2021 CSAT Questions MCQs

Passage: With respect to what are called denominations of religion, if everyone is left to be a judge of his own religion, there is no such things as religion that is wrong; but if they are to be a judge of each other's religion, there is no such thing as a religion that is right, and therefore all the world is right or all the world is wrong in the matter of religion. What is the most logical assumption that can be made from the passage given above?

No man can live without adhering to some religious denomination.
It is the duty of everyone to propagate one's religious denomination.
Religious denominations tend to ignore the unity of man.
Men do not understand their own religious denomination.

Explanation: The claim that no man can live without adhering to some religious denomination is incorrect because the passage does not comment on the necessity of belonging to a religious denomination for survival. The claim that it is the duty of everyone to propagate one's religious denomination is incorrect because there is no mention of any duty to spread religious beliefs. The assumption that religious denominations tend to ignore the unity of man is correct because it supports the central argument that judging others' religions leads to all religions being seen as wrong. The claim that men do not understand their own religious denomination is incorrect because the passage suggests people fail to understand others' religions, not necessarily their own.

Passage: It is certain, that seditions, wars, and contempt or breach of the laws are not so much to be imputed to the wickedness of the subjects, as to the bad state of a dominion. For men are not born fit for citizenship but must be made so. Besides, men's natural passions are everywhere the same; and if wickedness more prevails, and more offences are committed in one commonwealth than in another, it is certain that the former has neither enough pursued the end of unity, nor framed its laws with sufficient forethought; and that, therefore, it has failed in making quite good its right as a commonwealth. Which among the following is the most logical and rational inference that can be made from the passage given above?

Seditions, wars, and breach of the laws are inevitable in every dominion.
It is not the people, but the sovereign who is responsible for all the problems of any dominion.
That dominion is the best which pursues the aim of unity and has laws for good citizenship.
It is impossible for men to establish a good dominion.

Explanation: The assertion that seditions, wars, and breach of the laws are inevitable in every dominion is incorrect because the passage does not claim such problems are unavoidable. The claim that the sovereign alone is responsible for all problems is incorrect because it is overly simplistic to blame only the sovereign. The inference that the best dominion pursues the aim of unity and has laws for good citizenship is correct because it is directly supported by the passage. The claim that it is impossible to establish a good dominion is incorrect because the passage suggests good government requires preparation and education, not that it is unachievable.

Passage: Inequality violates a basic democratic norm: the equal standing of citizens. Equality is a relation that obtains between persons in respect of some fundamental characteristic that they share in common. Equality is, morally speaking, a default principle. Therefore, persons should not be discriminated on grounds such as race, caste, gender, ethnicity, disability, or class. These features of human condition are morally irrelevant. The idea that one should treat persons with respect not only because some of these persons some special features or talent, for example skilled cricketers, gifted musicians, or literary giants, but because persons are human being, is by now part of commonsense morality. With reference to the above passage, the following assumptions have been made: 1. Equality is a prerequisite for people to participate in the multiple transactions of society from a position of confidence. 2. Occurrence of inequality is detrimental to the survival of democracy. 3. Equal standing of all citizens is an idea that cannot actually be realised even in a democracy. 4. Right to equality should be incorporated into our values and day-to-day political vocabulary. Which of the above assumptions are valid?

1 and 2 only
2 and 3 only
1 and 4 only
3 and 4 only

Explanation: Assumption 1, which states that equality is a prerequisite for confident participation in societal transactions, is valid because the passage emphasizes equal standing as a foundational democratic norm. Assumption 2, which claims inequality threatens the survival of democracy itself, is not valid because the passage only says inequality violates democratic norms, not that it destroys democracy. Assumption 3, which claims equal standing cannot be realized even in a democracy, is not valid because the passage treats equality as a default moral principle rather than an unreachable ideal. Assumption 4, which states that the right to equality should be part of everyday values and political vocabulary, is valid because it aligns with the passage's moral argument. Therefore, only assumptions 1 and 4 are valid, making the correct choice the option that selects 1 and 4 only.

Passage: Aristocratic government ruins itself by limiting too narrowly the circle within which power is confined; oligarchic government ruins itself by the incautious scramble for immediate wealth. But even democracy ruins itself by excess of democracy. Its basic principle is the equal right of all to hold office and determine public policy. This is, at first glance, a delightful arrangement; it becomes disastrous because the people are not properly equipped by education to select the best rulers and the wisest courses. The people have no understanding and only repeat what their rulers are pleased to tell them. Such a democracy is tyranny or autocracy. – Plato Which one of the following statements best reflects the crux of the passage given above?

Human societies experiment with different forms of governments.
Any form of government tends to deteriorate by excess of its basic principle.
Education of all citizens ensures a perfect, functional and sustainable democracy.
Having a government is a necessary evil because tyranny is inherent in any form of government.

Explanation: The statement that human societies experiment with different forms of governments is incorrect because, although inferable, it is not explicitly stated as the author's main point. The statement that any form of government tends to deteriorate by excess of its basic principle is correct because the author explicitly says democracy ruins itself by excess of democracy and describes other governments through their excesses. The statement that education of all citizens ensures a perfect democracy is incorrect because it is speculative and goes beyond the passage. The statement that having a government is a necessary evil because tyranny is inherent in any form is incorrect because it is an extreme position that fails to capture the passage's main message.

In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English. The number of Indians who can speak English is

20
30
30 or less
30 or more

Explanation: Out of 120 persons, 80 are Indians and 40 are foreigners. Out of 120 persons, 70 can speak English and 50 cannot. To maximize the number of Indians who can speak English, assume all English speakers are Indians, giving a maximum of 70. To minimize it, assume all 40 foreigners speak English, leaving 30 Indians who must speak English. Therefore, the number of English-speaking Indians is between 30 and 70, which means the correct answer is the option stating 30 or more.

Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum. Which of the following is/are correct? 1. S is always divisible by 74. 2. S is always divisible by 9. Select the correct answer using the code given below:

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: There are only three non-zero digits that are multiples of 3: 3, 6, and 9. Since repetition is not allowed, the possible three-digit numbers are 369, 396, 639, 693, 936, and 963. Their sum S equals 3996. S is divisible by both 74 and 9, so both given statements are correct and the right choice is the option stating both 1 and 2.

There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B. Consider the following statements: 1. The average score of Class-B will definitely decrease. 2. The average score of Class-A will definitely increase. Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: In matters of averages, adding items below the existing average decreases the average. The lowest score in Class-B is higher than the highest score in Class-A. Therefore, any student moving from Class-A to Class-B will bring marks lower than Class-B's existing range, causing Class-B's average to definitely decrease. However, the four students leaving Class-A could be above or below Class-A's average. If they are above the average, Class-A's average would decrease; if below, it would increase. Since a definite increase cannot be confirmed, Statement 2 is incorrect. Thus, only Statement 1 is correct, making the right choice the option stating 1 only.

Consider two Statements and a Question: Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom. Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom. Question: What is Seema's rank from the top in the class of 40 students? Which one of the following is correct in respect of the Statements and the Question?

Statement-1 alone is not sufficient to answer the Question
Statement-2 alone is not sufficient to answer the Question
Either Statement-1 alone or Statement-2 alone is sufficient to answer the Question
Both Statement-1 and Statement-2 are required to answer the Question

Explanation: Since the total number of students is known, either statement alone can determine Seema's rank. From Statement-1, Priya is 31st from the bottom in a class of 40, so she is 10th from the top. Since Priya is 4 ranks below Seema, Seema is 6th from the top. From Statement-2, Ena is 37th from the bottom, so she is 4th from the top. Since Ena is 2 ranks above Seema, Seema is 6th from the top. Therefore, either statement alone is sufficient, making the correct choice the option stating that either Statement-1 alone or Statement-2 alone is sufficient.

Consider two Statements and a Question: Statement-1: Each of A and D is heavier than each of B, E and F, but none of them is the heaviest. Statement-2: A is heavier than D, but is lighter than C. Question: Who is the heaviest among A, B, C, D and E? Which one of the following is correct in respect of the Statements and the Question?

Statement-1 alone is sufficient to answer the Question
Statement-2 alone is sufficient to answer the Question
Both Statement-1 and Statement-2 are required to answer the Question
Neither Statement-1 alone nor Statement-2 alone is sufficient to answer the Question

Explanation: Statement-1 establishes that A and D are each heavier than B, E, and F, but it does not identify the heaviest overall because the relationship between A and D is unknown and a heavier item outside the mentioned set could exist. Statement-2 gives C > A > D, but by itself it says nothing about B, E, or F. Combining both statements yields the complete order C > A > D > B, E, F, proving C is the heaviest. Therefore, both statements are required, making the correct choice the option stating that both Statement-1 and Statement-2 are required.

In the English alphabet, the first 4 letters are written in opposite order, and the next 4 letters are written in opposite order and so on; and at the end Y and Z are interchanged. Which will be the fourth letter to the right of the 13th letter?

N
T
H
I

Explanation: The English alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ. Arranged as required, the groups become DCBA, HGFE, LKJI, PONM, TSRQ, XWVU, ZY. The 13th letter in this new arrangement is P. The fourth letter to the right of P is T.

Passage: India faces a challenging immediate future in energy and climate policy-making. The problems are multiple : sputtering fossil fuel production capability; limited access to electricity and modern cooking fuel for the poorest; rising fuel imports in an unstable global energy context; continued electricity pricing and governance challenges leading to its costly deficits or surplus supply; and not least, growing environmental contestation around land, water and air. But all is not bleak: growing energy efficiency programmes; integrated urbanisation and transport policy discussions; inroads to enhancing energy access and security; and bold renewable energy initiatives, even if not fully conceptualized, suggest the promise of transformation. Which one of the following statements best reflects the critical message conveyed by the passage given above?

India's energy decision-making process is ever more complex and interconnected.
India's energy and climate policy is heavily tuned to sustainable development goals.
India's energy and climate actions are not compatible with its broader social, economic and environmental goals.
India's energy decision-making process is straightforward supply-oriented and ignores the demand side.

Explanation: The statement that India's energy decision-making process is ever more complex and interconnected is correct because the passage discusses multiple overlapping problems and integrated policy discussions across energy, urbanisation, and transport. The statement that India's policy is heavily tuned to sustainable development goals is incorrect because the passage does not support such an extreme characterization. The statement that India's actions are incompatible with broader social, economic, and environmental goals is incorrect because it is speculative and not discussed in the passage. The statement that the decision-making process is straightforward supply-oriented and ignores demand is incorrect because the passage does not explicitly discuss demand-side versus supply-side orientation.

Passage: There are reports that some of the antibiotics sold in the market are fed to poultry and other livestock as growth promoters. Overusing these substances can create superbugs, pathogens that are resistant to multiple drugs and could be passed along humans. Mindful of that, some farming companies have stopped using the drugs to make chickens gain weight faster. Since Denmark banned antibiotic growth promoters in the 1990s, the major pork exporters says it is producing more pigs – and the animals get fewer diseases. Which one of the following statements best reflects the critical message conveyed by the passage given above ?

People should avoid consuming the products of animal farming.
Foods of animal origin should be replaced with foods of plant origin.
Using antibiotics on animals should be banned.
Antibiotics should only be used to treat diseases.

Explanation: The suggestion that people should avoid consuming animal farming products is speculative and not supported by the passage. The proposal to replace animal foods with plant foods is far-fetched and beyond the passage's scope. The proposal to ban all use of antibiotics on animals is incorrect because the passage appreciates companies that stopped using antibiotics for weight gain rather than calling for an outright ban. The statement that antibiotics should only be used to treat diseases is correct because the passage criticizes their use as growth promoters and highlights benefits when such non-therapeutic use is stopped.

Passage: Policy makers and media have placed the blame for skyrocketing food prices on a variety of factors, including high fuel prices, bad weather in key food producing countries, and the diversion of land to non-food production. Increased emphasis, however, has been placed on a surge in demand for food from the most populous emerging economies. It seems highly probable that mass consumption in these countries could be well poised to create a food crisis. With reference to the above passage, the following assumptions have been made: 1. Oil producing countries are one of the reasons for high food prices. 2. If there is a food crisis in the world in the near future, it will be in the emerging economies. Which of the above statements is/are valid?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: Assumption 1, which claims oil producing countries are a reason for high food prices, is incorrect because the passage only mentions high fuel prices generally, not specifically oil producers. Assumption 2, which claims a future food crisis will be confined to emerging economies, is incorrect because the passage discusses a general food price surge and does not narrow the crisis to specific regions. Therefore, neither assumption is valid, making the correct choice the option stating neither 1 nor 2.

Passage: A central message of modern development economics is the importance of income growth, by which is meant growth in Gross Domestic Product (GDP). In theory, rising GDP creates employment and investment opportunities. As incomes grow in a country where the level of GDP was once low, households, communities, and governments are increasingly able to set aside some funds for the production of things that make for a good life. Today GDP has assumed such a significant place in the development lexicon, that if someone mentions "economic growth", we know they mean growth in GDP. With reference to the above passage, the following assumptions have been made: 1. Rising GDP is essential for a country to be a developed country. 2. Rising GDP guarantees a reasonable distribution of income to all households. Which of the above assumptions is/are valid ?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: Assumption 1, which claims rising GDP is essential for a country to be developed, is speculative and not supported by the passage's discussion of GDP's dominance in development economics. Assumption 2, which claims rising GDP guarantees reasonable income distribution to all households, is also speculative and unsupported. Therefore, neither assumption is valid, making the correct choice the option stating neither 1 nor 2.

Seven books P, Q, R, S, T, U and V are placed side by side. R, Q and T have blue covers and other books have red covers. Only S and U are new books and the rest are old. P, R and S are law reports; the rest are Gazetteers. Books of old Gazetteers with blue covers are

Q and R
Q and U
Q and T
T and U

Explanation: Blue covers belong to R, Q, and T. Old books are P, Q, R, and T. Gazetteers are Q, T, and U. The intersection of old books, Gazetteers, and blue covers is Q and T. Therefore, the correct answer is the option identifying Q and T.

Replace the incorrect term by the correct term in the given sequence 3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40 where odd terms and even terms follow the same pattern.

0
1
3
6

Explanation: Separating the odd and even series: the odd series is 3, 7, 13, 21, 31, 43 with consistent gaps of 4, 6, 8, 10, 12. The even series is 2, 4, 10, 18, 28, 40 with gaps that should follow 2, 6, 8, 10, 12. Replacing the first term 2 with 0 makes the even series 0, 4, 10, 18, 28, 40, giving the correct gaps of 4, 6, 8, 10, 12. Therefore, the correct replacement is 0.

You are given two identical sequences in two rows: Sequence I 8 4 6 15 52.5 236.5 Sequence II 5 A B C D E What is the entry in the place of C for the Sequence-II?

2.5
5
9.375
32.8125

Explanation: Sequence I follows the pattern: 8 × 0.5 = 4; 4 × 1.5 = 6; 6 × 2.5 = 15; 15 × 3.5 = 52.5; 52.5 × 4.5 = 236.25. Sequence II follows the same multiplication pattern: 5 × 0.5 = 2.5 for A; 2.5 × 1.5 = 3.75 for B; 3.75 × 2.5 = 9.375 for the entry in place C.

A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1.5 km/hr and Y walks with a uniform speed of 1 km/hr in the first hour, with a uniform speed of 1.25 km/hr in the second hour and with a uniform speed of 1.5 km/hr in the third hour and so on. Which of the following is/are correct? 1. They take 5 hours to meet. 2. They meet midway between A and B. Select the correct answer using the code given below:

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: The total distance is 15 km. If they meet midway, each covers 7.5 km. At a uniform speed of 1.5 km/hr, X takes 5 hours to cover 7.5 km. Y's speeds over 5 equal hourly slots are 1, 1.25, 1.5, 1.75, and 2 km/hr, averaging 1.5 km/hr. In 5 hours at an average of 1.5 km/hr, Y also covers 7.5 km. Thus both statements are true, making the correct choice the option stating both 1 and 2.

A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?

2
3
4
5

Explanation: Since the marks are in strictly increasing proportions and the overall average is 60%, exactly half of the values must lie below the average and half above it. Therefore, three papers are below 60%. Alternatively, assuming 100 marks per paper gives a total of 600, and 60% overall is 360 total marks. Solving 5x + 6x + 7x + 8x + 9x + 10x = 360 yields x = 8. The marks become 40, 48, 56, 64, 72, and 80. In three of these papers the student scored less than 60, confirming the correct answer is the option stating 3.

Passage: Fig trees (genus Ficus) are considered sacred in India, East Asia and Africa and are common in agricultural and urban landscapes where other large trees are absent. In natural forests, fig trees provide food for wildlife when other resources are scarce and support a high density and diversity of frugivores (fruit-eating animals). If frugivorous birds and bats continue to visit to fig trees located in sites with high human disturbances, sacred fig trees may promote frugivore abundance. Under a favourable microclimate, plenty of seedlings of other tree species would grow around fig trees. On the basis of the passage given above, the following assumption have been made: 1. Fig trees can often be keystone species in natural forests. 2. Fig trees can grow where other large woody species cannot grow. 3. Sacred trees can have a role in biodiversity conservation. 4. Fig trees have a role in the seed dispersal of other tree species. Which of the above assumptions is/are valid?

1 and 2 only
3 only
2 and 4 only
1, 3 and 4 only

Explanation: Assumption 1, which states fig trees can often be keystone species in natural forests, is valid because the passage emphasizes their critical role in providing food and supporting wildlife diversity when other resources are scarce. Assumption 2, which claims fig trees can grow where other large woody species cannot, is not a valid assumption because negating it does not invalidate any statement in the passage; it is at best an inference. Assumption 3, which states sacred trees can have a role in biodiversity conservation, is valid because the passage links sacred fig trees to frugivore abundance and coexistence of species. Assumption 4, which states fig trees have a role in seed dispersal of other tree species, is valid because the passage connects visits by birds and bats to the presence of seedlings of other species around fig trees. Therefore, assumptions 1, 3, and 4 are valid, making the correct choice the option stating 1, 3 and 4 only.

Passage: At the heart of agroecology is the idea that agroecosystems should mimic the biodiversity levels and functioning of natural ecosystems. Such agricultural mimics, like their natural models, can be productive, pest-resistant, nutrient conserving, and resilient to shocks and stresses. In ecosystems there is no 'waste', nutrients are recycled indefinitely. Agroecology aims at closing nutrient loops, i.e., returning all nutrients that come out of the soil back to the soil such as through application of farmyard manure. It also harnesses natural processes to control pests and build soil fertility i.e., through intercropping. Agroecological practices include integrating trees with livestock and crops. Consider the following: 1. Cover crops 2. Fertigation 3. Hydroponics 4. Mixed farming 5. Polyculture 6. Vertical farming Which of the above farming practices can be compatible with agroecology, as implied by the passage?

1, 4 and 5 only
2, 3, 4 and 5 only
1, 2, 3 and 6 only
4 and 6 only

Explanation: Agroecology focuses on mimicking natural ecosystems. Fertigation, which delivers fertilizer through irrigation systems, is artificial and not seen in nature. Hydroponics, which grows plants in nutrient solutions without soil, is also artificial. Vertical farming, which stacks crops in layers, is unnatural. Cover crops, mixed farming, and polyculture align with natural processes such as nutrient cycling, intercropping, and integrating trees with crops and livestock. Therefore, practices 1, 4, and 5 are compatible, making the correct choice the option stating 1, 4 and 5 only.

Passage: Computers increasingly deal not just with abstract data like credit card details and databases, but also with the real world of physical objects and vulnerable human bodies. A modern car is a computer on wheels; an aeroplane is a computer on wings. The arrival of the "Internet of Things" will see computers baked into everything from road signs and MRI scanners to prosthetics and insulin pumps. There is little evidence that these gadgets will be any more trustworthy than their desktop counterparts. Hackers have already proved that they can take remote control of internet connected cars and pacemakers. Which one of the following statements best reflects the most critical inference that can be made from the passage given above?

Computers are not completely safe.
Companies producing the software do not take cyber security seriously.
Stringent data security laws are needed.
The present trend of communication technologies will affect our lives in future.

Explanation: The inference that computers are not completely safe is correct because the passage concludes that there is little evidence gadgets will be trustworthy and cites hackers taking remote control of cars and pacemakers. The claim that companies do not take cyber security seriously is speculative and not discussed. The claim that stringent data security laws are needed is a possible fallout but less central than the direct inference about safety. The statement that the present trend of communication technologies will affect our lives is too broad and does not capture the passage's specific focus on computer safety concerns.

Passage: A social and physical environment riddled with poverty, inequities, unhygienic and insanitary conditions generates the risk of infectious diseases. Hygiene has different levels: personal, domestic and community hygiene. There is no doubt that personal cleanliness brings down the rate of infectious diseases. But the entry of the market into this domain has created a false sense of security that gets conditioned and reinforced by the onslaught of advertisements. Experience in Western Europe shows that along with personal hygiene, general improvements in environmental conditions and components like clean water, sanitation and food security have brought down infant/child death/infections rates considerably. The obsession with hand hygiene also brings in the persisting influence of the market on personal health, overriding or marginalizing the negative impact on ecology and the emergence of resistant germs. On the basis of the passage given above, the following assumptions have been made: 1. People who are obsessed with personal hygiene tend to ignore the community hygiene. 2. Emergence of multi-drug resistant germs can be prevented by personal cleanliness. 3. Entry of the market in the domain of hygiene increases the risk of infectious diseases. 4. Scientific and micro-level interventions are not sufficient to bring down the burden of infectious diseases. 5. It is community hygiene implemented through public health measures that is really effective in the battle against infectious diseases. Which of the above assumptions are valid?

1 and 2 only
3 and 4 only
4 and 5 only
1, 2 and 4 only

Explanation: Assumption 1, which claims people obsessed with personal hygiene ignore community hygiene, is invalid because negating it does not affect the passage's conclusion. Assumption 2, which claims multi-drug resistant germs can be prevented by personal cleanliness, is invalid because the passage mentions resistant germs generally, not multi-drug resistant ones specifically, and assumptions should not be more specific than the passage. Assumption 3, which claims market entry increases disease risk, is an inference rather than a valid assumption because the passage links market entry to false security and ecological harm, not directly to increased infection risk. Assumptions 4 and 5 are valid because they serve as the missing link between community hygiene, environmental conditions, and reducing infectious diseases, which is the passage's central theme. Therefore, the valid assumptions are 4 and 5, making the correct choice the option stating 4 and 5 only.

A Statement followed by Conclusion-I and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statement, disregarding the commonly known facts. Statement: Some cats are almirahs. Some almirahs are chairs. All chairs are tables. Conclusion-I: Certainly some almirahs are tables. Conclusion-II: Some cats may not be chairs. Which one of the following is correct?

Only Conclusion-I
Only Conclusion-II
Both Conclusion-I and Conclusion-II
Neither Conclusion-I nor Conclusion-II

Explanation: Conclusion-I is valid because since all chairs are tables, substituting tables for chairs in the second premise yields 'some almirahs are tables'. Conclusion-II is valid because the first two premises do not establish that any cats are chairs, so it remains possible that some cats are not chairs. Therefore, both conclusions follow, making the correct choice the option stating both Conclusion-I and Conclusion-II.

A boy plays with a ball, and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing?

4
5
6
7

Explanation: Starting height is 150 cm. After the first hit, the bounce height is 120 cm. After the second, 96 cm. After the third, 76.8 cm. After the fourth, 61.44 cm. After the fifth, 49.15 cm. Since 49.15 cm is less than 50 cm, the ball does not bounce back after the fifth hit. Therefore, the ball hits the ground 5 times before stopping.

Images of consonants of the English alphabet (Capitals) are observed in a mirror. What is the number of images of these which do not look like their original shapes?

13
14
15
16

Explanation: The consonants are B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z, totaling 21. Those whose mirror images look like the original are H, M, T, V, W, X, and Y, totaling 7. Therefore, the number of consonants whose mirror images do not look like their original shapes is 21 minus 7, which equals 14.

A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house?

20 km
25 km
30 km
35 km

Explanation: Converting the route into cardinal directions: 10 km South, 20 km East, 40 km North, 5 km East, and 30 km South. The net North-South movement is 20 km South, and the net East-West movement is 25 km East. The shortest distance from the starting point is the straight-line distance, which equals the net eastward displacement of 25 km because the starting and ending points align horizontally. Therefore, the shortest distance is 25 km.

Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10?

6
7
8
9

Explanation: For integers between 700 and 1000, the first digit is 7, 8, or 9. If the first digit is 7, the remaining two digits must sum to 3, giving 703, 712, 721, and 730. If the first digit is 8, the remaining digits must sum to 2, giving 802, 811, and 820. If the first digit is 9, the remaining digits must sum to 1, giving 901 and 910. This yields a total of 9 integers. Therefore, the correct answer is the option stating 9.

A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point?

An angle less than 45 degrees South of East
An angle less than 45 degrees North of East
An angle more than 45 degrees South of East
An angle more than 45 degrees North of East

Explanation: The net displacement is 6 km North and 8 km East. Because the eastward distance is greater than the northward distance, the angle measured from the East axis towards North is less than 45 degrees. Therefore, the correct direction is an angle less than 45 degrees North of East.

Passage: Researchers simulated street lighting on artificial grassland plots containing pea-aphids, sap-sucking insects, at night. These were exposed to two different types of light – a white light similar to newer commercial LED lights and an amber light similar to sodium street lamps. The low intensity amber light was shown to inhibit, rather than induce, flowering in a wild plant of the pea family which is a source of food for the pea-aphids in grasslands. The number of aphids was also significantly suppressed under the light treatment due to the limited amount of food available. Which one of the following statements best reflects the most critical inference that can be made from the passage given above?

Low intensity light has more adverse effect on the plants as compared to high intensity light.
Light pollution can have a permanent adverse impact on an ecosystem.
White light is better for the flowering of plants as compared to the light of other colours.
Proper intensity of light in an ecosystem is important not only for plants but for animals too.

Explanation: The statement that low intensity light has more adverse effect than high intensity light is incorrect because the passage does not compare intensities. The inference that light pollution can have a permanent adverse impact on an ecosystem is correct because the passage demonstrates how artificial lighting disrupts plant flowering and suppresses aphid populations. The claim that white light is better for flowering than other colours is incorrect because the passage does not compare the effects of white and amber light on flowering. The statement that proper light intensity is important for both plants and animals is incorrect because the passage focuses on adverse impacts rather than defining what proper intensity would be.

Passage: Researchers simulated street lighting on artificial grassland plots containing pea-aphids, sap-sucking insects, at night. These were exposed to two different types of light – a white light similar to newer commercial LED lights and an amber light similar to sodium street lamps. The low intensity amber light was shown to inhibit, rather than induce, flowering in a wild plant of the pea family which is a source of food for the pea-aphids in grasslands. The number of aphids was also significantly suppressed under the light treatment due to the limited amount of food available. Which one of the following statements best reflects the most critical inference that can be made from the passage given above?

Low intensity light has more adverse effect on the plants as compared to high intensity light.
Light pollution can have a permanent adverse impact on an ecosystem.
White light is better for the flowering of plants as compared to the light of other colours.
Proper intensity of light in an ecosystem is important not only for plants but for animals too.

Explanation: The claim that low intensity light has more adverse effect than high intensity light is incorrect because the passage does not compare intensities. The inference that light pollution can have a permanent adverse impact on an ecosystem is correct because the passage demonstrates how artificial lighting disrupts plant flowering and suppresses aphid populations. The claim that white light is better for flowering than other colours is incorrect because the passage does not compare the effects of white and amber light on flowering. The statement that proper light intensity is important for both plants and animals is incorrect because the passage focuses on adverse impacts rather than defining what proper intensity would be.

Passage: Approximately 80 percent of all flowering plant species are pollinated by animals, including birds and mammals, but the main pollinators are insects. Pollination is responsible for providing us with a wide variety of food, as well as many plant-derived medicines. At least one-third of the world's agricultural crops depend upon pollination. Bees are the most dominant taxa when it comes to pollination and they are crucial to more than four hundred crops. Pollination is an essential service that is the result of intricate relationship between plants and animals, and the reduction or less of either affects the survival of both. Effective pollination requires resources, such as refuges of pristine natural vegetation. On the basis of the passage given above, the following assumptions have been made: 1. Sustainable production of India's cereal food grains is impossible without the diversity of pollinating animals. 2. Monoculture of horticultural crops hampers the survival of insects. 3. Pollinators become scarce in cultivated areas devoid of natural vegetation. 4. Diversity in insects induces diversity of plants. Which of the above assumptions is/are valid?

1 only
2, 3 and 4 only
1 and 2 only
3 and 4 only

Explanation: The assumption that sustainable production of India's cereal food grains is impossible without the diversity of pollinating animals is incorrect because it is too specific and goes beyond the general findings discussed in the passage. The assumption that monoculture of horticultural crops hampers the survival of insects is incorrect because the passage does not discuss monoculture practices. The assumption that pollinators become scarce in cultivated areas devoid of natural vegetation is correct because the passage states that effective pollination requires resources such as pristine natural vegetation, implying that their reduction affects pollinator presence. The assumption that diversity in insects induces diversity of plants is correct because the passage describes an intricate relationship where the reduction or loss of either plants or animals affects the survival of both. Therefore, only assumptions 3 and 4 are valid.

Passage: A study conducted on the impacts of climate change over the Cauvery basin of Tamil Nadu using regional climate models showed an increasing trend for maximum and minimum temperatures, and a decrease in the number of rainy days. These climatic shifts will have an impact on the hydrological cycles in the region, lead to more run-off and less recharge, and affect the groundwater tables. Further, there has been an increase in the frequency of droughts in the State. This has driven farmers to increase dependency on groundwater resources to secure their crops. Which one of the following statements best reflects the crux of the passage given above?

Development of regional climate models helps in choosing climate-smart agricultural practices.
Heavy dependence on groundwater resources can be reduced by adopting dry-land cropping systems.
Climate changes increase the criticality of water resources while simultaneously threatening it.
Climate changes cause the farmers to adopt unsustainable livelihoods and risky coping strategies.

Explanation: The statement that development of regional climate models helps in choosing climate-smart agricultural practices is not discussed in the passage. The statement that heavy dependence on groundwater can be reduced by adopting dry-land cropping systems is also not mentioned. The statement that climate changes increase the criticality of water resources while simultaneously threatening it accurately captures the main point about rising temperatures, reduced rainfall, droughts, and increased groundwater abuse. The statement that climate changes cause farmers to adopt unsustainable livelihoods is not the primary focus of the passage. Therefore, the correct answer is the option stating that climate changes increase the criticality of water resources while simultaneously threatening it.

Passage: Researchers were able to use stem cells to gauge the neurotoxic effects of the environmental pollutant Bisphenol A (BPA). They used a combination of biochemical and cell-based assays to examines the gene expression profile during the differentiation of mouse embryonic stem cells upon treatment with BPA, a compound known to cause heart diseases, diabetes, and developmental abnormalities in humans. They were able to detect and measure BPA toxicity towards the proper specification of primary germ layers, such as endoderm and ectoderm, and the establishment of neural progenitor cells. On the basis of the passage given above, the following assumptions have been made: 1. BPA may alter embryonic development in vivo. 2. Biochemical and cell-based assays are useful in finding out treatments for pollution-induced diseases. 3. Embryonic stem cells could serve as a model to evaluate the physiological effects of environmental pollutants. Which of the above assumptions are valid?

1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3

Explanation: The assumption that BPA may alter embryonic development is correct because the passage notes developmental abnormalities and effects on mouse embryonic stem cells upon treatment with BPA. The assumption that biochemical and cell-based assays are useful in finding treatments for pollution-induced diseases is incorrect because the passage only mentions using them to examine gene expression and measure toxicity, not to develop treatments. The assumption that embryonic stem cells could serve as a model to evaluate the physiological effects of environmental pollutants is correct because the passage explicitly demonstrates this use. Therefore, only assumptions 1 and 3 are valid.

If 3^2019 is divided by 10, then what is the remainder?

1
3
7
9

Explanation: The powers of 3 follow a repeating pattern for the unit digit: 3^1 = 3, 3^2 = 9, 3^3 = 27 (unit digit 7), 3^4 = 81 (unit digit 1), 3^5 = 243 (unit digit 3). The unit place repeats after every 4 steps. When the exponent 2019 is divided by 4, the remainder is 3. Therefore, the unit place of 3^2019 will be the same as that of 3^3, which is 7. Hence, when 3^2019 is divided by 10, the remainder will be 7.

The number 3798125P369 is divisible by 7. What is the value of the digit P?

1
6
7
9

Explanation: Using the divisibility rule for 7 by alternating triplets: (37) (981) (25P) (369). Calculate the difference between the sum of alternate triplets: (369 + 981) - (25P + 37) = 1350 - (250 + P + 37) = 1350 - 287 - P = 1063 - P. Dividing 1063 by 7 yields a remainder of 6 (since 1063 = 7 * 151 + 6). For the entire expression to be divisible by 7, the value (6 - P) must be a multiple of 7. The only single digit P that satisfies this condition is 6. Alternatively, testing the options directly shows that when P is 6, the resulting calculation is perfectly divisible by 7.

From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1m, where m = 1, 2, 3, …, 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is 69 + 0.15n for any n. On which date in the year 2021 are the prices of these two fuels equal?

21st May
20th May
19th May
18th May

Explanation: Determine the price of petrol on and after the 100th day of the year. On day 100, the price is 80 + 0.1(100) = 90 Rupees, and it remains constant after this day. Let's find the day n when the diesel price reaches 90 Rupees: 69 + 0.15n = 90. This simplifies to 0.15n = 21, which yields n = 140. We calculate the total number of days until the end of April, which is 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) = 120 days. Since n = 140, the required date falls in May. Subtracting the 120 days of the previous months from 140 gives the 20th day of May. Therefore, the prices are equal on 20th May.

A biology class at high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population?

P = 12 + 50n
P = 50 + 12n
P = 50 (2)^(12n)
P = 50 (2)^(n/12)

Explanation: The population doubles every 12 years, and the initial population in the year 2021 is 50 animals. This means after 12 years (when n=12), the population should be 100. Checking the mathematical models: substituting n=12 into P = 50 * 2^(n/12) gives P = 50 * 2^(12/12) = 50 * 2 = 100 animals. The linear models P = 12 + 50n and P = 50 + 12n, as well as the exponential model P = 50 * 2^(12n), do not yield 100 after 12 years. Thus, the equation P = 50 (2)^(n/12) is the correct representation.

In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys?

45%
40%
30%
20%

Explanation: Let the total number of students in the class be 100. The number of Indian students is 60, meaning the number of foreign students is 100 - 60 = 40. The total number of girl students in the class is 50. According to the data, 30% of the Indian students are girls, so there are 0.30 * 60 = 18 Indian girls. Consequently, the number of foreign girl students is the total girls minus Indian girls, which is 50 - 18 = 32. Since there are 40 foreign students in total and 32 are girls, the number of foreign boy students is 40 - 32 = 8. The percentage of boys among the foreign students is (8 / 40) * 100 = 20%.

A Statement followed by Conclusion-I and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statement, disregarding the commonly known facts. Statement: Some radios are mobiles. All mobiles are computers. Some computers are watches. Conclusion-I: Certainly some radios are watches. Conclusion-II: Certainly some mobiles are watches. Which one of the following is correct?

Only Conclusion-I
Only Conclusion-II
Both Conclusion-I and Conclusion-II
Neither Conclusion-I nor Conclusion-II

Explanation: Based on the statements provided, from 'some radios are mobiles' and 'all mobiles are computers', we can definitively conclude that some radios are computers. However, the statement 'some computers are watches' does not establish any necessary overlap or relationship between watches and radios, nor between watches and mobiles. Therefore, it is not certain that any radios are watches or that any mobiles are watches. Neither conclusion logically follows from the premises.

Passage: "........ most people would agree that telling deliberate lies is wrong, except perhaps in certain special situations where more harm will be done by telling the truth. Even the most truthful people probably tell a good many more lies that might be regarded as semantic lies; their use of words contains some measure of falsehood, more or less deliberate." The idea which the first part of the passage mention is

agreement about telling lies.
disagreement about telling lies.
disagreement about telling the truth.
disagreement about the harm in telling the truth.

Explanation: From the provided passage, it is stated that most people would agree that telling deliberate lies is wrong. Therefore, it is reasonable to conclude that the opening concept discusses an agreement among people regarding the general immorality of telling lies. The passage highlights a consensus on the act of lying before contrasting it with special situational exceptions regarding truth-telling.

Passage: "........ most people would agree that telling deliberate lies is wrong, except perhaps in certain special situations where more harm will be done by telling the truth. Even the most truthful people probably tell a good many more lies that might be regarded as semantic lies; their use of words contains some measure of falsehood, more or less deliberate." Which one of the following habits is found more often in good people ?

Mixing up the true and false
Intentional mixing up of truth with the false.
Falsification of facts
Complete concealment of truth

Explanation: The passage highlights in the final line that even the most truthful people use words that contain some measure of falsehood, more or less deliberate. This indicates that good people often intentionally mix truth with minor falsehoods or semantic lies to navigate situations, particularly to reduce the harm that blunt truth might cause. The passage does not support complete concealment or total falsification of facts.

Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ?

Monday
Wednesday
Thursday
Sunday

Explanation: The next meeting day for Joseph, Harsh, and Sumit can be determined by finding the least common multiple (LCM) of their visiting intervals. The LCM of 5, 24, and 9 is 360 days. To find the day of the week, we divide 360 by 7 (the number of days in a week), which gives 51 weeks and a remainder of 3 odd days. Adding these 3 odd days to the initial Sunday results in a Wednesday.

The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. Consider the following statements: 1. The sum of the two digits of the number can be determined only if the product of the two digits is known. 2. The difference between the two digits of the number can be determined. Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: Let the original number be 10x + y. The number obtained upon interchanging the digits is 10y + x. The difference between these two numbers is (10x + y) - (10y + x) = 9x - 9y = 9(x - y). We are given that this difference is 54. So, 9(x - y) = 54, which simplifies to x - y = 6. This confirms that the difference between the two digits can be determined definitively, making the statement that the difference between the two digits can be determined correct. The possible pairs of such digits are (7, 1), (8, 2), and (9, 3). While knowing the product of the digits would allow us to identify the specific pair and find their sum, knowing the ratio of the two digits would also allow us to do so. Therefore, the claim that the sum can be determined only if the product is known is incorrect.

X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements: 1. 8 years ago, the age of X was five times the age of Y. 2. After 14 years, the age of X would be two times the age of Y. Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: The present age of X is 42 years. Let the present age of Y be y years. At the time of Y's birth (which was y years ago), X's age was 42 - y. The problem states that X's age at that time was twice Y's present age. So, 42 - y = 2y. This simplifies to 3y = 42, making Y's present age 14 years. Checking the statement that 8 years ago X's age was five times Y's age: 8 years ago, X was 34 and Y was 6. Since 34 is not five times 6, this statement is incorrect. Checking the statement that after 14 years X's age would be two times Y's age: after 14 years, X will be 56 and Y will be 28. Since 56 is exactly two times 28, this statement is correct.

If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price?

0%
5% increase
5% decrease
Cannot be determined due to insufficient data

Explanation: Let the initial price of the article be Rs. 100. A 20% decrease reduces the price to 100 - (0.20 * 100) = Rs. 80. Subsequently, the new price is increased by 25%. A 25% increase on Rs. 80 equates to 80 + (0.25 * 80) = 80 + 20 = Rs. 100. Since the final price is identical to the initial price, there is a net change of 0%.

When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number?

15713
15723
15783
15873

Explanation: To find the correct number, multiply the candidates by 7 and check if the resulting product consists entirely of the digit 1. Testing the correct numerical string: 15873 multiplied by 7 equals 111111. Since this product comprises ones exclusively, 15873 is the correct number.

A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50%

24
21
18
15

Explanation: The man completes 7/8 of the job in 21 days. His rate of work is (7/8) / 21 = 1/24 of the job per day. This means completing the entire original job takes a total of 24 days. Since he has worked for 21 days, he has 3 days of work remaining to finish the original 1/8 of the job. The quantum of work is then increased by 50% of the total original job, adding an extra 1/2 of the original work. The time required to complete this additional 50% work is (1/2) / (1/24) = 12 days. The total additional days required is the sum of the time for the remaining original work and the newly added work, which is 3 + 12 = 15 days.

Passage: In our schools, we teach our children all that is there to know about Physics, maths and history and what-have you. But do we teach them about the bitter caste divide that plagues the country, about the spectre of famine that stalks large part of our land, about gender sensitivity, about the possibility of atheism as a choice, etc.? Equally important, do we teach them to ask question, or do we teach them only to passively receive our wisdom? From the cocooned world of school, suddenly, the adolescent finds himself/herself in the unfettered world of university. Here he/she is swept up in a turmoil of ideas and influences and ideologies. For someone who has been discouraged from asking questions and forming an opinion, this transition can be painful. Which one of the following best reflects the central idea of the passage given above ?

School curriculum is not compatible with the expectations of children and parents.
Emphasis on academic achievements does give time for development of personality and skills.
Preparing the children to be better citizens should be the responsibility of the education system.
To be a better citizen, the present world order demands societal and life-coping skills in addition to academic content.

Explanation: The passage explicitly emphasizes the need for societal awareness and life-coping skills alongside traditional academic content. It questions whether schools are effectively teaching students about real-world societal issues like caste divides, famine, and gender sensitivity, and whether they are being taught critical thinking. This directly aligns with the idea that modern citizenship demands these extra dimensions of education to prevent painful transitions into the real world. The statement that school curriculum is not compatible with the expectations of children and parents is not the central focus. The statement that emphasis on academic achievements does not give time for personality development is not explicitly framed that way in the passage. The statement that preparing children to be better citizens should be the responsibility of the education system is close, but the passage specifically stresses the need for societal and life-coping skills in addition to academics rather than broadly assigning responsibility.

There are three points P, Q and R on a straight line such that PQ:QR = 3:5. If n is the number of possible values of PQ:PR, then what is n equal to ?

1
2
3
4

Explanation: We must arrange the three points P, Q, and R on a straight line such that the ratio of lengths PQ : QR = 3 : 5. There are two viable geometric arrangements. In the first scenario, Q is positioned between P and R. This makes PR = PQ + QR = 3 + 5 = 8, resulting in a PQ:PR ratio of 3:8. In the second scenario, P is positioned between Q and R. This makes QR = PQ + PR, meaning 5 = 3 + PR, which yields PR = 2. This results in a PQ:PR ratio of 3:2. Therefore, there are exactly 2 possible values for the given ratio.

On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?

4
6
8
12

Explanation: A standard 8x8 chess board features two main diagonals, each consisting of exactly 8 squares. When selecting 6 consecutive squares along a single straight diagonal path of 8 squares, there are exactly 3 possible groupings (squares 1 to 6, squares 2 to 7, and squares 3 to 8). Because there are two such main diagonals on the board, the total number of ways to choose 6 consecutive squares is 3 + 3 = 6.

In the series_b_a_ba_b_abab_aab; fill in the six blanks (_) using one of the following given four choices such that the series follows a specific order.

bababa
baabba
bbaabb
ababab

Explanation: The given series follows a specific, repeating pattern of the blocks 'abb' followed sequentially by 'aab'. By substituting the characters 'ababab' into the respective empty blanks, the completed series reads: abb aab abb aab abb aab. This perfectly maintains the alternating three-letter block sequence.

Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed?

3
6
9
12

Explanation: For the generated five-digit number to be greater than 30000, it must explicitly start with the digit 3. This leaves four remaining positions to be filled by the remaining four digits: two 2s and two 3s. The number of ways to arrange these remaining items with repetitions is given by 4! / (2! * 2!) = 24 / 4 = 6. These distinct valid combinations are: 33322, 33232, 33223, 32332, 32323, and 32233.

Consider the following statements : 1. The sum of 5 consecutive integers can be 100. 2. The product of three consecutive natural numbers can be equal to their sum. Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: Analyzing the statement that the sum of 5 consecutive integers can be 100: Let the 5 consecutive integers be represented as x-2, x-1, x, x+1, and x+2. Their total sum equals 5x. Setting 5x = 100 yields x = 20. Thus, the integers are 18, 19, 20, 21, and 22, making this statement correct. Analyzing the statement that the product of three consecutive natural numbers can be equal to their sum: The first three natural numbers are 1, 2, and 3. Their sum is 1 + 2 + 3 = 6, and their product is 1 * 2 * 3 = 6. Since the product equals the sum, this statement is also correct. Therefore, both statements are correct.

A cubical vessel of side 1 m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel) ?

1000
10000
100000
1000000

Explanation: The total volume of the cubical vessel is calculated as Side * Side * Side = 1 m * 1 m * 1 m = 1 cubic meter. Standard conversion dictates that 1 cubic meter equals 1,000 liters. Since 1 liter is equivalent to 1,000 milliliters, multiplying 1,000 liters by 1,000 gives 1,000,000 milliliters.

There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place?

3
4
5
6

Explanation: Let the six individuals standing in the row be numbered sequentially from 1 to 6. The requirement is to select a group of 3 individuals such that no two selected individuals are standing next to each other. Systematically listing the valid, non-adjacent combinations yields: (1, 3, 5), (1, 4, 6), (1, 3, 6), and (2, 4, 6). Counting these shows there are exactly 4 distinct and valid combinations.

An amount of money was distributed among A, B and C in the ratio p : q : r. Consider the following statements : 1. A gets the maximum share if p is greater than (q+r). 2. C gets the minimum share if r is less than (p+q). Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Explanation: The money distribution is governed by the ratio p : q : r. Evaluating the statement that A gets the maximum share if p is greater than (q+r): Since ratio values are positive, if p > (q + r), it mathematically guarantees that p is independently larger than q and independently larger than r. Thus, A undoubtedly receives the largest share, making this statement correct. Evaluating the statement that C gets the minimum share if r is less than (p+q): If r < (p + q), it does not strictly guarantee that r is the smallest numerical value. For instance, if p = 2, q = 4, and r = 5, the condition 5 < (2 + 4) is met, yet r remains the largest share, not the smallest. Thus, this statement is incorrect. Therefore, only the statement regarding A getting the maximum share when p exceeds q+r is correct.

Passage: The best universities like Harvard and MIT, despite having the luxury of having some truly excellent teachers on their payroll, are increasingly embracing the "flipped classroom" format, where students listen to video lectures at home, and spend class time applying their knowledge, solving problems, discussing examples, etc. Professors guide that discussion and fill in wherever necessary, explaining those bits that seem to be eluding the students and throwing in advanced ideas that happen to be topical. These universities have made their video lectures available free for anyone in the world. They are also encouraging colleges and universities all over the world to integrate these online courses into their own pedagogy, picking the pieces that are appropriate for their needs and building a package around them. Which one of the following statements best reflects the central idea of the passage given above?

Efficacy of universities would be better in online mode of conducting classroom tuition as compared conventional method.
Availability of higher education can be made easier and cheaper without diluting the content.
We need not invest much in infrastructure related to higher education and yet develop better human and social capital.
Private sector institutions in higher education as well as coaching institutes can take advantage of this opportunity and thrive well.

Explanation: The passage does not argue for the absolute superiority of online education over conventional methods, nor does it explicitly focus on the private sector or coaching institutes. Instead, it underscores a collaborative global approach where institutions can freely adopt premium digital content to supplement their pedagogy. This suggests that institutions can leverage existing world-class digital resources without necessarily investing heavily in new physical infrastructure, thereby efficiently developing human capital. The statement about efficacy being better in online mode is not the central claim. The statement about availability being made easier and cheaper is partially true but not the core idea. The statement about private sector institutions thriving is beyond the passage's scope.

Passage: Our cities are extremely vulnerable to climate change because of large concentrations of populations and poor infrastructure. Moreover, population densities are increasing in them but we have not yet developed the systems to address climate change impacts. Our cities contribute to 65 percent of the GDP, but there are not enough facilities to cater to the needs of the people. It is important to address the issues of air quality, transport, etc., that are vital to identifying sustainable solutions. We need to involve citizens in city planning and create an ecosystem that meets the needs of people. Which among the following is the most logical and rational inference that can be made from the passage given above ?

Our cities need to have well-defined administrative set-up with sufficient autonomy.
Ever increasing population densities is a hindrance in our efforts to achieve sustainable development.
To maintain and develop our cities we need to adopt sustainability related interventions.
Public-Private Partnership mode of development is the viable long-term solution for the infrastructure and sustainability problems of India.

Explanation: The passage highlights the vulnerability of cities to climate change due to dense populations and inadequate infrastructure. It explicitly calls for addressing core issues like air quality and transportation as vital pathways to identifying sustainable solutions. Therefore, the most direct rational inference is the necessity of adopting sustainability-related interventions to properly maintain and develop urban centers. The statement about needing a well-defined administrative set-up is not the primary focus. The statement that ever-increasing population densities are a hindrance describes a problem but not the inference. The statement about public-private partnerships being the viable long-term solution is not discussed in the passage.

Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct ?

A pencil costs more than a pen.
The price of a pencil is equal to that of a pen
The price of a pen is two times the price of a pencil
The price of a pen is three times the price of a pencil

Explanation: Let the price of a single pen be defined as a, and the price of a single pencil be defined as b. Since Jay and Vijay spent identical total amounts at the store, their individual expenditures are equal: 3a + 5b = 2a + 7b. Subtracting 2a from both sides of the equation simplifies it to a + 5b = 7b. Subsequently subtracting 5b from both sides yields a = 2b. This algebraic proof definitively demonstrates that the price of one pen is exactly twice the price of one pencil.

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