For which of the following statements is/are always correct?
Given: 1/3 < x < y < 2
Statement I: x + 1/x < y + 1/y
Statement II: √(1+y²)/y < √(1+x²)/x
Select the answer using the code given below.
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Statement I is not always correct. For example, if x = 1/2 and y = 1, then x + 1/x = 2.5 and y + 1/y = 2, so the statement is false. Statement II is always correct. Since y > x > 0, we have 1/y < 1/x, so 1/y² < 1/x², hence 1 + 1/y² < 1 + 1/x², and taking square roots gives √(1+y²)/y < √(1+x²)/x. Therefore, Option b is correct.
What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?
Explanation: The key idea is to minimize the number of operations by using largest capacities first. Draw 100 litres thrice using the 100L container (3 measurements). After the third withdrawal, pour water from the 100L container into the 1L container until it is full, then empty the 1L container and repeat the process again so that 98L remains in the 100L container (2 more measurements). Thus, 298L is obtained in 5 measurements, which is the minimum.
There are four types of weights, namely 1kg, 2kg, 5kg and 10kg. What is the maximum number of different ways one can measure 20kg, if at least eight but not more than eleven weights of 1kg are to be used while measuring?
Explanation: Let x, y, z, w be the number of 1kg, 2kg, 5kg and 10kg weights respectively. Then x + 2y + 5z + 10w = 20 where 8 ≤ x ≤ 11. Case 1 (x=8): 2y + 5z + 10w = 12 gives 3 ways. Case 2 (x=9): 2y + 5z + 10w = 11 gives 1 way. Case 3 (x=10): 2y + 5z + 10w = 10 gives 3 ways. Case 4 (x=11): 2y + 5z + 10w = 9 gives 1 way. Total = 3 + 1 + 3 + 1 = 8 ways.
The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y, then y - x is
Explanation: Let the number of students be n. Increase in total marks due to first correction = 100 - 0 = 100. Since average increases by 4, 100/n = 4, so n = 25. The second correction reduces total marks by 81 - 56 = 25. Net change in total marks = 100 - 25 = 75. Therefore, net change in average = 75/25 = 3. Thus y - x = 3.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In contrast, people across the world have been exposed to HMPV for decades and the virus is well-studied. HMPV and SARS-CoV-2 belong to two very different virus families with fundamentally different characteristics and epidemiology, with strong seasonality seen in HMPV, unlike SARS-CoV-2. Both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. In general, HMPV causes milder illness with deaths being very rare and with no long-term post-viral symptoms.
Which of the following conclusions is/are valid?
1. Though SARS-CoV-2 and HMPV are similar viruses with somewhat different epidemiology, the former became a pandemic because it was novel and people had not been exposed to it in the past.
2. The two viruses have fundamentally different impacts on human populations and should not therefore be dealt with in a similar manner.
- 1 Only
- 2 Only
- Both 1 and 2
- Neither 1 Nor 2
Explanation: Statement 1 is incorrect. The passage clearly states that HMPV and SARS-CoV-2 belong to two very different virus families, not similar viruses. Statement 2 is correct. The passage states that both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. From this we can conclude that the two viruses have fundamentally different impacts on human populations and thus should not be dealt with in a similar manner.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In contrast, people across the world have been exposed to HMPV for decades and the virus is well-studied. HMPV and SARS-CoV-2 belong to two very different virus families with fundamentally different characteristics and epidemiology, with strong seasonality seen in HMPV, unlike SARS-CoV-2. Both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. In general, HMPV causes milder illness with deaths being very rare and with no long-term post-viral symptoms.
Which of the following reflect the intent of the writer in the above passage?
1. To evolve methodologies for objective analysis of the two viruses
2. To establish the epidemiological similarities and differences between the two viruses
3. To offer a better understanding of the remedies of HMPV when analysed in conjunction with SARS-CoV-2
- 1 and 2
- 2 and 3
- 1 and 3
- None of the above
Explanation: Statement 1 is incorrect. The author compares the impact of two viruses and does not propose a new methodology for their analysis. Statement 2 is incorrect. The passage notes that the viruses have fundamentally different characteristics and epidemiology, not similarities. Statement 3 is incorrect. The author does not discuss remedies for the treatment of HMPV or SARS-CoV-2.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In contrast, people across the world have been exposed to HMPV for decades and the virus is well-studied. HMPV and SARS-CoV-2 belong to two very different virus families with fundamentally different characteristics and epidemiology, with strong seasonality seen in HMPV, unlike SARS-CoV-2. Both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. In general, HMPV causes milder illness with deaths being very rare and with no long-term post-viral symptoms.
Which of the following statements reflect the logical and rational inferences that can be drawn from the passage?
1. HMPV has, historically, had longer documentation of studies when compared with SARS-CoV-2.
2. The two viruses are different from each other and this results in markedly different outcomes amongst those affected.
3. Long-term impacts of the two viruses are dissimilar and this is an important differentiator between them.
4. One of the common factors between the two viruses is seasonal specificity.
- 1 and 2 only
- 1, 2 and 3
- 3 and 4
- 1 and 3 only
Explanation: Statement 1 is correct. The passage states that SARS-CoV-2 was novel in 2019, while people across the world had been exposed to HMPV for decades and the virus is well-studied. Statement 2 is correct. The passage notes that the viruses have fundamentally different characteristics and epidemiology, and both cause different severity of symptoms. Statement 3 is correct. HMPV causes milder illness with no long-term post-viral symptoms, unlike SARS-CoV-2. Statement 4 is incorrect. The passage clearly mentions that seasonality is associated with HMPV unlike SARS-CoV-2.
Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}; then M - N is
Explanation: To maximize the expression, the largest numbers should be used in multiplication. Choose x=5, y=4, z=3. Then M = (5×4) + 3 = 23. To minimize the expression, the smallest numbers should be used in multiplication. Choose x=2, y=3, z=4. Then N = (2×3) + 4 = 10. Therefore, M - N = 23 - 10 = 13.
Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
Explanation: Since y is directly proportional to x², y = k₁x². Using y=50 and x=5: 50 = k₁(25), so k₁ = 2. Thus y = 2x². Since x is inversely proportional to z, x = k₂/z. Using x=5 and z=7/25: 5 = k₂/(7/25), so k₂ = 7/5. Thus x = 7/(5z). When y = 98: 98 = 2x², so x² = 49, giving x = 7. Substituting into x = 7/(5z): 7 = 7/(5z), so 5z = 1, giving z = 1/5.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimisation. However, penetration is limited to a small subset of tech-savvy farmers. In the US and in Europe, generative AI tools have started offering precision farming at scale, integrating large datasets to provide real-time agronomic insights. For at-scale integration and accessibility of AI tools in India, it would be helpful to develop Indian languages-based AI tools for smallholder farmers, partner with AgTechs to create affordable AI solutions, and disseminate AI-based advisory services through government programmes.
Which of the following assumptions is/are valid?
1. Agricultural productivity has marched ahead in the West because of the economies of scale facilitated by the adoption of AI tools.
2. Affordable AI tools rendered available in local languages can help AI-based solutions reach more and more small farmers.
3. Though penetration is as yet low, critical application areas deploying AI tools are already in use in India.
- 1, 2 and 3
- 2 only
- 1 and 3 only
- 2 and 3 only
Explanation: Statement 1 is invalid. The passage states that in the US and Europe, generative AI tools have started offering precision farming at scale, but it does not mention that this has led to greater productivity. Statement 2 is valid. The passage explicitly states that developing Indian languages-based AI tools for smallholder farmers and partnering with AgTechs to create affordable solutions would help. Statement 3 is valid. The passage notes that India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimization, though penetration is limited.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimisation. However, penetration is limited to a small subset of tech-savvy farmers. In the US and in Europe, generative AI tools have started offering precision farming at scale, integrating large datasets to provide real-time agronomic insights. For at-scale integration and accessibility of AI tools in India, it would be helpful to develop Indian languages-based AI tools for smallholder farmers, partner with AgTechs to create affordable AI solutions, and disseminate AI-based advisory services through government programmes.
Which of the following statements is/are not correct?
1. Tech-savvy farmers will drive the AgTech companies of the future.
2. The development of advisory services by the government programmes for the use of AI tools in agriculture would be helpful.
3. In the US and Europe, AI tools have replaced traditional agricultural practices.
4. The integration of large datasets for use in real-time agronomic analysis is already a reality.
- 1 and 3 only
- 1, 3 and 4
- 2 and 4
- 3 only
Explanation: Statement 1 is incorrect. While the passage states that penetration of AI in Indian agriculture is limited to tech-savvy farmers, it does not mention that these farmers would drive AgTech companies. Statement 2 is correct as the passage supports government advisory services. Statement 3 is incorrect. The passage highlights large-scale use of AI in the US and Europe but does not state that AI has replaced traditional farming. Statement 4 is correct as the passage mentions real-time agronomic insights through large datasets.
P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct?
I. If the rank of S is 3, then that of T is 2.
II. If the rank of Q is 3, then that of T is 5.
Select the answer using the code given below.
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Fixed ranks: R=1, P=4. Remaining ranks 2, 3, 5 for Q, S, T. Since Q≠5, Q can be 2 or 3. Since S≠2, S can be 3 or 5. Since T≠3, T can be 2 or 5.
Checking Statement I: If S=3, remaining ranks 2 and 5 go to Q and T. Since Q≠5, Q must be 2, so T must be 5. Thus T≠2, making Statement I false.
Checking Statement II: If Q=3, remaining ranks 2 and 5 go to S and T. Since S≠2, S must be 5, so T must be 2. Thus T≠5, making Statement II false.
Therefore, both statements are false.
Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Z, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct?
I. No one travels alone.
II. Only D travels with F.
III. Only C travels with B.
Select the answer using the code given below.
- I and II only
- I and III only
- II and III only
- All the three
Explanation: Car X has exactly 3 persons (A + 2 others). E and G are together alone in one car (2 persons). Total persons = 7, so the third car has 2 persons.
Since C travels by Z and B does not travel by Y, and A and B cannot be together in X, B must travel by Z. Thus Z = {B, C} (2 persons, full).
E and G cannot be in Z, so Y = {E, G} (2 persons, full).
Remaining persons D and F must be in X. Thus X = {A, D, F}.
Checking statements: I is correct (all cars have 2 or 3 persons). II is incorrect (F travels with A and D). III is correct (Z contains only B and C).
X and Y are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When X completed 7 rounds, Y did exactly 5. After completing 5 rounds, Y changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, X continued to run with the same speed. They stopped running when X completed exactly 21 rounds. How many times did X and Y meet after they had started and before they finally stopped?
Explanation: Initial speed ratio X:Y = 7:5. Let speed of X = 7k, initial speed of Y = 5k.
Before direction change (same direction): When X completes 7 rounds and Y completes 5, meetings = 7 - 5 = 2.
After Y changes direction at 5 rounds: Y's new speed = 10k. X continues at 7k. X runs 14 more rounds (from 7 to 21). In the same time, Y covers (10/7)×14 = 20 rounds in opposite direction. Meetings in opposite direction = 14 + 20 = 34.
Total meetings = 2 + 34 = 36. However, at the exact final instant both are at the starting point simultaneously. Excluding this last meeting, total = 35.
In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?
Explanation: Let x = correct answers, y = wrong answers. From first scheme: 5x - 2y = 69. From second scheme: 4x - y = 84. Multiplying the second equation by 2: 8x - 2y = 168. Subtracting the first equation: 3x = 99, so x = 33. Substituting: 4(33) - y = 84, so y = 48. Total questions = x + y = 33 + 48 = 81.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: The Juvenile Justice (Care and Protection of Children) Act, or the JJ Act, 2015 allows for the possibility for trying adolescents above 16 as adults if they are accused of committing a heinous offence. A heinous offence is one with a minimum punishment of seven years. Offences such as culpable homicide and causing death by negligence, which are common in drunken driving cases, are not heinous offences because they do not have a prescribed minimum punishment. The JJ Act, amended in 2021, now categorises an offence that has no minimum sentence, but has a maximum sentence of seven years or more as a serious offence which nonetheless, in the opinion of activists, does not merit the transfer of a case to the adult criminal justice system.
Which of the following conclusions is/are valid?
1. Only a serious offence as categorised by the revised JJ Act, justifies the transfer of a case to the adult judicial system.
2. The JJ Act, 2021, categorises an offence as a serious offence based on the maximum sentence it carries, rather than on the minimum sentence.
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is incorrect. The passage explicitly states that the JJ Act 2021 categorises an offence with no minimum sentence but maximum sentence of seven years or more as a serious offence which, in the opinion of activists, does not merit transfer to the adult criminal justice system. Statement 2 is correct. The passage states that the amended JJ Act categorises an offence based on having no minimum sentence but a maximum sentence of seven years or more.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: The Juvenile Justice (Care and Protection of Children) Act, or the JJ Act, 2015 allows for the possibility for trying adolescents above 16 as adults if they are accused of committing a heinous offence. A heinous offence is one with a minimum punishment of seven years. Offences such as culpable homicide and causing death by negligence, which are common in drunken driving cases, are not heinous offences because they do not have a prescribed minimum punishment. The JJ Act, amended in 2021, now categorises an offence that has no minimum sentence, but has a maximum sentence of seven years or more as a serious offence which nonetheless, in the opinion of activists, does not merit the transfer of a case to the adult criminal justice system.
Which of the following statements is/are correct?
1. If an offence has no minimum prescribed punishment, it cannot be considered heinous as per the JJ Act, 2015.
2. As per the JJ Act, 2021, an offence for which there is a provision for a maximum sentence of seven years or more, but no minimum sentence, is to be considered a serious offence.
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is correct. The passage states that a heinous offence is one with a minimum punishment of seven years, and offences without prescribed minimum punishment (like culpable homicide) are not heinous offences. Statement 2 is correct. The passage explicitly states that the JJ Act amended in 2021 categorises an offence with no minimum sentence but maximum sentence of seven years or more as a serious offence.
An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30 m/s, at what time did the explosion take place? Assume that the speed of sound is 300 m/s.
- 4:59:00 PM
- 4:59:02 PM
- 4:58:42 PM
- 4:56:32 PM
Explanation: The second drone starts at 5:02 PM and reaches at 5:05 PM, taking 3 minutes = 180 seconds. Distance D = 30 × 180 = 5400 metres. For the first picture: sound travels 5400m at 300 m/s (18 seconds), then first drone travels 5400m at 30 m/s (180 seconds = 3 minutes). Total time from explosion to first picture = 3 minutes 18 seconds. First picture received at 5:02 PM, so explosion time = 5:02:00 PM - 3 minutes 18 seconds = 4:58:42 PM.
The digit in the unit place of the number 6^129 × 7^307 is
Explanation: Powers of 6 always end in 6, so the unit digit of 6^129 is 6. The unit digits of powers of 7 follow a cycle of 4: 7, 9, 3, 1. Since 307 ÷ 4 leaves remainder 3, the unit digit of 7^307 is the same as 7^3, which is 3. Multiplying the unit digits: 6 × 3 = 18. Therefore, the unit digit is 8.
A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?
- 20% increase
- 30% increase
- 3% decrease
- 2% decrease
Explanation: Let initial salary be 100. Initial savings = 10, initial expenditure = 90. New salary = 100 + 12% of 100 = 112. New expenditure = 90 + 10% of 90 = 99. New savings = 112 - 99 = 13. Increase in savings = 3. Percentage increase = (3/10) × 100 = 30%.
P has a son and a daughter. S is the mother of T. S is R's spouse. Q and R are children of P. Then how is Q related to S?
- Q is a sister of S
- Q is a daughter of S
- Q is the mother of S
- Q is a sister of the husband of S
Explanation: Since S is R's spouse and S is the mother of T, S is female. Therefore R must be male (husband of S). Since P has one son and one daughter, and R is the son, Q must be the daughter. Thus Q is the sister of R. Since R is the husband of S, Q is the sister of the husband of S.
How many three-digit numbers can be expressed as an integral power of 2?
Explanation: A three-digit number lies between 100 and 999. Powers of 2: 2^5=32, 2^6=64, 2^7=128, 2^8=256, 2^9=512, 2^10=1024. The three-digit powers of 2 are 128, 256, and 512. Total = 3 numbers.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: The key source of the battle for clean skies and clear lungs is the fuel we burn—from household chulhas to the thermal power plants. In most cases, it is biomass or coal. The Supreme Court banned the use of pet coke. The Delhi Government banned the use of coal, which was later extended to the entire National Capital Region. It was also agreed that the thermal power plants would clean up or shut down. The lesson from the transition to CNG is that people need alternatives for a ban to be effective. When diesel buses were stopped, CNG supply had to be assured. The Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel.
Which of the following inferences is/are correct?
1. The source of the energy we consume is the key to the battle for cleaner air.
2. Bans are effective where the will is strong and the people are convinced that such bans are for the greater good of society.
3. There is judicial approval for a policy that intervenes fiscally to facilitate benevolent pricing for cleaner fuel.
- 1 and 2
- 2 and 3
- 1 and 3
- 1 only
Explanation: Statement 1 is correct. The passage states that the key source of the battle for clear skies and clear lungs is the fuel we burn. Statement 2 is incorrect. The passage explicitly mentions that people need alternatives for a ban to be effective, not just conviction. Statement 3 is correct. The passage mentions that the Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: The key source of the battle for clean skies and clear lungs is the fuel we burn—from household chulhas to the thermal power plants. In most cases, it is biomass or coal. The Supreme Court banned the use of pet coke. The Delhi Government banned the use of coal, which was later extended to the entire National Capital Region. It was also agreed that the thermal power plants would clean up or shut down. The lesson from the transition to CNG is that people need alternatives for a ban to be effective. When diesel buses were stopped, CNG supply had to be assured. The Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel.
Which of the following statements is/are correct?
1. Thermal power stations in Delhi were required to summarily shut down.
2. CNG supplies had to be assured once diesel vehicles were prohibited from plying.
3. The Supreme Court banned the use of coal across the National Capital Region.
- 1 and 2
- 3 only
- 2 only
- 2 and 3
Explanation: Statement 1 is incorrect. The passage states that thermal power plants would clean up or shut down, not summarily shut down. Statement 2 is correct. The passage explicitly states that when diesel buses were stopped, CNG supply had to be assured. Statement 3 is incorrect. The passage states that the Delhi Government banned coal, not the Supreme Court.
How many times does 5 appear in all two-digit positive integers?
Explanation: Count occurrences in the units place: 15, 25, 35, 45, 55, 65, 75, 85, 95 → 9 occurrences. Count occurrences in the tens place: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 → 10 occurrences. Total = 9 + 10 = 19. (Note: In 55, the digit 5 appears twice and both are counted.)
X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?
Explanation: Time taken by X: (1/5)×60 = 12 min; (2/10)×60 = 12 min; (3/4)×60 = 45 min. Total = 69 minutes. Time taken by Y: (1/4)×60 = 15 min; (2/10)×60 = 12 min; (3/5)×60 = 36 min. Total = 63 minutes. Difference = 69 - 63 = 6 minutes.
Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty?
Explanation: First weighing: Place 3 cubes on each pan, keep 1 aside. If equal, the cube kept aside is the lightest (identified in 1 attempt). If unequal, the lighter cube is among the 3 on the lighter pan. Second weighing: Take these 3 suspected cubes, place 1 on each pan and keep 1 aside. If equal, the one aside is lightest; if unequal, the one on the lighter side is lightest. Thus, maximum 2 attempts are required.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: Previous waves of customer-service technology, including email and those pesky voice menus, stoked concerns of job losses, only for them to fail to materialise. AI could yet prove different. And if it does, its effects may be salutary. Human agents could be freed up to spend more time on creative and rewarding tasks, like using feedback to make products and services better and thereby spend less time listening to irate customers!
Which one among the following statements most appropriately reflects the point of view of the given passage?
- If AI were to take over customer service, there would be no work left for human subjects to do
- Irritating voice menus and email did not achieve human redundancy to the extent that AI could
- The value of human intervention in the workplace affected by AI might be enhanced through redirection towards more fulfilling tasks
- Unlike previous waves in customer-service technology, AI has raised the alarm of worker redundancy without justification
Explanation: The passage highlights that the effect of AI in the workplace may be salutary. It explicitly mentions that human agents could be freed up to spend more time on creative and rewarding tasks, like using feedback to make products and services better.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: Previous waves of customer-service technology, including email and those pesky voice menus, stoked concerns of job losses, only for them to fail to materialise. AI could yet prove different. And if it does, its effects may be salutary. Human agents could be freed up to spend more time on creative and rewarding tasks, like using feedback to make products and services better and thereby spend less time listening to irate customers!
Which of the following conclusions, made on the basis of the given passage, is/are correct?
1. The advent of new customer-service technology had invariably sparked fears about job losses.
2. Often it is found that instead of job losses, alternative channels for employee engagement are discovered while certain tasks are replaced by technology.
3. The advent of technology inevitably leads to stressful outcomes.
- 1 and 3
- 2 only
- 3 only
- 1 and 2
Explanation: Statement 1 is correct. The passage states that previous waves of customer-service technology stoked concerns of job loss. Statement 2 is correct. The passage states that human agents would be freed up to spend more time on creative and rewarding tasks, indicating alternative channels for engagement. Statement 3 is incorrect as it solely focuses on negative impacts and ignores the opening up of new channels.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: Cattle from the nearby villages came to the common ground to graze, and there was still a cool freshness in the air. Hori took several deep breaths and thought of sitting down for a while, since he'd be dying of heat in the scorching 'loo' wind the rest of the day. A number of farmers were eager to lease this bit of land and had offered a good price, but Rai Sahib had plainly told them it was reserved for grazing and would not be relinquished for any price. If he'd been one of those selfish Zamindars, he'd have said the cattle could go to hell, that there was no reason for him to miss the chance to make a little money. But the Rai Sahib still held to the old values, feeling that any landlord who didn't look after his tenants was less than human.
Which of the following conclusions is/are correct?
1. All landlords essentially have some goodness trapped within them.
2. The common grazing grounds of a village are intended for use by the cattle of that village.
3. Landlords who believe in tradition tend to be more concerned about their tenants.
4. Winds later in the day tend to be cooler post the hot winds of the morning.
- 1 and 3
- 2 and 4
- 3 only
- 2 only
Explanation: Statement 1 is incorrect. The passage mentions that unlike Rai Sahib, some zamindars were selfish. Statement 2 is incorrect. While the passage states that cattle from nearby villages came to graze, it does not conclude that all common grounds were intended only for that village's cattle. Statement 3 is correct. The passage mentions that Rai Sahib held to old values, feeling that any landlord who didn't look after his tenants was less than human. Statement 4 is incorrect. The passage states there is cool air in the morning followed by scorching loo the rest of the day.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: Cattle from the nearby villages came to the common ground to graze, and there was still a cool freshness in the air. Hori took several deep breaths and thought of sitting down for a while, since he'd be dying of heat in the scorching 'loo' wind the rest of the day. A number of farmers were eager to lease this bit of land and had offered a good price, but Rai Sahib had plainly told them it was reserved for grazing and would not be relinquished for any price. If he'd been one of those selfish Zamindars, he'd have said the cattle could go to hell, that there was no reason for him to miss the chance to make a little money. But the Rai Sahib still held to the old values, feeling that any landlord who didn't look after his tenants was less than human.
Which of the following statements are not correct?
1. The landholdings of Rai Sahib were currently not being used for farming.
2. Temperamentally, Rai Sahib was as greedy as other landlords.
3. It cannot be ascertained that Rai Sahib could have made some money by leasing out the grazing land.
4. It may be asserted that Rai Sahib valued his tenants and wanted to protect their livelihood.
- 1 and 2 only
- 1 and 3 only
- 3 and 4
- 1, 2 and 3
Explanation: Statement 1 is incorrect. The passage states that a bit of Rai Sahib's land was used for grazing, but we cannot conclude whether other parts were used for farming. Statement 2 is incorrect. The passage explicitly highlights that Rai Sahib was unlike other selfish zamindars. Statement 3 is incorrect. The passage states that farmers were eager to lease this bit of land and had offered a good price, so Rai Sahib could have made money. Statement 4 is correct as the passage states Rai Sahib held to old values regarding tenant welfare.
In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is
Explanation: The sequence is: 1st term = 4, 2nd term = 7, 3rd term = 4+7 = 11, 4th term = 7+11 = 18, 5th term = 11+18 = 29, 6th term = 18+29 = 47.
The ratio of male to female workers in two companies A and B is 13:10 and 7:5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?
Explanation: Female ratio parts are 10 for A and 5 for B. LCM of 10 and 5 is 10. So Company B ratio is multiplied by 2: 7:5 becomes 14:10. Now A = 13:10 and B = 14:10. Total workers in A = 13+10 = 23. Total workers in B = 14+10 = 24. Required ratio = 23:24.
If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?
I. The difference of the numbers is an even number.
II. One of the numbers is a perfect square.
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: For any two numbers a and b: HCF(a,b) × LCM(a,b) = a × b. Given this equals a³, we get b = a². The two numbers are a and a² (distinct, so a ≠ 1). Checking Statement I: difference = a² - a = a(a-1). Since a and (a-1) are consecutive integers, one must be even, so their product is always even. Checking Statement II: b = a², so one number is always a perfect square. Both statements are correct.
If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x+y is divided by 11?
Explanation: The divisibility rule for 11 states that the difference between the sum of digits in odd positions and even positions must be a multiple of 11. For 4x5y790: Sum of odd positions (1st, 3rd, 5th, 7th) = 4 + 5 + 7 + 0 = 16. Sum of even positions (2nd, 4th, 6th) = x + y + 9. So (x + y + 9) - 16 = x + y - 7 must be a multiple of 11. Thus x + y = 11k + 7 for some integer k. The remainder when x+y is divided by 11 is 7.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: Was it the sun-dappled ambience, the strawberries and cream, the frustration of Flavio Cobolli's unforced errors against Serbian Novak Djokovic on Centre Court or simply the crushing weight of being a 64-year-old man in the third act of a very public life? Whatever the reason, Hugh Grant, the actor, deserves empathy. There he was, in the Royal Box at Wimbledon, flanked by Britain's well-dressed and well-rested spectators, watching the men's singles quarterfinals, when the actor did something quietly radical: head at a tilt, eyes closed, utterly unbothered, he took a nap. So praise be to Grant for serving up an unexpected ace. In that small, delicious moment, he didn't merely catch forty winks, he made an elegant case for surrender. Not to laziness, but to limits. To the body's quiet wisdom over society's relentless performance metrics. Wimbledon had its tennis. The perpetually sleep-deprived discovered a leading man, not of action, but of rest.
Which of the following statements is/are correct?
1. Radical action can also be attributed to mild surrender where against societal expectations one acts.
2. Submitting to one's limitations, given the effect of age and other factors, ought not to be conflated with laziness.
3. 'Leading man' usually refers to one who plays the lead role in a movie; in this instance the implication is that Hugh Grant is performing the role of not an action hero, but that of a resting one!
- 1 and 2 only
- 2 and 3 only
- 1, 2 and 3
- 3 only
Explanation: Statement 1 is correct. The passage describes Hugh Grant taking a nap at Wimbledon as a quietly radical act, making an elegant case for surrender against societal expectations. Statement 2 is correct. The passage explicitly states 'Not to laziness, but to limits. To the body's quiet wisdom over society's relentless performance metrics.' Statement 3 is correct. The passage states 'The perpetually sleep-deprived discovered a leading man, not of action, but of rest,' comparing his role as an actor to this moment of rest.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: Was it the sun-dappled ambience, the strawberries and cream, the frustration of Flavio Cobolli's unforced errors against Serbian Novak Djokovic on Centre Court or simply the crushing weight of being a 64-year-old man in the third act of a very public life? Whatever the reason, Hugh Grant, the actor, deserves empathy. There he was, in the Royal Box at Wimbledon, flanked by Britain's well-dressed and well-rested spectators, watching the men's singles quarterfinals, when the actor did something quietly radical: head at a tilt, eyes closed, utterly unbothered, he took a nap. So praise be to Grant for serving up an unexpected ace. In that small, delicious moment, he didn't merely catch forty winks, he made an elegant case for surrender. Not to laziness, but to limits. To the body's quiet wisdom over society's relentless performance metrics. Wimbledon had its tennis. The perpetually sleep-deprived discovered a leading man, not of action, but of rest.
Which of the following statements is/are correct?
1. Hugh Grant was watching, from the Royal Box, the men's semifinal match on Centre Court between Flavio Cobolli and Novak Djokovic.
2. The phrase 'unexpected ace' in the context uses a term from the game of tennis to highlight Hugh Grant's somewhat uncharacteristic act of catching 'forty winks'; an act that is viewed with opprobrium.
3. Grant subjects the demands of society to the wisdom of his body.
- 1 and 2
- 3 only
- 2 and 3
- 2 only
Explanation: Statement 1 is incorrect. The passage explicitly states that Hugh Grant was watching the men's singles quarterfinals, not semifinals. Statement 2 is incorrect. The passage does not describe Grant's act with opprobrium (criticism); rather, the author praises him. Statement 3 is correct. The passage explicitly states that Grant surrendered 'To the body's quiet wisdom over society's relentless performance metrics.'
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: The process by which countries close their labour-productivity gap with the technology leader is based on convergence theory. The convergence model divides economic eras into three phases: the breakaway, the catch-up, and the fine-tuning phase. It also divides economic entities into two categories: the technology leaders and the technology followers. The process begins with the development of a new technology, such as scavenging three million years ago (MYA), hunting—one MYA, farming—12 thousand years ago, and industrial technology a little more than 200 years ago. During the breakaway phase, the per capita income of the technology leaders rises, but is unchanged for the technology followers. In the catch-up phase, the followers adopt the new technology and close their per capita income gap with the technology leaders. In the fine-tuning phase, where participants try to extract the remaining benefits from an increasingly exhausted technology, leaders and followers have similar per capita incomes.
Which of the following conclusions are correct?
1. In the breakaway phase, economic progress is slow for the technology followers.
2. In the catch-up phase, leaders stagnate and followers, therefore, close the gap between them and the leaders.
3. In the fine-tuning technology is exhausted, as it were, phase, and both leaders and followers attempt to extract leftover benefits, leading to more or less similar per capita income levels.
4. Industrial technology followed scavenging, which preceded hunting, which itself was followed by farming.
- 3 and 4 only
- 1, 2, 3 and 4
- 1 and 2 only
- 2, 3 and 4 only
Explanation: Statement 1 is incorrect. The passage states that in the breakaway phase, economic progress is unchanged for technology followers, not slow. Statement 2 is incorrect. While followers catch up, the passage does not explicitly state that leaders stagnate. Statement 3 is correct. The passage states that in the fine-tuning phase, participants try to extract remaining benefits from an increasingly exhausted technology, and leaders and followers have similar per capita incomes. Statement 4 is correct regarding the chronological order of technologies mentioned.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: The process by which countries close their labour-productivity gap with the technology leader is based on convergence theory. The convergence model divides economic eras into three phases: the breakaway, the catch-up, and the fine-tuning phase. It also divides economic entities into two categories: the technology leaders and the technology followers. The process begins with the development of a new technology, such as scavenging three million years ago (MYA), hunting—one MYA, farming—12 thousand years ago, and industrial technology a little more than 200 years ago. During the breakaway phase, the per capita income of the technology leaders rises, but is unchanged for the technology followers. In the catch-up phase, the followers adopt the new technology and close their per capita income gap with the technology leaders. In the fine-tuning phase, where participants try to extract the remaining benefits from an increasingly exhausted technology, leaders and followers have similar per capita incomes.
Which of the following statements is/are correct?
1. The convergence model divides nations into three phases of economic progress.
2. At the heart of the convergence theory is the closing of the gap between labour and productivity.
3. Technology leaders typically have arrived earlier at different economic eras.
4. The time period covered by the convergence theory presented herein encompasses, as mentioned, 4012200 years.
- 2 and 4
- 2 and 3
- 3 only
- 1, 3 and 4
Explanation: Statement 1 is incorrect. The passage explicitly states that the convergence model divides economic eras into three phases, not nations. Statement 2 is incorrect. The passage refers to the labour-productivity gap between countries (as a single compound concept), not labour and productivity as separate entities. Statement 3 is correct. Technology leaders adopt new technologies before followers, creating the gap. Statement 4 is incorrect. The maximum timeline mentioned is three million years ago.
An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio should amounts of P and Q be mixed in order to get R?
Explanation: Alloy R must contain 50% copper and 50% zinc. Using the rule of alligation on copper percentages: P has 20%, Q has 60%, and R needs 50%. The differences are |60-50| = 10 and |50-20| = 30. Therefore, the ratio P:Q = 10:30 = 1:3.
A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A-B is a multiple of 27, where A > B, how many such different A's are possible?
Explanation: Let A = 10x + y and B = 10y + x where x ≠ y and x > y (since A > B). Then A - B = 9(x - y). For this to be a multiple of 27, x - y must be a multiple of 3. Since x and y are digits and x > y, possible values are x - y = 3 or 6. For x - y = 3: pairs are (4,1), (5,2), (6,3), (7,4), (8,5), (9,6) → 6 numbers. For x - y = 6: pairs are (7,1), (8,2), (9,3) → 3 numbers. Total = 6 + 3 = 9.
If ZERO is encoded as ADSN, then how do you encode STOP?
Explanation: Comparing ZERO and ADSN: Z→A (+1), E→D (-1), R→S (+1), O→N (-1). The pattern is +1, -1, +1, -1. Applying to STOP: S→T (+1), T→S (-1), O→P (+1), P→O (-1). Thus STOP is encoded as TSPO.
A train has to complete a journey of 800 km. If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing speed. On its way, the train meets with a minor accident after 200 km; and 400 km thereafter, it develops a mechanical defect. Had the train developed the mechanical defect after 200 km and met the minor accident 400 km thereafter, it would have taken 4 more hours to reach its destination. What was the original speed of the train in km per hour?
Explanation: Let original speed be s km/h. Case 1 (actual): 200/s + 400/(s/2) + 200/(s/8) = 200/s + 800/s + 1600/s = 2600/s hours. Case 2 (hypothetical): 200/s + 400/(s/4) + 200/(s/8) = 200/s + 1600/s + 1600/s = 3400/s hours. Given difference is 4 hours: 3400/s - 2600/s = 4, so 800/s = 4, giving s = 200 km/h.
In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are 0.2, 0.3 and 0.5, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected:
Candidate 1: Component scores 5, 4, 6
Candidate 2: Component scores 4, 6, 5
Candidate 3: Component scores 3, 2, 8
Candidate 4: Component scores 9, 4, 3
Candidate 5: Component scores 8, 8, 2
Explanation: Weighted scores: Candidate 1 = 0.2(5)+0.3(4)+0.5(6) = 5.2; Candidate 2 = 0.2(4)+0.3(6)+0.5(5) = 5.1; Candidate 3 = 0.2(3)+0.3(2)+0.5(8) = 5.2; Candidate 4 = 0.2(9)+0.3(4)+0.5(3) = 4.5; Candidate 5 = 0.2(8)+0.3(8)+0.5(2) = 5.0. Arranged in descending order: 5.2, 5.2, 5.1, 5.0, 4.5. Exactly three candidates are selected, so the cutoff is the score of the third candidate = 5.1.
Which among the following actions would constitute the most appropriate directive(s) in resolving interpersonal conflict in an office with culturally diverse personnel?
1. Direct personnel to practise activities that are the cultural markers of diverse groups
2. Allow conflicts to resolve naturally over time to set an appropriate precedent of leadership
3. Encourage personnel to seek each other's perspectives
- 1 and 3
- 2 only
- 3 only
- 2 and 3
Explanation: Statement 1 is incorrect. Directing personnel to practice activities of other groups might seem like imposition of cultures and not help in resolving conflict. Statement 2 is incorrect. Allowing conflicts to persist and taking no action may escalate the conflicts. Statement 3 is correct as it allows personnel to resolve conflicts by incorporating diverse views through discussions.
Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹17,000, how much profit will C get?
- ₹12,000
- ₹10,000
- ₹12,500
- ₹10,750
Explanation: Assume total capital = 12 units and total time = 12 units. A invests 4 units for 4 units of time → 4×4 = 16. B invests 3 units for 3 units of time → 3×3 = 9. C invests remaining 5 units for 12 units of time → 5×12 = 60. Profit ratio = 16:9:60. Total parts = 85. Value of one part = 17000/85 = 200. C's share = 60 × 200 = ₹12,000.
There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?
Explanation: Each time 1 litre is removed from 10 litres, only 9/10 of the previous amount of A remains. After 3 replacements: Remaining A = 10 × (9/10)³ = 10 × 729/1000 = 7.29 litres. Therefore, B = 10 - 7.29 = 2.71 litres. Percentage of B = (2.71/10) × 100 = 27.1% ≈ 27%.
X receives three coins of different denominations from {1, 2, 5, 10, 20}. If the total amount received by X is m, does X receive a coin of denomination 5?
Statement I: m is not a prime number.
Statement II: The sum of the digits of m is greater than 5.
Select the answer using the instructions for data sufficiency questions.
- The question can be answered using one of these statements alone, but cannot be answered using the other statement
- The question can be answered using either statement alone
- The question can be answered using both the statements together, but cannot be answered using either statement alone
- The question cannot be answered even using any of the statements
Explanation: Possible sums without 5: 13, 23, 31, 32 (digit sums 4, 5, 4, 5 respectively). Possible sums with 5: 8, 16, 17, 26, 27, 35 (digit sums 8, 7, 8, 8, 9, 8 respectively). Statement I is insufficient because both 32 (no 5) and 8 (has 5) are non-prime. Statement II is sufficient because all sums with 5 have digit sum > 5, while all sums without 5 have digit sum ≤ 5. Thus, II alone is sufficient but I alone is not.
If x and y are integers, then is x even?
Statement I: x²y² is even
Statement II: 1 + x² + y² is odd
Select the answer using the instructions for data sufficiency questions.
- The question can be answered using one of these statements alone, but cannot be answered using the other statement
- The question can be answered using either statement alone
- The question can be answered using both the statements together, but cannot be answered using either statement alone
- The question cannot be answered even using any of the statements
Explanation: From Statement I: x²y² = (xy)² is even, so xy is even, meaning at least one of x or y is even. This is insufficient because x could be odd with y even. From Statement II: 1 + x² + y² is odd, so x² + y² is even, meaning x and y have the same parity (both even or both odd). This is insufficient because both could be odd. Combining both: at least one is even (from I) and they have the same parity (from II), so both must be even. Therefore x is even. Both statements together are sufficient, but neither alone is sufficient.
If x, y and z are integers, each greater than 1, then is x a prime number?
Statement I: xy² = 116
Statement II: xz = 261
Select the answer using the instructions for data sufficiency questions.
- The question can be answered using one of these statements alone, but cannot be answered using the other statement
- The question can be answered using either statement alone
- The question can be answered using both the statements together, but cannot be answered using either statement alone
- The question cannot be answered even using any of the statements
Explanation: From Statement I: 116 = 2² × 29. Since y² must be a perfect square factor and y > 1, we have y² = 4, so y = 2 and x = 29, which is prime. Thus Statement I alone is sufficient. From Statement II: 261 = 3² × 29 = 9 × 29. Possible factor pairs with x, z > 1: (x=3, z=87) where x is prime, or (x=9, z=29) where x is composite. Thus Statement II alone is insufficient.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: 'Kalagram', the cultural village set up at the Maha Kumbh Mela, unfolded as a mosaic of India's diverse regions, each represented by seven meticulously crafted 'Sanskriti Angans'—stepping through the grand portal was like entering another world. These thematic zones, inspired by iconic temples like the Dakshineswar Kali Temple and the Brahma Mandir, were treasure troves of regional artistry. Bengal's Pattachitra paintings, Assam's bamboo crafts, Tamil Nadu's Thanjavur paintings, and Madhya Pradesh's tribal sculpture—all were showcased in these living galleries where 230 master artisans breathed life into them using age-old techniques, their hands shaping India's ancient history into creations to behold.
Which of the following conclusions are valid?
1. Seven Sanskriti Angans, representing different regions of India, had been showcased in Kalagram.
2. Regional artistry was recognised via the inspiration drawn from iconic temples.
3. India's ancient history had been crafted by the contemporary craftsmanship of 230 artisans into creations to behold.
4. Art forms from all regions of India had been showcased in these living galleries.
- 1 and 2 only
- 2, 3 and 4
- 1, 2 and 4
- 1 and 3
Explanation: Statement 1 is valid. The passage explicitly states that India's diverse regions, each represented by seven meticulously crafted 'Sanskriti Angans', were showcased at Kalagram. Statement 2 is valid. The passage mentions that these thematic zones, inspired by iconic temples, were treasure troves of regional artistry. Statement 3 is invalid. Contemporary artisans cannot create or craft ancient history; they can only replicate or be inspired by ancient traditions. Statement 4 is invalid. While the passage mentions several regions, we cannot conclude that art forms from all regions of India were showcased.
The weights of A, B, C, D, P, Q, R and S are measured. Given:
A + B + C + D = 17
A + C = 6
P + Q + S + D = 15
P + Q + R + B = 17
P = R and Q = S
Which one of the following statements is correct?
- B and D together weigh less than the total weight of P and Q.
- P and Q together weigh more than the total weight of A and C.
- P weighs more than Q.
- Q weighs more than P.
Explanation: From A+B+C+D=17 and A+C=6, we get B+D=11. Using P=R and Q=S: From P+Q+S+D=15, we get P+2Q+D=15. From P+Q+R+B=17, we get 2P+Q+B=17. Adding these two equations: 3P+3Q+B+D=32. Substituting B+D=11: 3(P+Q)=21, so P+Q=7. We have A+C=6, B+D=11, and P+Q=7. Therefore P+Q (7) > A+C (6), making option (b) correct. We cannot determine the individual relationship between P and Q.
How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning.
Explanation: The word QUEUE contains letters Q, U, E, U, E (U repeats twice, E repeats twice). Since Q must always be immediately followed by U, treat 'QU' as a single fixed block. Now we arrange the units: (QU), U, E, E. Here E repeats twice, so total arrangements = 4! / 2! = 24 / 2 = 12. We do not multiply by 2! for internal arrangement of QU because Q must come before U (fixed order only).
X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many times will they all land on the same mark (need not be at the same moment) between mark 195' and 1000', if all of them cross mark 1000' by 9 AM?
Explanation: Since all start from 199', common landing marks occur at intervals of LCM(4,6,5) = 60 feet. The common marks are 199 + 60k where k is an integer. For the range 195 ≤ 199 + 60k ≤ 1000: subtracting 199 gives -4 ≤ 60k ≤ 801, so -0.067 ≤ k ≤ 13.35. Integer values of k are 0, 1, 2, ..., 13, giving 14 values. Verification: k=0 gives 199 (valid), k=13 gives 199+780=979 (valid). Thus there are 14 common marks.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: Sport is not just about winning medals or getting jobs through a sports quota. Today's generation is struggling with issues like depression and anxiety. Parents often say that their children are inactive and rarely leave the house. Sport can help tackle these problems. From sport you can learn time management, fitness, teamwork, coordination, and so much more. We need to develop a culture in which sport is seen as a way of life—a path to building a healthier, happier society.
Which of the following conclusions are valid?
1. Sport is more than just games; it is a way of life.
2. Sport can help mitigate the problems of seclusion among the young.
3. Earning laurels in sport can help one secure a job on the basis of an assigned quota.
4. Standard corporate sector skills cannot be learnt through sport.
- 1 and 3 only
- 2 and 4 only
- 1, 2 and 4
- 1, 2 and 3
Explanation: Statement 1 is correct. The passage states that sport is seen as a way of life. Statement 2 is correct. The passage states that parents say children are inactive and rarely leave the house, and sport can help tackle these problems. Statement 3 is correct. The passage mentions getting jobs through a sports quota. Statement 4 is incorrect. The passage focuses on highlighting the value of sport rather than stating that corporate skills cannot be learnt from it.
A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?
Explanation: Let f = number of forward jumps and b = number of backward jumps. Then f + b = 31 and 5f - 2b = 15. Multiplying the first equation by 2: 2f + 2b = 62. Adding to the second equation: 7f = 77, so f = 11. Then b = 31 - 11 = 20. The difference = |f - b| = |11 - 20| = 9.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: How is deflation done? Most countries use a method called 'double deflation', where input and output prices are deflated separately. Consider a manufacturer importing oil for use in production. If oil prices fall, output prices do not and quantities remain the same, real value added should not change. But if the same deflator is used for inputs and outputs, as in India, it would look as if the manufacturer had become more productive.
Which of the following statements is/are correct?
1. Real value should not change in the instance of static output cost and unchanged quantities against falling oil prices.
2. Deflators are to be used separately for inputs and outputs, and this is a practice universally adopted by all economies.
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is correct. The passage explicitly states that if oil prices fall, output prices do not, and quantities remain the same, real value added should not change. Statement 2 is incorrect. The passage mentions that India does not use double deflation (separate deflators), so it is not universally adopted by all economies.
Read the following passage and answer the item that follows. Your answer should be based solely on the passage.
Passage: How is deflation done? Most countries use a method called 'double deflation', where input and output prices are deflated separately. Consider a manufacturer importing oil for use in production. If oil prices fall, output prices do not and quantities remain the same, real value added should not change. But if the same deflator is used for inputs and outputs, as in India, it would look as if the manufacturer had become more productive.
Which of the following assumptions is/are valid?
1. Deflation strategies can be used to make manufacturers appear to be doing better than they actually are.
2. When input and output prices are both deflated against a single input price, it is referred to as 'double deflation'.
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is correct. The passage states that if the same deflator is used for inputs and outputs, as in India, it could look as if the manufacturer had become more productive. Statement 2 is incorrect. The passage states that when input and output prices are deflated separately, it is referred to as double deflation, not when deflated against a single input price.
If 10^m × 1000 × n = 75^25 × 25^32 × 32^75, where n is not divisible by 10, then the value of m is
Explanation: LHS = 10^m × 10³ × n = 10^(m+3) × n = 2^(m+3) × 5^(m+3) × n. RHS: 75^25 = (3×5²)^25 = 3^25 × 5^50; 25^32 = (5²)^32 = 5^64; 32^75 = (2^5)^75 = 2^375. So RHS = 2^375 × 5^(50+64) × 3^25 = 2^375 × 5^114 × 3^25. Forming 10-pairs (2×5): min(375,114) = 114 pairs. So RHS = 10^114 × (2^261 × 3^25). Comparing: n = 2^261 × 3^25 (not divisible by 10, satisfied). Equating powers of 10: m+3 = 114, so m = 111.
The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
Explanation: Same direction relative speed = 100 - 4 = 96 km/h = 96 × (5/18) = 80/3 m/s. Length of train L = (80/3) × 15 = 400 metres. Opposite direction relative speed = 100 + 4 = 104 km/h = 104 × (5/18) = 260/9 m/s. Time = 400 / (260/9) = 400 × 9 / 260 = 3600/260 ≈ 13.846 seconds ≈ 13.85 seconds.