CSAT 2023 PAPER WITH EXPLANATIONS

2023 CSAT KEY & EXPLANATIONS

Directions for the following 3 (three) items :

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

Passage - 1

We often hear about conflicts among different States in India over river waters. Of the 20 major systems, 14 are already water-stressed; 75% of the population lives in water-stressed regions, a third of whom live in water-scarce areas. Climate change, the demands of rising population and the need for agriculture to keep pace, and increased rate of urbanization and industrialization will exacerbate water stress. According to the Constitution of India, water is a State subject and not that of the Union, except for regulation of inter-State rivers. Key to ensuring balance between competing demands of various stakeholders is a basin-based approach to allocate water amongst constituent regions and States. Allocating fair share of water requires assessments based on objective criteria, such as specificities of the river basin, size of dependent population, existing water use and demand, efficiency of use, projected future use, etc. while ensuring the environmental needs of the river and aquifers.

Which one of the following statements best reflects the most rational, practical and immediate action required to ensure fair and equitable allocation of water to different stakeholders ?

(a) A national, pragmatic, legal and policy framework for water allocation should be made.

(b) All river systems of the country should be linked and huge aquifers created.

(d) To mitigate water crisis, water demand of sectors such as agriculture and industry should be reduced.

Answer (d)

(d) To mitigate the water crisis, the water demand of sectors such as agriculture and industry should be reduced.

Of the given options, reducing the water demand of sectors like agriculture and industry is the most rational, practical, and immediate action required to ensure fair and equitable allocation of water to different stakeholders. This approach focuses on managing and optimizing water usage within existing resources rather than relying solely on large-scale infrastructure projects or interlinking of rivers, which can be costly, time-consuming, and potentially disruptive to ecosystems.

By implementing water conservation measures, promoting efficient irrigation practices, and encouraging industries to adopt sustainable water management strategies, the overall water demand can be reduced. This approach allows for a more balanced allocation of water among different sectors and stakeholders, taking into account the specificities of each river basin and the needs of the dependent population. It also helps in maintaining the environmental needs of the rivers and aquifers, ensuring long-term sustainability of water resources.

Passage - 2

More than half of Indian women and almost a quarter of Indian men of working age suffer from anemia. According to studies, they are anywhere from 5 — 15% less productive than they could be, as a result thereof. India also has the largest tuberculosis burden in the world, costing 170 million workdays to the country annually. But what is just as important as lost productivity now is lost potential in the future. It is becoming increasingly clear that on many measures of cognitive ability, malnourished Indian children perform two or three times worse than their adequately nourished peers. For an economy that will be more dependent on highly skilled workers, this poses a significant challenge. And it is one that really should be addressed given India’s demographic outlook.

2.Which one of the following statements best reflects what is implied by the passage ?

(a) Education system must be strengthened in rural areas.

(b) Large scale and effective implementation of skill development programme is the need of the hour.

(d) For rapid economic growth as envisaged by us, attention should be paid to health and nutrition of the people.

Answer (d)

The passage implies that for rapid economic growth, attention should be paid to the health and nutrition of the people. This is because a healthy and well-nourished population is more productive and has a higher potential for economic growth. The passage also mentions that India has a large number of people who are suffering from anemia and tuberculosis. These diseases can lead to lost productivity and lost potential in the future. Therefore, it is important to address these health issues in order to improve the productivity and potential of the Indian workforce.

The statement that best reflects this implication is (d) For rapid economic growth as envisaged by us, attention should be paid to health and nutrition of the people. This statement acknowledges the importance of health and nutrition for economic growth and suggests that the government should take steps to improve the health and nutrition of the people.

The other statements are not as accurate. Statement (a) suggests that the only way to improve economic growth is to strengthen the education system in rural areas. This is not necessarily true, as there are other factors that can also contribute to economic growth, such as health and nutrition. Statement (b) suggests that the only way to improve economic growth is to implement a large-scale skill development program. This is also not necessarily true, as there are other factors that can also contribute to economic growth, such as health and nutrition. Statement (c) suggests that only skilled workers need to be healthy and well-nourished in order to contribute to economic growth. This is not true, as all workers, regardless of their skill level, need to be healthy and well-nourished in order to be productive.

Therefore, the statement that best reflects what is implied by the passage is (d) For rapid economic growth as envisaged by us, attention should be paid to health and nutrition of the people.

Passage - 3

In India, a majority of farmers are marginal and small, less educated and possess low adaptive capabilities to climate change, perhaps because of credit and other constraints. So, one cannot expect autonomous adaptation to climate change. Even if it was possible, it would not be sufficient to offset losses from climate change. To deal with this, adaptation to climate change is paramount, alongside a fast mitigation response. Another solution is to have a planned or policy-driven adaptation, which would require the government to come up with policy recommendations . Perception is a necessary prerequisite for adaptation. Whether farmers are adapting agricultural practices to climate change depends on whether they perceive it or not. However, this is not always enough for adaptation. It is important how a farmer perceives the risks associated with climate change.

3.Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage ?

(a) Adaptation to climate change and mitigation response are basically the responsibilities of the government.

(b) Climate change causes a change in government policies regarding land use patterns in the country.

(c)Risk perceptions of farmers are important for motivating them for taking adaptation decisions.

(d) Since mitigation is not possible,governments should come up with policies for quick response to climate change.

Answer (c)

Risk perceptions of farmers are important for motivating them to take adaptation decisions.

The passage discusses the importance of adaptation to climate change and the role of farmers in this process. It emphasizes that farmers, particularly marginalized and small-scale farmers, may have limited education and adaptive capabilities to climate change due to various constraints. It also highlights that autonomous adaptation alone may not be sufficient to offset losses from climate change.

In this context, the passage suggests that perception is a necessary prerequisite for adaptation. It states that whether farmers are adapting agricultural practices to climate change depends on whether they perceive it or not. However, it also implies that perception alone is not enough for adaptation; how farmers perceive the risks associated with climate change is also important.

Option (a) is not the most logical and rational message conveyed by the author, as it oversimplifies the responsibilities of adaptation and mitigation to solely the government. Option (b) is not supported by the passage, as it does not discuss changes in government policies regarding land use patterns. Option (d) is not the best reflection of the passage, as it implies that mitigation is not possible, which is not explicitly stated in the passage.

Therefore, option (c) is the most logical and rational message conveyed by the author, as it emphasizes the importance of risk perceptions of farmers in motivating them to make adaptation decisions in response to climate change.

Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make ?

(a) 27

(b) 36

(d) 45

Answer: b

Raj has ten pairs of red shoes, so there are 20 red shoes in total. He also has nine pairs of white shoes and eight pairs of black shoes, for a total of 17 pairs of non-red shoes.

If Raj randomly picks shoes one by one from the box, he could pick all 17 pairs of non-red shoes before picking a red pair. This would require 17 x 2 = 34 attempts.

And now in the 35th attempt he picks a red shoe. And to get a pair of red shoes ,he has to make another attempt.So in total 34 + 2 =36 attempts required.

In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots ?

(a) 18

(b) 19

(d) 21

Answer (b)

The total runs scored by the batsman is 25. The batsman can score a single run, a four, or a six. We need to find the number of ways the batsman can score exactly 25 runs, irrespective of the sequence of scoring shots.

Let x be the number of singles, y be the number of fours, and z be the number of sixes. We know that x+4y+6z=25. We need to find the number of non-negative integer solutions to this equation.

One way to do this is to use stars and bars. We have 25 stars, and we need to divide them into 3 groups: one group for the singles, one group for the fours, and one group for the sixes. We can do this by placing 2 bars between the stars. For example, the following configuration represents 3 singles, 2 fours, and 1 six:

The number of ways to arrange 25 stars and 2 bars is (225+2)=(227)=351. However, not all of these arrangements are valid. For example, the following arrangement is not valid because it has 0 singles:

To find the number of valid arrangements, we need to subtract the number of arrangements with 0 singles, 0 fours, or 0 sixes. The number of arrangements with 0 singles is (223)=253. The number of arrangements with 0 fours is (225)=300. The number of arrangements with 0 sixes is (225)=300.

Therefore, the number of valid arrangements is 351−253−300−300+253=19.

Hence, the answer is (b).

There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements :

It is possible that exactly one letter goes into an incorrect envelope.

2.There are only six ways in which only two letters can go into the correct envelopes.

Which of the statements given above is/are correct ?

(a) 1 only

(b) 2only

(d) Neither 1 nor 2

Answer-b

Statement 1: It is possible that exactly one letter goes into an incorrect envelope.

This statement is incorrect. If there are four letters and four envelopes, and each letter is put into one envelope, it is not possible for exactly one letter to go into an incorrect envelope. Since each letter has only one corresponding envelope, all letters will go into their correct envelopes.

Statement 2: There are only six ways in which only two letters can go into the correct envelopes.

This statement is correct. To understand why, let's consider the possibilities:

The first letter can go into any of the four envelopes. Once the first letter is put into an envelope, there is only one correct envelope left for the second letter.

The second letter can go into any of the remaining three envelopes. Once the second letter is put into an envelope, there are only two correct envelopes left for the third letter.

The third letter can go into any of the remaining two envelopes. Once the third letter is put into an envelope, there is only one correct envelope left for the fourth letter.

Therefore, the total number of ways in which two letters can go into the correct envelopes is 4 × 3 × 2 × 1 = 24. However, this counts all possible permutations of the letters, so we need to divide by the number of ways the letters themselves can be arranged, which is 4 × 3 × 2 × 1 = 24. The result is 24/24 = 1.

So, there is only one way in which two letters can go into the correct envelopes, not six. Therefore, statement 2 is the only correct statement.

What is the remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100 ?

(a) 0

(b) 1

(d) 4

Answer (a)

The remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100 is 0.

This is because 85 x 87 x 89 x 91 x 95 x 96 is a multiple of 100.

A multiple of 100 is a number that can be divided by 100 with no remainder.

Therefore, the remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100 is 0.

What is the unit digit in the expansion of (57242)^9x7x5x3x 1 ?

(a) 2

(b) 4

(d) 8

Answer-A

The unit digit of the expansion of (57242) ^9×7×5×3×1 is 2.

The unit digit of a number is the digit in the ones place. The unit digit of a product of two numbers is the product of the unit digits of the two numbers. The unit digit of a power of a number is the unit digit of the number raised to the power.

The unit digit of 57242 is 2. The unit digit of 9 is 9. The unit digit of 7 is 7. The unit digit of 5 is 5. The unit digit of 3 is 3. The unit digit of 1 is 1.

The unit digit of (57242) 9×7×5×3×1 is the unit digit of 2 9×7×5×3×1

The unit digit of 2^ 1 is 2.

The unit digit of 2^ 2 is 4.

The unit digit of 2^ 3 is 8.

The unit digit of 2^ 4 is 6.

The unit digit of 2^ 5 is 2.

The unit digit of 2^ 6 is 4.

The unit digit of 2^ 7 is 8.

The unit digit of 2^ 8 is 6.

The unit digit of 2^ 9 is 2.

Therefore, the unit digit of (57242) ^9×7×5×3×1 is 2.

If ABC and DEF are both 3-digit numbers such that A, B, c, D, E and F are distinct non-zero digits such that ABC + DEF= 1111, then what is the value of A+B+C+D+E+F?

(a)28

(b)29

(d)31

Answer (c)

Since ABC and DEF are both 3-digit numbers, we can write them as follows:

ABC = 100A + 10B + C DEF = 100D + 10E + F

We are given that ABC + DEF = 1111, so we can substitute in the expressions above to get:

100A + 10B + C + 100D + 10E + F = 1111

Combining like terms, we get:

100(A + D) + 10(B + E) + (C + F) = 1111

Since A, B, C, D, E, and F are all distinct non-zero digits, we know that A + D must be a multiple of 10, B + E must be a multiple of 10, and C + F must be a multiple of 10.

The only way to satisfy these conditions is if A + D = 10, B + E = 10, and C + F = 10.

Therefore, A + B + C + D + E + F = 10 + 10 + 10 = 30.

So the answer is (c).

10.D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D?

(a) 0

(b) 7

(d) 9

Answer (a)

To find the difference between the digit at the hundred's place and the digit at the unit's place of D, we need to determine the number D that minimizes the ratio of the number to the sum of its digits.

Let's analyze the possible scenarios for D:

Case 1: D is a three-digit number with a leading digit of 1. In this case, let's assume D = 1AB, where A and B represent the digits at the tens and unit's places, respectively. The sum of the digits in D would be 1 + A + B. The ratio of D to the sum of its digits is (1AB) / (1 + A + B).

Case 2: D is a three-digit number with a leading digit greater than 1. In this case, let's assume D = XYZ, where X, Y, and Z represent the digits at the hundreds, tens, and unit's places, respectively. The sum of the digits in D would be X + Y + Z. The ratio of D to the sum of its digits is (XYZ) / (X + Y + Z).

To find the minimum ratio, we need to compare the ratios in both cases.

Case 1: Ratio for D = 1AB / (1 + A + B) = 100A + 10B + B / (1 + A + B) = 100A + 11B / (1 + A + B)

Case 2: Ratio for D = XYZ / (X + Y + Z) = 100X + 10Y + Z / (X + Y + Z)

Since we want to minimize the ratio, we need to find the smallest possible values for A, B, X, Y, and Z.

For A, B, X, Y, and Z, the digits range from 0 to 9, excluding 0 since D is a three-digit number.

By trying different values, we can find the minimum ratio for each case:

Case 1: The smallest ratio occurs when A = 0 and B = 1. Minimum ratio for Case 1: 100(0) + 11(1) / (1 + 0 + 1) = 11 / 2 = 5.5

Case 2: The smallest ratio occurs when X = 1, Y = 0, and Z = 0. Minimum ratio for Case 2: 100(1) + 10(0) + 0 / (1 + 0 + 0) = 100 / 1 = 100

Comparing the two cases, we see that the minimum ratio is smaller in Case 1 (5.5) compared to Case 2 (100).

Therefore, the minimum ratio is achieved when D = 101.

The difference between the digit at the hundred's place (1) and the digit at the unit's place (1) of D is 1 - 1 = 0.

Therefore, the correct answer is (a) 0.

Directions for the following 8 (three) items :

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

Passage- I

The emissions humans put into the atmosphere now will affect the climate in the middle of the century and onwards. Technological change, meanwhile, could make a future transition away from fossil fuels cheap or it might not, leaving the world with a terrible choice between sharply reducing emissions at huge cost or suffering through the effects of unabated warming. Businesses that do not hedge against the threat of uncertain outcomes fail. The world cannot afford such recklessness on climate change.

11.Which one of the following statements best reflects the crucial message conveyed by the author of the passage ?

(a)Businesses that cause emissions may need to close down or pay for pollution in future.

(b)The only solution is technological development related to the issues of climate change.

(c)Waiting to deal with carbon emissions until technology improves is not a wise strategy.

(d)Since future technological change is uncertain, new industries should be based on renewable energy sources.

Answer (c)

The correct answer is (c).

The passage states that "Businesses that do not hedge against the threat of uncertain outcomes fail." This means that businesses that do not take steps to reduce their emissions now, in anticipation of future technological change, may be forced to close down or pay for pollution in the future.

The passage also states that "The world cannot afford such recklessness on climate change." This means that the world cannot afford to wait until technology improves to deal with climate change. We need to take action now to reduce emissions, even if it is costly.

Therefore, the crucial message conveyed by the author of the passage is that waiting to deal with carbon emissions until technology improves is not a wise strategy.

The other options are not supported by the passage. Option (a) is not supported because the passage does not say that all businesses that cause emissions will need to close down or pay for pollution in the future. Option (b) is not supported because the passage does not say that technological development is the only solution to climate change. Option (d) is not supported because the passage does not say that new industries should be based on renewable energy sources.

Passage-2

Environmental problems cause health problems. Substantial changes in lifestyle can reduce environmental or health problems, but this idea appears almost impossible to adopt. With environmental problems, individual efforts can be perceived as having a negligible effect and therefore lead to inertia. With health, on the other hand, individual choices can make the difference between life and death, literally. And yet, barring a few, there seems to be the same collective lethargy towards making their choices.

12.Which one of the following statements best implies the most rational assumption that can be made from the passage ?

(a) We are likely to spend more money on cure than prevention.

(b) It is the job of the government to solve our environmental and public health problems.

(d) Loss of traditional lifestyle and the influence of western values led to some unhealthy ways of living.

Answer (a)

The most rational assumption that can be made from the passage is that we are likely to spend more money on cure than prevention. This is because the passage states that substantial changes in lifestyle can reduce environmental or health problems, but this idea appears almost impossible to adopt. This suggests that people are more likely to wait until they are sick to make changes to their lifestyle, which will cost more money in the long run.

The other options are not supported by the passage. Option (b) suggests that the government is responsible for solving environmental and public health problems, but the passage does not say anything about this. Option (c) suggests that health can be protected even if environmental problems go on unattended, but the passage states that environmental problems can cause health problems. Option (d) suggests that loss of traditional lifestyle and the influence of western values led to some unhealthy ways of living, but the passage does not mention this.

Therefore, the answer is (a).

Passage-3

Many people are not eating the right food. For some, it is simply a decision to stick with food they enjoy but which is not too healthy. This is leading to an increase in non-communicable diseases. This in turn leads to a major burden on our health-care systems that have the potential to derail the economic progress which is essential for the poor to improve their lives. For others, it is about limited access to nutritious food or a lack of affordability, leading to monotonous diets that do not provide the daily nutrients for them to develop fully. Part of the reason nutrition is under threat worldwide is that our food systems are not properly responding to nutritional needs. Somewhere along that long road from farm to

fork, there are serious detours taking place.

Which one of the following statements best reflects the crux of the passage ?

(a) The scheme of Universal Basic Income should be implemented worldwide as a way of poverty alleviation.

(b) We must place food-based nutrition at the centre of our policy debate.

(d) Using modern food processing technologies, we must fortify food items with required nutrient elements.

Answer (b)

The crux of the passage is that many people are not eating the right food, and this is leading to a number of problems. The passage discusses the reasons for this, including people's choices and limited access to nutritious food. It also discusses the consequences of this, including an increase in non-communicable diseases and a burden on healthcare systems.

Of the options given, only option (b) reflects the crux of the passage. This is because the passage argues that we need to place food-based nutrition at the center of our policy debate. This means that we need to make sure that people have access to nutritious food, and that they are aware of the importance of eating a healthy diet.

The other options are not supported by the passage. Option (a) suggests that we should implement a universal basic income as a way of poverty alleviation. This is not mentioned in the passage. Option (c) suggests that we should improve the nutritional status of food by creating appropriate genetically modified crops. This is one possible solution, but it is not the only one, and it is not mentioned in the passage. Option (d) suggests that we should fortify food items with required nutrient elements using modern food processing technologies. This is another possible solution, but it is also not mentioned in the passage.

Therefore, the answer is (b).

Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following:

p + q + r - s - t is definitely even.
2p + q + 2r - 2s + t is definitely odd.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(d )Neither 1 nor 2

Answer-a

The answer is (a) 1 only.

Statement 1: p + q + r - s - t is definitely even.

This is true because the sum of three even numbers and two odd numbers is always even.

Statement 2: 2p + q + 2r - 2s + t is definitely odd.

This is false because the sum of two even numbers and three odd numbers can be either even or odd.

For example, if p = 2, q = 4, r = 6, s = 1, and t = 3, then 2p + q + 2r - 2s + t = 4 + 4 + 12 - 2 + 3 = 21, which is odd.

However, if p = 2, q = 4, r = 6, s = 2, and t = 3, then 2p + q + 2r - 2s + t = 4 + 4 + 12 - 4 + 3 = 21, which is even.

Therefore, only statement 1 is correct.

Consider the following in respect of prime number p and composite number c.

p +c / p-c can be even.
2p + c can be odd.
pc can be odd.

Which of the statements given above are correct?

(a) 1 and 2 only

(b) 2 and 3 only

(d )1, 2 and 3

Answer-d

1.p+ c / p - c can be even.

This statement is correct. If p is a prime number and c is a composite number, then p - c will be negative or zero, as a composite number is always greater than a prime number. Therefore, p + c / (p - c) can be written as p + c / -(c - p), which simplifies to -(p + c) / (c - p). Since the numerator and denominator have opposite signs, the fraction will be negative. Hence, it can be an even number.

2.2p + c can be odd.

This statement is correct. If p is a prime number and c is any number (prime or composite), the sum 2p + c will always be odd. This is because multiplying a prime number by 2 gives an even number, and adding any number (even or odd) to an even number results in an odd number.

3.pc can be odd.

This statement is correct. If p is a prime number and c is any odd composite number, the product pc will be odd. This is because multiplying any number (prime or composite) by an odd number results in an odd number.

Therefore, all three statements are correct, and the correct answer is (d) 1, 2, and 3.

A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A+B+C?

(a) 18

(b) 16

(d )Cannot be determined due to insufficient data

Answer (c)

We have a 3-digit number ABC, and when it is multiplied by D, it results in the product 37DD. We know that A, B, C, and D are different non-zero digits.

Let's break down the multiplication to analyze the digits:

From the units place, we can determine that D multiplied by C should result in D in the units place of the product. This implies that C multiplied by D ends with D as the units digit. The only possible values for D are 1, 3, 7, or 9.

Now let's consider the tens place. We see that D multiplied by B plus the carried-over digit from the units place should result in D as the tens digit of the product. Since D is a non-zero digit, the carried-over digit must be 1. This implies that B multiplied by D plus 1 gives D as the tens digit. The only possible values for D that satisfy this condition are 4, 6, or 8.

From the hundreds place, we see that D multiplied by A plus the carried-over digit from the tens place should result in 3 as the hundreds digit of the product. Since the carried-over digit is 1, this implies that A multiplied by D plus 1 gives 3 as the hundreds digit. The only possible value for D that satisfies this condition is 2.

Therefore, we have determined the values of A, B, C, and D:

A = 3 B = 8 C = 4 D = 2

The value of A + B + C is 3 + 8 + 4 = 15.

Therefore, the correct answer is (c) 15.

For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by :

(a) 7 and 11 only

(b) 11 and 13 only

(d) 7, 11 and 13

Answer (d)

To determine the divisibility of a number, we need to consider the divisibility rules for each of the given divisors: 7, 11, and 13.

Divisibility by 7: For a number to be divisible by 7, the difference between twice the units digit and the remaining digits (excluding the units digit) must be divisible by 7.

In the given number, XYZXYZ, the units digit is the same as the thousands digit, so twice the units digit is equal to the remaining digits. Therefore, the difference between twice the units digit and the remaining digits is zero, which is divisible by 7.

Hence, XYZXYZ is divisible by 7.

Divisibility by 11: For a number to be divisible by 11, the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11.

In the given number, XYZXYZ, the sum of the digits in odd positions (X+Y+Z) is equal to the sum of the digits in even positions (X+Y+Z). Therefore, their difference is zero, which is divisible by 11.

Hence, XYZXYZ is divisible by 11.

Divisibility by 13: There is no specific rule based on the digits themselves to determine divisibility by 13.

To verify if XYZXYZ is divisible by 13 for any choices of values of X, Y, and Z, we can calculate its divisibility for all possible combinations of X, Y, and Z. However, doing so manually would be time-consuming.

Instead, we can make use of a divisibility rule for 13 that states if a number, represented as ABCDEF, is divisible by 13, then the number formed by (ABC - 2DEF) is also divisible by 13.

In the case of XYZXYZ, we have (XYZ - 2XYZ) = -XYZ, which is divisible by 13 since it is just the negative of XYZ.

Therefore, XYZXYZ is divisible by 13 for any choices of values of X, Y, and Z.

To summarize:

XYZXYZ is divisible by 7.
XYZXYZ is divisible by 11.
XYZXYZ is divisible by 13.

Hence, the correct answer is (d) 7, 11, and 13

18.125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side ?

(a) 27

(b) 25

(d) 18

Answer (a)

125 cubes arranged in cubical block means that the cubes are arranged in a 5x5x5 cube.

Only the inner cubes are surrounded by other cubes from each side. The inner cubes are 3x3x3.

Therefore, the number of cubes surrounded by other cubes from each side is 27.

So the answer is (a)

How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions?

(a) 12

(b) 18

(d) 72

Answer (c)

The number of ways to arrange the odd digits in the odd positions is 4!/2!2! = 6. The number of ways to arrange the even digits in the even positions is 4!/2!2! = 6. Therefore, the total number of ways to arrange the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions is 6 x 6 = 36. So the answer is (c)

A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on.

Consider the following statements :

The work will be finished on Thursday.
The work will be finished in 10 days.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer-a

To determine the correct statements, let's analyze the working schedule of A, B, and C:

A can complete the work in 8 days, which means A can do 1/8 of the work in a day.

B can complete the work in 16 days, which means B can do 1/16 of the work in a day.

C can complete the work in 12 days, which means C can do 1/12 of the work in a day.

Considering their individual working days, the schedule will look like this:

Day 1: A works (1/8 of the work is completed)

Day 2: B works (1/16 of the work is completed)

Day 3: C works (1/12 of the work is completed)

Day 4: A works (1/8 of the work is completed)

Now, let's determine if the statements are correct:

Statement 1: The work will be finished on Thursday.

On Thursday, A works again. Since A works every fourth day, the work will indeed be finished on Thursday. Therefore, statement 1 is correct.

Statement 2: The work will be finished in 10 days.

To calculate the total work completed in 10 days, we need to add the fraction of work done by A, B, and C on their respective working days:

1/8 + 1/16 + 1/12 = 6/48 + 3/48 + 4/48 = 13/48

Therefore, after 10 days, 13/48 of the work will be completed, which is less than half. Hence, statement 2 is incorrect.

In conclusion, only statement 1 is correct.

Directions for the following 3 (three) items:

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

Passage-1

To tackle the problem of pollution in cities, policy makers think that drastic actions like temporary use of odd-even number scheme for vehicles, closing schools, factories, construction activities, and banning the use of certain type of vehicles are a way forward. Even then the air is not clean. Vehicles more than 15 years old comprise one percent of the total; and taking them off the road will not make any difference. Banning certain fuels and car types arbitrarily is not proper. Diesel engines produce more PM 2·5 and less CO2 than petrol or CNG engines. On the other hand, both diesel and CNG engines produce more NOx than petrol engines. No one has measured the amount of NOx that CNG engines are emitting. Arbitrary bans on vehicles

that have passed mandated fitness tests and periodic pollution tests are unfair. What is needed is the scientific and reliable information about the source of pollutants on a continuing basis and the technologies that will work to reduce pollution from them.

21.Which one of the following statements best reflects the most logical and rational implication conveyed by the passage ?

(a) Arbitrary curbs on vehicles to reduce pollution are difficult to implement.

(b) Knee-jerk reactions cannot solve the problem of pollution but an evidence-based approach will be more effective.

(d) In the absence of laws to deal with the problems of pollution, the administration tends to make arbitrary decisions.

Answer (b)

The most logical and rational implication conveyed by the passage is that knee-jerk reactions cannot solve the problem of pollution but an evidence-based approach will be more effective. The passage states that policy makers think that drastic actions like temporary use of odd-even number scheme for vehicles, closing schools, factories, construction activities, and banning the use of certain type of vehicles are a way forward. However, the passage also states that even these drastic actions have not been effective in reducing pollution. The passage then goes on to explain that banning certain fuels and car types arbitrarily is not proper, and that arbitrary bans on vehicles that have passed mandated fitness tests and periodic pollution tests are unfair. The passage concludes by stating that what is needed is scientific and reliable information about the source of pollutants on a continuing basis and the technologies that will work to reduce pollution from them. This suggests that the author believes that an evidence-based approach to reducing pollution, rather than knee-jerk reactions, is more likely to be effective.

Therefore, the correct answer is (b)

Passage-2

Good corporate governance structures encourage companies to provide accountability and control. A fundamental reason why corporate governance has moved onto the economic and political agenda worldwide has been the rapid growth in international capital markets. Effective corporate governance enhances access to external financing by firms, leading to greater investment, higher growth and employment. Investors look to place their funds where the standards of disclosure, of timely and accurate financial reporting, and of equal treatment to all stakeholders are met.

22.Which of the following statements best reflects the logical inference from the passage given above?

(a) It is an important agenda of the countries around the world to ensure access to good external financing.

(b) Good corporate governance improves the credibility of the firms.

(d) Good corporate governance paves the way for robust supply chains.

Answer (b)

The logical inference from the passage given above is best reflected in option (b) - Good corporate governance improves the credibility of the firms.

The passage states that good corporate governance structures encourage companies to provide accountability and control. It also mentions that effective corporate governance enhances access to external financing by firms, leading to greater investment, higher growth, and employment. Furthermore, the passage highlights that investors look for standards of disclosure, timely and accurate financial reporting, and equal treatment to all stakeholders.

Based on these statements, it can be inferred that good corporate governance plays a crucial role in improving the credibility of firms. By adhering to principles of accountability, control, transparency, and meeting the standards expected by investors, companies gain credibility and trust. This, in turn, enhances their ability to attract external financing and contributes to their growth and development.

Therefore, option (b) best reflects the logical inference that good corporate governance improves the credibility of the firms.

Passage-3

Elephants are landscape architects, creating clearings in the forest, preventing overgrowth of certain plant species and allowing space for the regeneration of others, which in turn provide sustenance to other herbivorous animals. Elephants eat plants, fruits and seeds, propagating the seeds when they defecate in other places as they travel. Elephant dung provides nourishment to plants and animals and acts as a breeding ground for insects. In times of drought, they access water by digging holes which benefits other wildlife.

23.Which one of the following statements best reflects the most logical and rational inference that can be drawn from the passage ?

(a) The home range of elephants needs to be a vast area of rich biodiversity.

(b) Elephants are the keystone species and they benefit the biodiversity.

(d) Elephants are capable of regenerating forests with species as per their requirement.

Answer (b)

The most logical and rational inference that can be drawn from the passage is that elephants are keystone species and they benefit the biodiversity. The passage states that elephants create clearings in the forest, prevent overgrowth of certain plant species, and allow space for the regeneration of others. This helps to maintain a diverse range of plant species, which in turn provides sustenance to a variety of other animals. Elephants also help to spread seeds, which helps to regenerate forests. In times of drought, they dig holes to access water, which benefits other wildlife. All of these activities help to maintain a healthy and diverse ecosystem.

Therefore, the correct answer is (b)

If 7 EB 9 EB 10 = 8, 9 EB 11 EB 30 = 5, 11 EB 17 EB 21 = 13, what is the value of

23 EB 4 EB 15?

(a) 6

(b) 8

(d) 15

Answer: a

The answer is (a).

Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?

(a)10

(b) 11

(d) Infinitely many

Answer (a)

The correct answer is (a), 10.

Given that 7x + 96 is divisible by x, we can factor out x to get 7x + 96 = x(7 + 96/x). This means that x must be a factor of 96, which has 10 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Therefore, there are 10 possible values of x.

If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of

(p + q) /(r + s)?

(a) 230

(b) 225

(d) 221

Answer (b)

To find the greatest value of (p + q)/(r + s), we need to maximize the numerator and minimize the denominator.

Since p, q, r, and s are distinct single-digit positive numbers, the maximum possible value for p + q is 9 + 8 = 17.

To minimize the denominator, we need to choose the smallest possible values for r and s. The smallest single-digit positive numbers are 1 and 2, so the minimum value for r + s is 1 + 2 = 3.

Therefore, the greatest value of (p + q)/(r + s) is 17/3.

To compare the answer choices, we can convert 17/3 to a mixed fraction: 5 2/3.

The closest answer choice to 5 2/3 is (b) 225, which represents the mixed fraction 5 1/4.

Therefore, the correct answer is (b) 225.

A number N is formed by writing 9 for99 times. What is the remainder if N is divided by 13 ?

(a) 11

(b) 9

(d) 1

Answer (d)

The remainder when 9 is divided by 13 is 9. Therefore, the remainder when 999...99 (99 times) is divided by 13 is the same as the remainder when 9 + 9 + 9 + ... + 9 (99 times) is divided by 13. This is equal to 9 * 99 = 891. The remainder when 891 is divided by 13 is 1

Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?

(a) 64

(b) 80

(d) 100

Answer (c)

The correct answer is (c), 81.

The 9-digit number is 111111111. When multiplied by itself, the resulting number is 12345678901. The sum of the digits of this number is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 0 + 1 = 81.

What is the sum of all digits which appear in all the integers from 10 to 100?

(a) 855

(b) 856

(d) 911

Answer (c)

The correct answer is (c), 910.

Each of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 appears 10 times in the numbers from 10 to 100. The digit 0 appears 11 times, in the numbers 10, 20, 30, ..., 90, and 100. Therefore, the sum of all digits which appear in the integers from 10 to 100 is 10 * (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) + 11 * 0 = 910.

ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points ?

(a) 16

(b) 18

(d) 24

Answer (b)

The correct answer is (b), 18.

Let's label the points as follows: A, B, C, D are the vertices of the square, and E and F are the points on AB and CD, respectively. G and H are the points on BC, and I and J are the points on DA.

We can draw triangles using any three points as vertices out of these six points. However, we need to be careful not to count the same triangle twice. For example, the triangle AEI is the same as the triangle AIE, so we only count it once.

There are 18 distinct triangles that can be drawn using any three points as vertices out of these six points. Here is a list of all 18 triangles:

Directions for the following 5 (five) items :

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

Passage- I

In India, the segregation of municipal waste at source is rare. Recycling is mostly with the informal sector. More than three-fourths of the municipal budget goes into collection and transportation, which leaves very little for processing/resource recovery and disposal. Where does waste-to-energy fit into all this ? Ideally it fits in the chain after segregation (between wet waste and the rest), collection, recycling, and before getting to the landfill. Which technology is most appropriate in converting waste to energy depends on what is in the waste (that is biodegradable versus non-biodegradable component) and its calorific value. The biodegradable component of India's municipal solid waste is a little over 50 per cent, and biomethanation offers a major solution for processing this.

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

1.Collection, processing and segregation of municipal waste should be with government agencies.

2.Resource recovery and recycling require technological inputs that can be best handled by private sector enterprises.

Which of the assumptions given above is/are correct ?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: d

The passage does not make any assumptions about who should be responsible for collection, processing, and segregation of municipal waste. It simply states that more than three-fourths of the municipal budget goes into collection and transportation, which leaves very little for processing/resource recovery and disposal. This suggests that the government may not be able to afford to handle all aspects of waste management on its own.

The passage also does not make any assumptions about who should be responsible for resource recovery and recycling. It simply states that these activities require technological inputs that can be best handled by private sector enterprises. This suggests that the government may need to partner with private companies in order to effectively manage waste.

In conclusion, the passage does not make any assumptions about who should be responsible for waste management. It simply states that the current system is not working and that changes need to be made.

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

(a) Generation of energy from municipal solid waste is inexpensive.

(b) Biomethanation is the most ideal way of generating energy from municipal solid waste.

(d) The biodegradable component of India's municipal solid waste is not adequate to provide energy from waste efficiently/effectively.

Answer-c

The correct answer is (c).

The passage states that "the segregation of municipal solid waste is the first step in ensuring the success of waste-to-energy plants." This is because waste-to-energy plants can only process certain types of waste, and if the waste is not properly segregated, it can contaminate the entire batch of waste and make it unusable for energy production.

The passage also states that "the biodegradable component of India's municipal solid waste is not adequate to provide energy from waste efficiently/effectively." This is because biodegradable waste is not as energy-dense as other types of waste, such as plastic or paper. As a result, it takes more biodegradable waste to produce the same amount of energy, which makes it less efficient and effective.

Therefore, the statement that best reflects the crux of the passage is that segregation of municipal solid waste is the first step in ensuring the success of waste-to-energy plants.

Passage-2

There is a claim that organic farming is inherently safer and healthier. The reality is that because the organic farming industry is still young and not well-regulated in India, farmers and consumers, alike, are not only confused about what products are best for them, but sometimes use products in ways that could harm them as well. For example, since organic fertilizers are difficult to obtain on a large scale in India, farmers often use farmyard manure, which may contain toxic chemicals and heavy metals. Certain plant sprays, such as Datura flower and leaf spray, have an element called atropine. If it is not applied in the right dose, it can act on the nervous system of the consumer. Unfortunately, how much and when to use it are not well-researched or regulated issues.

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

1.Organic farming is inherently unsafe for both farmers and consumers.

2.Farmers and consumers need to be educated about eco-friendly food.

Which of the assumptions given above is/are correct?

(a)1 only

(b)2 only

(d) Neither 1 nor 2

Answer (b)

Based on the given passage, the correct assumption is:

(b) 2 only - Farmers and consumers need to be educated about eco-friendly food.

The passage mentions that the organic farming industry in India is still young and not well-regulated, leading to confusion among farmers and consumers. It also highlights the use of certain products, such as farmyard manure and plant sprays, which may contain toxic chemicals and pose risks if not used properly. This implies a need for education and awareness about eco-friendly food practices.

However, the passage does not state that organic farming is inherently unsafe for both farmers and consumers. It acknowledges the potential risks and confusion due to inadequate regulation and knowledge but does not make a definitive statement about the inherent safety of organic farming.

Therefore, the correct answer is (b) 2 only.

Which one of the following statements best reflects the most logical, rational and practical message conveyed by the author of the passage?

(a) In India, organic farming should not be promoted as a substitute for conventional farming.

(b) There are no safe organic alternatives to chemical fertilizers.

(d) The aim of organic farming should not be to generate huge profits as there is still no global market for its products.

Answer (c)

Based on the given passage, the most logical, rational, and practical message conveyed by the author is:

The passage highlights the challenges and shortcomings of the organic farming industry in India, such as the lack of regulation, confusion among farmers and consumers, and the use of potentially harmful products. However, it does not suggest that organic farming should not be promoted as a substitute for conventional farming or that there are no safe organic alternatives to chemical fertilizers. Additionally, it does not directly address the aim of generating profits or the global market for organic products.

Instead, the passage emphasizes the need to guide and assist farmers in making their organic farming practices sustainable. This implies that with proper support, education, and regulation, organic farming in India can be improved and made safer and healthier for both farmers and consumers.

Therefore, the best reflection of the message conveyed by the author is (c) In India, farmers need to be guided and helped to make their organic farming sustainable.

Passage-3

Food consumption patterns have changed substantially in India over the past few decades. This has resulted in the disappearance of many nutritious foods such as millets. While food grain production has increased over five times since independence, it has not sufficiently addressed the issue of malnutrition. For long,the agriculture sector focussed on increasing food production particularly staples, which led to lower production and consumption of indigenous traditional crops/grains, fruits and other vegetables, impacting food and nutrition security in the process. Further, intensive, monoculture agriculture practices can perpetuate the food and nutrition security problem by degrading the quality of land, water and food derived through them.

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

(1) To implement the Sustainable Development Goals and to achieve zero-hunger goal, monoculture agriculture practices are inevitable even if they do not address malnutrition.

(2) Dependance on a few crops has negative consequences for human health and the ecosystem.

(3) Government policies regarding food planning need to incorporate nutritional security.

(4) For the present monoculture agriculture practices, farmers receive subsidies in various ways and the government offers remunerative prices for grains and therefore they do not tend to consider crop diversity.

Which of the above assumptions are valid?

(a) 1,2 and 4 only

(b) 2 and 3 only

(d) 1,2,3 and 4

Answer (b)

The valid assumptions are (b) 2 and 3 only.

Assumption 1 is not valid because it is based on the premise that monoculture agriculture practices are inevitable in order to implement the Sustainable Development Goals and achieve zero-hunger. However, the passage does not provide any evidence to support this claim. In fact, the passage suggests that monoculture agriculture practices can have negative consequences for human health and the ecosystem.

Assumption 2 is valid because it is supported by evidence in the passage. The passage states that "Dependance on a few crops has negative consequences for human health and the ecosystem." This suggests that monoculture agriculture practices can be harmful to both human health and the environment.

Assumption 3 is valid because it is supported by evidence in the passage. The passage states that "Government policies regarding food planning need to incorporate nutritional security." This suggests that government policies should focus on ensuring that people have access to a variety of nutritious foods, rather than just a few staple crops.

Assumption 4 is not valid because it is based on the premise that farmers receive subsidies in various ways and the government offers remunerative prices for grains, and therefore they do not tend to consider crop diversity. However, the passage does not provide any evidence to support this claim. In fact, the passage suggests that farmers may be more likely to consider crop diversity if they were given more support from the government.

Therefore, the only valid assumptions are 2 and 3.

A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls.

Consider the following statements :

1.The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.

2.The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer-c

To determine the correctness of the statements, let's analyze the given information:

The box contains:

14 black balls

20 blue balls

26 green balls

28 yellow balls

38 red balls

54 white balls

Statement 1: The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one color is 175.

To evaluate this statement, let's consider the worst-case scenario, where the first n-1 balls drawn do not contain a full group of any color. In this scenario, the maximum number of balls drawn without fulfilling the condition is when we have drawn all balls except for one from each color group.

The maximum number of balls drawn without fulfilling the condition is: 13 (black balls) + 19 (blue balls) + 25 (green balls) + 27 (yellow balls) + 37 (red balls) + 53 (white balls) = 174.

Therefore, for n = 175, the condition is fulfilled, and any n balls drawn randomly will contain one full group of at least one color.

Hence, statement 1 is correct.

Statement 2: The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each color is 167.

To evaluate this statement, let's consider the worst-case scenario, where the first m-1 balls drawn do not contain at least one ball of each color. In this scenario, the maximum number of balls drawn without fulfilling the condition is when we have drawn all balls except for one color group, and one ball from another color group.

The maximum number of balls drawn without fulfilling the condition is: 14 (black balls) + 20 (blue balls) + 26 (green balls) + 28 (yellow balls) + 38 (red balls) = 126.

Therefore, for m = 167, the condition is fulfilled, and any m balls drawn randomly will contain at least one ball of each color.

Hence, statement 2 is correct.

Therefore, the correct answer is (c) Both 1 and 2.

If 'ZERO' is written as 'CHUR', then how is 'PLAYER' written?

(a) SOCAGT

(b) SODBGT

(d) SODBHU

Answer (d)

The letters in the word "ZERO" are shifted by 2 places to get the word "CHUR". Similarly, the letters in the word "PLAYER" are shifted by 2 places to get the word " SODBHU"

Consider the following statements :

1.A is older than B.

2.C and D are of the same age.

3.E is the youngest.

4.F is younger than D.

5.F is older than A.

How many statements given above are required to determine the oldest person/persons ?

(a) Only two

(b) Only three

(d) All five

Answer (c)

To determine the oldest person/persons based on the given statements, we need to find the statement(s) that directly or indirectly provide information about the age order. Let's analyze each statement:

A is older than B. This statement gives information about the relative age of A and B.
C and D are of the same age. This statement only provides information about the age of C and D relative to each other but does not give any information about their ages compared to others.
E is the youngest. This statement provides information about the relative age of E compared to others but does not directly reveal who the oldest person is.
F is younger than D. This statement gives information about the relative age of F and D.
F is older than A. This statement gives information about the relative age of F and A.

Based on the above analysis, statements 1, 4, and 5 provide direct information about the age order, and statement 3 provides information about the youngest person. So, a total of four statements (1, 3, 4, and 5) are required to determine the oldest person/persons.

Therefore, the correct answer is (c) Only four

Consider the following including the Question and the Statements :

There are 5 members A, B, C, D, E in a family.

Question : What is the relation of E to B ?

Statement: A and B are a married couple.

Statement-2 : D is the father of C.

Statement-3 : E is D's son.

Statement-4 : A and C are sisters.

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

(a) Statement-1,Statement-2 and Statement-3 are sufficient to answer the Question.

(b) Statement-1, Statement-3 and Statement-4 are sufficient to answer the Question.

(d) All four statements are not sufficient to answer the Question.

Answer (d)

To determine the relation of E to B, let's analyze the statements given:

Statement-1: A and B are a married couple. This statement establishes that A and B are married, but it does not provide any direct information about the relation of E to B.

Statement-2: D is the father of C. This statement informs us about the parentage of C, but it does not give any information about E or B.

Statement-3: E is D's son. This statement directly tells us that E is the son of D. However, it does not provide any information about the relation of E to B.

Statement-4: A and C are sisters. This statement establishes that A and C are sisters, which means they share the same parents. However, it does not provide any information about the relation of E to B.

Based on the analysis, none of the statements alone or in combination are sufficient to determine the relation of E to B. Therefore, the correct answer is (d) All four statements are not sufficient to answer the question.

Choose the group which is different from the others:

(a) 17,37,47,97

(b) 31, 41, 53, 67

(d) 83, 89, 91, 97

Answer (d)

The group that is different from the others can be identified by analyzing the numbers in each group.

In group (d) 83, 89, 91, 97, all the numbers are prime numbers.

In group (a) 17, 37, 47, 97, all the numbers except 97 are prime numbers, but 97 is the largest number in this group.

In group (b) 31, 41, 53, 67, all the numbers are prime numbers.

In group (c) 71, 73, 79, 83, all the numbers are prime numbers except for 83.

Therefore, the group that is different from the others is (d) 83, 89, 91, 97 because it contains one non-prime number, 91.

Directions for the following 3 (three) items:

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

Passage- I

Scientists studied the vernal window - transition period from winter to the growing season. They found that warmer winters with less snow resulted in a longer lag time between spring events and a more protracted vernal window. This change in the spring timetable has ecological, social and economic consequences - for agriculture, fisheries and tourism. As the ice melts earlier, the birds don't return, causing a delay, or lengthening in springtime ecological events.

41.With reference to the above passage, the following assumptions have been made :

1.Global warming is causing spring to come early and for longer durations.

2.Early spring and longer period of spring is not good for bird populations.

Which of the above assumptions is/are correct?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Will update Soon

Passage-2

A global analysis of nitrogen use efficiency - a measure of the amount of nitrogen a plant takes in to grow versus what is left behind as pollution - says that using too much fertilizers will lead to increased pollution of waterways and the air. Currently, the global average for nitrogen use efficiency is approximately 0·4, meaning 40 per cent of the total nitrogen added to cropland goes into the harvested crop while 60 per cent is lost to the environment, says a study. More than half of the world's population is nourished by food grown with fertilizers containing synthetic nitrogen, which is needed to produce high crop yields. Plants take the nitrogen they need to grow, and the excess is left in the ground, water and air. This results in significant emissions of nitrous oxide, a potent greenhouse and ozone depleting gas, and other forms of nitrogenpollution, including eutrophication of lakes and rivers and contamination of river water.

42.Which one of the following statements best reflects the most logical, rational and crucial message implied by the passage ?

(a) An enhanced efficiency of use of nitrogen is imperative for both food production and environment.

(b) Production of synthetic nitrogen fertilizers cannot be stopped as it will adversely affect global food security.

(d) Conventional agriculture using synthetic fertilizers should be replaced with agroforestry, agroecosystems and organic farming.

Answer: a

The most logical, rational, and crucial message implied by the passage is: (a) An enhanced efficiency of use of nitrogen is imperative for both food production and the environment.

The passage emphasizes that the current nitrogen use efficiency is low, with a significant portion of nitrogen being lost to the environment, leading to pollution of waterways and the air. Since a majority of the world's population relies on food grown with nitrogen fertilizers, it is crucial to improve nitrogen use efficiency to minimize environmental pollution while ensuring sufficient food production. This statement highlights the need to address the issue by finding ways to optimize nitrogen use without compromising food security.

Passage - 3

Along with sustainable lifestyles, climate justice is regarded as a significant principle in environmental parlance. Both the principles have bearings on political and economic choices of the nation. So far, in our climate change summits or compacts, both the principles have eluded consensus among nations. Justice, in the judicial sense, is well defined. However, in the context of climate change, it has scientific as well as socio-political connotations. The crucial question in the next few years will be how resources, technologies and regulations are used to support the victims of climate change. Justice in climate is not confined to actions relating to mitigation, but includes the wider notion of support for adaptation to climate change and compensation for loss and damage.

43.Which one of the following statements best reflects the most logical, rational and crucial message conveyed by the passage ?

(a) Climate justice should be ingrained in detail in the rules of all the new climate compacts/agreements.

(b) Environmental resources are unevenly distributed and exploited across the globe.

(d) Climate change in all its connotations is mostly due to developed countries and therefore their share of burden should be more.

Answer: a

The passage states that climate justice is a significant principle in environmental parlance, and that it has scientific as well as socio-political connotations. It also states that the crucial question in the next few years will be how resources, technologies and regulations are used to support the victims of climate change.

The most logical, rational, and crucial message conveyed by the passage is that climate justice should be ingrained in detail in the rules of all the new climate compacts/agreements. This is because climate justice is a complex issue with many different dimensions, and it is important to ensure that all of these dimensions are considered when developing new climate policies.

The other options are not as logical or rational as the first option. Option (b) is true, but it is not the most important message conveyed by the passage. Option (c) is also true, but it is not a new message. Option (d) is not supported by the passage.

Therefore, the answer is (a).

A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct ?

(a) R = S

(b) R > S

(d) R less than or equal to S

Answer c

The correct answer is (c).

When interest is compounded half-yearly, the effective rate of interest is higher than the nominal rate of interest. This is because the interest is earned on the interest that has already been earned, so the amount of interest grows exponentially.

When interest is compounded annually, the effective rate of interest is equal to the nominal rate of interest. This is because the interest is only earned on the original principal, so the amount of interest grows linearly.

Therefore, if a principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest, then the same principal P will become more than Q in 1 year when compounded annually with S% annual rate of interest. This means that R must be less than S.

45.How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers ?

(a) 6

(b) 7

(d) 9

Answer: c

The natural numbers that give a remainder of 31 when 1186 is divided by them are the divisors of 1186 - 31 = 1155.

The prime factorization of 1155 is 3 * 5 * 7 * 11.

Therefore, the divisors of 1155 are 1, 3, 5, 7, 11, 15, 21, 33, 55, 77, 165, 385, and 1155.

There are 8 divisors of 1155 that are less than 1155, and therefore there are 8 natural numbers that give a remainder of 31 when 1186 is divided by them.

46.Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements :

1.The number of possible values of p is 5.

2.The number of possible values of q is 6.

Which of the above statements is/are correct ?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: c

The correct answer is (c).

We are given that pp, qq, and rr are 2-digit numbers where p < q < r, and that pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero.

We can see that the sum of the three numbers must be a multiple of 10, and that the only way to achieve this is if one of the numbers is a multiple of 10 and the other two numbers are not.

Since p < q < r, we know that p cannot be a multiple of 10, and that r must be a multiple of 10. This leaves q as the only number that could potentially be a multiple of 10.

If q is a multiple of 10, then p must be a single-digit number and r must be a 2-digit number. This gives us 5 possible values for p (1, 2, 3, 4, 5) and 6 possible values for q (10, 20, 30, 40, 50, 60).

If q is not a multiple of 10, then p must be a 2-digit number and r must be a 3-digit number. This gives us 9 possible values for p (10, 11, 12, 13, 14, 15, 16, 17, 18) and 8 possible values for q (20, 21, 22, 23, 24, 25, 26, 27).

Therefore, the number of possible values of p is 5 or 9, and the number of possible values of q is 6 or 8. This means that both statements 1 and 2 are correct.

47.What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?

(a) 7998

(b) 8028

(d) 9238

Answer: b

The number of 4-digit numbers formed by the digits 1, 2, 3 and 4, where none of the digits is repeated is 4! = 24.

The sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated is:

1112 + 1123 + 1132 + 1142 + 1213 + 1221 + 1231 + 1242 + 1312 + 1321 + 1342 + 1412 + 1421 + 1432 + 2113 + 2121 + 2131 + 2142 + 2211 + 2231 + 2242 + 2311 + 2321 + 2342 + 2411 + 2421 + 2432 = 8028.

Therefore, the answer is (b).

48.What's the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction ?

(a)3

(b)11

(d)66

Answer: c

The number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction is 12.

There are 12 possible starting points, and once the starting point is chosen, the rest of the selection is determined. Therefore, there are 12 possible selections.

49.If today is Sunday, then which day is it exactly on 10^10 th day ?

(a)Wednesday

(b)Thursday

(c)Friday

(d) Saturday

Answer: a

The remainder when 10^10 is divided by 7 is 3. Therefore, the day of the week on the 10^10th day is 3 days after Sunday, which is Wednesday. Therefore, the answer is (a).

50.There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m, they together turn green. At what time will they change to green next, simultaneously ?

(a) 4:00 p.m.

(b) 4:10 p.m.

(d) 4:30 p.m.

Answer: b

The three traffic signals will change color from green to red and then from red to green in 25 seconds, 39 seconds, and 60 seconds, respectively. The durations for green and red colors are the same, so the three traffic signals will change color from green to red and then from red to green again in 50 seconds, 78 seconds, and 120 seconds, respectively.

The least common multiple of 50, 78, and 120 is 7800 seconds, or 130 minutes. Therefore, the three traffic signals will change to green simultaneously every 130 minutes.

At 2:00 p.m., the three traffic signals change to green simultaneously. The next time they change to green simultaneously will be 130 minutes later, at 4:10 p.m.

Directions for the following 3 (three) items :

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

Passage- I

Sourcing food from non-agricultural lands (uncultivated systems such as forests, wetlands, pastures, etc) in addition to agricultural lands enables a systemic approach to food consumption. It allows rural and tribal communities to sustain themselves for the whole year and steer clear of natural disasters and season-induced shortfalls of agricultural food. Since the productivity of trees is often more resilient to adverse weather conditions than annual crops, forest foods often provide a safety net during periods of food shortages caused by crop failure; forest foods also make important contributions during seasonal crop production gaps.

51.Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage ?

(a) Food yielding trees should replace other trees in rural and tribal areas and community owned lands.

(b) Food security cannot be ensured in India with the present practice of conventional agriculture.

(d) Agroecosystems should be developed in addition to or along with conventional agriculture.

Answer: d

The author of the passage is arguing that sourcing food from non-agricultural lands in addition to agricultural lands is a more sustainable and resilient way to ensure food security. The author cites the fact that the productivity of trees is often more resilient to adverse weather conditions than annual crops, and that forest foods often provide a safety net during periods of food shortages caused by crop failure.

Based on this information, the most logical and rational message conveyed by the author of the passage is that agro ecosystems should be developed in addition to or along with conventional agriculture. This would allow rural and tribal communities to sustain themselves for the whole year and steer clear of natural disasters and season-induced shortfalls of agricultural food.

Passage-2

While awareness on use/misuse and abuse of antibiotics is common knowledge, as is the impact of dosing poultry with antibiotics, the environmental impact of antibiotics-manufacturing companies not treating their waste has scarcely been discussed at any length or seriousness thus far. Pollution from antibiotics factories is fuelling the rise of drug-resistant infections. The occurrence of drug-resistant bacteria surrounding the pharma manufacturing plants is well known.

52.Which one of the following statements best reflects the most logical and practical message conveyed by the passage ?

(a) It is necessary to put proper effluent treatment protocols in place.

(b) It is necessary to promote environmental awareness among people.

(d) Pharma-manufacturing companies should be set up in remote rural areas, away from crowded towns and cities.

Answer: a

The passage states that the environmental impact of antibiotics-manufacturing companies not treating their waste is a serious problem that is not being discussed enough. The passage also states that pollution from antibiotics factories is fuelling the rise of drug-resistant infections.

Based on this information, the most logical and practical message conveyed by the passage is that it is necessary to put proper effluent treatment protocols in place. This would help to reduce the amount of pollution from antibiotics factories and would help to prevent the spread of drug-resistant infections.

Passage-3

Benefits of good quality school education accrue only when students complete and leave school after having acquired the gateway skills. Like one learns to walk before running, similarly one picks up advanced skills only after picking the basic foundational skills. The advent of the knowledge economy poses new challenges, and one of the severe consequences of having an uneducated workforce will be our inability to keep pace with the global economy. Without a strong learning foundation at the primary level, there can be no improvement in higher education or skill development.

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

(a) To become a global power, India needs to invest in universal quality education.

(b) India is unable to become a global power because it is not focussing or promoting

knowledge economy.

(d) Parents of many school children are illiterate and are unaware of the benefits of quality education.

Answer: a

The passage states that good quality school education is essential for India to become a global power. The passage also states that without a strong learning foundation at the primary level, there can be no improvement in higher education or skill development.

Based on this information, the statement that best reflects the crux of the passage is to become a global power, India needs to invest in universal quality education.

54.40 children are standing in a circle and one of them (say child-I) has a ring. The ring is passed clockwise. Child-I passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-I) will the ring be in the hands of child-I again ?

(a) 14

(b) 15

(d) 17

Answer: a

The ring is passed to every third child, so it will be passed to 40/3 = 13 children before it is passed back to child-I. Therefore, the ring will be in the hands of child-I again after 14 changes.

Therefore, the answer is (a).

55.What is the middle term of the sequence

Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, ... , A?

(a) H

(b) I

(d) M

Answer: d

To find the middle term of the given sequence, we need to determine the position of the middle term within the sequence.

The given sequence consists of repeating letters in descending order, starting with 'Z' and ending with 'A'.

The length of the sequence can be calculated by finding the number of terms between 'Z' and 'A' (inclusive).

In this case, the length is 26, as there are 26 letters in the English alphabet.

Since the sequence is symmetrical, the middle term will be the 13th term in the sequence.

Starting from 'Z', we can count 13 terms to reach the middle term.

The middle term is 'N'.

Therefore, the correct answer is (d) M.

56.Question : Is p greater than q ?

Statement- I : p x q is greater than zero.

Statement-2: p^2 is greater than q^2.

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

(a)The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

(b) The Question can be answered by using either Statement alone.

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

(d) The Question cannot be answered even by using both the Statements together.

Answer: d

Statement 1 only tells us that pq is positive, but this does not tell us whether p or q is greater. For example, both 2 * 3 and -2 * -3 are positive, but 2 is greater than 3 and -2 is less than -3.

Statement 2 only tells us that p^2 is greater than q^2, but this does not tell us whether p or q is greater. For example, both 2^2 and -2^2 are 4, but 2 is greater than -2 and -2 is less than 2.

Therefore, the question cannot be answered even by using both the statements together.

So the answer is (d).

57.Question: Is (p + q - r) greater than (p - q + r), where p, q and r are integers?

Statement- I : (p - q) is positive.

Statement-2: (p - r) is negative.

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

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

(b) The Question can be answered by using either Statement alone.

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

(d) The Question cannot be answered even by using both the Statements together.

Answer-c

The answer is (c).

Statement-1 only tells us that the difference between p and q is positive. This means that either p is greater than q or q is less than p. It does not tell us anything about the sign of r.

Statement-2 only tells us that the difference between p and r is negative. This means that either p is less than r or r is greater than p. It does not tell us anything about the sign of q.

When we combine both statements, we can see that if p is greater than q and r is greater than p, then (p + q - r) will be greater than (p - q + r). However, if p is less than q and r is less than p, then (p + q - r) will be less than (p - q + r).

Therefore, the question can be answered by using both statements together, but cannot be answered using either statement alone.

58.In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.

Question : How many persons attended the party?

Statement- I : 50 persons took milk.

Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

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

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

(b) The Question can be answered by using either Statement alone.

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

(d) The Question cannot be answered even by using both the Statements together.

Answer: d

Statement 1 tells us that 50 persons took milk. This is not enough information to answer the question, because we don't know how many people took only milk, and how many people took milk and another drink.

Statement 2 tells us that the number of persons who attended the party is five times the number of persons who took milk only. This is also not enough information to answer the question, because we don't know how many people took milk only.

Even if we know both statements, we cannot answer the question, because the two statements are contradictory. Statement 1 says that 50 persons took milk, but Statement 2 says that the number of persons who took milk only is zero. Therefore, both statements cannot be true, and we cannot answer the question.

59.Consider a 3-digit number.

Question : What is the number ?

Statement- I : The sum of the digits of the number is equal to the product of the digits.

Statement-2 : The number is divisible by the sum of the digits of the number.

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

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

(b) The Question can be answered by using either Statement alone.

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

(d) The Question cannot be answered even by using both the Statements together.

Answer: c

Statement I: The sum of the digits of the number is equal to the product of the digits.

Statement II: The number is divisible by the sum of the digits of the number.

To solve this problem, we need to consider both statements together.

Let's examine Statement I first.

For a 3-digit number, let's assume the digits are A, B, and C.

According to Statement I, we have the equation: A + B + C = A * B * C

We can see that this equation is only satisfied if A, B, and C are all equal to 3, as no other combination of digits can make this equation true.

Now let's move on to Statement II.

We need to check if the number is divisible by the sum of its digits.

For the number to be divisible by the sum of its digits, the sum of the digits should be a divisor of the number itself.

In our case, the sum of the digits is 3 + 3 + 3 = 9, which is a divisor of any 3-digit number that is divisible by 9.

Therefore, using both statements together, we can determine that the 3-digit number in question is 333.

We have successfully answered the question using both statements.

The correct option is (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

60.For five children with ages a < b < c < d < e; any two successive ages differ by 2 years.

Question : What is the age of the youngest child?

Statement-I : The age of the eldest is 3 times the youngest.

Statement-2 : The average age of the children is 8 years.

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

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

(b) The Question can be answered by using either Statement alone.

(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

(d) The Question cannot be answered even by using both the Statements together.

Answer: b

Let's assume the age of the youngest child is "a".

According to the given conditions, the ages of the other children can be expressed as: a, a+2, a+4, a+6, a+8

Now let's analyze Statement I.

It states that the age of the eldest child is 3 times the age of the youngest child.

So, we have:

a+8 = 3a

Simplifying this equation,

we find:

2a = 8 a = 4

Using Statement I alone, we can determine that the age of the youngest child is 4.

Now let's move on to Statement II.

It states that the average age of the children is 8 years.

We can calculate the average age using the given ages:

(a + a+2 + a+4 + a+6 + a+8) / 5 = 8

(5a + 20) / 5 = 8

Simplifying this equation,

we find:

a + 4 = 8

a = 4

Using Statement II alone, we can also determine that the age of the youngest child is 4. Therefore, both statements individually provide the same information, and we can determine that the age of the youngest child is 4 using either statement alone.

The correct option is (b) The Question can be answered by using either Statement alone.

Passage-4

The paradox of choice is illustrated by the story of Buridan's ass. Jean Buridan, the 14th century philosopher, wrote about free will and the inability to choose due to numerous choices and uncertainties. In the story, a donkey stands between two equally appealing stacks of hay. Unable to decide which to eat, it starves to death. Changes in technology and innovations such as smart phones and tablets only exacerbate our glut of choices. Constant connectivity and overconsumption of real-time data and social media can leave little room for self-reflection and rest, making decisions more difficult. Life is about choices. Many people are overwhelmed with attractive life choices, yet find themselves unhappy and anxious.

Which one of the following statements best reflects the most logical message implied by the above passage?

(a) Modern technology enfeebles societal structure and makes life difficult.

(b) Modern life is full of uncertainties and endless difficult choices.

(d) In our lives, having too few choices may not be a good thing, but having too many can be equally as difficult.

Answer: d

The most logical message implied by the passage is that having too many choices can be equally as difficult as having too few. This is supported by the story of Buridan's ass, which illustrates how an animal can be paralyzed by too many choices. The passage also mentions how modern technology can exacerbate the problem of too many choices. Constant connectivity and overconsumption of real-time data and social media can leave little room for self-reflection and rest, making decisions more difficult.

Passage-2

Household finance in India is unique. We have a tendency to invest heavily in physical assets such as gold and property. Steps to encourage the financialization of savings are critical. A populace accustomed to traditional processes will not simply jump into financialization. Hurdles to change include onerous bureaucracy, a scepticism of organized financial institutions, a lack of basic information about which of the myriad services and providers is best for each family, and how (and even if) one can make the transition between them if necessary.

62.Regarding the financialization of household savings, which of the following statements best reflect the solutions that are implied by the passage ?

1.A flexible environment is needed to develop solutions.

2.Households need customized solutions.

5.Innovations in financial technology are required.

Select the correct answer using the code given below:

(a) 1 and 2 only

(b) 2 and 3 only

(d) 1, 2 and 3

Answer: d

The correct answer is D.

The passage mentions that there are a number of hurdles to change in household finance in India. These hurdles include onerous bureaucracy, scepticism of organized financial institutions, and a lack of basic information about which of the myriad services and providers is best for each family.

The solutions that are implied by the passage are:

A flexible environment is needed to develop solutions. This means that the government and financial institutions need to be willing to experiment with new approaches and be open to feedback from households.
Households need customized solutions. This means that financial institutions need to offer a variety of products and services that meet the needs of different households.
Innovations in financial technology are required. This means that financial institutions need to use technology to make it easier for households to access and manage their finances.

All of these solutions are important, and they all need to be implemented in order to encourage the financialization of household savings in India.

Passage-3

Pharmaceutical patents grant protection to the patentee for the duration of the patent term. The patentees enjoy the liberty to determine the prices of medicines, which is time-limited to the period of monopoly, but could be unaffordable to the public. Such patent protection offered to the patentees is believed to benefit the public over the longer term through innovations and research and development (R&D), although it comes at a cost, in the nature of higher prices for the patented medicine. The patent regime and price protection - through a legally validated high price for the medicine during the currency of the patent - provide the patentee with a legitimate mechanism to get returns on the costs incurred in innovation and research.

63 Based on the above passage, the following assumptions have been made :

1.Patent protection given to patentees puts a huge burden on the public's purchasing power in accessing patented medicines.

2.Dependence on other countries for pharmaceutical products is a huge burden for developing and poor countries.

3.Providing medicines to the public at affordable prices is a key goal during the public health policy design in many countries.

4.Governments need to find an appropriate balance between the rights of patentees and the requirements of the patients.

Which of the above assumptions are valid ?

(a) 1 and 2

(b) 1 and 4

(d) 2 and 3

Answer: b

Based on the passage, the following assumptions can be considered valid:

Patent protection given to patentees puts a huge burden on the public's purchasing power in accessing patented medicines. This is supported by the statement that the prices of patented medicines determined by the patentees could be unaffordable to the public.

Providing medicines to the public at affordable prices is a key goal during the public health policy design in many countries. This is implied by the mention of the higher prices for patented medicines and the need for balance between the rights of patentees and the requirements of patients.

Therefore, the valid assumptions are: (b) 1 and 4

The correct answer is (b) 1 and 4.

Passage -4

India should ensure the growth of the digital economy while keeping personal data of citizens secure and protected. No one will innovate in a surveillance-oriented environment or in a place where an individual's personal information is compromised. The ultimate control of data must reside with the individuals who generate it; they should be enabled to use, restrict or monetise it as they wish. Therefore, data protection laws should enable the right kind of innovation - one that is user-centric and privacy protecting.

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

1.Protection of privacy is not just a right, but it has value to the economy.

2.There is a fundamental link between privacy and innovation.

Which of the above assumptions is/are valid ?

(a)1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: c

The passage states that India should ensure the growth of the digital economy while keeping personal data of citizens secure and protected. It also states that no one will innovate in a surveillance-oriented environment or in a place where an individual's personal information is compromised. This means that protection of privacy is not just a right, but it has value to the economy.

The passage also states that the ultimate control of data must reside with the individuals who generate it. This means that there is a fundamental link between privacy and innovation. If individuals do not have control over their data, they will be less likely to share it, which will stifle innovation.

Therefore, both assumptions are valid.

In an examination, the maximum marks for each of the four papers namely P, Q, Rand S are 100. Marks scored by the students are in integers. A student can score 99% m n different ways. What is the value of n?

(a) 16

(b) 17

(d) 35

Answer: c

To score 99% overall, the student must score 396 marks out of a possible 400. There are 23 ways to do this:

100 in P, Q, R, and S
99 in P, Q, and R, and 100 in S
99 in P, Q, and S, and 100 in R
99 in P, R, and S, and 100 in Q
99 in Q, R, and S, and 100 in P
100 in P, and 99 in Q, R, and S
100 in Q, and 99 in P, R, and S
100 in R, and 99 in P, Q, and S
100 in S, and 99 in P, Q, and R
98 in P, Q, and R, and 100 in S
98 in P, Q, and S, and 100 in R
98 in P, R, and S, and 100 in Q
98 in Q, R, and S, and 100 in P
100 in P, and 98 in Q, R, and S
100 in Q, and 98 in P, R, and S
100 in R, and 98 in P, Q, and S
100 in S, and 98 in P, Q, and R
99 in P, Q, and R, and 98 in S
99 in P, Q, and S, and 98 in R
99 in P, R, and S, and 98 in Q
99 in Q, R, and S, and 98 in P

A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?

(a) 12

(b) 18

(d) 36

Answer: c

Let's consider the possibilities for the first stripe:

If the first stripe is red, then the second stripe can be either green or yellow.

If the first stripe is green, then the second stripe can be either red or yellow.

If the first stripe is yellow, then the second stripe can be either red or green.

For each of these cases, we can continue determining the possibilities for the remaining two stripes.

Case 1:First stripe is red:

Second stripe can be either green or yellow (2 possibilities).

Third stripe cannot be the same color as the second stripe, so it has 2 possibilities.

Fourth stripe cannot be the same color as the third stripe, so it has 2 possibilities.

Total possibilities for this case: 2 * 2 * 2 = 8.

Case 2: First stripe is green:

Second stripe can be either red or yellow (2 possibilities).

Third stripe cannot be the same color as the second stripe, so it has 2 possibilities.

Fourth stripe cannot be the same color as the third stripe, so it has 2 possibilities.

Total possibilities for this case: 2 * 2 * 2 = 8.

Case 3: First stripe is yellow:

Second stripe can be either red or green (2 possibilities).

Third stripe cannot be the same color as the second stripe, so it has 2 possibilities.

Fourth stripe cannot be the same color as the third stripe, so it has 2 possibilities.

Total possibilities for this case: 2 * 2 * 2 = 8.

Adding up the possibilities from all cases:

Total possibilities = 8 + 8 + 8 = 24.

Therefore, the number of different ways to design the flag is 24, which corresponds to option (c).

A rectangular floor measures 4 m in length and 2·2 min breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor ?

(a) 6

(b) 7

(d) 9

Answer: a

To find the maximum number of tiles that can be accommodated on the rectangular floor without overlapping, we need to calculate how many tiles can fit along the length and breadth of the floor.

Length of the floor = 4 m = 400 cm

Breadth of the floor = 2 * 2 min = 200 cm

Size of each tile = 140 cm by 60 cm

To fit the tiles along the length, we divide the length of the floor by the length of each tile:

Number of tiles along the length = Length of the floor / Length of each tile

= 400 cm / 140 cm = 2.86

Since we cannot have a fraction of a tile, we can accommodate a maximum of 2 tiles along the length.

To fit the tiles along the breadth, we divide the breadth of the floor by the breadth of each tile:

Number of tiles along the breadth = Breadth of the floor / Breadth of each tile

= 200 cm / 60 cm = 3.33

Again, we cannot have a fraction of a tile, so we can accommodate a maximum of 3 tiles along the breadth.

To find the maximum number of tiles, we multiply the number of tiles along the length by the number of tiles along the breadth:

Maximum number of tiles = Number of tiles along the length * Number of tiles along the breadth = 2 * 3 = 6.

Therefore, the maximum number of tiles that can be accommodated on the floor is 6, which corresponds to option (a).

68.There are five persons P, Q, R, S and Teach one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done ?

(a) 6

(b) 12

(d) 24

Answer: d

There are 5 tasks and 5 persons. Task-1 cannot be assigned to either P or Q. Task-2 must be assigned to either R or S. Every person is to be assigned one task. In how many ways can the assignment be done?

There are 2 ways to assign Task-2: to R or S. If Task-2 is assigned to R, then Task-1 can be assigned to T or S. If Task-2 is assigned to S, then Task-1 can be assigned to T or R. In either case, there are 2 ways to assign Task-1.

Once Task-1 and Task-2 have been assigned, there are 3 people left to assign 3 tasks to. This can be done in 3! = 6 ways.

Therefore, the total number of ways to assign the tasks is 2 * 2 * 6 = 24.

So the answer is (d).

There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements :

1.To buy 78 gm of coins one must buy at least 7 coins.

2.To weigh 78 gm using these coins one can use less than 7 coins.

Which of the statements given above is/are correct?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: b

To determine which of the given statements is correct, let's analyze each statement:

Statement 1: To buy 78 gm of coins, one must buy at least 7 coins. Let's see if it is possible to buy 78 gm of coins with fewer than 7 coins. We can use a combination of different coin weights to achieve this. One possible combination is using a 50 gm coin, a 25 gm coin, and three 1 gm coins, which totals 78 gm. This combination requires only 5 coins, which is less than 7. Therefore, Statement 1 is incorrect.

Statement 2: To weigh 78 gm using these coins, one can use less than 7 coins. We need to determine if it is possible to weigh 78 gm using less than 7 coins. We can achieve this by using a combination of higher weight coins. For example, we can use a single 50 gm coin and a single 25 gm coin, totaling 75 gm. To reach 78 gm, we can add three 1 gm coins. This combination requires only 5 coins, which is less than 7. Therefore, Statement 2 is correct.

Based on the analysis, Statement 1 is incorrect, and Statement 2 is correct. Therefore, the correct answer is option (b) "2 only".

Consider the following :

1.A + B means A is neither smaller nor equal to B.

2.A - B means A is not greater than B.

3.Ax B means A is not smaller than B.

4.A/ B means A is neither greater nor equal to B.

5.A ± B means A is neither smaller nor greater than B.

Statement :P x Q, P - T, T -:- R, R ± S

Conclusion-I: Q ± T

Conclusion-2 : S + Q

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

(a) Only Conclusion-1 follows from the Statement.

(b) Only Conclusion-2 follows from the Statement.

(d) Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

Answer: d

Conclusion 1: Q ± T: Q is neither smaller nor greater than T.

This conclusion does not follow from the statement. The statement only tells us that P is not smaller than Q and P is not greater than T. It does not tell us anything about the relationship between Q and T.

For example, it is possible that P = Q and P = T. In this case, Q would be equal to T, which means that Q is neither smaller nor greater than T. However, the statement does not tell us that P = Q or P = T. Therefore, we cannot conclude that Q is neither smaller nor greater than T.

Conclusion 2: S + Q: S is neither smaller nor equal to Q.

This conclusion also does not follow from the statement. The statement only tells us that R is neither smaller nor greater than S. It does not tell us anything about the relationship between S and Q.

For example, it is possible that R = S and R = Q. In this case, S would be equal to Q, which means that S is neither smaller nor equal to Q. However, the statement does not tell us that R = S or R = Q. Therefore, we cannot conclude that S is neither smaller nor equal to Q.

Correct answer: (d) Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

Directions for the following 3 (three) items: Read the following three passages and answer the items that follow the passages. Your answers to these

items should be based on the passages only.

Passage -1

In India, while the unemployment rate is a frequently used measure of poor performance of the economy, under conditions of rising school and college enrolment, it paints an inaccurate picture. The reported unemployment rate is dominated by the experience of younger Indians who face higher employment challenges and exhibit greater willingness to wait for the right job than their older peers. The unemployment challenge is greater for people with secondary or higher education, and rising education levels inflate unemployment challenges.

71.Which one of the following statements most likely reflects as to what the author of the passage intends to say ?

(a) Enrolment in schools and colleges is high but there is no quality education.

(b) Unemployment must be seen as a function of rising education and aspirations of young Indians.

(d) The education system should be properly designed so as to enable the educated people to be self-employed.

Answer: b

The passage suggests that the reported unemployment rate in India does not accurately reflect the performance of the economy due to factors such as rising school and college enrolment and the employment challenges faced by younger Indians with higher education.

Based on this information, the most likely intention of the author can be inferred as follows: (b) Unemployment must be seen as a function of rising education and aspirations of young Indians.

This option captures the idea that the increasing levels of education and aspirations among young Indians contribute to the unemployment challenges they face. It aligns with the author's emphasis on the impact of rising education levels and the experiences of younger individuals on the accuracy of the unemployment rate. Regenerate response.

Passage-2

"Science by itself is not enough, there must be a force and discipline outside the sciences to coordinate them and point to a goal. It is not possible to run a course staright when the goal itself has not been rightly placed. What science needs is philosophy - the analysis of scientific method and the coordination of scientific purposes and results; without this, any science must be superficial. Government suffers, precisely like science, for lack of philosophy. Philosophy bears to science the same relationship which statesmanship bears to politics : movement guided by total knowledge and perspective, as against aimless and individual seeking. Just as the pursuit of knowledge becomes scholasticism when divorced from the actual needs of men and life, so the pursuit of politics becomes a destructive bedlam when divorced from science and philosophy."

72.Which one of the following statements best reflects the most rational, logical and practical message conveyed by the passage ?

(a) Modern statesmen need to be well trained in scientific methods and philosophical thinking to enable them to have a better perspective of their roles, responsibilities and goals.

(b) It is not desirable to have Governments managed by empirical statesmen unless well mixed with others who are grounded in learning and reflect wisdom.

(c) As the statesmen/bureaucrats are the products of a society, it is desirable to have a system of education in a society that focuses on training its citizens in scientific method and philosophical thinking from a very early age.

(d) It is desirable that all scientists need to be philosophers as well to make their work goal-oriented and thus purposeful and useful to society.

Answer: a

The most rational, logical, and practical message conveyed by the passage can be reflected in the following statement:

(a) Modern statesmen need to be well trained in scientific methods and philosophical thinking to enable them to have a better perspective of their roles, responsibilities, and goals.

The passage emphasizes the need for a force and discipline outside of science to coordinate and guide scientific endeavors towards a goal. It also highlights the importance of philosophy in analyzing scientific methods and coordinating scientific purposes and results. By drawing a parallel between government and science, the passage suggests that both can benefit from the guidance and perspective provided by philosophy. Therefore, the statement that modern statesmen should be well trained in scientific methods and philosophical thinking aligns with the passage's message of the need for coordination, perspective, and goal-oriented approaches.

Passage-3

"The last end of the state is not to dominate men, nor to restrain them by fear; rather it is so to free each man from fear that he may live and act with full security and without injury to himself or his neighbour. The end of the state, I repeat, is not to make rational beings into brute beasts and machines. It is to enable their bodies and their minds to function safely. It is to lead men to live by, and to exercise, a free reason; that they may not waste their strength in hatred, anger and guile, nor act unfairly toward one another."

73.Based on the above passage, which one of the following terms best expresses the ultimate goal of the state ?

(a) Personal safety

(b) Health of body and mind

(d) Liberty

Answer: d

Based on the passage, the term that best expresses the ultimate goal of the state is:

(d) Liberty The passage emphasizes that the end of the state is not to dominate or restrain individuals but to free them from fear and enable them to live and act with full security. It aims to allow individuals to exercise their free reason and live without wasting their strength in negative emotions or acting unfairly towards one another. This emphasis on freedom, security, and the ability to live and act without harm aligns with the concept of liberty.

What is the remainder if 2^192 is divided by 6?

(a) 0

(b) 1

(d) 4

Answer: a

2 to the power of any even number is always divisible by 4.

2 to the power of any odd number is always divisible by 2, but not by 4.

192 is an even number, so 2 to the power of 192 is divisible by 4.

Any number divisible by 4 is also divisible by 2.

Therefore, the remainder when 2 to the power of 192 is divided by 6 is 0.

Consider the sequence

ABC_ _ ABC_DABBCD_ABCD that follows a certain pattern.

Which one of the following completes the sequence?

(a) DACB

(b) CDAB

(d) DDCA

Answer: a

The sequence is a repetition of the following pattern:

ABC
D
ABC
DABB
BCD
ABCD

Therefore, the next two letters are DACB.

AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A + B + C equal to ?

(a) 6

(b) 7

(d) 9

Answer: b

We know that AB and CD are two-digit numbers, and multiplying them results in a three-digit number DEF. This means that AB and CD must both be less than 10, and DEF must be between 100 and 999.

We also know that E = 0 and F = 8. This means that D must be 1, since 08 is not a valid two-digit number.

Now, we can try to find AB and CD. We know that AB x CD = DEF, and DEF + GHI = 975. We can try to find all the possible values of AB and CD that satisfy these equations.

One possibility is AB = 1 and CD = 9. This would give us DEF = 9, and GHI = 966. However, this is not possible because GHI must be a three-digit number.

Another possibility is AB = 2 and CD = 4. This would give us DEF = 8, and GHI = 967. This is a valid solution, so AB = 2 and CD = 4.

Now, we can find A + B + C. A = 2, B = 1, and C = 4, so A + B + C = 7.

Therefore, the answer is (b).

Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false.

True Statement : One of P and Q was selected for the job.

False Statement : At least one of R and S was selected for the job.

True Statement : At most two of R, S and T were selected for the job.

Which of the following conclusions can be drawn?

1.At least four were selected for the job.

2.S was selected for the job.

Select the correct answer using the code given below:

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: d

The correct answer is (d).

The first statement tells us that either P or Q was selected for the job. The second statement tells us that R and S were not both selected for the job. The third statement tells us that at most two of R, S, and T were selected for the job.

We can conclude that at least one of P and Q was selected, and at most two of R, S, and T were selected. We cannot conclude anything about S or the number of people who were selected for the job.

Therefore, neither conclusion 1 nor conclusion 2 can be drawn.

78.Let P, Q, R, S and T be five statements such that:

I.If P Is true, then both Q and S are true.

II.If R and S are true, then T is false.

Which of the following can be concluded ?

1.If T is true, then at least one of P and R must be false.

2.If Q is true, then P is true.

Select the correct answer using the code given below:

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: a

Statement I tells us that if P is true, then Q and S must also be true.

Statement II tells us that if R and S are true, then T must be false.

We can conclude that if T is true, then R and S must be true. However, this does not tell us anything about P. It is possible that P is false, in which case Q would also be false.

Therefore, we can conclude that if T is true, then at least one of P and R must be false. However, we cannot conclude that if Q is true, then P is true.

Therefore, only conclusion 1 can be drawn.

A cuboid of dimensions 7 cm x 5 cm x 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions

7 cm x 5 cm, 5 cm x 3 cm, 7 cm x 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct?

There are exactly 15 small cubes with no paint on any face.

There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.

Select the correct answer using the code given below:

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Answer: c

The correct answer is (c).

The cuboid has a total of 7 x 5 x 3 = 105 small cubes.

The cubes with no paint on any face are the ones that are located in the interior of the cuboid. There are 7 - 2 = 5 rows of cubes along the length of the cuboid, 5 - 2 = 3 rows of cubes along the width of the cuboid, and 3 - 2 = 1 row of cubes along the height of the cuboid. Therefore, there are 5 x 3 x 1 = 15 cubes with no paint on any face.

The cubes with exactly two faces painted blue and green are the ones that are located on the edges of the cuboid, and that are adjacent to both a blue face and a green face. There are 2 x 3 x 1 = 6 such cubes.

Therefore, both statements 1 and 2 are correct.

The letters of the word "INCOMPREHENSIBILITIES" are arranged alphabetically in reverse order. How many positions of the letter/letters will remain unchanged?

(a) None

(b) One

(d) Three

Answer: c

To solve this problem, let's arrange the letters of the word "INCOMPREHENSIBILITIES" in alphabetical order:

B C E E E H I I I I I L M N N O P R S S T

Now, we need to determine the number of positions where the letters remain unchanged when compared to the original word.

Looking at the two arrangements, we can observe that the following letters remain in the same positions:

I appear in the same position (7th position) in both arrangements.

N appears in the same position (13th position) in both arrangements.

Therefore, there are two positions (7th and 13th) where the letters remain unchanged.

The correct answer is (c) Two.

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