrangements.

Q6. During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Earth-Moon distances is closest to

1. 328
2. 382
3. 238
4. 283

Answer: 382

In a right triangle formed by the Earth, Moon, and Sun during the half-moon phase, the angle of 89.85° indicates that the Earth-Sun distance is significantly larger than the Earth-Moon distance. Using the sine function, the ratio of the distances can be calculated, leading to the conclusion that the closest ratio is approximately 382.

Q7. The probability that a student passes only in Mathematics is 1/3. The probability that the student passes only in English is 4/9. The probability that the student passes in both of these subjects is 1/6. The probability that the student will pass in at least one of these two subjects is

1. 17/18
2. 11/18
3. 14/18
4. 1/18

Answer: 17/18

P(at least one) = P(only Math) + P(only English) + P(both) = 1/3 + 4/9 + 1/6 = 6/18 + 8/18 + 3/18 = 17/18 (option 0), not the stored 11/18.

Q8. Is there any good show ________ television tonight? Select the most appropriate option to complete the above sentence.

1. in
2. at
3. within
4. on

Answer: on

The correct option 'on' is used to indicate that something is being broadcast or available through a medium, in this case, television. It is the standard preposition used to refer to programs or shows that are airing.

Q9. As the police officer was found guilty of embezzlement, he was ________ dismissed from the service in accordance with the Service Rules. Select the most appropriate option to complete the above sentence.

1. sumptuously
2. brazenly
3. unintentionally
4. summarily

Answer: summarily

The term 'summarily' means to dismiss someone immediately and without the usual formalities, which is appropriate in the context of a police officer being found guilty of a serious crime like embezzlement.

Q10. “Why do they pull down and do away with crooked streets, I wonder, which are my delight, and hurt no man living? Every day the wealthier nations are pulling down one or another in their capitals and their great towns: they do not know why they do it; neither do I. It ought to be enough, surely, to drive the great broad ways which commerce needs and which are the life-channels of a modern city, without destroying all history and all the humanity in between: the islands of the past.” (From Hilaire Belloc’s “The Crooked Streets”) Based only on the information provided in the above passage, which one of the following statements is true?

1. The author of the passage takes delight in wondering.
2. The wealthier nations are pulling down the crooked streets in their capitals.
3. In the past, crooked streets were only built on islands.
4. Great broad ways are needed to protect commerce and history.

Answer: The wealthier nations are pulling down the crooked streets in their capitals.

The passage explicitly states that wealthier nations are demolishing crooked streets in their capitals, indicating that this statement accurately reflects the author's observations.

Q11. Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?

1. 64 6/11
2. 66 5/13
3. 65 5/11
4. 66 6/13

Answer: 65 5/11

The hour and minute hands coincide once every 12/11 hours, i.e. 720/11 = 65 5/11 minutes. So the time Rohit spent is 65 5/11 minutes, not 66 5/13.

Q12. “His face ________ with joy when the solution of the puzzle was ________ to him.” The words that best fill the blanks in the above sentence are

1. shone, shown
2. shone, shone
3. shown, shone
4. shown, shown

Answer: shone, shown

The correct option uses 'shone' to describe the face emitting light or happiness, and 'shown' as the past participle of 'show,' indicating that the solution was revealed to him.

Q13. “Although it does contain some pioneering ideas, one would hardly characterize the work as ________.” The word that best fills the blank in the above sentence is

1. innovative
2. simple
3. dull
4. boring

Answer: innovative

The term 'innovative' implies a high level of creativity and originality, which contrasts with the idea of merely containing 'some pioneering ideas.' Thus, the sentence suggests that while there are new concepts, the overall work does not reach the level of being truly innovative.

Q14. a + a + a +... + a (n times) = a² b and b + b + b +... + b (m times) = ab², where a, b, n and m are natural numbers. What is the value of (m + m + m +... + m (n times))(n + n + n +... + n (m times))?

1. 2a²b²
2. a⁴b⁴
3. ab(a + b)
4. a² + b²

Answer: a⁴b⁴

The expressions given simplify to a²b and ab², respectively. When calculating (m times b) and (n times a), we find that multiplying these results leads to a⁴b⁴, as each term contributes to the overall exponentiation of a and b.

Q15. A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?

1. 27
2. 72
3. 81
4. 84

Answer: 84

The number of ways to form a committee of 3 members from 9 people is calculated using the combination formula, which is C(n, r) = (n!)/(r!(n-r)!). Here, n = 9 and r = 3, leading to C(9, 3) = (9!)/(3!(9-3)!) = 84.

Q16. For non-negative integers, a, b, c, what would be the value of a + b + c if log a + log b + log c = 0?

1. 3
2. 1
3. 0
4. −1

Answer: 3

The equation log a + log b + log c = 0 implies that a * b * c = 1, since the logarithm of a product is the sum of the logarithms. For non-negative integers, the only values that satisfy this condition are a = 1, b = 1, and c = 1, leading to a + b + c = 3.

Q17. In manufacturing industries, loss is usually taken to be proportional to the square of the deviation from a target. If the loss is Rs. 4900 for a deviation of 7 units, what would be the loss in Rupees for a deviation of 4 units from the target?

1. 400
2. 1200
3. 1600
4. 2800

Answer: 1600

Loss is proportional to deviation squared: 4900 = c*7^2 gives c = 100. For a deviation of 4, loss = 100*4^2 = 1600 rupees. The stored answer 400 is wrong.

Q18. A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 15th July of the same year?

1. 12:45 PM
2. 12:58 PM
3. 1:00 PM
4. 2:00 PM

Answer: 12:58 PM

The faulty clock gains 15 minutes every 24 hours, which means in the 4 days from 9 AM on July 11 to 2 PM on July 15, it gains a total of 1 hour (15 minutes x 4). Therefore, when the faulty clock shows 2 PM, the actual time is 1 hour earlier, resulting in 12:58 PM.

Q19. Given that (log P)/(y-z)=(log Q)/(z-x)=(log R)/(x-y)=10 for x ≠ y ≠ z, what is the value of the product PQR?

1. 0
2. 1
3. xyz
4. 10^xyz

Answer: 1

The equations imply that log P = 10(y-z), log Q = 10(z-x), and log R = 10(x-y). Adding these gives log P + log Q + log R = 10[(y-z) + (z-x) + (x-y)] = 10(0) = 0, which means log(PQR) = 0, leading to PQR = 10⁰ = 1.

Q20. Each of the letters in the figure below represents a unique integer from 1 to 9. The letters are positioned in the figure such that each of (A + B + C), (C + D + E), (E + F + G) and (G + H + K) is equal to 13. Which integer does E represent?

1. 1
2. 4
3. 6
4. 7

Answer: 4

The sum of the integers in each group must equal 13, and since E is part of multiple groups, it must be a value that allows the other integers to also be unique and fit within the range of 1 to 9. Testing the options, E = 4 allows for valid combinations with the other letters, while maintaining the uniqueness of the integers.

Q21. Daytime temperatures in Delhi can ____ 40°C.

1. get
2. stand
3. reach
4. peak

Answer: reach

The verb 'reach' is appropriate here as it conveys the idea of attaining a specific temperature, which is commonly used in the context of weather.

Q22. The growth rate of ABC Motors in 2017 was the same ______ XYZ Motors in 2016.

1. as off
2. as those of
3. as that off
4. as that of

Answer: as that of

The phrase 'as that of' correctly compares the growth rate of ABC Motors in 2017 to the growth rate of XYZ Motors in 2016, maintaining proper grammatical structure and clarity.

Q23. Suresh wanted to lay a new carpet in his new mansion with an area of 70 × 55 sq. mts. However an area of 550 sq. mts. had to be left out for flower pots. If the cost of carpet is Rs. 50 per sq. mts., how much money (in Rs.) will be spent by Suresh for the carpet now?

1. Rs. 1,65,000
2. Rs. 1,92,500
3. Rs. 2,75,000
4. Rs. 1,27,500

Answer: Rs. 1,65,000

Carpet area = 70x55 = 3850 sq m, minus 550 for flower pots = 3300 sq m. At Rs 50/sq m the cost = 3300 x 50 = Rs 1,65,000.

Q24. A retaining wall with measurements 30m × 12m × 6m was constructed with bricks of dimensions 8cm × 6cm × 6cm. If 60% of the wall consists of bricks, the number of bricks used for the construction is ______ lakhs.

1. 30
2. 40
3. 45
4. 75

Answer: 45

Wall volume = 30*12*6 = 2160 m^3; bricks occupy 60% = 1296 m^3. One brick = 0.08*0.06*0.06 = 0.000288 m^3. Number of bricks = 1296/0.000288 = 4,500,000 = 45 lakhs (option 2), not 75.

Q25. Hima Das was ____ only Indian athlete to win ____ gold for India.

1. the, many
2. the, a
3. an, a
4. an, the

Answer: the, a

The correct option uses 'the' to specify Hima Das as the unique athlete in this context, and 'a' to indicate that she won one gold medal, which is an indefinite quantity.

Q26. Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that x is greater than y. Let P be the ratio of population of state X to state Y in a given year. The percentage increase in P from 2001 to 2011 is ________.

1. x / y
2. x − y
3. 100(x−y) / (100+x)
4. 100(x−y) / (100+y)

Answer: 100(x−y) / (100+y)

The correct option is derived from the formula for percentage change in ratios, which accounts for the different growth rates of the two populations. Since state X's population grows faster than state Y's, the change in their ratio reflects the difference in their percentage increases, adjusted for the initial size of state Y's population.

Q27. The Newspaper reports that over 500 hectares of tribal land spread across 28 tribal settlements in Mohinitamapuram forest division have already been “alienated”. A top forest official said, “First the tribals are duped out of their land holdings. Second, the families thus rendered landless are often forced to encroach further into the forests”. On the basis of the information available in the paragraph, ________ is/are responsible for duping the tribals.

1. forest officials
2. landless families
3. The Newspaper
4. it cannot be inferred who

Answer: it cannot be inferred who

The passage does not provide specific information about who is responsible for duping the tribals; it only mentions that a top forest official made a statement regarding the situation. Therefore, it cannot be definitively inferred who is responsible.

Q28. An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the tank is full and the drainage hole is open, the oil is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it take for the tank to be filled? (Assume that the rate of drainage is independent of the Head)

1. 1.50
2. 2.00
3. 2.50
4. 4.00

Answer: 2.50

Fill rates: X = 1/5, Y = 1/4 per hour; drain = 1/20 per hour. Net rate = 1/5 + 1/4 - 1/20 = (4+5-1)/20 = 8/20 = 2/5 tank per hour. Time = 1/(2/5) = 2.5 hours (index 2).

Q29. “Popular Hindi fiction, despite – or perhaps because of – its wide reach, often does not appear in our cinema. As ideals that viewers are meant to look up to rather than identify with, Hindi film protagonists usually read books of aspirational value: textbooks, English books, or high value literature.” Which one of the following CANNOT be inferred from the paragraph above?

1. Though popular Hindi fiction has wide reach, it often does not appear in the movies
2. Protagonists in Hindi movies, being ideals for viewers, read only books of aspirational value
3. Textbooks, English books or high literature have aspirational value, but not popular Hindi fiction
4. People do not look up to writers of textbooks, English books or high value literature

Answer: People do not look up to writers of textbooks, English books or high value literature

The statement about people not looking up to writers of textbooks, English books, or high value literature cannot be inferred from the paragraph, as it focuses on the reading preferences of protagonists rather than the public perception of the writers.

Q30. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

1. 1
2. 1/2
3. 1/3
4. 1/4

Answer: 1/4

Each die shows an even number (2,4,6) with probability 3/6 = 1/2. For both dice independently, the probability is 1/2 * 1/2 = 1/4.