1. If every alternative letter of the English alphabet from B onwards (including B) is written in lower case (small letters) and the remaining letters are capitalized, then how is the first month of the second half of the year written?

a) JuLY

b) jULy

c) jUly

d) jUlY

Sol. Ans is (d).

To rewrite the English alphabet in the described format, each pair of letters alternates between lowercase and uppercase: ab, Cd, Ef, etc., until reaching the end with yz. Therefore, July would be rendered as jUlY.

Mentally, you can visualize these pairs as transitioning from lowercase to uppercase. In the case of July, 'y' is the last letter, so it would be in uppercase ('Y'). As for 'j', it would be in lowercase. Consequently, options (b) and (c) are eliminated since 'Y' is uppercase. Furthermore, since 'j' is lowercase, option (a) is also eliminated. Thus, the correct answer is option (d).

2. Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is

a) 13 units

b) 15 units

c) 16 units

d) 30 units

Sol. Ans is (d).

The only three single digit odd prime numbers are 3, 5 and 7. So the length of the first piece = (3+ 5 + 7)/3 = 5. Now let the length of the second piece = Y units.

Then by the condition given in question we have – Length of the third piece = Y + 5. Length of the second piece = Y = 5 + (Y + 5)/3.

Solve this to get Y = 10. So, length of the first piece = 5, second piece = 10 and third piece = 15. So length of the original sheet = 5 + 10 + 15 = 30 units. Ans.(d)

3. In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7?

a) 1

b) 2

c) 3

d) None

Sol. Ans is (a).

In the given sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, there is only one such 5 that is not preceded immediately by 3, but immediately followed by 7. It is the one in bold – 1, 5, 7, 3, 5, 7, 4, 3, 5, 7.

4. A joint family consists of seven members A, B, C, D, E, F and G with three females. G is a widow and sister-in-law of D's father F. B and D are siblings and A is daughter of B. C is cousin of B. Who is E?

Wife of F

Grandmother of A

Aunt of C

Select the correct answer using the code given below:

a) 1 and 2 only

b) 2 and 3 only

c) 1 and 3 only

d) 1, 2 and 3

Sol. Ans is (d)

All the statements are accurate: E is F's spouse, A's grandmother, and C's aunt. This information aligns with the provided diagram.

Therefore, the correct answer is option (d).

5. Each face of a cube can be painted in black or white colours. In how many different ways can the cube be painted?

a) 9

b) 10

c) 11

d) 12

Sol. Ans is (b)

There are many cases possible. Basic assumption is that all faces are identical and not identified by different numbers.

Case I: All the faces are painted black. ONE case.

Case II: Five faces are painted black and one face is painted white. ONE case (Since cube is symmetrical figure on all its faces, that is why six cases will reduce to ONE)

Case III:Four faces are painted black and two faces is painted white. Two cases. First when the two white faces are on opposite faces and second when the two white faces are on adjacent faces.

Case IV: Three faces are painted black and three faces is painted white. Two cases. This can be done in two ways.

Case V: Two faces are painted black and four faces is painted white. Similar to case III. Two cases. First when the two white faces are on opposite faces and second when the two white faces are on adjacent faces.

Case VI: One face is painted black and five faces are painted white. Similar to case II. ONE case (Since cube is symmetrical figure on all its faces, that is why six cases will reduce to ONE)

Case VII: All the faces are painted white. ONE case.

So, total 1 + 1 + 2 + 2 + 2 + 1 + 1 = 10 cases are possible.

A simpler way to look at it will be –

0 sides White : 1 way (all sides Black)

1 side White : 1 way (all other sides Black)

2 sides White : 2 ways (1 way with adjacent sides White, and 1 way with opposite sides White)

3 sides White : 2 ways (1 way where three White sides have same corner, and 1 way where opposite sides are White and one center side is White)

4 sides White : 2 ways (same as 2 sides Black)

5 sides White : 1 way (same as 1 side Black)

6 sides White : 1 way (same as 0 sides Black)

So total=1+1+2+2+2+1+1 = 10 ways.

6. How many triplets (x, y, z) satisfy the equation x + y + z = 6, where x, y and z are natural numbers?

a) 4

b) 5

c) 9

d) 10

x, y and z are natural numbers. So, x, y and z will be greater than zero. It also means that minimum 1 will be there at all places in (x, y, z).

So we can conclude that x' + y' + z' = 6 – (1 + 1 + 1) = 3, where x', y', and z' can take value 0 too.

Now this is a problem of distributing three objects at three places (i.e. with two partitions). This can be done in 5!/(3!×2!) = 10 ways.

The other, simpler way to do it is to manually check. We get 10 sets of triplets : (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1),(1,1,4), (1,4,1), (4,1,1), (2,2,2).

7. If \$ means 'divided by'; @ means 'multiplied by'; # means 'minus', then the value of 10#5@1\$5 is

a) 0

b) 1

c) 2

d) 9

Sol. Ans is (d)

After changing the expression as per the conditions given in the question, we get 10#5@1\$5 = 10 - 5 × 1 ÷ 5.

Using BODMAS, we first get 1 / 5 = 1/5. Then we get 5 x 1/5 = 1. Then we get 10 – 1 = 9. Hence, we have answer 9. Ans.(d)

8. An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible?

a) 2

b) 3

c) 4

d) 6

This is a question based on rules of divisibility. The rule of divisibility of 3 is that the sum of all the digits of the number should be divisible by 3. We have 4 + 2 + 5 + 2 + 7 + 4 + 6 + B = 30 + B, which is completely divisible by three. So B can take value as 0, 3, 6, or 9.

Hence 4 values are possible for B.

Directions for the following 3 (three) items:

Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least.

In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.

9. If F stands second in the ranking, then the position of B is

a) Third

b) Fourth

c) Fifth

d) Sixth

10. If B scores the least, the rank of C will be

a) Second

b) Third

c) Fourth

d) Second or third

11. If E is ranked third, then which one of the following is correct?

a) E gets more marks than C

b) C gets more marks than E

c) A is ranked fourth

d) D is ranked fifth

Solution for Q. 9 to 11:

Let’s first number the conditions given in question. There are eight conditions in all.

i. Six students A, B, C, D, E and F appeared in several tests.

ii. Either C or F scores the highest.

iii. Whenever C scores the highest, then E scores the least.

iv. Whenever F scores the highest, B scores the least.

v. In all the tests they got different marks;

vi. D scores higher than A, but they are close competitors;

vii. A scores higher than B;

viii. C scores higher than A

If F stands second, then by condition (ii), C will be first. If C is first (i.e., score highest) by condition (iii), E scores the least. And using conditions v, vi, vii and viii, we got the following order - C – F – D – A – B – E. Hence B stood fifth.

Sol 10. Answer is (d). B scores last means C is not on the first position (condition iii). So on the first position there must be F (condition ii). Now out of six positions first and last positions are fixed. F _ _ _ _ B.

The middle four positions will be filled by E, C, D and A. In which C, D and A will come in following order (conditions v, vi, vii and viii) – F _ C _ D _ A _ B In this arrangement E can occupy four positions. In every case C can be either occupy second or third place. Ans.(d)

Sol 11. Answer is (b). E is ranked third, it means it is not ranked last, it means C is not first, it means F is first, it means B is last (using conditions given in question). So we have following arrangement -

F _ E _ _ B

Now by using conditions v to viiii we have final order –

F C E D A B

Ans.(b)

Directions for the following 2 (two) items:

Read the following statements SI and S2 and answer the two items that follow:

S1: Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.

S2: Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.

12. Which one of the following statements is correct?

a) Weight of Mohan is greatest

b) Weight of Sohan is greatest

c) Weight of Rohan is greatest

d) Whose weight is greatest' cannot be determined

Sol 12.

Let weight of Sohan = S, weight of Mohan = M and weight of Rohan = R.

Then by the condition given we have :

2S < M, even double of S is less than M. So, S < M.

2S < R, even double of S is less than R. So S < R.

So, we can conclude that S is less than M and R. But we do not know the order relation between M and R. Again, 2R > M, means either R = M or R > M or R < M. So we cannot conclude relation between R and M.

2R > S is obvious as we have concluded R > S above. So not give any fruitful information. Ans.(d)

13. Which one of the following statements is correct?

a) Weight of Mohan is least

b) Weight of Sohan is least

c) Weight of Rohan is least

d) 'Whose weight is least' cannot be determined

Solution for Q. 12 to 13:

Sol 13. Answer is (b). It is clear that weight of Sohan is least.

Directions for the following 7 (seven) items:

Passage — 1

India's economic footprint, given its population, still remains small compared to the US, the European Union or China. It has much to learn from other economies, yet must implement solutions that fit its unique circumstances. India especially needs an effective long-term regulatory system based on collaboration rather than the ' current top-down approach. Regulations seek desirable outcomes yet are repeatedly used as political tools to push one agenda or another. Often, regulations fail to consider impacts on jobs and economic growth — or less restrictive alternatives. Regulations may be used to protect local markets at the expense of more widely shared prosperity in the future. Additionally, regulations inevitably result in numerous unintended consequences. In today's hyper competitive global economy, regulations need to be viewed as "weapons" that seek cost-justified social and environmental benefits while improving the economic well-being of most citizens.

14. Which one of the following is the most logical, rational and crucial inference that can be derived from the above passage ?

a) A better regulatory system will help India achieve the size of economy appropriate to its population.

b) In a competitive global economy, India must use regulations strategically.

c) Regulations in India do not favour its integration with today's hyper competitive global economy.

d) Job creation and economic growth should be dominant considerations in developing India's regulatory system.

15. On the basis of the above passage, the following assumptions have been made :

In today's global economy,

regulations are not effectively used to protect local markets.

social and environmental concerns are generally ignored by the governments across the world while implementing the regulations.

Which of the above assumptions is/are valid ?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Solution for Q. 14 to 15:

Solution 14: The correct answer is (a). Option (c) isn't the primary inference being drawn; it's simply one of the discussed issues. Similarly, option (d) is another issue discussed but not the main inference. Option (b) is close to being the most logical inference, but (a) is better. Why? The passage initially focuses on India's economic size, then delves into the regulatory system's problems. Therefore, (a) is preferable to (b).

Solution 15: The correct answer is (a). The first assumption is valid, as the passage indicates that regulations might be used to protect local markets at the expense of other factors. However, the second assumption appears incorrect because the passage suggests governments prioritize social and environmental concerns over economic ones, rather than maintaining a balance. Thus, only assumption 1 (option (a)) appears correct.

Passage — 2

In a study, scientists compared the microbiomes of poorly nourished and well nourished infants and young children. Gut microbes were isolated from faecal samples of malnourished and healthy children. The microbiome was "immature" and less diverse in malnourished children compared to the better developed "mature" microbiome found in healthy children of the same age. According to some studies, the chemical composition of mother's milk has shown the presence of a modified sugar (sialylated oligosaccharides). This is not utilized by the baby for its own nutrition. However, the bacteria constituting the infant's microbiome thrive on this sugar which serves as their food. Malnourished mothers have low levels of this sugar in their milk. Consequently, the microbiomes of their infants fail to mature. That in turn, leads to malnourished babies.

16. Which one of the following is the most logical, rational and crucial inference that can be derived from the above passage ?

a) If malnourished condition in children is caused by gut bacteria, it cannot be treated.

b) The guts of malnourished babies should be inoculated with mature microbiomes.

c) Babies of malnourished mothers should be fed with dairy milk fortified with sialylated oligosaccharides instead of mother's milk.

d) Research on benign effects of gut bacteria on nutrition has policy implications.

Solution: The correct answer is (c). Option (a) is incorrect because finding the cause can lead to treatment. Option (b) seems unlikely and is not mentioned in the passage. Option (c) appears plausible, although its technical correctness isn't explicitly stated. The issue with it lies in the phrase "instead of mother’s milk." Option (d) also seems logical, pertaining to policy choices regarding nutrition, but the passage doesn't hint at such governmental decisions; it solely discusses scientific aspects. Hence, option (c) is chosen over (d).

17. On the basis of the above passage, the following assumptions have been made :

Processed probiotic foods are a solution to treat the children suffering from malnutrition due to immature gut bacteria composition.

The babies of malnourished mothers generally tend to be' malnourished. Which of the above assumptions is/are valid?

Which of the above assumptions is/are valid?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Solution: The correct answer is (c). Assumption 1 seems correct as it could compensate for early-year problems due to inadequate mother's milk. Assumption 2 is clearly supported by the passage, particularly in the last two sentences.

Passage — 3

Temperatures have risen nearly five times as rapidly on the Western Antarctic Peninsula than the global average over the past five decades. Researchers have now found that melting glaciers are causing a loss of species diversity among benthos in the coastal waters off the Antarctic Peninsula, Impacting an entire seafloor ecosystem. They Believe increased levels of suspended sediment in water to be the cause of the dwindling biodiversity in the coastal region.

18. On the basis of the above passage, the following assumptions have been Made :

Regions of glaciers warm faster than other regions due to global warming.

Global warming can lead to seafloor sedimentation in some areas.

Melting glaciers can reduce marine biodiversity in some areas.

Which of the above assumptions is/are valid?

a) 1 and 2 only

b) 3 only

c) 2 and 3 only

d) 1, 2 and 3

Sol. Answer is (c). All three assumptions seem to be valid.

Passage — 4

A research team examined a long-term owl roost. Owls prey on small mammals and the excreted remains of those meals that accumulated over the time, provide us an insight into the composition and structure of small mammals over the past 'millennia. The research suggested that when the Earth went through a period of rapid warming about 13,000 years ago, the small mammal community was stable and resilient. But, from the last quarter of the nineteenth century, human-made changes to the environment had caused an enormous drop in biomass and energy flow. This dramatic decline in energy flow means modern ecosystems are not adapting as easily as they did in the past.

19. On the basis of the above passage, the following assumptions have been made :

Global warming is a frequently occurring natural phenomenon.

The impending global warming will not adversely affect small mammals.

Humans are responsible for the loss of the Earth's natural resilience.

Which of the above assumptions is/are valid ?

a) 1 and 2 only

b) 3 only

c) 2 and 3 only

d) 1, 2 and 3

Sol.

Assumption 1 cannot be inferred solely from the paragraph due to the limited example provided, thus ruling out options (a) and (d). Assumption 2 conflicts with the passage, eliminating option (c). Consequently, option (b) emerges as the correct choice. Notably, Assumption 3 aligns with the explicit mention in the paragraph.

Passage — 5

Food varieties extinction is happening all over the world --- and it is happening fast. For example, of the 7,000 apple varieties that were grown during the nineteenth century, fewer than o hundred remain. In the Philippines, thousands of varieties of rice once thrived; now only up to a hundred are grown there. In China, 90 percent of the wheat varieties cultivated just a century ago have disappeared. Farmers in the past painstakingly bred and developed crops well suited to the peculiarities of their local climate and environment. In the recent past, our heavy dependence on a few high yielding varieties and technology-driven production and distribution of food is causing the dwindling of diversity in food crops. If some mutating crop disease or future climate change decimates the few crop plants we have come to depend on to feed our growing population, we might desperately need some of those varieties we have let go extinct.

20. On the basis of the above passage, the following assumptions have been made :

Humans have been the main reason for the large scale extinction of plant species.

Consumption of food mainly from locally cultivated crops ensures crop diversity.

The present style of production and distribution of food will finally lead to the problem of food scarcity in the near future.

Our food security may depend on our ability to preserve the locally cultivated varieties of crops.

Which of the above assumptions are valid ?

a) 1 and 3

b) 2 and 4

c) 2 and 3

d) 1 and 4

After reevaluation, it becomes evident that assumption 3 is context-specific, applicable primarily during crises like mutating crop diseases or future climate change, rather than universally valid. Consequently, options (a) and (c) are ruled out. Assumption 1 focuses on the extinction of plant species, which differs from the passage's discussion of food varieties. However, assumption 2 stands as accurate. Thus, assumptions 2 and 4 hold true, making option (b) the correct choice.

21. What is X in the sequence 132, 129, 124, 117, 106, 93, X ?

a) 74

b) 75

c) 76

d) 77

Sol. Ans is (c).

The series is reducing by 3, 5, 7, 11, 13 ... i.e., by prime numbers starting with 3. So, the next prime will be 17. The value of X will be 93 – 17 = 76.

22. A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time ?

a) 5:36 p.m.

b) 5:30 p.m.

c) 5:24 p.m.

d) 5:18 p.m.

In 24 hours, the correct clock moves 24 × 60 = 1440 minutes, whereas the incorrect clock will move 1440 + 10 = 1450 minutes. So we establish a basic relationship: for every 1440 minutes the correct clock moves, the incorrect clock moves 1450 minutes.

Now by the condition given in question the INCORRECT clock has moved 24 + 24 + 10 = 58 hours (i.e. 58×60 minutes).

If the INCORRECT clocks moves 1450 minutes, CORRECT clock moves 1440 minutes.

If the INCORRECT clock moves 1 minute, CORRECT clock moves 1440/1450 minutes.

But in our case INCORRECT clock has moved 58 hrs × 60 min /hr = 3480 minutes.

So, if the INCORRECT clock moved 3480 minutes, the correct clock will have moved (1440×3480)/1450 = 3456 minutes.

Converting 3456 min into hours we have 3456/60 = 573/5 or 57 hours 36 minutes. Ans.(a)

23. If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is

a) always less than the original fraction

b) always greater than the original fraction

c) always equal to the original fraction

d) such that nothing can be claimed definitely

We can apply the fundamental property of ratios: when the numerator is less than the denominator, adding the same positive quantity to both the numerator and denominator results in a fraction greater than the original one.

a/b<(a+x)/(b+x) .

But in above case we do not whether the fraction is positive or negative. If it is positive, then the answer will be different from when it will be negative. Hence we can't say anything.

24. What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X ?

a) 48

b) 64

c) 125

d) 256

Sol. Answer is (b). The series can be seen as 4 (=22), 196 (=142), 16 (=42), 144 (=122), 36 (=62), 100 (=102), 64 (=82), X (?2).

Observing every alternate term, value of X will be square of 8 i.e., 64.

25. In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is

a) 10

b) 9

c) 5

d) 4

In a group of 15 people 3 cannot read any of two languages.

So, n(A ∪ B) = 12, n(A) = 7, n(B) = 8. And we have n(A ∪ B) = n(A) + n(B) - n(A ∩ B) By putting the values, we have 12 = 7 + 8 - n(A ∩ B).

So, n(A ∩ B) = 3.

So, total number of people who can read exactly one language = (7 - 3) + (8 - 3) = 4 + 5 = 9.

This can also be solved using a Venn diagram

26. A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have ?

a) 1040

b) 1048

c) 1049

d) 1050

Digits required to print one digit numbers (1 to 9) = 9×1 = 9

Digits required to print two digit numbers (10 to 99) = 90 × 2 = 180

Digits required to print three digit numbers (100 to 999) = 900 × 3 = 2700.

So, upto 999 pages we have 2700 + 180 + 9 = 2889 digits.

Now from here onwards each number will use 4 digits and we are remaining with 3089 - 2889 = 200 digits.

So 200/4 = 50 more numbers are there. i.e., 999 + 50 = 1049 pages in the book.

27. Consider the following sequence that follows some arrangement :

c_accaa_aa_bc_b

The letters that appear in the gaps are

a) abba

b) cbbb

c) bbbb

d) cccc

By breaking down the sequence into groups of 5 characters, and applying the given options, we find that the correct sequence is "ccacc aabaa bbcbb" when using option (b) – c-b-b-b.

28. A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother?

a) 48 kg

b) 50 kg

c) 52 kg

d) 54 kg

We know that – Average x Number of people = Total.

Average of weight of two children and their mother (i.e. total 3 members) = 50. So, the sum of the weight of two children and mother = C1 + C2 + M = 50 × 3 = 150 ... (1) (where C1 and C2 are the weights of two children and M is the weight of the Mother)

Again if the weight of the Father is F, we have C1 + C2 + F = 52 × 3 = 156 ... (2)

Now it is given that the weight of the father = F = 60.

By putting this value in equation (2), we have C1 + C2 = 156 - 60 = 96.

by using equation (1) we have M = 150 - 96 = 54 kg.

29. Suppose you have sufficient amount of rupee currency in three denominations : Rs. 1, Rs. 10 and Rs. 50. In how many different ways can you pay a bill of Rs. 107 ?

a) 16

b) 17

c) 18

d) 19

Case I: We use TWO Rs. 50 notes - One possibility - 50(×2) + 1(×7) = 107

Case II: We use ONE Rs. 50 note -

Six possibilities (by adding Rs.10 note from none to five) –

50(×1) + 10(×0) + 1(×47) = 107; 50(×1) + 10(×1) + 1(×47) = 107; 50(×1) + 10(×2) + 1(×37) =

107; 50(×1) + 10(×3) + 1(×27) = 107; 50(×1) + 10(×4) + 1(×17) = 107; 50(×1) + 10(×5) + 1(×7) = 107;

Case III: We use no Rs. 50 note (Only Rs. 10 and 1 notes) - Ten possibilities –

10(×10) + 1(×7) = 107; 10(×9) + 1(×17) = 107; 10(×8) + 1(×27) = 107; 10(×7) + 1(×37) = 107; 10(×6) + 1(×47) = 107; 10(×5) + 1(×57) = 107; 10(×4) + 1(×67) = 107; 10(×3) + 1(×77) = 107; 10(×2) + 1(×87) = 107; 10(×1) + 1(×97) = 107;

Case IV: We use only Rs. 1 note - One possibility - 1 (×107) = 107.

Hence, total 18 possibilities.

30. 'A' started from his house and walked 20 m towards East, where his friend B joined him. They together walked 10 m in the same direction. Then 'A' turned left while 'B' turned right and travelled 2 m and 8 m respectively. Again 'B' turned left to travel 4 m followed by 5 m to his right to reach his office. 'A' turned right and travelled 12 m to reach his office. What is the shortest distance between the two offices?

a) 15 m

b) 17 m

c) 19 m

d) 20 m

Shortest Distance = Hypotenuse = √(〖15〗^2+8^2 )=√(225+64)=√289=17.

31. Consider two statements S1 and S2 followed by a question:

S1: p and q both are prime numbers.

S2: p + q is an odd integer.

Question: Is pq an odd integer?

Which one of the following is correct ?

a) S1 alone is sufficient to answer the question

b) S2 alone is sufficient to answer the question

c) Both S1 and S2 taken together are not sufficient to answer the question

d) Both S1 and S2 are necessary to answer the question

Consider following rules -

1. odd × odd = odd; 2. odd×even = even; 3. even × even = even; 4. odd + odd = even; 5. even + even = even and 6. even + odd = odd.

By above rules p×q = even, if both p and q are even or they form a pair of odd and even numbers and p×q = odd, if p and q both are odd.

Statement I: Information given is not sufficient as in a set of prime number two numbers can be even and odd or odd and odd. So, p×q can be even or odd.

Statement II: Information given is not sufficient as it is not known that whether p and q are integers are not. They may be fractions.

By combining statements I and II: we have p and q as prime number and there sum is odd. So, the two prime numbers should be one even and one odd. So now we have that one is even and one is odd. In this case p×q will always be even. So we can answer the question that No, p×q is not an odd integer.

32. Which year has the same calendar as that of 2009?

a) 2018

b) 2017

c) 2016

d) 2015

Sol. Answer is (d).To have the same calendar two things should be matched. First – the first day of the year and second – the year type i.e., ordinary or leap. Let the first day of year 2009 is X day. It means first day of 2010 will be X+1 day, as there is one odd day in one ordinary year.

It means first day of 2011 will be X+2 day. (As there is one odd day in one ordinary year)

It means first day of 2012 will be X+3 day. (As there is one odd day in one ordinary year)

It means first day of 2013 will be X+5 day. (As there are TWO odd days in one LEAP year)

It means first day of 2014 will be X+6 day. (As there is one odd day in one ordinary year); and

It means first day of 2015 will be X+7 day. (As there is one odd day in one ordinary year)

After every 7 days, the same day appears. So, the first day of 2015 will be same as 2009.

Since both are ordinary years. We can use the calendar of 2009 in 2015.

33. Number 136 is added to 5B7 and the sum obtained is 7A3, where A and B are integers. It is given that 7A3 is exactly divisible by 3. The only possible value of B is

a) 2

b) 5

c) 7

d) 8

It is given 136 + 5B7 = 7A3.

Add the unit’s numbers to get 6 + 7 = 13. So, carry over 1.

=> 1 + 3 + B = 1A => 1 + 3 + B = 10 + A => B – A = 6.

Which means if A = 0, B = 6; if A = 1, B = 7, if A = 2, B = 8 and if A = 3, B = 9.

But given 7A3 is completely divisible by 3. So, as per rules of divisibility, 7 + A + 3 = 10 + A should also be completely divisible by 3.

So the possible values of A are 2, 5 and 8. (12 / 15 / 18 divisible by 3) Out of these, only 2 satisfies both the conditions so A = 2, so B = 8. Ans.(d)

Directions for the following 7 (seven) items:

Passage — 1

What stands in the way of the widespread and careful adoption of 'Genetic Modification (GM)' technology is an `Intellectual Property Rights' regime that seeks to create private monopolies for such technologies. If GM technology is largely corporate driven, it seeks to maximize profits and that too in the short run. That is why corporations make major investments for herbicide-tolerant and pest-resistant crops. Such properties have only a short window, as soon enough, pests and weeds will evolve to overcome such resistance. This suits the corporations. The National Farmers Commission pointed out that priority must be given in genetic modification to the incorporation of genes that can help impart resistance to drought, salinity and other stresses.

34. Which one of the following is the most logical, rational and crucial message conveyed by the above passage?

a) Public research institutions should take the lead in GM technology and prioritise the technology agenda.

b) Developing countries should raise this issue in WTO and ensure the abolition of Intellectual Property Rights.

c) Private corporations should not be allowed to do agribusiness in India, particularly the seed business.

d) Present Indian circumstances do not favour the cultivation of genetically modified crops.

Sol 34.The correct answer is (a).

Option (b) is irrelevant to the passage's context. Option (c) represents an extreme viewpoint not explicitly mentioned in the passage. Option (d) is incorrect as the passage contradicts it (as indicated in the last part). Option (a) best aligns with the passage's criticism of private corporations and its suggestion of what India truly requires, a task that private firms are unlikely to undertake, leaving it to public enterprises.

35. On the basis of the above passage, the following assumptions have been made:

The issue of effects of natural calamities on agriculture is not given due consideration by GM technology companies.

In the long run, GM technology will not be able to solve agricultural problems arising due to global warming.

Which of the above assumptions is/are valid?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Sol 35. The correct answer is (a).

Assumption 1 is indeed accurate, as it's explicitly stated in the passage. However, Assumption 2 appears overly broad, suggesting that GM technology will "never" achieve certain goals, which may not be entirely accurate. Therefore, option (a) is the most suitable choice.

Passage — 2

Most invasive species are neither terribly successful nor very harmful. Britain's invasive plants are not widespread, not spreading especially quickly, and often less of a nuisance than vigorous natives such as bracken. The arrival of new species almost always increases biological diversity in a region; in many cases, a flood of newcomers drives no native species to extinction. One reason is that invaders tend to colonise disturbed habitats like polluted lakes and post-industrial wasteland, where little else lives. They are nature's opportunists.

36. Which one of the following is the most logical and rational inference that can be made from the above passage?

a) Invasive species should be used to rehabilitate desert areas and wastelands of a country.

b)Laws against the introduction of foreign plants are unnecessary.

c)Sometimes, the campaigns against foreign plants are pointless.

d)Foreign plants should be used to increase the biodiversity of a country.

Sol.

Options (b), (c), and (d) are unsuitable due to their use of terms like "foreign plants" or suggesting extreme measures not directly supported by the passage. Even without this reasoning, option (b) appears too extreme, as there may be cases where such laws are necessary. Option (c) is not the most logical inference due to the term "sometimes," and option (d) suggests a questionable approach to conservation. Therefore, (a) is the most appropriate choice, as it aligns with the passage's content.

Passage — 3

Diarrhoeal deaths among Indian children are mostly due to food and water contamination. Use of contaminated groundwater and unsafe chemicals in agriculture, poor hygiene in storage and handling of food items to food cooked and distributed in unhygienic surroundings; there are myriad factors that need regulation and monitoring. People need to have awareness of adulteration and ways of complaining to the relevant authorities. Surveillance of food-borne diseases involves a number of government agencies and entails good training of inspection staff. Considering the proportion of the urban population that depends on street food for its daily meals, investing in training and education of street vendors is of great significance.

37. On the basis of the above passage, the following assumptions have been made:

Food safety is a complex issue that calls for a multipronged solution.

Great investments need to be made in developing the manpower for surveillance and training.

India needs to make sufficient legislation for governing food processing industry.

Which of the above assumptions is/are valid?

a) 1 and 2 only

b) 3 only

c) 1 and 3 only

d) 1, 2 and 3

Assumption 2 assumes "Great investments need to be made..." which is not explicitly stated in the passage. Therefore, we can eliminate options (a) and (d). Assumption 1, however, is clearly supported by the beginning of the passage. Thus, the best answer is option (c).

Passage — 4

The interests of working and poor people have historically been neglected in the planning of our cities. Our cities are increasingly intolerant,', unsafe and unlivable places for large numbers of citizens and yet we continue to plan via the old ways — the static Development Plan — that draws exclusively from technical expertise, distanced from people's live experiences and needs, and actively excluding large number of people, places, activities and practices that are an integral part of the city.

38. The passage seems to argue

a) against the monopoly of builders and the interests of elite groups.

b) against the need for global and smart cities.

c) in favour of planning cities mainly for working class and poor people.

d) in favour of participation of peoples' groups in city planning.

Options (a) and (b) are indeed incorrect, while option (c) is not wrong since it aligns with the logic presented at the beginning of the passage. However, option (d) provides a broader perspective, encompassing option (c) and suggesting that involving community groups in city planning would not only address the needs of the working class and poor but also potentially achieve much more. Therefore, option (d) seems to be the best choice as it offers a more comprehensive solution.

Passage — 5

A vast majority of Indians are poor, with barely 10 percent employed in the organised sector. We are being convinced that vigorous economic growth is generating substantial employment. But this is not so. When our economy was growing at 3 percent per year, employment in the organised sector was growing at 2 percent per year. As the economy began to grow at 7 - 8 percent per year, the rate of growth of employment in the organised sector actually declined to 1 percent per year.

39. The above passage seems to imply that

most of modern economic growth is based on technological progress.

much of modern Indian economy does not nurture sufficient symbiotic relationship with labour-intensive, natural resource-based livelihoods.

service sector in India is not very labour-intensive.

literate rural population is not willing to enter organised sector.

Which of the statements given above are correct?

a) 1 and 2 only

b) 3 and 4 only

c) 1, 2 and 3 only

d) 1, 2, 3 and 4

Statement 4 isn't referenced in the passage, eliminating options (b) and (d). Now, consider statement 3. Assuming the service sector is synonymous with the organized sector, especially considering the significant contribution of the service sector to economic growth, is a substantial assumption not explicitly stated in the passage. Thus, statement 3 isn't accurate. Consequently, option (c) is dismissed, leaving option (a) as the best choice.

Passage — 6

India has banking correspondents, who help bring people in the hinterland into the banking fold. For them to succeed, banks cannot crimp on costs. They also cannot afford to ignore investing in financial education and literacy. Banking correspondents are way too small to be viewed as a systemic risk. Yet India's banking regulator has restricted them to serving only one bank, perhaps to prevent arbitrage.'Efforts at banking outreach may succeed only if there are better incentives at work for such last-mile workers and also those providers who ensure not just basic bank accounts but also products such as accident and life insurance and micro pension schemes.

40. Which one of the following is the most logical, rational and crucial inference that can be derived from the above passage?

a) Efforts to bring people in India's hinterland into the banking system are not successful.

b) For meaningful financial inclusion, India's banking system needs more number of banking correspondents and other such last-mile workers.

c) Meaningful financial inclusion in India requires that banking correspondents have diverse skills

d) Better banking outreach would be impossible unless each banking correspondent is allowed to serve a number of banks

Option (c) is evidently incorrect since the passage does not center on the skills of banking correspondents. Similarly, option (a) is inaccurate as the passage does not draw such a conclusion. Considering options (b) and (d), option (d) is more pertinent as it addresses the core issue under discussion.

41. The number of times the digit 5 will appear while writing the integers from 1 to 1000 is

a) 269

b) 271

c) 300

d) 302

From 1 to 1000, the numbers in which 5 can occur could be of one digit, two digits or three digits.

Case I – If the number is of one digit – 5 will appear only one time, i.e. in 5.

Case II – If the number is of two digits – then

(a) There is only one 5, this can happen in two ways _5 and 5_. In the first case (_5) the blank Place can be filled in 8 ways(as 0 and 5 cannot appear at that place), while in the second case (5_) the blank place can be filled in 9 ways (5 cannot appear there). Total 9 + 8 = 17 ways.

(b) There are two 5s. In this case only ONE possibility.

Case III – If the number is of three digits – then

(a) Only one 5. Then, 5 can occupy three positions. 5 _ _ or _ 5 _ or _ _ 5. In the first case (5_ _), remaining two positions can be filled in 9 way each. So total 9 × 9 = 81 possibilities. In the second case (_ 5 _) first position can be filled in 8 ways and last position can be filled in 9 ways. So total 9 × 8 = 72 possibilities. Same will be true for the third (_ _ 5) case. So total 72 possibilities.

(b) Only two 5. This can be done in three ways 55_ or 5_5 or _55. In first (55_) and second (5_5) case it can be filled in 9 ways each. While in the third case (_55) it can be filled in 8 ways. So total 9 + 9 + 8 = 26 possibilities.

(c) All three digits are 5. This can be done in only ONE way. i.e, 555.

So, total = 1 + 17 + 1 + 81 + 72 + 72 + 26 + 1 = 271.

42. A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?

a) 4

b) 6

c) 8

d) 10

Sol. Answer is (c).According to the condition described in the question, the cube can be divided as depicted below. For simplicity, let's assume the side of the original cube to be 12 units. Thus, the new structure appears as shown in the image. The desired cubes, marked with "R," total to 8 cubes, with 4 on each side having only one face painted.

43. A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?

a) 60%

b) 45.5%

c) 40%

d) 37.5%

Sol. Answer is (d). Let the weight of A be 100 kg.

So, the combined weight of A + B will 160 kg. Out of this 160 kg, 60 kg is reduced now.

60 is what percent of 160? 60×100/160 = 37.5%.

44. Mr 'X' has three children. The birthday of the first child falls on the 5th Monday of April, that of the second one falls on the 5th Thursday of November. On which day is the birthday of his third child, which falls on 20th December?

a) Monday

b) Thursday

c) Saturday

d) Sunday

November has 30 days, meaning each day of the week occurs 4 times (7 days × 4 = 28), with two days occurring 5 times. These two days will be the first two or last two days of the month. Therefore, if a day occurs 5 times, it must be at the beginning or end of the month. Since the second child's birthday falls on the fifth Thursday, it must be at the end of November.

Thus, either November 29th is Thursday or November 30th is Thursday.

If November 29th is Thursday, then December 20th will be a Thursday.

If November 30th is Thursday, then December 20th will be a Wednesday. Since this option is not provided, the answer must be Thursday, making option (b) the correct choice.

45. Consider the following Statements and Conclusions:

Statements:

Some rats are cats.

Some cats are dogs.

No dog is a cow.

Conclusions:

No cow is a cat.

No dog is a rat.

Some cats are rats.

Which of the above conclusions is/are drawn from the statements?

a) I, II and III

b) Only I and II

c) Only III

d) Only II and III

The conclusion that 'Some rats are cats' leads to 'Some cats are rats' is valid, which supports conclusion III. However, since both statements I and II start with 'some', no conclusion can be drawn regarding rats and dogs. Therefore, conclusion II is not valid, eliminating all options but (c).

Regarding cats and cows, the only valid conclusion would be 'Some cats are not cows'. Therefore, conclusion I is not valid.

46. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is

a) 18

b) 24

c) 32

d) 36

In the diagram, let’s count the parallelograms one by one.

Case I - Parallelograms of 1 × 1 (ABFE type) - ABFE, BCGF, CDHG, EFJI, FGKJ, GHLK, IJNM, JKON, KLPO – total 9.

Case II - Parallelograms of 1 × 2 (ACGE type) - ACGE, BDFH, EGKI, FHLJ, IKOM, JLPN – total 6.

Case III - Parallelogram of 2 × 1 (ABJI type) - ABJI, EFNM, BCKJ, FGON, CDLK, GHPO – total 6.

Case IV - Parallelograms of 1 × 3 (ADHE type) - ADHE, EHLI, ILPM – total 3.

Case V - Parallelograms of 3 × 1 (ABNM type) - ABNM, BCON, CDPO – total 3.

Case VI - Parallelograms of 2 × 2 (ACKI type) - ACKI, BDLJ, EGOM, FHPN – total 4.

Case VII - Parallelograms of 3 × 2 (ADLI type) - ADLI, EHPM – total 2.

Case VIII - Parallelograms of 2 × 3 (ACOM type) - ACOM, BDPN – total 2.

Case IX -Parallelograms of 3 × 3 (ADPM type) – ADPM – total 1.

Total 36.

A much shorter method is by using permutations and combinations.

Select any two of the first set of 4 lines. That can be done in 4C2 ways.

Now select any two of the second set of 4 lines. That can also be done in 4C2 ways.

So the total number of ways of doing it = 4C2 x 4C2 = 6 x 6 = 36 ways.

47. In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football?

a) 4

b) 8

c) 10

d) 12

To find a number completely divisible by both 4 and 6, it must be divisible by the least common multiple (LCM) of 4 and 6, which is 12. Hence, there are 8 possible numbers meeting this condition: 12, 24, 36, 48, 60, 72, 84, and 96. Therefore, the answer is (b).

48. When a runner was crossing the 12 km mark, she was informed that she had completed only 80% of the race. How many kilometres was the runner supposed to run in this event?

a) 14

b) 15

c) 16

d) 16.5

This can be solved mentally. 12 km is 8/10 = 4/5 of the whole race. So whole race must be 15 km.

In this question 12 km is 80% of the total race.

=> 12 km = 0.8 R => R = 12 / 0.8 = 15.

So total race will be of 15 km.

49. Raju has Rs. 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows 2000 from a friend. Then

a) Raju still does not have enough amount to buy the handset.

b) Raju has exactly the same amount as required to buy the handset.

c) Raju has enough amount to buy the handset and he will have 500 with him after buying the handset.

d) Raju has enough amount to buy the handset and he will have 1000 with him after buying the handset.

In this scenario, Rs. 9000 represents 75% of the total cost of the mobile phone. Therefore, the total cost of the mobile phone is Rs. 12000 (calculated as 9000 / 0.75). If he borrows Rs. 2000, he will still be short of Rs. 1000 to purchase the phone.

50. In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?

a) 1992

b) 1994

c) 1996

d) 1998

Sol. Answer is (b). Let Meenu’s age in 2002 be M and Meera’s age in 2002 be X.

In 2002, Meenu = 1/3 of Meera. => M = X/3

In 2010, Meenu = 1/2 of Meera. So, M + 8 = (X + 8) / 2

Solving these two, we get M = 8. So, in 2002, Meenu was 8 years old. So she was born in 1994.

51. Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent 1300 and Rajesh spent 1500. If each racket costs three times a ball does, then what is the price of a racket?

a) Rs. 70

b) Rs. 90

c) Rs. 210

d) Rs. 240

Let the cost of each ball is Rs. X. Then cost of each racket will be 3X.

Cost of 10 balls = 10X, and cost of 10 rackets = 30X.

So total cost = 10X + 30X = 40X.

By the condition given in question, we have

40X = 1300 + 1500 or 40X = 2800 or X = 70. Price of each racket = Rs. 210.

52. In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct?

At least 30 Indian participants are vegetarian.

At least 10 Indian participants are non-vegetarian.

Select the correct answer using the codes given below:

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Let's focus on maximizing the number of Indian vegetarians. Out of the 70 Indians, all 60 vegetarians can be considered Indian. This leaves at least 10 Indians who are non-vegetarians. The number of non-vegetarian Indians can increase based on the total number of vegetarian Indians.

Now, let's aim to minimize the number of Indian vegetarians. To achieve this, we need to maximize the number of non-Indian vegetarians. Out of the 30 non-Indians, all can be vegetarians, leaving 30 vegetarians. However, these 30 vegetarians still fall under the Indian category. Therefore, there will be at least 30 Indians who are vegetarians. Hence, both statements are correct.

Directions for the following 8 (eight) items :

Passage — 1

Political theorists no doubt have to take history of injustice, for example, untouchability, seriously. The concept of historical injustice takes note of a variety of historical wrongs that continue into the present in some form or the other and tend to resist repair. Two reasons might account for resistance to repair. One, not only are the roots of injustice buried deep in history, injustice itself constitutes economic structures of exploitation, ideologies of discrimination and modes of representation. Two, the category of historical injustice generally extends across a number of wrongs such as economic deprivation, social discrimination and lack of recognition. This category is complex, not only because of the overlap between a number of wrongs, but because one or the other wrong, generally discrimination, tends to acquire partial autonomy from others. This is borne out by the history of repair in India.

53. What is the main idea that we can infer from the passage ?

a) Untouchability in India has not been taken seriously by political theorists.

b) Historical injustice is inevitable in any society and is always beyond repair.

c) Social discrimination and deprivation have their roots in bad economies.

d) It is difficult, if not impossible, to repair every manifestation of historical injustice.

54. On the basis of the above passage, the following assumptions have been made :

Removal of economic discrimination leads to removal of social discrimination.

Democratic polity is the best way to repair historical wrongs.

Which of the above assumptions is/are valid ?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2.

Solution for Q. 53 to 54:

Solution 53: Option (d) is the answer. Option (b) is dismissed as it introduces the concept of irreparability, not mentioned in the passage. Option (c) does not align with the passage's wording. Although option (a) seems plausible, it implies that only political theorists take the issue seriously, which isn't explicitly stated. Option (d) aligns best with the passage's message.

Solution 54: Option (d) is correct. The passage indicates that historical injustice encompasses various aspects like economic deprivation, social discrimination, and lack of recognition. Assumption 1 isn't necessarily true, as historical injustice isn't confined to a single category. Assumption 2 isn't explicitly stated in the passage, rendering both assumptions invalid.

Passage — 2

Education plays a great transformatory role in life, particularly so in this rapidly changing and globalizing world. Universities are the custodians of the intellectual capital and promoters of culture and specialized knowledge. Culture is an activity of thought, and receptiveness to beauty and human feelings. A merely well informed man is only a bore on God's earth. What we should aim at is producing men who possess both culture and expert knowledge. Their expert knowledge will give them a firm ground to start from and their culture will lead them as deep as philosophy and as high as art. Together it will impart meaning to human existence.

55. On the basis of the above passage, the following assumptions have been made :

A society without well educated people cannot be transformed into a modern society.

Without acquiring culture, a person's education is not complete.

Which of the above assumptions is/are valid ?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

In assumption 1, we interpret "Well Educated" to encompass both knowledge and cultural awareness, which aligns with the passage's context. Therefore, assumption 1 is indeed correct. Assumption 2 is explicitly stated in the passage, making it undoubtedly correct.

Passage — 3

Soil, in which nearly all our food grows, is a living resource that takes years to form. Yet it can vanish in minutes. Each year 75 billion tonnes of fertile soil is lost to erosion. That is alarming — and not just for food producers. Soil can trap huge quantities of carbon dioxide in the form of organic carbon and prevent it from escaping into the atmosphere.

56. On the basis of the above passage, the following assumptions have been made :

Large scale soil erosion is a major reason for widespread food insecurity in the world.

Soil erosion is mainly anthropogenic.

Sustainable management of soils helps in combating climate change.

Which of the above assumptions is/are valid ?

a) 1 and 2 only

b) 3 only

c) 2 and 3 only

d) 1, 2 and 3

Assumption 1 is incorrect because the passage does not establish a direct connection between soil erosion and food insecurity. Additionally, the use of the word "alarming" does not necessarily imply that food insecurity has already occurred. Assumption 2 is also incorrect as there is no mention in the passage that humans are responsible for soil erosion. Assumption 3, however, is undoubtedly correct, as supported by the final line of the passage.

Passage — 4

Inequality is visible, even statistically measurable in many instances, but the economic power that drives it is invisible and not measurable... Like the force of gravity, power is the organising principle of inequality, be it of income, or wealth, gender, race, religion and region. Its effects are seen in a pervasive manner in all spheres, but the ways in which economic power pulls and tilts visible economic variables remain invisibly obscure,

57. On the basis of the above passage, the following assumptions have been made :

Economic power is the only reason for the existence of inequality in a society.

Inequality of different kinds, income, wealth, etc, reinforces power.

Economic power can be analysed more through its effects than by direct empirical methods.

Which of thy above oasomptions is/are valid ?

a) 1 and 2 only

b) 3 only

c) 1 and 3 only

d) 1, 2 and 3

Assumption 1 is incorrect because the phrase "only reason" suggests a singular cause, which may not be accurate in complex socio-political contexts. Assumption 2 is flawed because it reverses the relationship between power and inequality; it is power that typically reinforces and perpetuates existing inequalities. Assumption 3, however, is valid, as supported by the initial statement in the passage.

Passage — 5

Climate change may actually benefit some plants by lengthening growing seasons and increasing carbon dioxide. Yet other effects of a warmer world, such as more pests, droughts, and flooding, will be less benign. How will the world adapt ? Researchers project that by 2050, suitable croplands for four commodities — maize, potatoes, rice and wheat — will shift, in some cases pushing farmers to plant new crops. Some farmlands may benefit from warming, but others won't. Climate alone does not dictate yields; political shifts, global "demand, and agricultural practices will influence how farms fare in the future.

58. Which one of the following is the most logical and rational inference that can be made from) the above passage ?

a) Farmers who modernize their methods and diversify their fields will be. in an advantageous position in future.

b) Climate change will adversely affect the crop diversity.

c) Shifting ma' r crops to new croplands will lead to a gr t increase in the total area under culti tion and thus an increase in overall agricultural production.

d) Climate change is the most important factor affecting the agricultural economy in the future.

Option (a) cannot be guaranteed in all situations, as there may be other factors preventing farmers from gaining advantages despite implementing sustainable practices. Option (b) is not addressed in the passage. Option (c) does not align with the discussion presented. Option (d) emerges as the most appropriate choice, as it reflects the overarching theme of the passage.

Passage — 6

A bat's .wings may look like sheets of skin. But underneath, a bat has the same five fingers as an orangutan or a human, as well as a wrist connected to the same cluster of wrist bones connected to the same long bones of the arm. What can be more curious than that the hand of a man, formed for grasping, that of a mole for digging, the leg of the horse, the-paddle of the porpoise, and the wing of the bat, should all be constructed on the some pattern ?

59. Which one of the following is the most logical, scientific and rational inference that can be made from the above passage ?

a) Different species having similar structure of hands is an example of biodiversity.

b) Limbs being used by different species for different kinds of work is an example of biodiversity.

c) Man and the aforementioned animals having similar structure of limbs is an example of coincidence in evolution.

d) Man and the aforementioned animals have a shared evolutionary history.

Option (a) lacks specific mention in the passage. Option (b) references "biodiversity," but the varied use of limbs does not directly relate to biodiversity. Option (c) may seem plausible, but it's not explicitly supported by the passage as "coincidence in evolution" is not mentioned. Option (d) stands out as the most suitable choice, as it refers to "a shared evolutionary history," which aligns with the passage's discussion of a "very curious situation."

Passage — 7

Around 56 million years ago, the Atlantic Ocean had not fully opened and animals, perhaps including our primate ancestors, could walk from Asia to North America through Europe and across Greenland. Earth was warmer than it is today, but as the Palaeocene epoch gave way to Eocene, it was about to get much warmer still —rapidly and radically. The cause was a massive geologically sudden release of carbon. During this period called Palaeocene - Eocene Thermal Maximum or PETM, the carbon injected into the atmosphere was roughly the amount that Would be injected today if humans burned all the Earth's reserves of coal, oil and natural gas. The PETM lasted for about 1,50,000 years, until the excess carbon was reabsorbed. It brought on drought, floods, insect plagues and a few extinctions. Life on Earth survived — indeed, it prospered — but it was drastically different.

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

Global warming has a bearing on the planet's biological evolution.

Separation of land masses causes the release of huge quantities of carbon into the atmosphere.

Increased warming of Earth's atmosphere can change the composition of its flora and fauna.

The present man-made global warming will finally lead to conditions similar to those which happened 56 million years ago.

Which of the assumptions given above are valid ?

a) 1 and 2

b) 3 and 4

c) 1 and 3

d) 2 and 4

Assumption 1 is clearly valid based on the information provided in the passage. Assumption 2, however, is quite far-fetched and cannot be deduced from the passage. Assumption 3 is valid, as it is explicitly stated. Assumption 4, on the other hand, is also far-fetched as the amounts mentioned in the passage are too high to support such a conclusion.

61.A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor.

Consider the following statements:

The middle three floors are painted in different colours.

The second (II) and the fourth (IV) floors are painted in different colours.

The first (I) and the fifth (V) floors are painted red.

To ensure that any two consecutive floors have different colours

a) Only statement 2 is sufficient

b) Only statement 3 is sufficient

c) Statement 1 is not sufficient, but statement 1 along with statement 2 is sufficient

d) Statement 3 is not sufficient, but statement 3 along with statement 2 is sufficient.

Sol. Answer is (b). Precondition: Five floors are painted with four different colors.

Statement 1: The statement that the middle three floors are painted in different colors does not ensure that any two consecutive floors will have different colors, as floors I and II or floors IV and V could potentially have the same color.

Statement 2: Similarly, stating that the second (II) and the fourth (IV) floors are painted in different colors does not guarantee that any two consecutive floors will have different colors, as floors I and II, II and III, III and IV, or IV and V could share the same color.

Statement 3: This statement ensures that any two consecutive floors will have different colors since there are only four colors to be used, leaving the remaining three floors with different colors.

Therefore, the correct answer is (b)

62. P, Q and R are three towns. The distance between P and Q is 60 km, whereas the distance between P and R is 80 km. Q is in the West of P and R is in the South of P. What is the distance between Q and R?

a) 140 km

b) 130 km

c) 10 km

d) 100 km

Sol. Answer is (d). A direct application of Pythagoras theorem.

Using Pythagoras theorem –

Distance between Q and R = √(〖80〗^2+〖60〗^2 )=√(6400+3600)=√10000=100 km. Ans.(d)

63. All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data?

40% members went for shopping as well as sightseeing.

20% members went for only shopping.

Select the correct answer using the code given below:

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Only statement (1) is correct.

64. In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two-wheeler. Which of the following conclusions cannot be drawn from the above data?

60% of the students do not have two-wheelers.

No cricketer has a two-wheeler.

Cricket players do not play football.

Select the correct answer using the code given below:

a) 1 and 2 only

b) 2 and 3 only

c) 1 and 3 only

d) 1, 2 and 3

Conclusions 1 and 2 cannot be inferred. It's possible for a cricket player to also own a two-wheeler.

65. The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs is

a) 5

b) 4

c) 3

d) 2

Let the ten's digit of two digit number ab be 'a' and unit’s digit be 'b'. So the number will be of the form 10a + b.

After reversing the digits the number will be 10b + a.

By the condition given in question we have (10a+b)/(10b+a)=4/7 which means a/b=1/2

So by putting the values, total possible pairs (12, 21), (24, 42), (36, 63), (48, 84).

Thus, four pairs are possible.

66. In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored?

a) 360

b) 380

c) 400

d) 420

Sol. Answer is (b). Check options directly.

Let’s start with (a). If B is 360, A will be 380. Now, 5% of 380 = 19. So B will become 380 – 19 = 361. Hence this option is wrong (B is 360, not 361).

If B is 380, A will be 400. Now, 5% of 400 = 20. So B will be 400 – 20 = 380. Hence (b) is correct.

67. Seeta and Geeta go for a swim after a gap of every 2 days and every 3 days respectively. If on 1st January both of them went for a swim together, when will they go together next?

a) 7th January

b) 8th January

c) 12th January

d) 13th January

Seeta goes swimming every 3rd day, and Geeta goes swimming every 4th day. The least common multiple (LCM) of 3 and 4 is 12. So, they will swim together every 12th day. Therefore, on the 12th day after January 1, they will go swimming together, which is January 13th.

68. X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?

a) 20

b) 25

c) 30

d) 35

In the 1000 m race, X gives Y 40 m start. That means Y starts race 40 m ahead of X.

In the 1000 m race, X gives Z 64 m start. That means Z starts race 64 m ahead of X

So, this means Y gives a lead of 24 m in a 1000 – 40 = 960 m race.

So, by unitary method, lead given by Y in 1000 m = 24/960×1000 = 25 m.

69. If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?

a) x is greater than y

b) (y - x) is greater than 15

c) (y - x) is less than or equal to 15

d) (x - y) is greater than or equal to 65

Given that x is greater than or equal to 25. Also, y is less than or equal to 40.

Let’s try to find the various values of y – x.

If y = 40, x can take various values like 25, 26, 27, ....... (not necessarily integers – not given in question) In that case y – x will take values like 15, 14, 13, 12,......0, - 1 etc.

If y = 39, x can take various values 25, 26, 27.... (not necessarily integers) In that case y – x will take values like 14, 13, 12, 11 ..... 0, - 1 etc.

Similarly, if y = 38, values of y – x will be 13, 12, 11, ..... 0, -1 etc. and so on.

So, we can say that value of y – x is less than or equal to 15 in all cases.

70. Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?

a) 22 years

b) 23 years

c) 24 years

d) 25 years

Ena's present age = 13

Ena's mother's present age = 13 + 24 = 37.

Ena's father's present age = 37 + 3 = 40.

Now at present Ena is 13 years old and her parents got married 4 years before she was born.

So, Ena's parents got married 13 + 4 = 17 years earlier.

So at the time of marriage her father would be of 40 – 17 = 23 years old.

71. Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered?

a) 15%

b) 20%

c) 25%

d) 30%

Discount = Marked Price – Selling Price. Let the Marked Price of 10 articles = Rs. 100.

So, Marked Price of 8 articles = Rs. 80. (so each was marked at Rs.10)

So, as per the question, Rakesh purchased 10 mobile phones for Rs. 80

So, the selling price of 10 mobile phones = Rs. 80 (so each bought at Rs.8)

The discount is 2 rupees on 10 which is 20%.

72. The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are

a) 39

b) 39.7

c) 40

d) 40

Given, average marks of 100 students = 40.

So, total marks of 100 students = 40 × 100 = 4000.

But in this total the error is 83 – 53 = 30, more than the actual total.

So, Actual total = 4000 – 30 = 3970.

So the correct Mean = 3970/100 = 39.70.

Directions for the following 8 (eight) items:

Passage — 1

Low-end IoT (Internet of Things) devices are cheap commodity items: addressing security would add to the cost. This class of items is proliferating with new applications; many home appliances, thermostats, security and monitoring devices and personal convenience devices are part of the IoT. So are fitness trackers, certain medical implants and computer-like devices in automobiles. The IoT is expected to expand exponentially — but new security challenges are daunting.

73. Which one of the following statements is the most logical and rational inference that can be made from the above passage?

a) Development of enabling technologies in India can be a big boost to its manufacturing sector.

b) India is not yet fully ready to adopt IoT in view of the imminent security challenges.

c) Life becomes more comfortable with the development of cheap low-end IoT devices.

d) As we go digital, we must recognise the huge threat to Internet security from some IoT devices.

Sol. Answer is (d). Option (a) is indeed irrelevant to the given passage. Option (b) is also not applicable as the passage does not discuss "India." Option (c) does not align with the theme of the passage. The most suitable answer is option (d).

Passage — 2

With the digital phenomenon restructuring most social sectors, it is little surprise that global trade negotiations are now eyeing the digital area in an attempt to pre-emptively colonise it. Big Data is freely collected or mined from developing countries, and converted into digital intelligence in developed countries. This intelligence begins to control different sectors and extract monopoly rents. A large foreign company providing cab service, for instance, is not a work of cars and drivers, it is digital intelligence about commuting, public transport, roads, traffic, city events, presonal behavioural characteristics of commuters and driver and so on.

74. Which one of the following is the most logical and rational corollary to the above passage?

a) Globalization is not in the interests of India as it undermines its socio-economic structures.

b) India should be careful to protect its digital sovereignty in global trade talks.

c) India should charge monopoly rents from multinational companies in exchange for Big Data.

d) The loss of Big Data from India is proportional to the degree/value of its foreign trade.

Options (a), (c), and (d) are incorrect. The passage primarily discusses how ownership of digital data is becoming crucial for trade and business advantages, emphasizing the risks associated with foreign firms holding Indian data. Option (b) provides the best guidance for the future based on the passage's context.

Passage — 2

With the digital phenomenon restructuring most social sectors, it is little surprise that global trade negotiations are now eyeing the digital area in an attempt to pre-emptively colonise it. Big Data is freely collected or mined from developing countries, and converted into digital intelligence in developed countries. This intelligence begins to control different sectors and extract monopoly rents. A large foreign company providing cab service, for instance, is not a work of cars and drivers, it is digital intelligence about commuting, public transport, roads, traffic, city events, presonal behavioural characteristics of commuters and driver and so on.

75. Which of the following is most definitively implied by the above passage?

a) 7 Big Data is the key resource in the digital space.

b) Big economies create Big Data.

d) Access to and possession of Big Data is a characteristic of developed countries.

The central idea revolves around the notion that data ownership is becoming increasingly vital for trade and business advantages. Option (b) merely states a fact without addressing the broader context. Option (c) is incorrect as developed countries typically do not assert such rights. Option (d) is partially correct but lacks completeness in capturing the essence of the passage.

Passage — 3

The rural poor across the world, including India, have contributed little to human-induced climate change, yet they are on the frontline in coping with its effects. Farmers can no longer rely on historical averages for rainfall and temperature, and the more frequent and extreme weather events, such as droughts and floods, can spell disaster. And there are new threats, such as sea level rise and the impact of melting glaciers on water supply. How significant are small farms? As many as two billion peopre worldwide depend on them for their food and livelihood. Small-holder farmers in India produce 41 percent of the country's food grains, and other food items that contribute to local and national food security.

76. What is the most logical and rational Corry to the above passage?

a) Supporting small farmers is an important part of any agenda regarding environmentally sustainable development.

b) Poor countries have little role to play in the mitigation of global warming.

c) Due to a large number of farmer households, India will not have food security problem in the foreseeable future.

d) Only small-holder farmers in India can ensure food security.

77. The above passage implies that

There is a potential problem of food insecurity in India.

India will have to strengthen its disaster management capabilities.

Which of the above assumptions is/are valid?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Solution for Q. 76 to 77:

Solution 76: The correct answer is (a). Options (b), (c), and (d) are incorrect. Option (b) misinterprets the passage by suggesting that the poor are not involved in contributing to climate change, whereas they may play a role in mitigating it. Option (c) involves a significant assumption that may not hold true. Option (d) is not mentioned in the passage, and the use of "only" makes it incorrect. Option (a) is the best choice.

Solution 77: The answer is (c). Both assumptions appear valid based on the passage. Assumption 1 is supported by the passage's indication that small farms contribute significantly to food production but are under threat. Assumption 2 reflects a clear message directed towards India, evident from the tone of the passage.

Passage – 4

A changing climate, and the eventual efforts of governments (however reluctant) to deal with it, could have a big impact on investors' returns. Companies that produce or use large amounts of fossil fuels will face higher taxes and regulatory burdens. Some energy producers may find it impossible to exploit their known reserves, and be left with "stranded assets" — deposits of oil and coal that have to be left in the ground. Other industries could be affected by the economic damage caused by more extreme weather — storms, floods, heat waves and droughts.

78. On the basis of the above passage, the following assumptions have been made:

Governments and companies need to be adequately prepared to face the climate change.

Extreme weather events will reduce the economic growth of governments and companies'in future.

Ignoring climate change is a huge risk for investors.

Which of the above assumptions is/are valid?

a) 1 and 2 only

b) only

c) 1 and 3 only

d) 1, 2 and 3

Assumption 3 is undoubtedly correct, eliminating option (a). Assumption 2 is oddly phrased with "economic growth of governments," making it unsuitable. Therefore, options (a) and (d) are discarded. This leaves us with option (c) as the only viable choice.

Passage – 5

Access to schooling for those coming of school age is close to universal, but access to quality exhibits a sharp gradient with socio-economic status. Quotas for the weaker sections in private schools is a provision introduced by the Right of Children to Free and Compulsory Education Act, 2009. The quotas have imposed a debate on issues of social integration and equity in education that private actors had escaped by and large, The idea of egalitarian education system with equality of opportunity as its primary goal appears to be outside the space that private school principals inhabit. Therefore, the imposition of the quotas has led to resistance, sometimes justified.

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

Making equality of opportunity a reality is the fundamental goal of the Indian education system.

The present Indian school system is unable to provide egalitarian education.

Abolition of private schools and establishment of more government schools is the only way to ensure egalitarian education.

Which of the above assumptions is/are valid?

a) 1 and 2 only

b) 2 only

c) 2 and 3 only

d) 3 only

You're right. Assumption 2 is indeed supported by the passage, eliminating option (d). Assumption 3 appears too strongly worded and is not explicitly mentioned, especially considering the passage's partial support for private schools towards the end. Thus, assumption 3 can be ruled out. With options (a) and (b) remaining, assumption 1 is explicitly stated in the passage, leading us to choose option (a) as the answer.

Passage – 6

A majority of the TB infected in India are poor and lack sufficient nutrition, suitable housing and have little understanding of prevention. TB then devastates families, makes the poor poorer, particularly affects women and children, and leads to ostracisation and loss of employment. The truth is that even if TB does not kill them, hunger and poverty will. Another truth is that deep-seated stigma, lack of counselling, expensive treatment and lack of adequate support from providers and family, coupled with torturous side-effects demotivate patients to continue treatment — with disastrous health consequences.

80. Which one of the following is the most logical, rational and crucial message conveyed by the above passage?

a) TB is not a curable disease in Indian circumstances.

b) Curing TB requires more than diagnosis and medical treatment.

c) Government's surveillance mechanism is deficient; and poor people have no access to treatment.

d) India will be free from diseases like TB only when its poverty alleviation programmes are effectively and successfully implemented.