**Directions for the following 3 (three) items:**

**Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.**

*Passage–1*

The main threat to maintaining progress in human development comes from the increasingly evident unsustainability of production and consumption patterns. Current production models rely heavily on fossil fuels. We now know that this is unsustainable because the resources are finite. The close link between economic growth and greenhouse gas emissions needs to be served for human development to become truly sustainable. Some developed countries have begun to alleviate the worst effects by expanding recycling and investing in public transport and infrastructure. But most developing countries are hampered by the high costs and low availability of clean energy sources. Developed countries need to support developing countries' transition to sustainable human development.

**Q1.** Unsustainability in production pattern is due to which of the following?

1. Heavy dependence on fossil fuels

2. Limited availability of resources

3. Expansion of recycling

Select the correct answer using the code given below.

(a) 1 and 2 only

(b) 2 only

(c) 1 and 3 only

(d) 1, 2 and 3

**Ans. **(a)

__Solution:__

**Statement 1** is correct: The passage indeed highlights the heavy reliance on fossil fuels in current production models.

**Statement 2 **is correct: The passage emphasizes the unsustainability of relying on finite resources, which aligns with the statement.

**Statement 3** is incorrect: While the passage discusses the importance of recycling as a solution to sustainability challenges, it does not state that the expansion of recycling is the reason for the unsustainability of current production models. Therefore, this statement is incorrect.

**Q2. **Consider the following statements:

Developed countries can support developing countries' transition to sustainable human development by

1. making clean energy sources available at low cost

2. providing loans for improving their public transport at nominal interest rates

3. encouraging them to change their production and consumption patterns

Which of the statements given above is/are correct?

(a) 1 only

(b) 1 and 2 only

(c) 2 and 3 only

(d) 1, 2 and 3

**Ans. **(b)

__Solution:__

**Statement 1 **is correct: The passage does suggest that developed countries should support developing countries in transitioning to sustainable human development, as indicated by the mention of high costs and low availability of clean energy sources.

**Statement 2** is correct: The passage highlights the challenges faced by developing countries due to high costs, which implies that they may require support from developed countries in their transition efforts.

**Statement 3** is incorrect: While encouraging developing countries to change their production and consumption patterns may indeed be beneficial for transitioning to sustainable human development, the passage does not explicitly mention this as a call for action directed towards developed countries. Therefore, this statement cannot be inferred directly from the passage.

*Passage–2*

Unless the forces and tendencies which are responsible for destroying the country's environment are checked in the near future and afforestation of denuded areas is taken up on a massive scale, the harshness of the climatic conditions and soil erosion by wind and water will increase to such an extent that agriculture, which is the mainstay of our people, will gradually become impossible. The desert countries of the world and our own desert areas in Rajasthan are a grim reminder of the consequences of large-scale deforestation. Pockets of desert-like landscape are now appearing in other parts of the country including the Sutlej-Ganga Plains and Deccan Plateau. Where only a few decades back there used to be lush green forests with perennial streams and springs, there is only brown earth, bare of vegetation, without any water in the streams and springs except in the rainy season.

**Q3. **According to the passage given above, deforestation and denudation will ultimately lead to which of the following?

1. Depletion of soil resource

2. Shortage of land for the common man

3. Lack of water for cultivation

Select the correct answer using the code given below.

(a) 1 and 2 only

(b) 2 and 3 only

(c) 1 and 3 only

(d) 1, 2 and 3

**Ans.** (c)

__Solution:__

**Statement 1** is correct: The passage explicitly mentions that unless afforestation efforts are undertaken, harsh climatic conditions and soil erosion by wind and water will increase significantly. This implies that afforestation can mitigate these issues.

**Statement 2** is incorrect: The passage does not discuss the availability of land for the common man. It focuses on the consequences of deforestation, such as soil erosion and climatic changes.

**Statement 3 **is correct: The passage highlights the depletion of water resources, indicating that the drying up of natural water sources could impact agricultural irrigation. Therefore, the statement logically follows from the information provided in the passage.

**Q4.** What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X?

(a) 105

(b) 120

(c) 150

(d) 225

**Ans. **(d)

__Solution:__

*20 × 0.5 = 1010 × 1 = 1010 × 1.5 = 1515 × 2 = 3030 × 2.5 = 7575 × 3 = 225*

*Therefore, answer is (d) 225.*

**Q5.** An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?

(a) 8

(b) 9

(c) 11

(d) 12

**Ans.** (a)

__Solution:__

*Divisibility Rule of 2 - If a number is even or a number whose last digit is an even number i.e. 2,4,6,8 including 0, it is always completely divisible by 2.*

*Divisibility Rule of 3 - A number is divisible by 3 if the sum of its digits is divisible by 3*

*Divisibility Rule of 5 - Numbers, which last with digits, 0 or 5 are always divisible by 5.*

*The 7 digit number is ABCDEFG and we have to find the value of C + D + E (middle 3 digits) *

*After deleting 1 digit from the right, the resulting number (ABCDEF) is divisible by 6. Hence by divisibility rule of 2, F = 2, 4 or 8 (i.e. an even number).*

*The remaining number (ABCDEF) is divisible by 3, then G must be 9 to satisfy the divisibility test of 3.*

*After deleting 2 digits from the right, the resulting number (ABCDE) is divisible by 5. It means that, E = 5. Now, C+D can be between 3 to 7 (as per 4 choices given)*

*After deleting 3 digits from the right, the resulting number (ABCD) is divisible by 4. It means that, D = 2 or 4 (as per divisibility test and 8 can be dropped due to above condition)*

*After deleting 5 digits from the right, the resulting number (AB) is divisible by 2. It means that, B = 2, 4 or 8 (i.e. an even number).*

*So, F, D and B are even numbers (2, 4 or 8). Therefore, A & C are 1 or 7 (only two remaining choices. *

*After deleting 4 digits from the right, the resulting number (ABC) is divisible by 3, so now as per the divisibility rule, B must be 4 (A & C are already known as 1 or 7, A+B+C must be divisible by 3)*

*Now, C & D cannot be 7 and 8 as then C+E or D+E will exceed highest option 12, so won't fit any of the options. So, C = 1 and D = 2*

*So, C+D+E = 1+2+5 = 8*

**Q6.** Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40m. Then X turns left and runs 50m and stops, while Y turns right and runs 50 m and then stops. How far are the two friends from each other now?

(a) 100 m

(b) 90 m

(c) 60 m

(d) 50 m

**Ans.** (a)

__Solution:__

*Considering the turning point as the starting point and both facing north, we ignore the initial 50 meters.*

*X moves 60 meters East and then 50 meters South, while Y moves 40 meters West and then 50 meters South.*

*We calculate the distance by only considering the horizontal movement, which is 60 meters (East) + 40 meters (West). The 50 meters South can be ignored as it is common for both paths, having been already accounted for in the initial position.*

**Q7.** Which date of June 2099 among the following is Sunday?

(a) 4

(b) 5

(c) 6

(d) 7

**Ans.** (d)

__Solution:__

*Considering June 5th, 2022, Sunday, as the reference date (the day UPSC CSE prelims 2022 was conducted), we can determine the Sundays for June 2099 as well.*

*Each regular year consists of 364 days plus one additional day, while a leap year consists of 364 days plus two additional days.*

*So, on June 5th, 2023, it will be Monday (+1 day).*

*On June 5th, 2024, it will be Wednesday (+2 days).*

*The difference between the two years is 2099 - 2022 = 77 years.The number of leap years within this period is 77/4 = 19 (quotient).*

*Thus, until 2099, there will be 58 regular years and 19 leap years.The total number of days to be added is (58 * 1) + (19 * 2) = 58 + 38 = 96 days.*

*When we divide 96 by 7, we get a remainder of 5.*

*Therefore, on June 5th, 2099, it will be Sunday + 5 = Friday.*

*Thus, June 7th, 2099, will be a Sunday.*

**Q8.** A bill for 1,840 is paid in the denominations of 50, 20 and 10 notes. 50 notes in all are used. Consider the following statements:

1. 25 notes of 50 are used and the remaining are in the denominations of 20 and 10.

2. 35 notes of 20 are used and the remaining are in the denominations of 50 and 10.

3. 20 notes of 10 are used and the remaining are in the denominations of 50 and 20.

Which of the above statements are not correct?

(a) 1 and 2 only

(b) 2 and 3 only

(c) 1 and 3 only

(d) 1, 2 and 3

**Ans.** (d)

__Solution:__

*Total amount = Rs. 1840*

*Let the number of 50, 20, and 10 denomination notes be x, y and z respectively. So, 50x+20y+10z = 1840.*

**Statement 1:** 25 notes of 50 denomination were used. So, remaining amount = 1840 – (25 × 50) = 1840 – 1250 = 590.

*Now, even if we assume all the remaining 25 notes are of 20 denomination (highest denomination remaining), we will only get 500 (25x20) So, Statement 1 is incorrect.*

**Statement 2:** 35 notes of 20 denomination were used. So, remaining amount = 1840 – (35 × 20) = 1840 – 700 = 1140.

*Now, even if we assume all the remaining 15 notes are of Rs. 50 denomination (highest denomination remaining), we will only get 750 (15x50). So, Statement 2 is also incorrect.*

**Statement 3: **20 notes of 10 denomination were used. So, remaining amount = 1840 – (20 × 10) = 1840 – 200 = 1640.

*Now, even if we assume all the remaining 30 notes are of Rs. 50 denomination (highest denomination remaining), we will only get 1500 (30x50). So, Statement 3 is also incorrect.*

**Q9.** Which number amongst 240, 321, 418 and 812 is the smallest?

(a) 240

(b) 321

(c) 418

(d) 812

**Ans.** (b)

__Solution:__

*The given numbers 240, 321, 418, and 812 can be simplified to 240, 321, 236, and 236. Now, 240 cannot be the smallest, and since we cannot have two correct answers, the answer must be 321.*

*If there were a need to find the smallest between 236 and 321, we can factorize them to compare, and usually, there is a significant difference so that we don't have to calculate completely.*

*For example:236 = 2 × 2 × 59321 = 3 × 107*

*Observing the factors, it's evident that the second number is smaller.*

**Q10.** The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?

(a) 4

(b) 3

(c) 2

(d) 1

**Ans.** (c)

__Solution:__

*We can only use three of the four digits – 2, 3, 7, and 9, in the first row.*

*Also, since third row is also a 3 digit number and thrice the first row number, maximum value of first row can be 987/3 ie. 329. So, we are left with following combinations only: 237, 273, 239, 293, 279, 297, 327, and 329.*

*We will check these numbers by doubling and tripling respectively to check feasibility - *

*237 × 2 = 474 (digit repetition, so eliminated)273 × 2 = 546; 273 × 3 = 819 (passes both)239 × 2 = 478; 239 × 3 = 717 (digit repetition, so eliminated)293 × 2 = 586; 293 × 3 = 879 (digit repetition, so eliminated)279 × 2 = 558 (digit repetition, so eliminated)297 × 2 = 594 (digit repetition, so eliminated)327 × 2 = 654; 327 × 3 = 981 (passes both)329× 2 = 658; 329× 3 = 987 (digit repetition, and so eliminated)*

*So, only two cases are possible. answer is (c)*

**Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.**

*Passage–1*

"In simple matters like shoe-making, we think only a specially trained person will serve our purpose, but in politics, we presume that everyone who knows how to get votes knows how to administer a State. When we are ill, we call for a trained physician, whose degree is a guarantee of specific preparation and technical competence – we do not ask for the handsomest physician, or the most eloquent one: well then, when the whole State is ill should we not look for the service and guidance of the wisest and the best?"

**Q11. **Which one of the following statements best reflects the message of the author of the passage?

(a) We assume that in a democracy, any politician is qualified to administer a State.

(b) Politicians should be selected from those trained in administration.

(c) We need to devise a method of barring incompetence from public office.

(d) As voters select their administrators, the eligibility of politicians to administer a State cannot be questioned.

**Ans.** (c)

__Solution:__

**Option (a) **is incorrect because it only captures the premise of the passage and fails to include the conclusion, which is the suggestion made by the author to choose the best administrators when the state is malfunctioning.

**Option (b)** is incorrect because it uses the word "selected" instead of "elected," which is not suggested by the author. The author does not oppose elections.

**Option (c)** is correct because the passage suggests that there should be a method in place to prevent incompetence from occupying public office. This implies the need for a system that ensures individuals in positions of power have the necessary qualifications, expertise, and competence to administer a state effectively. Therefore, statement (c) best reflects the message conveyed by the author.

**Option (d)** is incorrect because it contradicts the suggestion of the author.

*Passage –2*

The poverty line is quite unsatisfactory when it comes to grasping the extent of poverty in India. It is not only because of its extremely narrow definition of 'who is poor' and the debatable methodology used to count the poor, but also because of a more fundamental assumption underlying it. It exclusively relies on the notion of poverty as insufficient income or insufficient purchasing power. One can better categorize it by calling it income poverty. If poverty is ultimately about deprivations affecting human well-being, then income poverty is only one aspect of it. Poverty of a life, in our view, lies not merely in the impoverished state in which the person actually lives, but also in the lack of real opportunity given by social constraints as well as personal circumstances–to choose other types of living. Even the relevance of low incomes, meagre possessions, and other aspects of what are standardly seen as economic poverty relate ultimately to their role in curtailing capabilities, i.e., their role in severely restricting the choices people have to lead variable and valued lives.

**Q12.** Why is the methodology adopted in India to count the 'poor' debatable?

(a) There is some confusion regarding what should constitute the 'poverty line'.

(b) There are wide diversities in the condition of the rural and urban poor.

(c) There is no uniform global standard for measuring income poverty.

(d) It is based on the proposition of poverty as meagre income or buying capacity.

**Ans.** (d)

__Solution:__

**Option (a)** is incorrect. The methodology for counting the 'poor' is debatable because it primarily emphasizes the income dimension, excluding other dimensions of poverty such as lack of opportunity. Therefore, this answer option is incorrect.

**Option (b)** is incorrect because the passage does not discuss the classification of urban and rural poverty, making it beyond the scope of the passage.

**Option (c) **is incorrect because the passage focuses on the Indian scenario and does not mention global standards of poverty estimation. Therefore, this answer option is incorrect.

**Option (d)** is correct because it highlights why the poverty estimation methodology used in India is debatable. The passage states that the methodology exclusively relies on the notion of poverty as insufficient income or purchasing power, indicating a limitation. It suggests that poverty should not be solely defined by lack of income but should also consider other social and personal circumstances that limit access to improved living standards.

**Q13. ** Why is income poverty only one measure of counting the 'poor'?

(a) It talks of only one kind of deprivation ignoring all others.

(b) Other deprivations in a human life have nothing to do with lack of purchasing power.

(c) Income poverty is not a permanent condition, it changes from time to time.

(d) Income poverty restricts human choices only at a point of time.

**Ans. **(a)

__Solution:__

**Option (a)** is correct: According to the passage, the poverty line exclusively relies on the notion of poverty as insufficient income or insufficient purchasing power. It also says, “...if poverty is ultimately about deprivations affecting human well-being, then income poverty is only one aspect of it.” Therefore, it is correct to say that it ignores other kinds of deprivations.

**Q14.** What does the author mean by 'poverty of a life'?

(a) All deprivations in a human life which stem not only from lack of income but lack of real opportunities

(b) Impoverished state of poor people in rural and urban areas

(c) Missed opportunities in diverse personal circumstances

(d) Material as well as non-material deprivations in a human life which restrict human choices permanently.

**Ans.** (a)

__Solution:__

**Option (a)** is correct. The passage says, “Poverty of a life, lies not merely in the impoverished state in which the person actually lives but also in the lack of real opportunity given by social constraints as well as personal circumstances - to choose other type of living.” The term ‘Poverty of a life’ is used to highlight the multi-dimensional nature of poverty. In addition to economic or income deprivations, poverty encompasses other aspects like lack of opportunity, curtailed capabilities, inability to choose a better alternative etc. All these are effectively captured in this answer option.

**Q15. ** X and Y run a 3 km race along a circular course of length 300m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?

(a) 2

(b) 3

(c) 4

(d) 5

**Ans.** (b)

__Solution:__

*Since speeds are in ratio of 3:2, when X completes 3km race ie 10 full rounds of the circular course, Y would have completed 6.66 rounds only (2/3*10). *

*Now, X and Y meet every two rounds. So, by the time X completes, they meet only thrice. Hence, the correct answer is (B).*

**Q16. **If the order of the letters in the English alphabet is reversed and each letter represents the letter whose position it occupies, then which one of the following represents 'LUCKNOW'?

(a) OGXPMLD

(b) OGXQMLE

(c) OFXPMLE

(d) OFXPMLD

**Ans. **(d)

*Solution:*

*To find the reverse letter of each of the letters in LUCKNOW -*

*27 – 12 = 15 ie O27 – 21 = 6 ie F27 – 3 = 24 ie X27 – 11 = 16 ie P27 – 14 = 13 ie M27 – 15 = 12 ie L27 – 23 = 4 ie D*

*Therefore, the answer is OFXPMLD.*

**Q17.** In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?

(a) 151

(b) 150

(c) 149

(d) 148

**Ans. **(c)

__Solution:__

*The tournament starts with 150 players.*

*After first round 75 remain (75 matches are held & 75 players are eliminated).After second round 38 remain (37 matches are held & 37 players are eliminated, 1 qualifies directly to next round)*

*Similarly, after third round 19 remain.(19 matches)*

*After fourth round, 10 remain.(9 matches)After fifth round 5 remain.(5 matches)After sixth round 3 remain.(2 matches)After seventh round (in which 1 match is held): 1 player is eliminated, and 2 remain.After eighth round (in which 1 match is held): 1 player is eliminated, and 1 remain.*

*So, total number of matches = 75 + 37 + 19 + 9 + 5 + 2 + 1 + 1 = 149*

**Q18.** How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?

(a) 8

(b) 12

(c) 16

(d) 24

**Ans.** (b)

*Solution:*

*We need to find three-digit numbers in which:All digits are odd. So, the three digits must be from amongst 1, 3, 5, 7, and 9.The number is divisible by 5, i.e. the units digit is 5.The number of ways we can fill the first two digits from amongst 4 distinct digits = 4 × 3 = 12.*

**Q19.** Consider the Question and two Statements given below:

Question: Is x an integer?

Statement-1: x/3 is not an integer.

Statement-2: 3x is an integer.

Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the Question

(b) Statement-2 alone is sufficient to answer the Question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Ans. **(d)

__Solution:__

*Let’s consider the two statements one by one.*

**Statement 1:** x/3 is not an integer.

x may or may not be an integer. For example, if x = 1, x/3 is not an integer.

**Statement 2: **3x is an integer.

x may or may not be an integer. For example, if x = 1/3, 3x will be an integer.

*On combining the two statements also, x may or may not be an integer. For example, if x = 1, even then x/3 will not be an integer. But 3x = 3 will be an integer.*

*If x = 1/3, even then 3x will be an integer. But x/3 = 1/9 will not be an integer.*

**Q20.** The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?

(a) 5%

(b) 10%

(c) 12.5%

(d) 15%

**Ans.** (b)

__Solution:__

*Let the initial price be Rs. 100.*

*After 25% rise, the new price = 100 + 25% of 100 = Rs. 125After 20% fall, the new price = 125 – 20% of 125 = Rs. 100After 10% rise, the new price = 100 + 10% of 100 = Rs. 110So, final percentage increase in price = 10%*

**Directions for the following 3 (three) items:**

**Read the following passage and answer the items that follow the passage. Your answers to these items should be based on the passage only.**

*Passage*

In some places in the world, the productivity of staples such as rice and wheat has reached a plateau. Neither new strains nor fancy agrochemicals are raising the yields. Nor is there much unfarmed land left that is suitable to be brought under the plough. If global temperature continues to rise, some places will become unsuitable for farming. Application of technology can help overcome these problems. Agricultural technology is changing fast. Much of this change is brought about by affluent farmers in the West/Americas. Techniques developed in the West are being adapted in some places to make tropical crops more productive. Technology is of little use if it is not adapted. In the developing world, that applies as much to existing farming techniques as it does to the latest advances in genetic modification. Extending to the smallholders and subsistence farmers of Africa and Asia the best of today's agricultural practices, in such simple matters as how much fertilizers to apply and when, would lead to a greatly increased availability of food for humanity. So would things like better roads and storage facilities, to allow for the carriage of surpluses to markets and reduce wastage.

**Q21. **Based on the above passage, the following assumptions have been made:

1. Development of agricultural technology is confined to developed countries.

2. Agricultural technology is not adapted in developing countries.

Which of the above assumptions is/are valid?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans.** (d)

__Solution:__

**Statement 1** is incorrect because it overgeneralizes by stating that agricultural techniques are "confined to developed countries." The passage mentions that techniques developed in the West are being adapted in some places to make tropical crops more productive, implying that such techniques are not exclusive to developed countries. Therefore, this answer option is incorrect.

**Statement 2** is also incorrect because it contradicts the information provided in the passage, which clearly states that agricultural techniques developed in the West are being adapted in certain regions. Therefore, this answer option is incorrect.

**Q22. **Based on the above passage, the following assumptions have been made:

1. Poor countries need to bring about change in their existing farming techniques.

2. Developed countries have better infrastructure, and they waste less food.

Which of the above assumptions is/are valid?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans.** (a)

__Solution:__

**Assumption 1 **is indeed valid. The passage suggests the need to extend modern agricultural practices, such as adjusting the timing and quantity of fertilizer usage, to improve food security in regions like Africa and Asia. Therefore, assuming that changing agricultural practices is necessary aligns with the author's recommendation.

**Assumption 2**, however, is not valid. While the passage does mention the importance of infrastructure and reducing food wastage in ensuring food security, negating this assumption does not necessarily weaken the argument presented in the passage. Even without infrastructure improvements or reduced food wastage, implementing modern agricultural practices could still contribute significantly to enhancing food security in Africa and Asia. Therefore, this assumption cannot be considered valid based on the information provided in the passage.

**Q23. **Based on the above passage, the following assumptions have been made:

1. Growing enough food for future generation will be a challenge.

2. Corporate farming is a viable option for food security in poor countries.

Which of the above assumptions is/are valid?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans.** (a)

__Solution:__

**Assumption 1** is indeed valid. The passage does highlight various challenges to food security, including the plateauing of wheat and rice production, difficulties in increasing yields through technology, and limitations in cultivating new areas. Addressing these challenges is crucial for ensuring food security for future generations, as mentioned in the passage. Therefore, assuming that overcoming these challenges is necessary aligns with the author's argument.

**Assumption 2**, however, is invalid. The passage does not discuss corporate farming or its implications for food security. Instead, it focuses on the potential of technology to address challenges in agricultural productivity. Therefore, assuming a stance on corporate farming goes beyond the scope of the passage and cannot be considered a valid assumption based on the information provided.

**Q24.** The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?

(a) 12

(b) 18

(c) 24

(d) 36

**Ans. **(c)

__Solution:__

*The following four arrangements are possible:*

*A _ _ E __ A _ _ EE _ _ A __ E _ _ A*

*The three blank spaces can be filled by three distinct letters in 3 × 2 × 1 = 6 waysSo, total possible arrangements = 6 × 4 = 24*

**Q25. **Consider the Question and two Statements given below:

Question: Is Z brother of X?

Statement-1 : X is a brother of Y and Y is a brother of Z.

Statement-2 : X, Y and Z are siblings.

Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the Questions

(b) Statement-2 alone is sufficient to answer the Question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Ans.** (d)

__Solution:__

**Statement 1:** Given that X is the brother of Y, and Y is the brother of Z, we know that all three individuals are siblings. However, the gender of only X and Y is specified. Without knowing whether Z is male or female, we cannot determine whether Z is the brother or sister of X.

**Statement 2:** Simply stating that X, Y, and Z are siblings does not provide information about their genders. Without knowing the gender of Z, we cannot determine whether Z is the brother or sister of X. Combining the two statements does not resolve the ambiguity regarding Z's gender, so we cannot definitively answer the question.

**Q26.** On one side of a 1.01 km long road, 101 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants?

(a) 40 m

(b) 40.4 m

(c) 50 m

(d) 50.5 m

Ans. (b)

__Solution:__

*101 plants are planted at equal distance from each other. So, there will be 100 gaps between those plants.*

*Length of each gap = 1010/100 = 10.1 m*

*Now, there are 4 gaps between 5 consecutive plantsSo, required distance = 4 × 10.1 = 40.4 m*

**Q27.** A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?

(a) 10

(b) 13

(c) 15

(d) 36

**Ans.** (c)

__Solution:__

*Number of ways to go directly from A to C = 3.Number of ways to go from A to B = 3, and Number of ways to go from B to C = 4.Therefore, Number of ways to go from A to C, via B = 3 × 4 = 12So, total number of ways to go from A to C = 3 + 12 = 15*

**Q28. **A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now, is the smallest two-digit number. How many coins does A have in the beginning?

(a) 76

(b) 68

(c) 60

(d) 52

**Ans.** (d)

__Solution:__

*Assume number of coins with A, B, C and D before giving as A, B, C & D respectively. The number of coins with D = 10 (smallest 2 digit number).*

*Let’s work backwards now.*

*D = (C/2) + 2Or C/2 = 10 – 2 = 8Or C = 16*

*Similarly,*

*C = (B/2) + 2Or B/2 = 16 – 2 = 14Or B = 28*

*And finally,*

*B = (A/2) + 2Or A/2 = 28 – 2 = 26Or A = 52*

*So, A initially had 52 coins.*

**Q29.** In the series AABABCABCDABCDE.., which letter appears at the 100th place?

(a) G

(b) H

(c) I

(d) J

**Ans.** (c)

__Solution:__

*The given series is: AABABCABCDABCDE…The pattern being followed here is: A, AB, ABC, ABCD, ABCDE, …*

*Number of alphabets increase in arithmetic progression.*

*If we have an arithmetic series, 1, 2, 3 …, then:Sum of first n terms = (n/2) (2a + (n-1)d), where ‘n’ is the number of terms in the series, ‘a’ the first term, and ‘d' the difference between two terms i.e. 1.*

*So, n(n+1)/2 >= 100, solving/estimating we get n=14.*

*For n=13, we have sum = 13x14/2 = 91. so, 92nd is A, 93rd is B and so, 100th is I.*

**Q30.** Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons between A and B, and 7 persons between B and C. If there are 11 persons ahead of C and 13 behind A, what could be the minimum number of persons in the queue?

(a) 22

(b) 28

(c) 32

(d) 38

**Ans. **(a)

__Solution:__

*There are 4 persons between A and B, and 7 persons between B and C. So, there are four cases possible:*

*A_ _ _ _ B _ _ _ _ _ _ _ CB_ _ _ _ A _ _ CC_ _ _ _ _ _ _ B _ _ _ _ AC _ _ _ _ A _ _ B*

*there are 11 persons ahead of C and 13 behind A. As there are more than 11 persons ahead of C in first case depicted above, we can eliminate it. We can proceed with the remaining three cases and eliminate all but second one.*

*_ _ _B_ _ _ _ A _ _ C _ _ _ _ _ _ _ _ _ _*

*Minimum possible number of people in the queue = 22.*

**Directions for the following 4 (four) Items:**

**The following two passages and answer items that follow the passages. Your answers to these items should be based on the passages only.**

*Passage-1*

Natural selection cannot anticipate future environments on the earth. Therefore, the set of existing organisms can never be fully prepared for environmental catastrophes that await life. An outcome of this is the extinction of those species which cannot overcome environmental adversity. This failure to survive, in modern terms, can be attributed to the genomes which are unable to withstand geological vagaries or biological mishaps infections, diseases and so on). In biological evolution on the earth, extinction of species has been a major feature. The earth may presently have up to ten million species, yet more than 90% of species that have ever lived on the earth are now extinct. Once again, the creationist doctrines fail to satisfactorily address why a divine creator will firstly bother to create millions of species and then allow them to perish. The Darwinian explanation for extinct life is once again simple, elegant and at once convincing organisms go extinct as a function of environmental or biological assaults for which their inheritance deems them ill-equipped. Therefore, the so-called Darwinian theory of evolution is not a theory at all. Evolution happens-this is a fact. The mechanism of evolution (Darwin proposed natural selection) is amply supported by scientific data. Indeed, to date no single zoological, botanical, geological, paleontological, genetic or physical evidence has refuted either of the central two main Darwinian ideas. If religion is not taken into consideration, Darwinian laws are acceptable just like the laws proposed by Copernicus, Galileo, Newton and Einstein-sets of natural laws that explain natural phenomena in the universe.

**Q31. **According to the passage, natural selection cannot anticipate future environments on the earth as

1. species not fully prepared to face the environmental changes that await them will face extinction

2. all the existing species would get extinct as their genomes will not withstand biological mishaps

3. inability of the genome to withstand environmental changes would result in extinction

4. extinction of species is a common feature

Select the correct answer using the code given below.

(a) 1, 2 and 3

(b) 2, 3 and 4

(c) 1, 3 and 4

(d) 1, 2 and 4

**Ans.** (c)

__Solution:__

**Statement 1** is correct. The passage explicitly states that species go extinct when they are ill-equipped to handle environmental or biological challenges, which implies that natural selection cannot predict future environmental changes.

**Statement 2 **is incorrect. It makes a broad and pessimistic prediction about the extinction of all existing species in the future, which is not supported by the passage. Its elimination helps identify the correct answer, option (c).

**Statement 3 **is correct. The passage suggests that species fail to survive due to genomes that are unable to adapt to geological or biological challenges, indicating that natural selection cannot foresee and adapt to future environmental changes.

**Statement 4** is correct. The passage implies that if natural selection could anticipate future environmental changes, species would not face extinction as frequently as they do, making extinction less common. Therefore, the prevalence of species extinction suggests that natural selection cannot predict future environmental conditions.

**Q32. **The passage suggests that Darwinian theory of evolution is not a theory at all because

(a) it does not satisfy the creationist doctrine

(b) extinction is a function of environment and biological assaults

(c) there are no evidences to refute it

(d) existence of organisms is attributed to a creator

**Ans.** (c)

__Solution:__

*Option (c) is correct. The passage explains that Darwin's theory, which explains evolution and extinction, is not merely a theory but rather a law. It is well-supported by scientific evidence and has not been refuted, making it more akin to a scientific law than a theory.*

**Q33.** With reference to the passage, the following assumptions have been made:

1. Only species that have the ability to overcome environmental catastrophes will survive and perpetuate.

2. More than 90% of the species on the earth are in the danger of getting extinct due to drastic changes in the environment.

3. Darwin's theory explains all the natural phenomena,

Which of the above assumptions is/are valid?

(a) 1 only

(b) 1 and 2 only

(c) 3 only

(d) 1, 2 and 3

**Ans. **(a)

__Solution:__

**Statement 1 **is correct. The passage indeed emphasizes that species ill-equipped to handle environmental challenges due to their genetic makeup are likely to face extinction, while those that can adapt will survive. This aligns with the idea that natural selection cannot fully anticipate future environmental changes.

**Statement 2 **is incorrect because it extrapolates the current rate of extinction to predict future outcomes, which the passage does not explicitly support. While the passage mentions past extinctions, it does not make specific predictions about the extent of future extinction.

**Statement 3 **is incorrect because Darwin's theory specifically addresses the process of evolution by natural selection, not all natural phenomena. It focuses on how species change over time through adaptation to their environment.

*Passage-2*

With steady economic growth, higher literacy and increasing skill levels, the number of Indian middle-class families has gone up exponentially. Direct results of the affluence have been changes in dietary patterns and energy consumption levels. People have moved to a higher protein-based diet like milk products, fish and meat, all of which need significantly more water to produce than cereal-based diets. Increasing use of electronic and electric machines/gadgets and motor vehicles needs more and more energy and generation of energy needs water.

**Q34.** Which one of the following statements best reflects the crux of the passage?

(a) People should be persuaded to continue with the mainly Indian traditional cereal-based diets.

(b) India needs to focus on developing agricultural productivity and capacity for more energy generation in the coming years.

(c) Modern technological developments result in the change of cultural and social behaviour of the people.

(d) Water management practices in India need to change dramatically in the coming years.

**Ans. **(d)

__Solution:__

**Option (a)** is incorrect because it suggests reversing the emerging trend of food consumption, which is impractical. Also, the passage does not solely deal with dietary trends. It also talks about trends in transportation and gadget use.

**Option (b)** is incorrect. The statement seems logical but is not the crux of the passage because it suggests improving agricultural and energy efficiency separately without dealing with the core issue of water use efficiency that is common to both agriculture and energy production.

**Option (c) **is incorrect. According to the passage, the changing trends in consumption behavior are due to the growing affluence among the middle class, and not solely due to modern technological developments. It is affluence that enables access to modern technological developments like gadgets and vehicles.

**Option (d)** is the correct answer. The passage clearly mentions that switching from cereal-based to protein-based diets entails increased water consumption. Increasing use of machines and vehicles also requires more energy, which in turn needs water to generate. Both changing dietary practices and energy use practices put a strain on water resources. As the number of middle-class families with water-intensive habits is set to rise exponentially, water management practices will also need to change dramatically in the coming years.

**Q35.** How many seconds in total are there in x weeks, x days, x hours. x minutes and X seconds?

(a) 11580x

(b) 11581x

(c) 694860x

(d) 694861x

**Ans. **(d)

__Solution:__

*x minutes = 60x secondsx hours = 60x minutes = 3600x secondsx days = 24x hours = 1440x minutes = 86400x secondsx weeks = 7x days = 7 × 86400x seconds = 604800x seconds*

*So, total time in seconds = 604800x + 86400x + 3600x + 60x + x = 694861x seconds.*

**Q36.** P, Q, R, S, T and U are six members of a family. R is the spouse of Q, U is the mother of T and S is the daughter of U. P's daughter is T and R's son is P. There are two couples in the family. Which one of the following is correct?

(a) is the grandfather of T

(b) is the grandmother of T

(c) R is the mother of P

(d) T is the granddaughter of Q

**Ans.** (d)

**Q37. **Consider the Question Statements given below in respect of and two three cities P, Q and R in a State:

Question: How far is city P from city Q ?

Statement-1: City Q is 18 km from city R.

Statement-2: City P is 43 km from city R.

Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the Question

(b) Statement-2 alone is sufficient to answer the Question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Ans. **(d)

__Solution:__

*As we do not know the relative positions of P and Q, we cannot find the distance between them.*

**Q38.** Two Statements followed by four Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows follow from the Statements, disregarding the commonly known facts :

Statement-1 : All pens are books.

Statement-2 : No chair is a pen.

Conclusion-I : All chairs are books.

Conclusion-II : Some chairs are pens.

Conclusion-III : All books are chairs.

Conclusion-IV : No chair is a book.

Which one of the following is correct?

(a) Only Conclusion-I

(b) Only Conclusion-II

(c) Both Conclusion-III and Conclusion-IV

(d) None of the Conclusion follows

**Ans. **(d)

**Q39.** Three Statements followed by three Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/ follow from the Statements, disregarding the commonly known facts:

Statement-1: Some doctors are teachers.

Statement-2: All teachers are engineers.

Statement-3: All engineers are scientists.

Conclusion-I: Some scientists are doctors.

Conclusion-II: All engineers are doctors.

Conclusion-III: Some engineers are doctors.

Which one of the following is correct?

(a) Only Conclusion-I

(b) Only Conclusion-II

(c) Both Conclusion-I and Conclusion-III

(d) Both Conclusion-I and Conclusion-II

**Ans. **(c)

__Solution:__

*We can draw the possible Venn diagrams and see that conclusions 1 and 3 follow.*

**Q40.** Eight students A, B, C, D, E, F, G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. B and D sit neither adjacent to C nor opposite to C A sits in between E and D. and sits in between B and H. Which one of the following is definitely correct?

(a) B sits in between A and G

(b) C sits opposite to G

(c) E sits opposite to F

(d) None of the above

**Ans. **(d)

**Directions for Read the following 4 (four) Items:**

**following two passages and answer that follow the passages. Your answer to these items should be based on the passages only.**

*Passage-1*

For two or three generations past, ever-increasing number of individuals have been living as workers merely, not as human beings. An excessive amount of labor is rule today in every circle of society, with the result that man's spiritual element cannot thrive. He finds it very difficult to spend his little leisure in serious activities. He does not want to think; or he cannot even if he wants to. He seeks not Self-improvement, but entertainment which would enable him to be mentally idle and to forget his usual activities. Therefore, the so-called culture of our age is dependent more on cinema than on theatre, more on newspapers, magazines and crime stories than on serious literature.

**Q41. **The passage is based on the idea that

(a) man should not work hard

(b) the great evil of our age is overstrain

(c) man cannot think well

(d) man cannot care for his spiritual welfare

**Ans. **(b)

__Solution:__

*The passage emphasizes the detrimental effects of overwork on individuals, highlighting how it leaves them mentally drained and unable to engage in meaningful activities outside of work. These activities include self-reflection, personal growth, and spiritual pursuits. Instead, overworked individuals often opt for passive forms of entertainment that require less mental effort. Despite their capability for constructive thinking and personal development, the demands of overwork prevent them from engaging in these activities.*

*Based on this discussion, options (c) and (d) can be disregarded.*

*The author is not opposed to hard work itself but rather to the negative impacts of overworking individuals. Therefore, option (a) is incorrect, and option (b) emerges as the correct answer.*

**Q42.** Man does not seek self-improvement because he

(a) is not intellectually capable

(b) has no time to do so

(c) is distracted by materialism

(d) loves amusement and is mentally idle

**Ans.** (b)

__Solution:__

*Option (b) is correct as excessive work does not leave adequate time to engage in self-improvement.*

*Passage-2*

The demographic dividend, which has begun in India and is expected to last another few decades, is a great window of opportunity. The demographic dividend is basically a swelling in the working age population, which conversely means that the relative ratio of very young and very old will, for a while, be on the decline. From the experience of Ireland and China, we know that this can be a source of energy and an engine of economic growth. The demographic dividend tends to raise a nation's savings rate since in any nation, it is the working age population that is the main saver. And since the savings rate is an important driver of growth, this should help elevate our growth rate. However, the benefits of demographic dividend depend on the quality of the working age population. And this implies bringing back the importance of education, acquisition of skills and human capital.

**Q43.** Which of the following would invariably happen in a country, when the demographic dividend has begun to operate?

1. The number of illiterate people will decrease.

2. The ratio of very old and very young will decrease for a while.

3. Population growth rate will quickly stabilize.

Select the correct answer using the code given below.

(a) 1 and 2 only

(b) 2 only

(c) 1 and 3 only

(d) 1, 2 and 3

**Ans.** (b)

__Solution:__

*Statement 2 is correct. The passage talks precisely about this increase in relative ratio of the very old and the very young. Hence, this statement is correct.*

**Q44.** With reference to the passage, which of the following inferences can be drawn?

1. Demographic dividend is an essential condition for a country to rapidly increase its economic growth rate.

2. Promotion of higher education is an essential condition for a country for its rapid economic growth.

Select the correct answer using the code given below.

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans. **(d)

__Solution:__

**Statement 1 **is incorrect because the passage does not suggest that the demographic dividend is an essential or necessary condition for economic growth. While it does highlight the potential benefits of a demographic dividend, it does not imply that economic growth cannot occur without it. Therefore, the statement is too extreme and not supported by the passage.

**Statement 2** is also incorrect because the passage does not claim that the promotion of higher education is an essential condition for economic growth. While it discusses the importance of education in leveraging the demographic dividend, it does not state that economic growth cannot occur without a focus on higher education. Using the extreme word "essential" makes this statement too categorical and unsupported by the passage.

**Q45.** Five friends P. O, X, Y and Z purchased some notebooks. The relevant information is given below:

1. Z purchased 8 notebooks more than X did.

2. P and Q together purchased 21 notebooks.

3. O purchased 5 notebooks less than P did.

4. X and Y together purchased 28 notebooks.

5. P purchased 5 notebooks more than X did.

If each notebook is priced 40, then what is the total cost of all the notebooks?

(a) 2,600

(b) 2,400

(c) 2,360

(d) 2,320

**Ans. **(a)

Solution:

As per the information provided in the question:

Statement 1 -> Z = X + 8 ….(i)

Statement 2 -> P + Q = 21 ….(ii)

Statement 3 -> Q = P – 5 ….(iii)

Statement 4 -> X + Y = 28 ….(iv)

Statement 5 -> P = X + 5 ….(v)

Total number of Books = P + Q + X + Y + Z

Solving equations (ii) and (iii), we get:

P = 13

Q = P – 5 = 8

Using above result and equation (v), we get: X = P – 5 = 8

Using above result and equation (i), we get: Z = X + 8 = 16

Using (iv), we get: Y = 28 – 8 = 20

So, P + Q + X + Y + Z = 13 + 8 + 8 + 20 + 16 = 65

So, total cost of all the notebooks = 65 × 40 = Rs. 2600

**Q46.** A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1.25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is

(a) 10 minutes slow

(b) 5 minutes slow

(c) 10 minutes fast

(d) 5 minutes fast

**Ans.** (d)

__Solution:__

*Total time taken by the man to come back home = 14:30 to 16:00 = 90 minutes*

*Now subtract time for which he stayed in the village ie 25 minutes.Therefore, total travelling time = 90 – 25 = 65 minutes*

*Using, time speed distance formula, total time t1 + t2 = (distance 1/speed 1) + (distance 2/speed 2)*

*65 = d/s + 1.25d/2s *

*Solving we get, d/s = 65x2/3.25 = 40So, the man took 40 minutes to reach to the village.*

*So, the correct time = 14:30 + 40 minutes = 15:10 hoursTherefore, the village clock is 15:15 – 15:10 = 5 minutes fast.*

**Q47. **A person X wants to distribute some pens among six children A B C D E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?

(a) 147

(b) 150

(c) 294

(d) 300

**Ans. **(c)

__Solution:__

*Now, this is a classical problem, but with a twist pens with A B C D E and F - all should be even. Otherwise, we could have solved by simply taking LCM, ie LCM of 2, 3, 4, 5, and 6 = 60.*

*But now we have to check all values, B C D E F*

*number of pens with B = 60/2 = 30number of pens with C = 60/3 = 20number of pens with D = 60/4 = 15 (an odd number)number of pens with E = 60/5 = 12number of pens with F = 60/6 = 10*

*Now since adding is not an option, we can simply multiply by 2 convert odd numbers to even. Therefore A becomes 60 × 2 = 120*

*Similarly doubling all and adding we get total number of pens bought by X = 120 + 60 + 40 + 30 + 24 + 20 = 294*

**Q48.** Six Persons A, B, C, D, E and F are sitting equidistant form each other around a circular table (facing the centre of the table).

Consider the Question and two statements given below:

Question: Who is sitting on the immediate left of A?

Statement-1: B is sitting opposite to C and D is sitting opposite to E.

Statement -2: F is sitting on the immediate left of B.

Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the question

(b) Statement-2 alone is sufficient to answer the question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

** Ans.** (d)

*Solution:*

*Neither of the two statements is sufficient alone due to lack of information. *

**Q49.** Consider the Question and two Statements given below:

Question: What is the age of Manisha?

Statement 1: Manisha is 24 years younger than her mother.

Statement 2: 5 years later, the ages of Manisha and her mother will be in the ratio 3: 5.

Which one of the following is correct in respect of the Question and the Statement?

(a) Statements-1 alone is sufficient to answer the Question

(b) Statement-2 alone is sufficient to answer the question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Ans.** (c)

__Solution:__

*Since each statement alone has only one equation while solving for two variables generally requires two unique equations, neither of the two statements is sufficient alone.*

*Now we check if both the statements are sufficient together.*

*Let the present ages of Manisha and her mother be x and y respectively.*

*As per statement 1, y = x + 24As per statement 2, (x + 5)/(y + 5) = 3/5*

*Or 5x + 25 = 3y + 15Or 3y – 5x = 10Or 3(x + 24) – 5x = 10 (using statement 1)Or 3x + 72 – 5x = 10Or x = 31*

*So, Manisha is 31 years old at present. Both statements together are sufficient to answer the question. *

**Q50.** Six lectures A B C D E and F, each of one hour duration, are scheduled between 8:00 am, and 2:00 p.m.

Consider the Question and two Statements given below:

Question: Which lecture is in the third period?

Statement-1: Lecture F is preceded by A and followed by C

Statement-2: There is no lecture after lecture B.

Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the question

(b) Statement-2 alone is sufficient to answer the question

(c) Both Statement-1 and Statement-2 are sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

**Ans.** (d)

__Solution:__

*Since each statement has too little information, neither of the two statements is sufficient alone.*

*Even after using both statements, we get multiple possible cases. *

*So, Both Statement-1 and Statement-2 are not sufficient to answer the Question*

**Directions for the following 3 (three) Items:**

**Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.**

*Passage-1*

In an economic organization, allowing mankind to benefit by the productivity of machines should lead to a very good life of leisure, and much leisure is apt to be tedious except to those who have intelligent activities and interests. If a leisured population is to be happy, it must be an educated population, and must be educated with a view to enjoyment as well as to the direct usefulness of technical knowledge.

**Q51.** Which of the following statements best reflects the underlying tone of the passage?

(a) Only an educated population can best make use of the benefits of economic progress.

(b) All economic development should be aimed at the creation of leisure.

(c) An increase in the educated population of a country leads to an increase in the happiness of its people.

(d) Use of machines should be encouraged in order to create a large leisured population.

**Ans.** (c)

__Solution:__

*Option (c) is correct. Refer to the last line or the conclusion. It conveys the tone clearly that author is advocating education as one of the solutions that increases happiness. Therefore, we can choose this as the correct answer.*

*Passage-2*

If presents bring less thrill now that we are grown up, perhaps it is because we have too much already, or perhaps it is because we have lost the fullness of the joy of giving and with it the fullness of the joy of receiving. Children's fears are poignant, their miseries are acute, but they do not look too forward nor too far backward. Their joys are clear and complete, because they have not yet learnt always to add 'but' to every proposition. Perhaps we are too cautious, too anxious, too sceptical. Perhaps some of our cares would shrink if we thought less about them and entered with more single-minded enjoyment into the happiness that come our way.

**Q52.** With reference to the passage, which one of the following statements is correct?

(a) It is not possible for adults to feel thrilled by presents.

(b) There can be more than one reason why adults feel less thrilled by presents.

(c) The author does not know why adults feel less thrilled by presents.

(d) Adults have less capacity to feel the joy of loving or being loved.

**Ans.** (b)

__Solution:__

*According to the author, as individuals mature, they tend to become more cautious, anxious, and skeptical. This shift towards overthinking prevents them from fully enjoying the present moment, as they are preoccupied with concerns about the future or dwelling on past experiences. The passage outlines these reasons for why adults may feel less thrilled by presents. Therefore, options (a), (c), and (d) are incorrect.*

*Option (b) remains as the most appropriate answer, as it aligns with the author's explanation of why adults may feel less excitement when receiving gifts.*

**Q53.** The author of the passage is against

(a) worrying too much about the past and future

(b) being in the habit of thinking about presents

(c) not being thrilled by new things

(d) giving and receiving joy only partially

**Ans.** (a)

__Solution:__

*Option (a) is correct. The core agenda of the passage is discussing the importance of enjoying the present. This includes being thrilled by presents or gifts. According to the passage, as we grow there is a reduction in enjoying the moment. That’s because we tend to worry too much about the past and future. Option (a) talks precisely about the same - the author is against worrying too much about past and future.*

**Q54.** Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition.

Consider the following statements:

1. The 4-digit least value of x is 1332.

2. The 3-digit greatest value of x is 888

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans. **(a)

__Solution:__

*The three-digit numbers have been represented by ABC, wherein A, B, and C are non-zero digits.*

*Using 3 distinct digits we can make 3 × 2 × 1 = 6 three-digit numbers.So, x will be the sum of these 6 three-digit numbers.*

*We need to find the two values of x closest to 1000, one just below it (which will be the greatest 3-digit value of x), and the other just above it (which will be the lowest 4-digit value of x).*

*Now, we have to do a bit of hit and try, so that the value of x reaches close to 1000.*

*Let the three digits be the minimum possible ones, i.e. 1, 2, and 3.So, we get x = 123 + 132 + 213 + 231 + 312 + 321 = 1332*

*This is the least possible value of x. So, statement 1 is correct, but statement 2 is incorrect.*

**Q55.** There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?

(a) 6

(b) 8

(c) 10

(d) 12

**Ans.** (c)

__Solution:__

*The PIN contains three digits out of – 1, 2, 3, 4, 5, 6, and 7*

*Case I: The rightmost digit is 1The possible combinations are: 531, 631, 731, 641, 741, 751 (i.e. 6 possible combinations)*

*Case II: The rightmost digit is 2The possible combinations are: 642, 742, 752 (i.e. 3 possible combinations)*

*Case III: The rightmost digit is 3The possible combinations are: 753 (i.e. 1 possible combination)*

*The rightmost digit cannot be more than 3. (due to difference of 2 between each)*

*So, the total number of possible combinations of the PIN = 6 + 3 + 1 = 10*

**Q56.** There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?

(a) 24

(b) 16

(c) 12

(d) 8

**Ans.** (a)

__Solution:__

*Given a circle with eight equidistant points - A, B, C, D, E, F, G, and H - we can form four unique diameters by connecting opposite points. Each diameter, with its opposite vertex on the circle, forms a right-angled triangle. Therefore, using the remaining six points, we can create six unique right-angled triangles for each diameter.*

*Hence, the total number of right-angled triangles that can be formed is 4 (diameters) × 6 (unique triangles per diameter) = 24.*

**Q57. **24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?

(a) 30 days

(b) more than 30 days

(c) Less than 30 days or more than 30 days

(d) Data is inadequate to draw any conclusion

**Ans.** (d)

__Solution:__

*Since we have only one equation and 2 variables, it is not possible to solve.*

**Q58.** What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?

(a) 3

(b) 2

(c) 1

(d) 0

**Ans.** (d)

__Solution:__

*The key to solving this question is knowledge of divisibility tests. We check 1261 with all prime numbers one by one. First hit is 13 (2, 3 & 5 can easily be ruled out. Then try 7 and 11). *

*Remaining number ie 1261/13 is 97.1261 = 1 × 13 × 97*

*Now, 91 is divisible by 13 and 97 itself is present. So, 1261 will completely divide the expression.*

*Hence, the remainder = 0*

**Q59.** Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:

1. It is possible to cut the sheet exactly into 4 square sheets.

2. It is possible to cut the sheet into 10 triangular sheets of equal area.

Which of the above statements is are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans. **(c)

__Solution:__

**Statement I: **It is not possible to cut a rectangle into exactly 4 square sheets. But the 4 squares don't have to be equal in area. So, we can have 4 squares - 8x8, 8x8, 4x4, 4x4

**Statement II:** Now we know that by merging two equal area congruent triangles we can form a rectangle. So, we have 5 equal sized rectangles instead of 10 triangles. We can easily cut 1 rectangle into 5 equal sized rectangles.

*Hence, both statements 1 and 2 are correct.*

**Q60.** When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. which one of the following is correct?

(a) z < x < y

(b) x < y < z

(c) y < x < z

(d) z < y < x

**Ans. **(a)

__Solution:__

*To simplify*,* we write percentages in decimal form,*

*0.7 x + y = 1.65 yOr 0.7 x = 0.65 yOr x/y = 0.65/0.70, which is less than 1.*

*Hence, x < y …..(i)*

*Now, 0.6 x + z = 1.65 zOr 0.6 x = 0.65 zOr x/z = 0.65/0.60, which is greater than 1.*

*Hence, x > z …..(ii)*

*From (i) and (ii), we get: z < x < y*

**Directions for the following 3 (three) items:**

*Passage–1*

The majority of people who fail to accumulate money sufficient for their needs, are generally, easily influenced by the opinions of others. They permit the newspapers and the gossiping neighbours to do their thinking for them. Opinions are the cheapest commodities on the earth. Everyone has a flock of opinions ready to be wished upon by anyone who will accept them. If you are influenced by opinions when you reach decisions, you will not succeed in any undertaking.

**Q61.** Which one of the following is implied by the passage?

(a) Most of the people do not accumulate money for their needs.

(b) Most of the people never fail to accumulate money for their needs.

(c) There are people who fail to accumulate money for their needs.

(d) There is no need to accumulate money.

**Ans.** (c)

__Solution:__

*To answer this question, we need to simplify the first line of the passage. It states that among those who fail to accumulate sufficient money, the majority are easily influenced by external opinion. The author doesn't suggest that most people fail to accumulate sufficient money, nor does the author imply that most people succeed in accumulating sufficient money. The passage maintains a balanced perspective and emphasizes the importance of money. Option (c) best reflects these aspects.*

**Q62.** What is the main idea of the passage?

(a) People should not be influenced by the opinions of others.

(b) People should accumulate as much money as they can.

(c) People should neither give nor accept the opinions.

(d) People will succeed in any undertaking if they do not accept any opinion at all

**Ans.** (a)

__Solution:__

*Statement (a) is correct. The author indeed discusses the influence of others' opinions from the very beginning of the passage. In the last line, the author emphasizes that one cannot succeed in any initiative if they are influenced by the opinions of others. Therefore, there is a clear suggestion throughout the passage against being influenced by others' opinions.*

*Passage–2*

"The social order is a sacred right which is the basis of all other rights. Nevertheless, this right does not come from nature, and must therefore be founded on conventions."

**Q63**. With reference to the above passage which of the following statements is/are correct?

1. Conventions are the sources of rights of man.

2. Rights of man can be exercised only when there is a social order.

Select the correct answer using the code given below.

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans.** (c)

__Solution:__

**Statement 1** is correct. The author indeed argues that social order does not naturally arise but is established through convention. This order serves as the foundation for all other rights. Therefore, social order emerges from conventions, as stated in the passage.

**Statement 2 **is also correct. If we negate this statement, it contradicts the passage's assertion that social order is the basis for all other rights. Therefore, this statement aligns with the passage's argument.

**Q64.** Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?

(a) 15000

(b) 12000

(c) 9600

(d) 5000

**Ans. **(a)

__Solution:__

*Since there are only two candidates, if X got 56%, Y got 44%. Difference is of 12%.*

*Now, Difference is given as 1440 (12% of votes casted). Therefore, total casted votes = 12000*

*Now, only 80% voted, so total voters = 12000/.80 = 15000*

**Q65.** What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?

(a) 1063

(b) 1073

(c) 1083

(d) 1183

**Ans. **(c)

__Solution:__

*LCM of 6, 9, 12, 15 and 18 = 180*

*Smallest number greater than 1000 which is a multiple of 180 is 1080.*

*So, the required number with remainder 3 = 1080 + 3 = 1083*

**Q66.** Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p x q = 2430, then what is the difference between p and q?

(a) 45

(b) 27

(c) 18

(d) 9

**Ans. **(d)

__Solution:__

*The given product p × q = 2430 ...(i)*

*The last digit is 0, so one two of the digits must be 5 and other one an even number 2, 4, 6 or 8.*

*Let this unknown digit be x.So, p = 10x + 5 and q = 50 + xputting in (i), (10x + 5) × (50 + x) = 2430*

*Now, try 2, 4, 6 and 8, x = 4 *

*Therefore, p = 45 and q = 54Required difference = q - p = 54 – 45 = 9*

**Q67.** Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:

1. p x q can be an odd number.

2. q / p can be a prime number.

3. p + q can be a prime number.

Which of the above statements are correct?

(a) 1 and 2 only

(b) 2 and 3 only

(c) 1 and 3 only

(d) 1, 2 and 3

**Ans. **(d)

*Solution:*

*p is a prime number. So, p can be 2, 3, 5, 7, 11, 13, .….q is a composite number. So, q can be 4, 6, 8, 9, 10, .….*

**Statement 1:** p × q can be an odd number, e.g. (3 × 9 = 27). Thus, statement 1 is correct.**Statement 2: **q/p can be a prime number, e.g. (4/2 = 2). Thus, statement 2 is correct.**Statement 3: **p + q can be a prime number, e.g. (3 + 4 = 7). Thus, statement 3 is correct.

*Thus, all the statements 1, 2 and 3 are correct.*

**Q68. **Consider the following statements :

1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.

2. Between 4:58 p.m. and 4:59 p.m.. both minute hand and second hand coincide.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**Ans.** (c)

*Solution:*

**Statement 1** is correct. At 3:16 PM, the hour hand covers 192×0.5=96

192×0.5=96 degrees, and the minute hand covers 16×6= 96

16×6=96 degrees in the same time span.

*Therefore, both hands coincide at this time.*

**Statement 2 **is also correct. The second-hand travels through the entire clock face in one minute, so it will coincide with the minute hand between 4:58 PM and 4:59 PM.

*Therefore, both statements 1 and 2 are correct.*

**Q69. **There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

(a) m=n

(b) m> n

(c) m<n

(d) Cannot be determined due to insufficient data

**Ans.** (a)

__Solution:__

*After 20 ml of milk transferred from container X to container Y, Milk in container X = 100 – 20 = 80 mlAmount of solution in container Y becomes = 100 ml water + 20 ml milk = 120 ml*

*Ratio of milk in container Y solution = 20 : 120 = 1 : 6By corollary, ratio of water in Y solution = 5 : 6 (100 : 120)*

*After 20 ml of milk transferred from container Y to container X, Milk in container X = 80 + 1/6 *20 = 83.33 mlAmount of water in Y = 5/6 * 100 = 83.33 ml*

*Thus, m = n*

**Q70. **A pie chart gives the expenditure on five different items A, B, Q D and E in a household. If B, C, D and E correspond to 90o, 50o, 45o, and 75o respectively, then what is the percentage of expenditure on item A?

(a) 112/9

(b) 125/6

(c) 155/9

(d) 250/9

**Ans. **(d)

__Solution:__

*Angle A in the pie-chart = 360 – (90 + 50 + 45 + 75) = 100*

*Percentage of expenditure on item A = (100/360) × 100 = (250/9)%*

**Directions for the following 3 (three) items:**

*Passage–1*

To encourage research is one of the functions of a university. Contemporary universities have encouraged research, not only in those cases where research is necessary, but on all sorts of entirely unprofitable subjects as well. Scientific research is probably never completely valueless. However silly and insignificant it may seem, however mechanical and unintelligent the labours of the researchers, there is always a chance that the results may be of value to the investigator of talent, who can use the facts collected for him by uninspired but industrious researchers as the basis of some fruitful generalization. But where research is not original, but consists in the mere rearrangement of existing materials, where its objects is not scientific but literary or historical, then there is a risk of the whole business becoming merely futile.

**Q71.** The author's assumption about scientific research is that

(a) it is never very valuable

(b) it is sometimes very valuable

(c) it is never without some value

(d) it is always very valuable

**Ans. **(c)

__Solution:__

*The author adopts an optimistic approach towards the outcome of scientific research. The only concern is with reference to the nature of research. According to the author, it should be original and not literary or historical. Hence, (C) is the correct answer.*

**Q72. **According to the author

(a) not many research results can be of value to an intelligent investigator

(b) a research result is always valuable to an intelligent investigator

(c) any research result can be of value to an intelligent investigator

(d) a research result must always be of some value to an intelligent investigator

**Ans.** (c)

__Solution:__

*To determine the correct answer, consider the author's tone throughout the passage.*

*The line "…there is always a chance that the result is of value to the investigator of talent…" suggests that scientific research findings may be valuable to an intelligent investigator in some cases. However, the author does not claim that the result is always valuable to such an investigator, stopping short of an extreme stance. Option (c) appropriately reflects this cautious perspective of the author.*

*Passage–2*

How best can the problems of floods and droughts be addressed so that the losses are minimal and the system becomes resilient? In this context, one important point that needs to be noted is that India gets "too much' water (about 75% of annual precipitation) during 120 days (June to September) and "too little' for the remaining 245 days. This skewed water availability has to be managed and regulated for its consumption throughout the year.

**Q73. **Which one of the following best reflects the practical, rational and lasting solutions?

(a) Constructing huge concrete storage tanks and canals across the country

(b) Changing the cropping patterns and farming practices

(c) Interlinking of rivers across the country

(d) Buffer stocking of water through dams and recharging aquifers

**Ans.** (d)

__Solution:__

*Option (d) is indeed correct. Buffer stocking of water, achieved through methods such as dams and recharging aquifers, involves storing excess water above and below ground to be utilized during periods of low rainfall or drought. This management and regulation of water resources ensure availability for future consumption, especially during lean seasons.*

**Q74.** 15 x 14 x 13 x ... x 3 x 2 x 1 = 3m x n

Where m and n are positive integers, then what is the maximum value of m?

(a) 7

(b) 6

(c) 5

(d) 4

**Ans.** (b)

__Solution:__

*15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3m × n*

*Numbers which are multiple of 3 = 15 × 12 × 9 × 6 × 3 = (3 × 5) × (3 × 4) × (3 × 3) × (3 × 2) × 3 = (3x3x3x3x3x3) × (5 ×4 × 2)*

*Therefore, the maximum value of m is 6.*

**Q75.** What is the value of X in the sequence 2, 12, 36, 80, 150, X?

(a) 248

(b) 252

(c) 258

(d) 262

**Ans.** (b)

__Solution:__

*1 x 1 x 2, 2 x 2 x 3, 3 x 3 x 4, 4 x 4 x 5, 5 x 5 x 6, .....*

*Next number is 6 x 6 x 7 = 252*

*Hence, option (b) is the correct answer.*

**Q76.** One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated?

(a) 105

(b) 525

(c) 945

(d) 1050

**Ans.** (c)

__Solution:__

*There are 9 non-zero digits ie 1, 2, 3, 4, 5, 6, 7, 8 or 9*

*There are 5 vowels and 21 consonants in English alphabet (capitals only)*

*The password starts with a vowel and ends with a consonant. So, the digit will come at the middle.*

*The number of such passwords = 5 × 9 × 21 = 945*

*Hence, 945 such passwords can be generated.*

**Q77.** There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?

(a) 18

(b) 27

(c) 54

(d) 81

**Ans.** (d)

__Solution:__

*The cups will be arranged in a 3 × 3 matrix. We need to remove cases where any one row contains only Tea ie all 3 Teas in a single row.*

*This can happen in 3 ways - first, second or third row. Therefore 3 cases need to subtracted from total combinations possible.*

*Total arrangements = 9! /(6! x 3!) (by formula)Required answer = total arrangements possible - 3 = 84 - 3 = 81Hence, option (d) is the correct answer.*

**Q78. **The sum of three consecutive integers is equal to their product. How many such possibilities are there?

(a) Only one

(b) Only two

(c) Only three

(d) No such possibility is there

**Ans. **(c)

__Solution:__

*Let the 3 consecutive integers be x - 1, x, and x + 1*

*According to the question, sum = product, therefore(x – 1) + x + (x + 1) = (x - 1) × x × (x + 1)⇒ 3x = x × (x - 1) × (x + 1)⇒ x = 0, 2 or -2*

*Therefore, there are 3 such possibilities.*

*Hence, option (c) is the correct answer.*

**Q79.** What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?

(a) 72

(b) 81

(c) 90

(d) 100

**Ans.** (a)

__Solution:__

*Since X and Y are distinct non-zero digits - 1 to 9*

*XY can be arranged in = 9 × 8 ways = 72*

**Q80.** The average weight of A, B, C is 40 kg, the average weight of B, D, E is 42 kg and the weight of F is equal to that of B. What is the average weight of A, B, C, D, E and F?

(a) 40.5 kg

(b) 40.8 kg

(c) 41 kg

(d) Cannot be determined as data is inadequate

**Ans.** (c)

__Solution:__

*(A + B + C)/3 = 40 (given)=> (A + B + C) = 120 ………(a)*

*(B + D + E)/3 = 42 (given)=> (B + D + E) = 126 ..……(b)*

*F = B .…….(c)*

*From equations (a) and (b), we get:A + B + C + B + D + E = 120 + 126Or A + B + C + D + E + F = 246 (replacing one B with F as F = B from equation c)*

*So, average weight of A + B + C + D + E + F = 246/6 = 41*

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