1. In the sum

for which digit does the symbol ® stand?

a) 2

b) 3

c) 4

d) 5

Sol.

For option (a),

2 + 12 + 52 + 22 + 21 = 109 (which is not 122). So option (a) is wrong.

For option(b)

3 + 13 + 53 + 33 + 31 = 133. So option (b) is correct.

2.If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure?

a) 0.05 foot

b) 0.25 foot

c) 1 foot

d) 3.25 feet

Sol.

Correct answer is HCF of 7.5 and 3.25, which is 0.25.

3.A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ..... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?

a)34

b) 36

c) 38

d) 40

Sol. Ans.(c).

We can see that by subtracting 1 from each term, we will get a sequence of primes.

14 – 1 = 13; 18 – 1 = 17; 20 – 1 = 19; 24 – 1 = 23; 30 -1 = 29; 32 – 1 = 31.

So the next term will be 38 – 1 = 37 which is also a prime number. Ans is ©

4.One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages Is 195. The torn page contains which of the following numbers?

a) 5, 6

b) 7, 8

c) 9, 10

d) 11, 12

Sol.

We know that the sum of n consecutive natural numbers = n(n+1)/2.

Natural numbers are integers starting with 1.

Now according the information given in question our value of n(n+1)/2 should be greater than 195.

Why? Because one page is torn, so the sum is less than what it should be. Right?

If we take n = 19 we will get n(n+1)/2 = 19 × 20/2 = 190 which is less than 195.

So taking next number let’s assume n = 20.

In this case – n(n+1)/2 = 20×21/2 = 210. But two consecutive numbers were removed, so 210 – 195 = 15. It means that the sum of the two consecutive torn pages should be 15. Only option (b) matches.

5.Consider the following arrangement that has some missing letters:

abab_b_bcb_dcdcded_d

The missing letters which complete the arrangement are

a) a, b, c, d

b) a, b, d, e

c) a, c, c, e

d) b, c, d, e

Sol.

By examining the sequence and trying various options, we can discern that the correct sequence follows a repeated pattern of ababa, bcbcb, cdcdc, deded. Only option (c) matches this pattern.

If we were to choose option (a), the sequence would be ababa, bbbcb, cdcdc, deddd—there is no discernible pattern in it.

Option (b) would yield the sequence ababa, bbbcb, ddcdc, deded—again, there is no recognizable pattern.

Similarly, option (d) results in ababb, bcbcb, ddcdc, deded—lacking a clear repeating pattern.

Therefore, the correct choice is (c) as it aligns with the observed repeated pattern.

6.Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D?

a) 1

b) 2

c) 3

d) 4

Sol.

Each letter represents a different digit from the set {4, 5, 6, 7, 8, 9}. These digits must be greater than 3. Thus, A - D (or D - A) is to be found.

Given that C + F ends with 2, C can only be 8 or 7. If C is 8, then F is 4; if C is 7, then F is 5. Considering the carry, B + 2 + 1 must end with 0, implying B = 7. Hence, C cannot be 7, so C = 8 and F = 4.

Now, with F + 3 + 1 ending with 9, E must be 5. This results in no carry for the next term, A + D = 15, with remaining digits 9 and 6. Thus, 9 + 6 = 6 + 9 = 15.

Therefore, the difference between A and D is 3, making the correct option (c).

7.Two statements S1 and S2 are given below followed by a Question:

S1: There are not more than two figures on any page of a 51-page book.

S2: There is at least one figure on every page.

Question:

Are there more than 1oo figures in that book?

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

a) Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

b) S1 alone is sufficient to answer the Question.

c) S1 and S2 together are not sufficient to answer the Question.

d) S2 alone is sufficient to answer the Question.

Sol.

Using Statement 1 alone, the number of figures on any page could range from 0 to 2. Thus, the total number of figures could be anywhere between 0 (if every page contains 0 figures) and 102 (if every page contains 2 figures). Therefore, Statement 1 alone is not sufficient to answer the question definitively.

Similarly, Statement 2 alone allows for the number of figures on any single page to range from 1 to infinity, thus not providing a unique answer.

Even when combining both statements, the number of figures on any page could be either 1 or 2, leading to a minimum of 51 (if every page contains 1 figure) and a maximum of 102 figures (if every page contains 2 figures). Hence, even by combining both statements, the question cannot be answered definitively.

8.Consider the following data:

What is the value of x in the above table?

a) 7.8

b) 7.6

c) 7.4

d) 7.2

Sol. Ans.(a).

Let the number of boys = b and number of girls = g.

So by the condition given in question we have 9g + 8b = 8.8 (b + g). That gives us ratio b:g = 1:4. It means that if there are p boys number girls will be 4p, where p is any positive integer.

Again by the condition given in question 8×4p + 7×p = X (4p + p)

=> 32p + 7p = 5p × X => 39p = 5pX => 39 = 5X or X = 39/5 or X = 7.8.

9.A family of two generations consisting of six members P, Q, R, S, T and U has three males and three females. There are two married couples and two unmarried siblings. U is P’s daughter and Q is R’s mother-in-law. T is an unmarried male and S is a male. Which one of the following is correct?

a) R is U's husband.

b) R is S's wife.

c) S is unmarried.

d) None of the above

Sol. Ans.(b).

10.If in a particular year 12th January is a Sunday, then which one of the following is correct?

a) 15th July is a Sunday if the year is a leap year.

b) 15th July is a Sunday if the year is not a leap year.

c) 12th July is a Sunday if the year is a leap year.

d) 12th July is not a Sunday if the year is a leap year.

Sol. Ans.(c).

In a non-leap year, the total number of odd days between January 12 and July 12 is calculated as follows:

Remaining days of January: 19

February: 28

March: 31

April: 30

May: 31

June: 30

July: 12

Summing these gives a total of 181 days. When divided by 7, the remainder is 6, indicating that there are 6 odd days.

If January 12 is a Sunday, then July 12 will be a Saturday in a non-leap year.

However, in a leap year, July 12 will be a Sunday due to the additional day added in February (February 29).

11.A man walks down the backside of his house straight 25 meters, then turns to the right and walks 50 meters again; then he turns towards left and again walks 25 meters. If his house faces to the East, what is his direction from the starting point?

a) South-East

b) South-west

c) North-East

d) North-west

Sol. Ans.(d).

Draw diagram to solve the question

12.Two Statements are given followed by two Conclusions:

Statements:

All numbers are divisible by 2.

All numbers are divisible by 3.

Conclusion-I

All numbers are divisible by 6.

Conclusion-Il

All numbers are divisible by 4.

Which of the above Conclusions logically follows/follow from the two given Statements?

a) Only Conclusion-I

b) Only Conclusion-II

c) Neither Conclusion-I nor conclusion-II

d) Both Conclusions-I and Conclusion-II

Sol. Ans.(a).

Given statements are – first, all numbers are divisible by 2 and second, all numbers are divisible by 3. If a number is divisible by 3 and 2 then it will surely be divisible by 6 (which is 2 x 3), but will not be necessarily divided by 4.

13.Two Statements are given followed by two Conclusions:

Statements:

All cats are black.

Conclusion-I:

All dogs are black.

Conclusion-II:

Some dogs are not black.

Which of the above Conclusions logically follows/follow from the two given Statements disregarding commonly known facts?

a) Only Conclusion-I

b) Only Conclusion-II

c) Neither Conclusion-I nor Conclusion-II

d) Both Conclusions-I and Conclusion-Il

Sol. Ans.(c).

Solve by drawing venn diagram and analysing

14.Consider the following sequence of numbers:

How many odd numbers are followed by the odd number in the above sequence?

a) 5

b) 6

c) 7

d) 8

Sol. Ans.(b).

Given sequence is – 5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6.

It happens six times when an odd number is followed by another odd number. See the bold digits (51, 73, 39, 57, 31 and 15).

15.A is 16th from the left end in a row or boys and V is 18th from the right end. Q is 11th from A towards the right and 3rd from V towards the right end. How many boys are there in the row?

a) 40

b) 41

c) 42

d) Cannot be determined due to insufficient data

Sol. (b)

A is 16th from left so 15 students will be there to A’s left. G is 11th to right from A and 3rd to right from V. So there will be 7 students between A and V and 2 students between V and G. Consequently there will 14 students to the right of G. So total number of Students will 15 + 7 + 2 + 14 + A(1) + V(1) + G (1) = 41.

16.Three Statements S1, S2 and S3 are given below followed by a Question:

S1: C is younger than D, but older than A and B.

S2: D is the oldest.

S3: A is older than B.

Question:

Who among A, B, C and D is the youngest?

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

a) S1 alone is sufficient to answer the Question.

b) S1 and S2 together are sufficient to answer the Question.

c) S2 and S3 together are sufficient to answer the Question.

d) S1 and S3 together are sufficient to answer the Question.

Sol. Ans.(d).

a) Option (a): S1 alone is not sufficient. Because there is no clarity about A and B as to who will be younger.

b) Option (b): S1 and S2 together will also be not sufficient as again there will be not clarity about A and B as who will be younger.

c) Option (c): Combination S2 and S3 will not be sufficient as it does not provide any information about C.

d) Option (d): Combination S1 and S3 will give order D > C > A > B. So, the youngest person will be B.

17.How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?

a) 5

b) 11

c) 12

d) 13

Sol. Ans.(c).

Between 1 and 100 there are 19 such integers which have 4 as a digit – 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84 and 94.

Out of these, only 7 integers – 4, 24, 40, 44, 48, 64 and 84 are divisible by 4.

So correct answer will be 19 – 7 = 12. A mechanical question but can be done.

18. Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m / x and V = n / y. which one or the following is correct?

a) u = 4v

b) u = 2v

c) v = u

d) v = 4u

Sol. Ans.(a).

Let the side of P = a, so the side of Q = 2a.

Volume of P (x) = a3 volume of Q (y) = 8a3

Also, It is given that, mass of P (m) = u × X = u × a3 ….. (1) and

Mass of Q (n) = v × y = v × 8a3 …..(2)

It is also given that Mass of Q (n) = 2 × mass of P (m).

So, by using equations 1 and 2 we have v × 8a3 = 2 × u × a3  4v = u.

So option (a) is correct.

19.The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?

a) 25 years

b) 30 years

c) 35 years

d) 45 years/li>

Sol. Ans.(c).

Traditional Method Let the age of Teachers is T years and the three students is a years (Given age of all three student is same). According to question,

(T + 3a)/4 = 20 or T + 3a = 80 ….(1)

T – a = 20 ….(2) (assuming that teachers age will be greater than the students)

By solving equations 1 and 2 simultaneously we have a = 15 and T = 35. Option (c) is correct.

20.A person bought a car and sold it for Rs. 3, 00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?

a) Rs. 3, 60,000

b) Rs. 3, 65,000

c) Rs. 3, 70,000

d) Rs. 3, 75,000

Sol. Ans.(d).

SP = Rs 3,00,000; Loss% = 20%.

CP = (SP × 100)/(100 – Loss%)

=>P = 3,00,000 × 100 / 80 =>CP = Rs. 3, 75,000. So, option D is correct.

Alternative method – Since loss is 20%, so 80% of CP = 3,00,000. => 0.8 CP = 300000 So CP = 3,75,000.

Directions for the following 6 (six) items:

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

Passage — 1

In India, over the last decade or so, labour has been departing agriculture, but is only going to construction and unregistered manufacturing which are not markedly better jobs. Services, where labour tends to be most productive, are not generating the additional jobs the country needs. India will need 24 million or so jobs over the next decade. The new sector, e-commerce, can at best close only half the jobs gap. Only those sectors that drive domestic demand such as health and education can comfortably fill the other half.

21. Which one of the following is best Implied in the passage?

a) Strong measures need to be taken to reduce the rural to urban migration of labour.

b) The working condition in construction and unregistered manufacturing needs to be improved.

c) Service sector has been reducing the problem of unemployment.

d) Increased social sector spending is imperative for large-scale job creation.

Sol. Ans.(d). Theme is “Jobs in India”.

Clearly option (d) is the answer.

Clearly, option (d) is the correct answer.

Option (a) is incorrect as the passage does not discuss reducing labor movement out of rural areas.

Option (b) is incorrect as it does not capture the central idea conveyed in the passage.

Option (c) is the opposite of what is stated in the passage. The passage emphasizes that only sectors like health and education, which drive domestic demand, can fulfill the country's job requirements.

Option (d) may seem slightly indirect, but it aligns with the passage's content. The health and education sectors are part of the social sector, and substantial investments in these areas can indeed create numerous job opportunities.

Passage — 2

In India, the current focus on the right to privacy is based on some new realities of the digital age. A right is a substantive right only if it works in all situations, and for everyone. A right to free expression for an individual about her exploitation, for instance, is meaningless without actual availability of security that guarantees that private force cannot be used to thwart this right. The role of the State, therefore, is not just to abstain from preventing rightful free expression, but also to actively ensure that private parties are not able to block it.

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

State should have some institutions to ensure its appropriate role in a digital society.

State should ensure that private parties do not violate the citizens' right to privacy.

Digital economy is not compatible with the idea of not violating the citizens’ privacy.

Which of the above assumptions is/are valid?

a) 1 and 2

b) 3 Only

c) 1 and 3

d) 2 only

Sol. Ans.(a).

The theme is "Rights of Citizens in the 21st century".

Statement 3 is evidently incorrect as it is not assumed or implied anywhere in the passage. Therefore, options (b) and (c) are eliminated.

Focusing on the options, we need to determine the accuracy of Statement 1. It appears to be correct because the phrase "to actively ensure" implies the necessity of institutional mechanisms rather than one-off or ad hoc responses. Hence, only option (a) seems correct.

The passage initially discusses the "right to privacy" and then elaborates on the significance of this right with an example related to the "right to free expression". Towards the end, it mentions the "role of the state" in guaranteeing the "right to free expression" through both acts of omission and commission.

Passage — 3

One of the biggest ironies around water is that it comes from rivers and other wetlands. Yet it is seen as divorced from them. While water is used as a resource, public policy does not always grasp that it is a part of the natural ecosystem. Efforts at engineering water systems are thus efforts at augmenting water supply rather than strengthening the capacities of ecological systems.

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

a) Rivers and other wetlands should be protected under Ramsar Convention.

b) Engineering water systems should be modernized and further augmented.

c) Wetlands need to be reinforced as more than just open sources or water.

d) Water supply should not be free of cost so as to prevent its misuse or overuse.

Sol. Ans.(c). Theme is “Water as a resource”.

Passage does not talk about ‘Ramsar Convention’ neither does it talk about ‘cost of its supply’, so options (a) and (d) are ruled out.

Passage talks about ‘strengthening the capacities of ecological systems’. For this you have to give more respect to the wetlands, from where the water is sourced, and that can be done by considering them more than just open sources of water. So option (c) is correct.

Option (b) is not the most logical inference as modernization of water systems does not necessarily mean respecting natural ecosystems.

Passage — 4

Asset allocation is the most important investment decision we will ever make, and sadly, most of us do not give that decision the importance it deserves. We are adamant about seeking predictability with our future. We tend to think of investing in risky assets as extremely volatile and value eroding. We also dislike fluctuating returns and the loss of control of investment. We think our money is best left idle unproductive but safe. There is no asset that is risk-free. We could lose our jobs, our homes can lose value, our banks can go bankrupt, our bonds can default, the government can collapse and companies we chose fondly may cease to exist. But we cannot live life assuming that all these extreme events are waiting to happen, and all at the same time. All these extreme forms or risks we know will not manifest at the same time.

24.Which one of the following statements best implies the suggestion given by the author of the passage?

a) Distribute your wealth across different kinds of assets so that your risks would be minimized.

b) Risk-taking behaviour should be a necessary component of your Personality if you want to generate wealth.

c) While making investments, find a trustworthy asset management organization which would manage your wealth for you.

d) You should know that investing your money is a risky business.

Sol. Ans.(a). The theme is "Investment and Asset Allocation."

Given that "Asset allocation" involves implementing an investment strategy to balance risk and reward by adjusting the percentage of each asset in a portfolio based on the investor's risk tolerance, goals, and investment time frame, let's evaluate the options:

Option (c) can be dismissed as it is not mentioned in the passage.

Option (d) is too vaguely worded and can be discarded.

Option (b) implies a goal of generating wealth, which is not explicitly discussed in the passage.

Therefore, we are left with Option (a). Towards the end of the passage, it discusses the importance of diversifying assets to lower risk, stating that extreme forms of risks are unlikely to manifest simultaneously. The passage emphasizes diversification of risk rather than risk-taking, and there is no mention of an "asset management organization."

Hence, Option (a) aligns best with the content of the passage.

Passage — 5

Although most of the Genetically Modified (GM) crops cultivated now are genetically engineered for a single trait, in future, crops genetically engineered for more than one trait will be the norm. Thus, biotechnology's role in agriculture and the regulation or the same cannot be understood solely in the context of the current generation of GM crops. Instead, there is a need to take a comprehensive look, taking into account various aspects, including socio-economic impacts, so that the potential or the technology can be harnessed while minimizing negative impacts. Given the importance of biotechnology in developing varieties that can help in climate change mitigation and adaptation, not using biotechnology as a part of the climate change action plan cannot be an option. Domestic regulation of biotechnology cannot be viewed in isolation of trade policy and obligations under various international treaties and conventions.

25.with reference to the above passage, the following assumptions have been made:

a) Biotechnology regulation is an evolving process.

b) Participation of people is needed in policy decisions regarding biotechnology regulation.

c) Biotechnology regulation should take into account socio-economic aspects in decision-making.

d) Wider involvement of political executive in biotechnology regulation improves its effectiveness in dealing with the country’s trade Policies and international obligations.

Which of the above assumptions are valid?

1, 2 and 4 only

1 and 3 only

2, 3 and 4 only

1, 2, 3 and 4

Sol. Ans.(d). The theme is "Evolving Nature of Biotechnology."

Given that this passage contains two questions, both must be addressed.

Statement 1 is undoubtedly correct as biotechnology is indeed constantly evolving. Therefore, option (c) can be eliminated.

Between statements 2 and 3, statement 3 is more comprehensive and aligns better with the wording of the passage. In fact, statement 3 encompasses what is stated in statement 2. Hence, statement 3 is certainly correct, and statement 2 may or may not be correct.

Statement 4 is definitely accurate as the involvement of the political executive is essential in this context.

Therefore, the only option containing all of statements 1, 3, and 4 is option (d), which also includes statement 2.

So, option (d) is the correct choice.

26.Which one of the following statements best implies the crux of the passage?

a) Precautionary principle is not given importance in current debate on developing GM crops.

b) Biotechnology is not currently used in climate change mitigation and adaptation mechanisms.

c) Biotechnology’s role is not confined to the current priorities of developing GM crops.

d) The negative Impacts of not biotechnology are properly understood.

Sol. Ans.(c). Theme is “Evolving nature of biotechnology”.

We are now asked the “crux of the passage”.

The passage is talking mainly about what biotechnology is being used for today, and what is can be and must be used for in the coming years. Hence, option (c) best summarises the crux.

27.How many zeroes are there at the end of the following product?

a) 10

b)12

c) 14

d) 15

Sol. Ans.(a).

In a multiplication problem, 0 can be produced in two ways. First when a number is multiplied by 10 or second when 5 is multiplied by 2 or any even number.

So to count the number of zeroes in the given multiple let’s break the whole multiplication in to 10, 5 and 2.

We get 1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60

= 1 × 5 × 10 × (3 × 5) × (2×10) × (5×5) × (3×10) × (7×5) × (4×10) × (9×5) × (5×10) × (11×5) × (6×10)

= 1 × (10 × 10 × 10 × 10 × 10 × 10) × (5 × 5 × 5 × 5 × 5 × 5 × 5 × 5) × (2 × 4 × 6) × (3 × 3 × 7 × 9 × 11)

= 1 × (10 × 10 × 10 × 10 × 10 × 10) × (5 × 5 × 5 × 5 × 5 × 5 × 5 × 5) × {2 × (2 × 2) × (2×3)} × (3 × 3 × 7 × 9 × 11)

Now you can see in above multiplication we have six 10s, eight 5s and four 2s.

Six 10s will give us six 0s while four 2s when combined with four 5s (out of the eight available) will give us additional four 0s.

So in the multiplication six + four = ten 0s will be there.

28.Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by

a) 3

b) 9

c) 37

d) (X + Y + Z)

Sol. Ans.(b).

XYZ is a 3-digit number not divisible by 3.

We know that expanded form of XYZ will be 100 X + 10Y + Z. (basic decimal number system)

So, XYZ + YZX + ZXY = (100 X + 10Y + Z) + (100 Y + 10Z + X) + (100 Z + 10X + Y)

= 111X + 111Y + 111Z = 111 (X + Y + Z)

(note 3 and 37 are prime numbers and X + Y + Z is not a multiple of 3 (given), so it will not be multiple of 9 too)

So, the correct option is (b).

29.Let p, q, r and s be natural numbers such that p - 2016 = q + 2017 = r – 2018 = s + 2019 which one of the following is the largest natural number?

a) p

b) q

c) r

d) s

Sol. Ans.(c).

From the given relations, we have p – q = 4033; r – q = 4035 which clearly means r > p > q. Also r – s = 4037 which means r > s.

Thus, r is the greatest of all. So the correct option is (c).

30.How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?

a) Zero

b) One

c) Nine

d) Ten

Sol. Ans.(a).

A number is prime if it is divisible by only 1 and itself.

Now take the digits 1,2,3,4 and 5 and add them. We get 15 as the sum.

“If the sum of the digits of a number is divisible by 3 then number will be divisible by 3”.

So any number formed using these five digits will be divisible by 3. So it cannot be prime. Hence zero.

Directions for the following 7 (Seven) items:

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

Passage — 1

Private investment in general is volatile. Foreign private investment is more volatile because the available investment avenues are significantly greater (i.e., the entire world). Therefore, the responsibility of providing employment cannot be left to Foreign Direct investment (FDl). The current FDI inflows are volatile over time and across sectors and regions, which is a necessary consequence of their search for the highest returns. The adverse consequences are unstable employment and an accentuation of income and regional inequalities. A probable positive consequence of foreign investment is the inflow of new technology and its subsequent diffusion. However, the technology diffusion is not at all certain because the existing state of physical and human capital in India may prove inadequate for the diffusion.

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

Relying on foreign investment in the long run is not an economically sound policy.

Policies must be undertaken to reduce volatility in foreign private investment.

Policies must be undertaken to strengthen domestic private investment.

Public investment should be given priority over private investment.

Substantial public investment in education and health should be undertaken. Which of the above assumptions is/are valid?

a) 1, 2 and 4

b) 1, 3 and 5

c) 2, 4 and 5

d) 3 only

Sol. Ans.(b). Theme is “nature of private investment and employment”.

The passage is talking about the nature of private investment and its fickle tendency. It explains why employment generation cannot be left to foreign private investment, and even its positive effects may get diluted due to inherent problems in Indian human capital.

So, statement 1 is surely correct.It is definitely assumed in it. Why? When we are constantly worried about the fickle nature of FDI (and local private investment), and its negative relation with employment generation, how can we rely on it as an economic policy? If 1 is correct, then options (a) and (b) are possible answers but not (c) or (d).

Now between (a) and (b), we have to check 2 and 3.

Focus on 2 – India can do nothing to reduce volatility in FDI because it is the inherent nature of FDI to seek higher returns (hence fickle – moves from here to there). Note the phrase “a necessary consequence”. So 2 is wrong. But 3 may be right, and 5 is surely right

Why is 5 right? Education and health are bottlenecks (in absorbing new technology) so public investments will help.

Hence, correct answer is option (b). Also note that 4 is not explicitly talked about anywhere.

Passage — 2

Many opportunities to harness the highly skewed, seasonal and spatial distribution of monsoon flows, which occur in a four-month period from June to September annually, have been lost. Since these few months account for most or the rainfall and consequent freshwater availability, the need for holding rainwater in reservoirs, for subsequently releasing it for use over the year, is a necessity nobody can afford to overlook. Climate change will continue to affect weather conditions and create water shortages and excesses. While millions suffer from droughts and floods, waters in the country's many rivers flow unutilized, and are discharged into the sea every year.

32.With reference to the above passage, which of the following could be the most rational and practical implications for India?

Inter-linking of rivers should be undertaken.

A network of dams and canals should be built across the country for proper distribution of water.

Farmers should be provided easy loans for digging borewells.

Usage or water for agriculture should be regulated by law.

Distribution of river water among regions should be regulated by the Union Government.

Select the correct answer using the code given below.

a) 1 and 2

b) 2, 4 and 5

c) 1, 3 and 4

d) 2, 3 and 5

Sol. Ans.(a).

The theme is "Water Resources and Utilization."

The passage discusses water shortages and excesses resulting from the unpredictable nature of the Indian monsoon. It also mentions the issue of unutilized water flowing in rivers.

Statement 3 does not align with the implications of the passage and can be eliminated. Therefore, we are left with options (a) and (b).

To address the challenge of unutilized water discharging into the oceans, statements 1 and 2 propose potential solutions. Interlinking rivers could facilitate the utilization of excess water in deficit regions, while a network of dams and canals could ensure the timely harnessing of skewed monsoon flows.

Hence, option (a) seems most suitable. Additionally, since statement 3 is incorrect, options (c) and (d) are ruled out.

Passage — 3

People will invest in education whenever they are granted the economic freedom to fully enjoy benefits Again, this is for the obvious reason that the return on education increases as the level of economic freedom rises. When people, thanks to lower tax rates, are allowed to retain of the higher income that they gain from incremental level of education, it makes sense to invest in education. On the other hand, when the government decides to tax the higher income of educated individuals at even higher rates, it makes very little sense to invest in educating oneself further. The same incentives apply to parents who decide on whether to invest in their children's education.

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

Lower tax rates in a country invariably translate into greater investments in higher education.

Investment in the education of children ensures their economic freedom.

Economic freedom has a positive impact on building up human capital.

Which of the above assumptions is/are valid?

a) 1 only

b) 2 only

c) 3 only

d) 1, 2 and 3

Sol. Ans.(a).

The theme is "Education and Taxation."

The term "human capital" is not explicitly mentioned in the passage, and its assumption cannot be confirmed. Therefore, statement 3 is ruled out, leading to the elimination of options (c) and (d).

Statement 2 is also incorrect. Investment in children's education by parents depends on various factors, including whether the education will lead to economic freedom. Therefore, it is not accurate to conclude that "investment in education ensures economic freedom."

Thus, the best answer is option (a).

Passage-4

Our urban bodies cannot possibly ensure sustainable delivery of water in our cities unless financing mechanisms are put in place. Water delivery requires heavy investment in collecting it from a natural source, treating it to make it potable, and laying a distribution network of pipes for delivery to the users. It also requires investments in sewerage infrastructure and sewage treatment plants so that the sewers can carry the wastewater to these plants to ensure that no untreated sewage is discharged back into natural water bodies. If our cities were rich enough to meet the entire cost, water could be delivered free. They are not.

34.What is the most logical and crucial message conveyed by the passage?

a) Urban local bodies must recover costs through user charges.

b) Urban local bodies are not efficient enough to meet the water requirements of our cities.

c) Water shortage in our cities is a perennial problem that cannot be solved.

d) In view of the water crisis in our cities, there is an urgent need to limit the population of cities by adopting an upper limit of population size.

Sol. Ans.(a). Theme is “Cost of supplying water”.

Try this passage as it has two questions.

Option (c) is clearly wrong, as it says “…cannot be solved”.

Option (d) is wrong as it is nowhere mentioned in the passage.

Between (a) and (b), when we look at (b), it talks of “ULBs not being efficient enough”. But efficiency is not being discussed in the passage, rather financial viability is. So (b) is not entirely correct.

So (b) is not entirely correct. crucial message being given – “recovering costs through user charges” – which can be a financing mechanism to ensure sustainability of water supply.

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

Rich cities only can ensure sustainable delivery of water.

Sustainable delivery of water in cities means much more than supplying water to households.

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. Ans.(b). Theme is “Cost of supplying water”.

Statement 1 is not correct, as “rich cities could supply water for free” is mentioned. We are talking of sustainability in statement 1.

Statement 2 is correct as sustainable delivery includes many aspects other than just supplying water to households.

Hence option (b) is right.

Passage-5

In India, agriculture still engages about half of workforce, and about 85 per cent of its farms mall and marginal. Compared to China Vietnam, which have experienced fast structural and rural transformation, India's story is of slow transformation. As a result, poverty reduction in India was at a much slower pace during 1988—2014, compared to China and Vietnam. India's poverty reduction was slow during 1988-2005, but during 2005-2012, it accelerated dramatically—almost three times faster than during the earlier period. What did India do during this period? Research reveals that the relative price scenario changed significantly (by more than 50%) in favour of agriculture in the wake of rising global prices. This boosted private investments in agriculture by more than 5o%. As a result, agri-GDP growth touched 4/1% during 2007-2012 as against 2.4% during 2002—2007. The net surplus or agri-trade touched \$25 billion in 2013-2014: real farm wages rose by 7% per annum. All this led to unprecedented fall in poverty.

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

Structural and rural transformation is impossible when farms are mainly small arid marginal.

A good price incentive can trigger investments in agriculture.

India needs to build value chains for high-value agri-products like livestock and horticulture.

Higher global prices of agricultural commodities are essential for India's poverty reduction.

Which of the above assumptions are valid?

a) 1 and 3

b) 2 and 4

c) 2 and 3

d) 3 and 4

Sol. Ans.(b).

The theme is "Agricultural Prices and Poverty Reduction," a topic with significant historical context.

Statement 2 is unquestionably correct, as it reflects an assumption explicitly mentioned in the paragraph: good price incentives indeed stimulate agricultural investments. Therefore, options (b) and (c) remain as possibilities.

Statement 3 is not mentioned anywhere in the passage, even indirectly. Thus, only option (b) remains.

While statement 4 may initially seem simplistic in suggesting that India's poverty reduction is dependent on higher global agricultural prices, it is a fact that such price increases do directly assist in poverty alleviation.

37.Which one of the following statements best reflects the critical message of the passage?

a) India should create large- scale off-farm rural employment to reduce poverty in the near future.

b) India should create a large number of farmer producer companies

c) Private investment in agriculture should be given priority over public investment.

d) Inclusive agricultural growth is key to reduce poverty in the near future.

Sol. Ans.(d).

The theme is "Agricultural Prices and Poverty Reduction."

The passage does not discuss topics such as "off-farm rural employment," "farmer produce companies," or the prioritization of private investment in agriculture over public investment. These concepts are not mentioned in the passage at all, and considering them relevant would be purely speculative.

Therefore, options (a), (b), and (c) are ruled out.

The passage strongly implies that the rate of poverty reduction was higher when the growth rate of agricultural GDP was higher. Hence, option (d) is correct.

38.Two Statements S 1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question:

S1: R is greater-than P as well as Q.

S2: S is not the largest one.

Among four numbers P, Q, R and S which one is the largest?

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

a) S1 alone is sufficient to answer the Question.

b) S2 alone is sufficient to answer the Question.

c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

d) S1 and s2 together are not sufficient to answer the Question.

Sol. Ans.(c).

The question asks, "Among four numbers P, Q, R, and S, which one is LARGEST?"

Statement 1 alone is not sufficient to answer the question as it does not provide any information about S.

Statement 2 alone cannot be sufficient because it only specifies that S is not the largest, but it does not provide any indication about the relative sizes of R, P, and Q.

By combining Statements 1 and 2, we know that S cannot be the largest. However, Statement 2 indicates that R is greater than both P and Q. Therefore, R must be the largest among P, Q, and R.

Hence, the correct answer is option (c).

39.Two Statements Si and S2 are given below followed by a Question:

S1: n is a prime number.

S2: n leaves a remainder of 1 when divided by 4.

If n is a unique natural number between 10 and 20, then what is n?

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

a) S1 alone is sufficient to answer the Question.

b) S2 alone is sufficient to answer the Question.

c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

d) S1 and S2 together are not sufficient to answer the Question.

Sol. Ans.(d).

Neither of the S1 and S2 together or alone can give you the value of n.

Using S1 alone you have four prime numbers between 10 and 20 -> 11, 13, 17, and 19.

Using S2 alone there are two numbers 13 (= 4×3 + 1) and 17 (= 4×4 + 1) are possible.

Even after combining both you will get set of two numbers i.e., 13 and 17. So correct answer is option (d).

40.Two Statements S1 and S2 are given below with regard to two numbers followed by a Question:

S1: Their product is 21.

S2: Their sum is 10.

Question:

What are the two numbers?

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

a) S1 alone is sufficient to answer the Question.

b) S2 alone is sufficient to answer the Question.

c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

d) S1 and S2 together are not sufficient to answer the Question.

Sol. Ans.(c).

S1 alone gives you a × b = 21 (where a and b are two numbers) which have multiple possibilities like 3×7 = 21, 1.5×14 = 21 or 6 × 3.5 = 21. (it is not mentioned that numbers are integers)

So S1 alone is not sufficient.

S2 alone will also not sufficient as it will give you a + b = 10, and again multiple possibilities of a and b like (1, 9); (2, 8); (3, 7)… etc.

By combining bothwe have a + b = 10 or b = 10 – a …(1) and a × b = 21 …(2)

Putting the value of b in equation 2, we have a × (10 – a) = 21 =>a2 – 10a +21 = 0

=> a2 – 7a – 3a +21 = 0 => a(a – 7) – 3 (a – 7) = 0 =>a – 7) (a – 3) = 0

=> If a = 7, b = 3 and If a = 3, b = 7.

So both S1 and S2 are required to find the numbers. Option (c) is correct.

41.What is the greatest length x such that 3 ½ m and 8 ¾ m are integral multiples of x?

a) 1 ½ m

b) 1 1/3 m

c) 1 ¼ m

d) 1 ¾ m

Sol. Ans.(d). Find HCF

42.Consider the following data:

For which period was the natural growth rate maximum?

a) 1911 - 1921

b) 1941 - 1951

c) 1961 - 1971

d) 1971 - 1981

Sol. Ans.(d).

Growth rate = Birth rate – Death rate

Growth rate for 1911-1921 = 48.1 – 35.5 = 12.6

Growth rate for 1941-1951 = 39.9 – 27.4 = 12.5

Growth rate for 1961-1971 = 41.1 – 18.9 = 22.2

Growth rate for 1971-1981 = 37.1 – 14.8 = 22.3

We have to assume the simple formula for natural growth rate, as above, because nothing else is mentioned. And check only for the options given, not all seven years.

43.The recurring decimal representation 1.272727... is equivalent to

a) 13/11

b) 14/11

c) 127/99

d) 137/99

Sol. Ans.(b).

Given that X = 1.272727…

So 100 x = 127.272727…

=>Subtract the first from second, to get – 99 X = 126

=>X = 126/99 = 14/11.

So the correct option is (c).

44.What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?

a) 1012

b) 1022

c) 1122

d) 1222

Sol. Ans.(b).

Desired number = (Least multiple of four digit of LCM of 3, 4 and 5) + 2

So the LCM of 3, 4, 5 and 6 is 60.

The least 4-digit number divisible by 60 is 1020.

So with remainder 2 it will be 1020 + 2 = 1022. Answer is (b).

45.In adult Population or a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?

a) 33 1/7%

b) 34%

c) 34 2/7%

d) 35%

Sol. Ans.(c).

Traditional Method - Let total no. of men = X and Total population be 100.

Total women = (100 − X)

Married men = 40 X/100 …(i) and Married women = (100 − X) × 30/100 …(ii)

But, No. of married men = No. of married women. (as per conditions given)

So, from (i) and (ii) X = 300/7

So, married Men = 300/7 X 40/100 = 120/7 and Married women = 120/7.

Total married population = Men + Women = 240/7

Required percentage = 240/7 % = 342/7 %. So the correct option is (c).

Alternative method: No man marries more than one woman and no woman marries more than one man. It means the Number of married men = Number of married women = 120 (let). Married adult population = 240.

Number of men = 120×100/40 = 300 and Number of women 120 × 100/30 = 400. So, total population = 300 + 400 = 700.

Required percentage 240×100/700 = = 240/7 % = 342/7 %

46.What is the remainder when 51 x 27 x 35 x 62 x 75 is divided by 100?

a) 50

b) 25

c) 5

d) 1

Sol. Ans.(a).

When a number is divided by 100, last two digits of that number will always be remainder. For example 312/100 will give 12 as remainder or 5759 will give 59 as remainder.

So our question is basically reduced to find last two digits of 51 × 27 × 35 × 62 × 75.

However, present question can be solved by looking at only unit digit of the above multiplication.

In the multiplication of two numbers, the unit’s place of the resultant number always be the product of the unit’s place digits of the number which are multiplying. For example, the unit’s digit of 51 × 27 will 1 × 7 = 7.

In above we will get unit digit as 1 × 7 × 5 × 2 × 5 = ..0. Only matching option is (a).

47.A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6 . What is the difference between the maximum share and the minimum share?

a) Rs. 300

b) Rs. 350

c) Rs. 400

d) Rs. 450

Sol. Ans.(c).

Ratio 1/2 : 3/4 : 5/6 can be written as 6 : 9 : 10.

The total amount is Rs. 2500. Clearly the shares are Rs. 600, Rs. 900 and Rs. 1000 respectively.

The difference between the greatest and the smallest is Rs. 400. So the correct answer is (c).

48.For what value of it, the sum of digits in the number (10n + 1) is 2?

a) For n= 0 only

b) For any whole number n

c) For any positive integer n only

d) For any read number n

Sol. Ans.(b).

(10n + 1) will have sum of digits 2 for any whole number n. Whole numbers are integers starting with 0. Just put different value of n and observe yourself.

For n = 0, 100 + 1 = 1 + 1. So sum is 2.

For n = 1, 101 + 1 = 11. So sum is 1 + 1 = 2.

For n = 2, 102 + 1 = 100 + 1 = 101. So sum is 1 + 1 = 2.

So the correct option is (b).

49.In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?

a) It increases.

b) It decreases.

c) It remains the same.

d) No conclusion can be drawn due to insufficient data.

Sol. Ans.(c).

The class average will remain unchanged since there is no addition or removal of individuals from the class. The equilibrium of the average weight will stay the same as before the shifting. Any alteration in the average weight would only occur if individuals were added to or removed from the group(s), which is not the case here.

1. How many different sums can be formed with the denominations Rs. 50, Rs. 100, Rs. 200, Rs. 500 and Rs. 2,000 taking at least three denominations at a time?

a) 16

b) 15

c) 14

d) 10

Sol. Ans.(a).

We have to choose at least three denominations out of five. So we can either choose 3 denominations out of 5 or choose 4 out of 5 or choose all 5.

Mathematically it will be written as –

Total number of ways = 5C3 + 5C4 + 5C5 = 10 + 5 + 1 = 16 ways.

Don’t worry about ‘different sums’, they will be ‘different’ as each time we are taking a different set of denominations.

Manually, these combinations will be –

(a) Three denomination combinations –

50+100+200; 50+100+500; 50+100+2000; 50+200+500; 50+200+2000; 50+500+2000; 100+200+500; 100+200+2000; 100+500+2000; 200+500+2000; TOTAL 10

(b) Four denomination combinations –

50+100+200+500; 50+100+200+2000; 50+100+500+2000; 50+200+500+2000; 100+200+500+2000; TOTAL 5

(c) Five denomination combinations –

50+100+200+500+2000; TOTAL 1

So total = 10 + 5 + 1 = 16.

51.A person X can complete 20% of work in 8 days and another person y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

a) 6

b) 8

c) 10

d) 12

Sol. Ans.(a).

X can complete 20% of the work in 8 days. So X can complete the entire work in 40 days. Thus, work done by X in 1 day = 1/40.

Y can complete 25% of the same work in 6 days. So work entire work in 24 days and work done by Y in 1 day = 1/24.

Work done by X and Y in 1 day = 1/40 + 1/24 = 8/120 = 1/15.

That means X and Y can together complete the entire work in 15 days.

So, time taken to finish 40% or 2/5th of the work = 15 × 2/5 = 6 days. So the correct option is (a).

52.A car travels from a place X to place Y at an average speed of v km/hr from y to X at an average speed of 2v km/hr, again from X to y at an average speed of 3v km/hr and again from y to x at an average speed of 4v km/hr. Then the average speed of the car for the entire journey

a) is less than v km/hr

b) lies between v and 2v km/hr

c) lies between 2v and 3v km/hr

d) lies between 3v and 4v km/hr

Sol. Ans.(b).

Average Speed = Total distance ÷ Total time.

Let us assume that distance between X and Y be ‘a’. Then, total distance = a + a + a + a = 4a.

And total time = Distance/Speed = a/v + a/2v + a/3v +a/4v = 25a/12v

So, average speed for the entire journey = 4a/ (25a/12v) = 48v/25 = 1 .92v.

So the correct option is (b) i.e. between v and 2v.

53.Consider the following statements:

The minimum number of points of intersection of a square and a circle is 2.

The maximum number of points of intersection of a square and a circle is 8.

Which of the above statements is/are correct?

a) 1 only

b) 2 only

c) Both 1 and 2

d) Neither 1 nor 2

Sol. Ans.(c).

54.A man takes half time in rowing a certain distance downstream than upstream. What is the ratio or the speed in still water to the speed of current?

a) 1 : 2

b) 2 : 1

c) 1 : 3

d) 3 : 1

Sol. Ans.(d).

Let the speed in still water = s kmph and the speed of current = c kmph. Let distance is D km.

Speed upstream = Speed in still water + Speed of current = s + c.

Speed downstream = Speed in still water – Speed of current = s – c.

Time upstream = Distance/Speed upstream = D/(s –c) …(1) and

Time downstream = Distance/Speed downstream = D/(s+c) …(2)

By the condition given in question Time upstream/2 = Time downstream

55.How many pairs of natural numbers are there such that the difference of whose squares is 63?

a) 3

b) 4

c) 5

d) 2

Sol. Ans.(a).

Natural numbers are integers starting with 1.

Let the two numbers be a and b then

a2 – b2 = 63 =>(a + b) (a – b) = 63. Now 63 = 9 × 7 = 21 × 3 = 63 × 1 So,

Case I: a + b = 9; a – b = 7. Here we will get a = 8 and b = 1

Case II: a + b = 21; a – b = 3. Here we will get a = 12 and b = 9.

Case III: a + b = 63; a – b = 1. Here we will get a = 32 and b = 31

Since 63 has only these 3 pairs of factors, so the correct option is (a).

56.Which one of the following will have minimum change in its value if s is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?

a) 2/3

b) 3/4

c) 4/5

d) 5/6

Sol. Ans.(d).

Value of this percent will depend on ‘a’. As numerator is a constant value and ‘a’ is in denominator, the higher the value will be the shorter the percentage will be. Hence correct option is (d).

57.A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?

a) 2n

b) 3n

c) 2n + 4

d) 3n + 1

Sol. Ans.(d).

A digit n > 3 is divisible by 3 but not divisible by 6 is 9.

So n = 9. Of all given options 2n, 3n, 2n+4, and 3n + 1, only the last one ( = 3×9 + 1 = 28 ) will be divisible by 4.

58.If 1 litre of water weighs 1 kg, then how many cubic millimeters of water will weigh 0.1 gm?

a) 1

b) 10

c) 100

d) 1000

Sol. Ans.(c).

Given 1 litre = 1 kg.

We know that 1 m3 (1 cubic metre) is exactly 1000 Litres.

=>1000 litre = 109 cubic millimetres.

(How? 1 m x 1 m x 1 m = 100 cm x 100 cm x 100 cm = 1000 mm x 1000 mm x 1000 mm = 109 mm3)

=>1 litre = 106 cubic millimetres = 1 kg = 1000 gm

So 0.1 gram = 102 mm3 = 100 cubic millimetres.

59.A vessel full of water weighs 4o kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?

a) 10 kg

b) 15 kg

c) 20 kg

d) 25 kg

Sol. Ans.(a).

Regular method: Let the weight of empty vessel = v and weight of water = w, then by the conditions given we have

v + w = 40 …. (1) and

v + w/3 = 20 …. (2)

By solving equations (1) and (2) simultaneously we have w = 30 and v = 10.

60.A frog tries to come out of a dried well 4.5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. what is the number of jumps required for the frog to come out of the well?

a) 28

b) 29

c) 30

d) 31

Sol. Ans.(b).

Total distance to be jumped by frog to come out = 4.5 m = 450 cm.

Frog jumps 30 cm and slips 15 cm, which means that, in a jump he ascends 30 – 15 = 15 cm.

In 28 such jumps he will ascend to 28 × 15 = 420 cm.

Now only 30 cm remain to come out, which the frog will jump in the next (29th) jump.

In the last jump frog will not slip because he will be outside the well.

Directions for the following 6 (six) items:

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

Passage — 1

Spanish ships in the late 16th century first brought the potato tuber from South America to Europe whereby in the early 19th century, it bad become a reliable backup to cereal crops, particularly in the cold, rain-soaked soils of Ireland. The Irish were soon almost wholly dependent on the potato as their staple food. And they were planting primarily one prodigious variety, the ‘Lumper' potato, whose genetic frailty would be cruelly exposed by the fungus 'Phytophthora infestans’. In 1845, spores of the deadly fungus began spreading across the country, destroying nearly all the Lumpers in its path. The resulting famine killed or displaced millions.

61.Which one or the following statements best reflects the critical message or the passage?

a) For introducing any foreign plant into a country, the soil and climate conditions of that country should be suitable.

b) As a staple food of a country, tuber crops like potato cannot replace cereal crops.

c) Some or the fungal infections or plants cannot be prevented or stopped from spreading across large areas.

d) Relying on a homogeneous food source is not desirable.

Sol. The theme is "Crop Dependence of Nations."

Soil and climate conditions were not the reasons for the destruction of the homogenous potato crop throughout Ireland. Therefore, options (a) and (d) are not relevant.

The passage does not discuss the prevention of fungal infections, so option (c) is not correct. Additionally, the passage does not address whether tuber crops can replace cereal crops, so option (b) is not correct either.

The fundamental message conveyed in the passage is that nations should not rely solely on a homogenous food source because a single disease can devastate the entire food economy.

Therefore, the correct answer is option (a).

Passage-2

India is at once among the fastest growing global economies and home to the largest number of malnourished children in the world. There are regions where malnutrition is not the exception but the norm. And across the country, malnutrition is the cause of death for roughly half the 1-3 million children who die before their fifth birthday each year. Even those children who survive suffer permanently from the damage that has already been done to their bodies and minds from not getting enough of the right foods and nutrients. Around 44 million children under 5 are stunted. That makes it harder for them to learn in school and subsequently earn a living as adults. Their lifetime earnings potential is almost a quarter less than that or their healthy peers.

62.With reference to the above passage, which of the following is/are the most rational and practical implication/ Implications?

a) India’s Public Distribution System should be monitored by the Union Government.

b) Girls should be encouraged to delay marriage and first pregnancy.

c) Mothers should be encouraged to breastfeed their children immediately after birth.

d) The supply of safe drinking water and proper sanitation facilities to all should be ensured.

e) Authorities should ensure the vaccination as prescribed

Select the correct answer using the code given below.

1, 2, 3 and 4

2, 3, 4 and 5

1 only

3 and 5 only

Sol.The theme is "Malnutrition in India."

The passage focuses solely on the issue of malnutrition and does not discuss topics such as vaccination, water/sanitation, or breastfeeding.

Therefore, if we focus solely on addressing malnutrition, it implies ensuring food supply for all citizens, especially the weaker sections. This suggests the need for a better Public Distribution System (PDS). Statement 1 aligns with this perspective, suggesting that if the Union government can monitor the PDS with the aim of eliminating malnutrition, the problem can be mitigated.

Since statement 5 is not mentioned in the passage, options (b) and (d) can be eliminated.

Additionally, option (a) is eliminated because statement 2 is not immediately relevant to addressing malnutrition.

Hence, the correct answer is option (c).

Passage—3

The pulse variety ‘Pusa Arhar 16’ has the potential to be grown in the paddy-growing of Punjab, Haryana and Uttar Pradesh and eventually in all of India. Its yield (about 2000 kg/hectare) will be significantly greater than those of the existing varieties and because its size will be uniform, it will be amenable to mechanical harvesting, an attractive feature for farmers in northern India who currently use this technology for paddy. Most important, Arhar straw, unlike paddy straw, is green arid can be ploughed back into the soil. In Paddy straw, the problem is the high silica content, which does not allow for easy decomposition. In the case of Arhar, the farmer, even after combine harvesting, just needs to run a rotovator to cut the leftover straw into pieces, which can be ploughed back and will decompose very fast. AU this is difficult with leftover paddy stalks that cannot be easily salvaged or ploughed back. Farmers, therefore, choose the easiest option of simply burning it.

63.Which of the following are the most rational inferences that can be made from the passage?

a) Farmers' income will be higher with pulse cultivation than with paddy cultivation.

b) Pulse cultivation causes less pollution as compared to paddy cultivation.

c) Pulse straw can be used to improve soil quality.

d) In the context of northern Indian agriculture, paddy straw has no usefulness.

e) Mechanized agriculture is the main cause for stubble burning.

Select the correct answer using the code given below.

2, 3 and 5

1, 4 and 5

2 and 3 only

1 and 4 only

Sol. Ans.(c).

The theme is "Paddy versus Pulses in North Indian Farms."

Statement 5 is incorrect as it suggests that mechanized agriculture is the reason for burning paddy stalks. However, the passage mentions that paddy stalks are tough to collect or plough back into the ground, leading farmers to choose burning as an alternative. Therefore, options (a) and (b) can be ruled out.

Statement 1 is also not correct as it is not explicitly mentioned whether a direct comparison between pulse cultivation and paddy cultivation is feasible.

Thus, options (a) and (d) are ruled out.

Therefore, the only remaining option is (c), which includes statements 2 and 3 only.

Passage-4

In India, authorities always look to store the maximum amount of water in reservoirs during the monsoon season, which is then used for irrigation and generation of electricity during the summer months. It is an internationally accepted practice that the water level or a reservoir should be kept below a certain level before the onset of monsoon season. This is so that when monsoon rains come, there is space to store the excess rainwater and also so that water can be released in a regulated manner. But the authorities store the maximum amount of water in reservoirs even before the close of the monsoon, only to ensure greater electricity generation and irrigation.

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

High risks involved in holding maximum water in reservoirs are due to our over-dependence on hydro power projects.

Storage capacity of dams should not be fully used before or during monsoon season.

Role of dams in flood control is underestimated in India.

Which of the above assumptions is/are valid?

a) 1 and 2 only

b) 2-only

c) 3 only

d) 1, 2 and 3

Sol. Ans.(c). Theme is “Water reservoirs and monsoon”

Three options have statement 2 in them. So focus on 2 first.

Statement 2 says – “Storage capacity of dams should not be fully used before or during monsoon season”. But the passage says that reservoirs must be used during monsoon rains to store excess rainwater. So statement 2 does not seem right.

Hence, only option (c) is correct.

Passage-5

Economic liberalization in India was shaped largely by the economic problems of the government than by the economic priorities of the people or by the long-term development objectives. Thus, there were limitations in conception and design which have been subsequently validated by experience. Jobless growth, persistent poverty and rising inequality have mounted as problems since economic liberalization began. And all these years later, four quiet crises confront the economy: agriculture infrastructure, industrialization and education as constraints on the country’s future prospects. These problems must be resolved if economic growth has to be sustained and transformed into meaningful development.

65.Which of the following is/are the most rational and logical Inference/ Inferences that can be made from the passage?

It is essential to rethink and redefine the economic role of the state in the quest for development.

India has not made effective implementation of its policies in social sectors nor made sufficient investments in them.

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

Sol. Ans.(a).

The theme is "Economic Liberalization in India," and there are two questions to be addressed.

Statement 1 suggests the need to reconsider the economic role of the State in the pursuit of development. The passage indicates that the Indian liberalization process stemmed from the government's economic challenges rather than the people's issues, leading to various design flaws. These flaws are now evident in the shortcomings across multiple sectors. Therefore, it seems rational to infer that rethinking and redefining the State's economic role are necessary for proper development. Hence, the answer could be (a) or (c).

Statement 2 discusses the implementation of policies and insufficient investments. However, the passage primarily focuses on the conception and design of policies rather than their implementation. Additionally, the term "social sectors" is not explicitly defined in the passage. Therefore, it is difficult to infer statement 2 from the passage. Thus, the final answer is (a).

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

India's economy needs to be greatly integrated with global economy so as to create large number of jobs and to sustain its growth momentum.

Economic liberalization would cause large economic growth which would reduce poverty and create sufficient employment in the long run.

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. Ans.(d).

The theme is "Economic Liberalization in India."

Upon closer examination, it becomes apparent that neither statement 1 nor statement 2 is valid.

The passage does not discuss the integration of the Indian economy with the global economy, as suggested by statement 1. Additionally, the passage does not mention the potential for high growth being the driver of economic liberalization in India, as implied by statement 2.

Therefore, both statements are incorrect.

67.A shop owner offers the following discount options on an article to a customer:

Successive discounts or 10% and 20%, and then pay a service tax of 10%

Successive discounts of 20% and 10%, and then pay a service tax of 10%

Pay a service tax or 10% first, then successive discounts of 20% and 10%

Which one of the following is correct?

a) 1 only is the best option for the customer.

b) 2 only is the best option for the customer.

c) 3 only is the best option for the customer.

d) All the options are equally good for the customer.

Sol. Ans.(d).

Case 1 –Let the price of the article = 100, after first discount of 10% it will be of 90. After second discount of 20% it will be 90 – 18 (20% of 90) = 72. And after services tax, it will become 72 – 7.2 (10% of 72) = 64.8.

Case 2 Let the price of the article = 100, after first discount of 20% it will be of 80. After second discount of 10% it will be 80 – 8 (10% of 80) = 72. And after services tax, it will become 72 – 7.2 (10% of 72) = = 64.8.

Case 3 Let the price of the article = 100, after 10% service it will be of 90. After second discount of 20% it will be 90 – 18 (20% of 90) = 72. And after the last discount of 10% it will become 72 – 7.2 (10% of 72) = 64.8.

68.The letters from A to Z are numbered from 1 to 26 respectively. If GHI = 1578 and DEF = 912, then what is ABC equal to?

a) 492

b) 468

c) 262

d) 246

Sol. Ans.(d).

It is given that A to Z are numbered in same order as 1 to 26 (the word “respectively”).

Now, GHI must logically become 789. But we are given GHI = 1578.

Note that 789 x 2 = 1578.

Also given that DEF = 912. But 912 = 456 x 2 and 456 = DEF in the given coding scheme.

So logic is “doubling of give number code”.

So correct answer would be ABC = 123 = 246.

1. What is the missing term in the following?

ACPQ : BESU:: MNGI: @

a) NPJL

b) NOJM

c) NPIL

d) NPJM

Sol. Ans.(d).

ACPQ : BESU :: MNGI : @

Here A + 1 = B; C + 2 = E; P + 3 = S; Q + 4 = U (So ACPQ becomes BESU)

Similarly, M + 1 = N; N + 2 = P; G + 3 = J; I + 4 = M.

So the correct option is (d) as MNGI will become NPJM.

70.what is the largest number among the following?

a) (1/2)-6

b) (1/4)-3

c) (1/3)-4

d) (1/6)-2

Sol. Ans.(c).

(1/2)– 6 = 64;

(1/4)– 3 = 64;

(1/3)– 4 = 81;

(1/6)–– 2 = 36;

So the correct option is (c).

Directions for the following 6 (six) items:

Passage — 1

Bank credit to the industrial sector has started shrinking. Its decline has been a serious concern as credit growth is essential to revive investment. The problem's Origins lie in the incomplete reforms of the last 25 years. An institutional change that should have followed the 1991 reforms should have been setting up of a resolution corporation for banks. In a market economy with booms and busts, banks should be allowed to be set up and to fail. Today, we cannot shut down banks because there is no proper system to shut them down. Weak loss-making banks continue to need more capital.

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

Indian banking system is not able to help the country in its economic growth.

Economic reforms that started in 1991 have not helped in improving the economy to expected levels.

India lacks the institutional mechanism to deal with the failure of banks.

Encouraging the foreign investments in our industrial sector is a good alternative to this sector's dependence on banks for credit.

Sol. Ans.(c). The theme is "Failing Banks and Resolution Process."

a) Option (a) is too broad and does not directly relate to the limitations of the Indian banking system discussed in the passage.

b) Option (b) is too generalized and does not specifically address the issues highlighted in the passage.

c) Option (c) is precise and accurately reflects the actual inference that can be drawn from the passage. The passage focuses on the limitations of the Indian banking system, particularly the lack of a formal resolution process for failing banks.

d) Option (d) is irrelevant to the discussion of failing banks and resolution processes.

Therefore, option (c) is the most appropriate inference based on the content of the passage.

Passage — 2

India has tremendous potential for solar energy. We all realize that we have to stop burning fossil fuels to meet our energy needs. But certain renewable resources are still going through their cost Curves and learning curves to get the required amount of output. The Indian Government has strongly committed to its targets of reducing emissions by 33 percent by 2030, and towards this it has initiated a strong push towards a gas-based economy and has also invested heavily in renewable energy. However, business houses are wary of investing too heavily in renewable energy at a time when the technology is not yet ready.

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

a) India's commitment to reduce emissions by 33% is unlikely to be achieved.

b) India should import gas rather than invest in renewable resources.

c) Getting renewable resources to market too soon may be costly.

d) India should put in more efforts in the exploration of natural gas.

Sol. Ans.(c).

The theme is "India's Emissions and Renewables Push."

The passage highlights India's potential for solar energy and its commitment to shifting towards renewable sources, despite their current costliness and technological imperfections. The government aims to reduce emissions by 33% by 2030 and has made efforts in both the gas-based economy and renewable energy sectors. However, business-houses are hesitant to invest in renewable energy due to technological limitations.

Option (b) is ruled out as the passage does not compare gas with renewable sources or suggest that gas should be preferred over renewables.

Option (d) proposes a policy prescription, which is not explicitly mentioned in the passage, so it is also ruled out.

Between options (a) and (c), it is a difficult choice. However, option (c) more accurately reflects the emphasis on reducing emissions through the promotion of renewable energy sources and the challenges associated with technological limitations. Therefore, we will go with option (c).

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

Governments often provide inefficient and costly subsidies for technologies that may not be ready in the near future.

India’s commitment of reducing emissions by 33% by 2030 shall be on the basis of gas-based economy.

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. Ans.(d).

The theme is "India's Emissions and Renewables Push."

The passage does not mention subsidies; rather, it focuses on investment from corporations. Therefore, statement 1 can be ruled out, eliminating options (a) and (c).

Statement 2 is only partially correct because it implies a predetermined outcome for the year 2030. However, considering that the passage refers to the current situation in 2020 and plans for 2030, it is possible that circumstances may change in the intervening years. Thus, statement 2 may not be entirely accurate.

Since both statements 1 and 2 are not entirely correct, the answer is (d).

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

Genome editing does not require the transfer of genes from one plant to another.

Through genome editing, the chosen genes can be altered precisely in a manner akin to the natural process that helps plants to adapt to the environmental factors.

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. Ans.(c). T

heme is “Genome editing”.

Both the assumptions are valid.

Statement 1 is evident from ‘Researchers use ‘molecular scissors’ to dissect the genome and repair it..’.

Statement 2 looks like the summary of the passage. It is correct.

Passage — 4

Many people understand the connection n solid waste management and health in terms of the consequences of unattended heaps of garbage which become home for flies and other Vermin. However, there is another aspect that is not well-understood, that is, what happens when unscientific solid waste management combines with poor drainage and dumping of untreated sewage into drains which are meant to carry storm water during rains. The result is choked drains which are full of stagnant water breeding mosquitoes, resulting in the spread of water-borne diseases.

75.In the context of India, which one of the following statements best reflects the eritical message of the passage?

a) In India, the drainage networks are not separate for sewerage and storm water.

b) Urban local bodies do not have enough resources and legislative authority to deal with the problems or waste management.

c) Solid waste management should be integrated with the maintenance of drainage and sewerage networks.

d) Bad management of solid waste and sewerage systems by our municipalities is the reason for drinking water shortages in our cities.

Sol. Ans.(c). The theme is "Solid Waste Management."

The passage does not discuss the resources of urban local bodies or drinking water shortages, so options (b) and (d) can be ruled out.

Between options (a) and (c), option (c) is supported by the passage, as it mentions the consequences of unscientific solid waste management combined with poor drainage. This indicates that solid waste mismanagement contributes to environmental pollution and health hazards, leading to adverse effects on public health.

Therefore, the correct answer is option (c).

Passage — 5

In Part III of the constitution which assures people certain fundamental rights, Article 25 proclaims that “all persons are equally entitled to freedom of conscience and the right freely to profess, practice and propagate religion”. What people fail to notice is that this Proclamation is prefixed with the words “subject to public order, morality, health and to the other provisions of this Part”, Which set conditions precedent for the legal protection of religious practices of any Community. The closing words of this prefatory rider in Article 25 virtually constitute a subordination clause placing other fundamental rights mentioned in Part Ill over and above the right to religious freedom. Among those other fundamental rights is the rights to equality before law and equal protection of laws-assured at the outset and elaborated in later articles to mean, inter alia, that the State shall not deny equal protection of laws to any person or group of persons on the basis of religion alone.

76.What is the most logical inference from the above passage?

a) State shall not interfere with the religious affairs of the Citizens.

b) Religious freedom under the Constitution is open to State intervention

c) Religious freedom of the citizens is not covered under fundamental rights.

d) Religious practices of any Community are immune to State laws.

Sol. Ans.(b).

Theme is “Freedom of Religion u/Art 25”.

The passage wants to say that our constitution provides the fundamental right of religious freedom with certain conditions. If it is harmful for the society in any way, the state can intervene.

Options (c) and (d) are both extreme and can be immediately rejected.

Option (a) is not correct at all.

77.How many different 5-letter words (with or without meaning) can be constructed using all the letters of the word ‘DELHI’ so that each word has to start with D and end with I?

a) 24

b) 18

c) 12

d) 6

Sol. Ans.(d).

D _ _ _ I

We have three places and three letters E, H, L which can be arranged in 3! = 6 ways.

So the correct option is (d). This is a question from permutations and combinations. If you don’t know the topic, you can try doing it manually as well which may take some time.

78.A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it d replaced by same quantity of liquid B. Again 4 litre of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?

a) 4 : 1

b) 5 : 1

c) 16 : 9

d) 17 : 8

Sol. Ans.(c).

Successive replacement case – If y units of some other liquid is replaced in x units of original liquid n times then the ratio of the quantity of original liquid to the total quantity of liquid after n operation = ((x-y)/x)^n.

Applying to our case x = 20, y = 4, n = 2.

So at the end of the 2nd operation the ratio of the quantity of liquid A to the total quantity of liquid =

It means out of the total quantity of 25 units liquid A is 16 units and liquid B is 26 – 16 = 9 units.

Hence required ratio is 16 : 9.

79.The average score of a batsman after his 50th innings was 46.4. After 60th innings, his average Score increases by 2.6. What was his average score in the last ten innings?

a) 122

b) 91

c) 62

d) 49

Sol. Ans.(c).

Regular method:Average of 50 innings = 46.4.

Sum of 50 innings = 50 × 46.4 = 2320 …(i)

Average of 60 innings = 46.4 + 2.6 = 49

Sum of 60 innings = 60 × 49 = 2940 …(ii)

So runs scored in last ten innings = 2940 – 2320 = 620.

Average = 620/10 = 62. So the correct option is (c).

80.As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for Rs. 1,200. What Was the Original price of rice per kg?

a) Rs. 30

b) Rs. 40

c) Rs. 50

d) Rs. 60

Sol. Ans.(b).

Let the original price be P. So, 1.25 P is the new price.

Earlier quantity purchased = 1200 / P kg.

New quantity purchased = 1200 / 1.25P kg

Difference = 6 kg = 1200/P – 1200/1.25P.

Solve for P

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