Explanation:

Step 1: Assume Total Candidates = 100

• Men: 60% × 100 = 60
• Women: 40% × 100 = 40

Step 2: Number of Candidates Clearing the Qualifying Test

• Men clearing qualifying test: 70% × 60 = 42
• Women clearing qualifying test: 75% × 40 = 30

Step 3: Number of Candidates Passing the Final Test

• Men passing final test: 80% × 42 = 33.6 ≈ 34 
• Women passing final test: 70% × 30 = 21

Step 4: Overall Success Rate

• Total successful candidates: 34 + 21 = 55
• Overall success rate:

$$ \text{Success Rate = } \frac{55}{100} \times 100 = 55%$$

Step 5: Compare Success Rates

Success rate for men:

Success rate for men

$$ \text{Success rate for men = } \frac{34}{60} \times 100 = 56.67% $$

Success rate for women:

$$ \text{Success rate for women} = \frac{21}{40} \times 100 = 52.5% $$

The success rate is higher for men compared to women.

Step 6: Analyze Each Option

1. (a) Success rate is higher for women.
   • Incorrect, as the success rate for men (56.67%) is higher than for women (52.5%).
2. (b) Overall success rate is below 50%.
   • Incorrect, the overall success rate is 55%, which is above 50%.
3. (c) More men cleared the examination than women.
   • Correct, 34 men cleared the exam compared to 21 women.
4. (d) Both (a) and (b) are correct.
   • Incorrect, as neither (a) nor (b) is correct.

Correct Answer: (c) More men cleared the examination than women.

Explanation:

Step-by-Step Solution

The total number of marbles in the box is:

Total marbles = White marbles + Red marbles + Green marbles.

Substitute the values:

$$.$$

Correct Answer: (b) 28

Explanation:

Problem Analysis

We are given that:

1. The cost of a cow is more than 4 goats but less than 5 goats.
2. The cost of a goat is between ₹600 and ₹800.

We need to determine the most valid conclusion about the cost of the cow.

Step-by-Step Calculation

1. Cost of 4 goats:

• Minimum cost: 4 × 600 = 2400
• Maximum cost: 4 × 800 = 3200

Thus, the cost of the cow must be greater than ₹2400.

2. Cost of 5 goats:

• Minimum cost: 5 × 600 = 3000
• Maximum cost: 5 × 800 = 4000

Thus, the cost of the cow must be less than ₹4000.

3. Range for the cow’s cost:

Combining the above:

Cost of the cow ∈ (2400, 4000)

Options Analysis

1. (a) A cow costs more than ₹2,500.
   • This is not specific enough since it only partially describes the range of the cow’s cost.
2. (b) A cow costs less than ₹3,600.
   • This is incorrect because the cost of the cow can exceed ₹3600.
3. (c) A cow costs between ₹2,600 and ₹3,800.
   • This is too restrictive. While the range 2600−3800 lies within the broader range, it excludes valid possibilities such as a cow costing ₹2501 or ₹3900.
4. (d) A cow costs between ₹2,400 and ₹4,000.
   • This is accurate and fully describes the valid range for the cow’s cost based on the calculations.

Correct Answer: (d) A cow costs between ₹2,400 and ₹4,000.

Explanation:

Step-by-Step Analysis

Step 1: Assign initial categories

• $C$ and $D$ are friends, meaning they cannot both be cowards (since two cowards are always enemies).
  Therefore, C and $D$ are fighters.

Step 2: Analyze $A$ and $B$

• $A$ and $B$ are enemies.
  • If $A$ is a fighter, $B$ must be a coward.
  • If $A$ is a coward, $B$ must be a fighter.
  • From later clues ($A$ and $E$ are not enemies), $A$ must be a fighter (otherwise $E$ must also be a coward, making them enemies, which is not true).

Thus, $A$ is a fighter, and $B$ is a coward.

Step 3: Analyze $E$

• A and E are not enemies, so $E$ must also be a fighter (a fighter is indifferent to another fighter).

Step 4: Analyze $F$

• $E$ and $F$ are indifferent to one another, so $F$ must also be a fighter (fighters are indifferent to each other).

Step 5: Verify $B$ and $F$

• $B$ and $F$ are enemies. Since $B$ is a coward, $F$ must be a fighter, which matches our earlier conclusion.

Final Categories

• Fighters: A, C, D, E, F.
• Cowards: $B$.

Option Analysis

1. (a) $,$ and $F$ are cowards.
   • Incorrect: C and $F$ are fighters, not cowards.
2. (b) $,$ and $F$ are fighters.
   • Correct: Based on the analysis, $,$ and $F$ are indeed fighters.
3. (c) B and $E$ are in the same category.
   • Incorrect: B is a coward, and E is a fighter.
4. (d) $A$ and F are in different categories.
   • Incorrect: A and $F$ are both fighters.

Correct Answer: (b) $,$ and $F$ are fighters.

Explanation:

Given Information:

1. The group consists of two men (Anil and David) and two women (Shabnam and Rekha).
2. Languages spoken:
   • Two members speak Tamil, and the other two speak Marathi.
   • Shabnam speaks Marathi.
   • Anil speaks Tamil.
3. Driving abilities:
   • Rekha and David can drive a car.
   • Only one man and one woman can drive.

Step 1: Assign languages to all members

• Shabnam speaks Marathi, so the other Marathi speaker must be David.
• Anil speaks Tamil, so the other Tamil speaker must be Rekha.

Thus, the language distribution is:

• Tamil speakers: Anil and Rekha.
• Marathi speakers: Shabnam and David.

Step 2: Assign driving abilities

• Rekha (woman) and David (man) are the only two who can drive.

Step 3: Verify the options

(a) Both the Tamil speakers can drive a car.

• Tamil speakers: Anil and Rekha.
• Only Rekha can drive, so this is false.

(b) Both the Marathi speakers can drive a car.

• Marathi speakers: Shabnam and David.
• Only David can drive, so this is false.

(c) Both of those who can drive a car speak Marathi.

• Drivers: Rekha (Tamil speaker) and David (Marathi speaker).
• This is false, as Rekha does not speak Marathi.

(d) One of those who can drive a car speaks Tamil.

• Drivers: Rekha (Tamil speaker) and David (Marathi speaker).
• This is true, as Rekha speaks Tamil.

Correct Answer: (d) One of those who can drive a car speaks Tamil.

Explanation:

Problem Analysis

We are tasked with finding the average speed of a car that travels from city A to city B at a speed of 40 km/hr and returns from city B to city A at a speed of 60 km/hr.

Step 1: Formula for average speed

The formula for the average speed of a round trip when the distances are equal but the speeds differ is given by:
$$
\text{Average Speed} = \frac{2 \cdot v_1 \cdot v_2}{v_1 + v_2},
$$
where:

$v_1 = 40$ km/hr (speed from A to B),
$v_2 = 60$ km/hr (speed from B to A).

Step 2: Substitute the values

Substitute $v_1 = 40$ and $v_2 = 60$ into the formula:
$$
\text{Average Speed} = \frac{2 \cdot 40 \cdot 60}{40 + 60}.
$$

Simplify:
$$
\text{Average Speed} = \frac{2 \cdot 2400}{100}.
$$
$$
\text{Average Speed} = \frac{4800}{100} = 48 \, \text{km/hr}.
$$

Step 3: Verify the result

The total distance for the round trip is:
$$
\text{Total Distance} = 360 \, \text{km (A to B)} + 360 \, \text{km (B to A)} = 720 \, \text{km}.
$$

The total time taken is:
$$
\text{Time for A to B} = \frac{360}{40} = 9 \, \text{hours},
$$
$$
\text{Time for B to A} = \frac{360}{60} = 6 \, \text{hours}.
$$
$$
\text{Total Time} = 9 + 6 = 15 \, \text{hours}.
$$

The average speed is:
$$
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{720}{15} = 48 \, \text{km/hr}.
$$

Final Answer:

The average speed of the car is:
$$
\boxed{\text{(b) 48 km/hr}}
$$

Explanation:

Problem Analysis

The monthly incomes of Peter and Paul are in the ratio of $4:3$, and their expenses are in the ratio of $3:2$. Each of them saves Rs. $6000$ at the end of the month. We need to calculate their monthly incomes.

Step 1: Represent the incomes and expenses

1. Let Peter’s monthly income be $4x$ and Paul’s monthly income be $3x$ (since the income ratio is $4:3$).

2. Let Peter’s monthly expense be $3y$ and Paul’s monthly expense be $2y$ (since the expense ratio is $3:2$).

3. The savings for both Peter and Paul are:
$$
\text{Savings of Peter} = \text{Income of Peter} – \text{Expense of Peter} = 4x – 3y.
$$
$$
\text{Savings of Paul} = \text{Income of Paul} – \text{Expense of Paul} = 3x – 2y.
$$

Step 2: Use the given savings

Since both Peter and Paul save Rs. $6000$, we set up the equations:
1. For Peter:
$$
4x – 3y = 6000.
$$
2. For Paul:
$$
3x – 2y = 6000.
$$

Step 3: Solve the equations

From the first equation:
$$
4x – 3y = 6000 \quad \text{(1)}.
$$
From the second equation:
$$
3x – 2y = 6000 \quad \text{(2)}.
$$

Multiply equation (2) by 3 and equation (1) by 2 to eliminate $y$:
$$
9x – 6y = 18000 \quad \text{(3)}.
$$
$$
8x – 6y = 12000 \quad \text{(4)}.
$$

Subtract equation (4) from equation (3):
$$
(9x – 6y) – (8x – 6y) = 18000 – 12000.
$$
$$
x = 6000.
$$

Step 4: Find $y$

Substitute $x = 6000$ into equation (2):
$$
3(6000) – 2y = 6000.
$$
$$
18000 – 2y = 6000.
$$
$$
2y = 12000 \implies y = 6000.
$$

Step 5: Calculate incomes

1. Peter’s income:
$$
4x = 4(6000) = 24000 \, \text{Rs.}
$$

2. Paul’s income:
$$
3x = 3(6000) = 18000 \, \text{Rs.}
$$

Final Answer:

The monthly incomes of Peter and Paul are:
$$
\boxed{\text{(a) 24000 and 18000}}
$$

Explanation:

Problem Analysis

We need to determine the time between 6 PM and 7 PM when the minute hand of a clock is ahead of the hour hand by 3 minutes.

Step 1: Formulate the problem

1. At exactly 6:00 PM, the hour hand is at the 6-hour mark, and the minute hand is at the 12-hour mark.

2. The hour hand moves at a rate of 0.5° per minute(since it completes 360° in 12 hours or 30° per hour).

3. The minute hand moves at a rate of 6° per minute(since it completes 360° in 60 minutes).

4. We are tasked to find the time $t$ (in minutes past 6:00) when the minute hand is 3 minutes ahead of the hour hand. In terms of degrees:
$$
\text{Minute hand position} – \text{Hour hand position} = 3 \times 6 = 18°.
$$

Step 2: Express positions of the hands

1. Minute hand position at time $t$:
$$
\text{Position of minute hand} = 6t \, \text{(in degrees)}.
$$

2. Hour hand position at time $t$:

At 6 PM, the hour hand is at $180°$, and it moves $0.5t$ degrees in $t$ minutes. Thus:
$$
\text{Position of hour hand} = 180 + 0.5t \, \text{(in degrees)}.
$$

3. Condition for the minute hand to be 18° ahead of the hour hand:
$$
6t – (180 + 0.5t) = 18.
$$

Step 3: Solve the equation

Simplify:
$$
6t – 180 – 0.5t = 18.
$$
$$
5.5t = 198.
$$
$$
t = \frac{198}{5.5} = 36 \, \text{minutes}.
$$

Step 4: Determine the time

The time $t = 36$ minutes past 6:00 corresponds to:
$$
6:36 \, \text{PM}.
$$

Step 5: Verify the options

(a) 6:15 PM: Incorrect, as the calculation shows $t = 36$ minutes.
(b) 6:18 PM: Incorrect.
(c) 6:36 PM: Correct.
(d) 6:48 PM: Incorrect.

Final Answer:

The correct time is:
$$
\boxed{\text{(c) 6:36 PM}}
$$

Explanation:

Analyzing the Passage

The passage primarily focuses on the financial challenges faced by developing countries in implementing climate change adaptation and mitigation plans. It emphasizes the debate in multilateral negotiations under the UNFCCC regarding the responsibility of developed countries to provide financial support, given their historical contributions to the stock of greenhouse gases (GHGs). The key focus is the financial and support-related conflict between developed and developing countries.

Options Analysis

(a) Conflict between developed and developing countries regarding support for mitigation.

• This is the central theme of the passage. The passage discusses the responsibility of developed countries to provide financial support for climate change efforts and the debate surrounding this issue in multilateral negotiations.
• This is the correct answer.

(b) Occurrence of climate change due to excessive exploitation of natural resources by the developed countries.

• While the passage mentions the developed countries’ contribution to GHGs, it does not focus on the exploitation of natural resources as the cause of climate change. The discussion revolves around funding responsibilities rather than causes of climate change.
• This is incorrect.

(c) Lack of political will on the part of all the countries to implement adaptation plans.

• The passage does not suggest a lack of political will. Instead, it emphasizes the financial challenges and debates regarding funding responsibilities under the UNFCCC framework.
• This is incorrect.

(d) Governance problems of developing countries as a result of climate change.

• The passage does not discuss governance issues in developing countries. It focuses on the financial and resource challenges these countries face in addressing climate change.
• This is incorrect.

Correct Answer:

(a) Conflict between developed and developing countries regarding support for mitigation.

Explanation:

Analyzing the Passage

The passage discusses the financial challenges faced by developing countries due to climate change, particularly in implementing adaptation and mitigation plans. It emphasizes the inadequacy of domestic finances to address these challenges and highlights the need for global funding mechanisms. However, the passage does not mention multilateral trade or any implications of climate change on trade.

Options Analysis

Statement 1: Domestic finances

• The passage explicitly states that domestic finances of developing countries are insufficient to meet the costs of climate change mitigation and adaptation:
  

  “Given the magnitude of the task and the funds required, domestic finances are likely to fall short…”

• This statement is correct.

Statement 2: Capacity for multilateral trade

• The passage does not mention trade or how climate change might affect the capacity for multilateral trade in developing countries.
• This statement is incorrect.

Correct Answer: (a) 1 only

The passage focuses on the financial constraints of developing countries in addressing climate change and does not discuss trade. Therefore, only Statement 1 is supported by the passage.

Explanation:

Options Analysis

Statement 1: The scale and size of required financial support.

• This is explicitly mentioned in the passage as a key issue in UNFCCC negotiations:
  

  “The scale and magnitude of the financial support required by developing countries… are a matter of intense debate.”

• Therefore, this statement is correct.

Statement 2: The crop loss due to climate change in the developing countries.

• The passage does not mention crop loss as part of the debate in multilateral negotiations. While climate change might indirectly affect agriculture, this specific issue is not addressed in the passage.
• Therefore, this statement is incorrect.

Statement 3: To enhance the mitigation and adaptation actions in the developing countries.

• The passage clearly states that financial support is needed to enhance mitigation and adaptation actions in developing countries. This is directly tied to the debate under UNFCCC:
  

  “Global funding… will enhance their domestic capacity to finance the mitigation efforts.”

• Therefore, this statement is correct.

Correct Answer: (c) 1 and 3 only

• The passage focuses on the scale of financial support and the need to enhance mitigation and adaptation actions. It does not mention crop loss as part of the debate in the UNFCCC negotiations. Thus, statements 1 and 3 are correct, while statement 2 is incorrect.

Explanation:

Analyzing the Passage

The passage discusses the ongoing conflict between the individual and the State, which has persisted throughout history. While attempts have been made to resolve this conflict, a permanent solution remains elusive due to the dynamic nature of human society, where old ideas are constantly replaced by new ones. The passage also argues that absolute freedom of speech and action for individuals would lead to chaos, ruin, and anarchy.

Options Analysis

(a) The conflict between the claims of State and individual remains unresolved.

• This option directly captures the central theme of the passage: that despite centuries of effort, the tension between the rights of individuals and the authority of the State continues due to the evolving nature of society. This aligns well with the author’s viewpoint.

(b) Anarchy and chaos are the obvious results of democratic traditions.

• The passage does not criticize democratic traditions. Instead, it warns against absolute freedom of speech and action, which could lead to anarchy. This option misinterprets the author’s argument.

(c) Old values, ideas and traditions persist despite the dynamic nature of human society.

• The passage explicitly states that old values and ideas are replaced by new ones in a dynamic society. This option contradicts the passage and is incorrect.

(d) Constitutional guarantee of freedom of speech is not in the interest of society.

• The passage does not reject constitutional guarantees of freedom of speech. Instead, it argues against absolute freedom, which would lead to chaos. This option is overly extreme and misrepresents the author’s view.

Correct Answer:

(a) The conflict between the claims of State and individual remains unresolved.

Explanation:

The passage makes it clear that the responsibility for financial support is based on the historical contribution of developed countries to the stock of GHGs, not their per capita incomes or GDP size. Only statement 3 is supported by the passage.

Explanation:

Analyzing the Passage

The passage argues that no Right is absolute, exclusive, or inviolable, including the Right of personal property. It suggests that this Right must align with the principles of liberty, equality, and cooperation, which are foundational to justice. Therefore, personal property rights cannot be viewed in isolation but must be reconciled with the rights of others in a broader socio-economic context.

Options Analysis

(a) The Right of personal property is a Natural Right duly supported by statutes and scriptures.

• This option suggests that the Right of personal property is absolute, which contradicts the passage’s central argument that no Right is absolute or exclusive. Hence, this is incorrect.

(b) Personal property is a theft and an instrument of exploitation. The Right of personal property is therefore violative of economic justice.

• This option reflects an extreme viewpoint that labels personal property as theft. The passage does not suggest that the Right of personal property is inherently exploitative but rather emphasizes the need for balancing it with other principles like liberty, equality, and cooperation. Thus, this is incorrect.

(c) The Right of personal property is violative of distributive justice and negates the principle of cooperation.

• This option is partially aligned with the passage but overly one-sided. The passage does not argue that the Right of personal property inherently violates distributive justice or cooperation; it argues for reconciling personal property rights with these principles. Hence, this option is not convincing.

(d) The comprehensive idea of economic justice demands that the Right of each person to acquisition of property has to be reconciled with that of others.

• This is the most logical interpretation of the passage. It aligns with the idea that no Right is absolute and that the Right of personal property must be balanced with the principles of liberty, equality, and cooperation to ensure economic justice.

Correct Answer:

(d) The comprehensive idea of economic justice demands that the Right of each person to acquisition of property has to be reconciled with that of others.

Explanation:

Analyzing the Passage

The passage discusses persistent high inflation in India and attributes it to several factors, including administered price increases, demand and supply imbalances, imported inflation (exacerbated by rupee depreciation), and speculation. Importantly, the passage notes that many of these factors are outcomes of economic reforms, specifically citing trade liberalization and the effort to reduce subsidies.

The key takeaway is that economic reforms can inadvertently lead to inflationary pressures, especially in a socio-economic context like India’s.

Options Analysis

(a) Under the present circumstances, India should completely avoid all trade liberalisation policies and all subsidies.

• This is too extreme. The passage does not suggest completely avoiding trade liberalization or subsidies, but rather implies that these reforms have consequences that need to be managed.

(b) Due to its peculiar socio-economic situation, India is not yet ready for trade liberalisation process.

• The passage does not explicitly argue against trade liberalization in principle. It only highlights the inflationary challenges that result from such reforms. Therefore, this is an incorrect interpretation.

(c) There is no solution in sight for the problems of continuing poverty and inflation in India in the near future.

• The passage does not claim that there is no solution. It focuses on the link between economic reforms and inflation, without suggesting hopelessness regarding the issue.

(d) Economic reforms can often create a high inflation economy.

• This is the correct answer. The passage directly implies that economic reforms, such as trade liberalization and subsidy reduction, have contributed to India’s high inflation. This aligns with the most logical and rational interpretation of the passage.

Correct Answer: (d) Economic reforms can often create a high inflation economy.

Explanation:

Problem Analysis

The problem provides a set of comparisons about the running speeds of Usha, Kamala, Priti, and Swati. We are tasked with determining the slowest runner based on the given information.

Step 1: Restate the relationships

1. Usha runs faster than Kamala:

$U > K$

(Usha is faster than Kamala).

2. Priti runs slower than Swati:

$P < S$

(Priti is slower than Swati).

3. Swati runs slower than Kamala:

$S < K$

(Swati is slower than Kamala).

Step 2: Combine the relationships

Using the inequalities:

From (1), Kamala is slower than Usha: $U > K$.
From (3), Swati is slower than Kamala: $S < K$.
From (2), Priti is slower than Swati: $P < S$.

By combining these:
$$
P < S < K < U
$$

This implies:

– Priti is the slowest runner.

Step 3: Verify the options

(a) “Kamala”:

This is incorrect because Kamala is faster than both Swati and Priti.

(b) “Priti”:

This is correct because Priti is slower than all the others.

(c) “Swati”:

This is incorrect because Swati is faster than Priti but slower than Kamala and Usha.

(d) “Usha”:

This is incorrect because Usha is the fastest runner.

Final Answer:

The slowest runner is:
$$
\boxed{\text{(b) Priti}}
$$

Explanation:

Analyzing the given statements:

1. Life on other heavenly bodies is considered to be a possibility.
   • Suggests that there is a chance, though not confirmed, that life might exist on other heavenly bodies.
2. Voyage to space is now an established fact.
   • Indicates that humans have traveled to space, which is a proven fact.

Conclusions:

(a) UFOs are heavenly bodies.

• The statements do not mention UFOs directly or imply they are heavenly bodies. This conclusion cannot be drawn.

(b) UFOs are sent from other heavenly bodies.

• There is no direct or implied connection between UFOs and the possibility of life on other heavenly bodies. This conclusion cannot be drawn either.

(c) Some living species in other heavenly bodies are more intelligent than man.

• While life on other heavenly bodies is considered a possibility, there is no information in the statements about the existence or intelligence of such species. This conclusion cannot be drawn.

(d) Nothing definite can be said about the UFOs.

• The statements do not provide any evidence or information about UFOs. Therefore, nothing definite can be concluded about them.

Correct Answer: (d) Nothing definite can be said about the UFOs.

Explanation:

Problem Analysis

The problem involves comparing the expenditure on food by two families, A and B, based on the proportions and total monthly expenditures provided in the bar charts. The details are as follows:

Family A:
– Total monthly expenditure: ₹20,000
– Proportion spent on food: $50%$
– Amount spent on food:
$$
50% \times 20,000 = 0.5 \times 20,000 = ₹10,000
$$

Family B:
– Total monthly expenditure: ₹1,00,000
– Proportion spent on food: $10%$
– Amount spent on food:
$$
10% \times 1,00,000 = 0.1 \times 1,00,000 = ₹10,000
$$

Step 1: Compare the expenditures on food

From the calculations:

– Family A spends ₹10,000 on food.
– Family B also spends ₹10,000 on food.

Thus, both families spend the same amount on food.

Step 2: Evaluate the options

(a) “Family A spent more money on food than Family B”:

This is incorrect, as both families spent the same amount on food.

(b) “Family B spent more money on food than Family A”:

This is also incorrect, as the amounts are equal.

(c) “Family A and Family B spent the same amount on food”:

This is correct, as both families spent ₹10,000 on food.

(d) “The expenditure on food by Family A and Family B cannot be compared”:

This is incorrect, as the expenditures are directly calculated from the given data.

Final Answer:

The correct option is:
$$
\boxed{\text{(c) Family A and Family B spent the same amount on food.}}
$$

Explanation:

Problem Breakdown:

We are tasked with finding the values of $D$ and $E$ such that: ABC × DEED = ABC ABC where ABC ABC is the number formed by writing ABC twice (a six-digit number). Here, $A$, $B$, $C$, $D$, and $E$ are different digits.

Step-by-step Solution:

1. Structure of $ABC$:
   • ABC ABC can be expressed mathematically as: ABC ABC = ABC × 1001
   • Therefore, the equation becomes: ABC × DEED = ABC × 1001
   • Dividing both sides by ABC(since ABC ≠ 0): DEED = 1001
2. Properties of DEED:
   • DEED is a four-digit number in the form D E E D.
   • The only valid value for DEED to equal 1001 is D = 1 and $0$.
3. Verification:
   • Substituting D = 1 and E = 0, DEED = 1001, which satisfies the given equation.

Correct Answer: (c) D = 1, E = 0

Explanation:

Problem Analysis

Two pipes, A and B, can independently fill a tank in 20 minutes and 30 minutes, respectively. When both pipes are opened simultaneously, we need to calculate the total time required to fill the tank completely.

Step 1: Determine the rates of A and B

– The rate of pipe A is:
$$
\text{Rate of A} = \frac{1}{20} \, \text{(tank per minute)}.
$$

– The rate of pipe B is:
$$
\text{Rate of B} = \frac{1}{30} \, \text{(tank per minute)}.
$$

When both pipes are opened together, their combined rate of filling the tank is:
$$
\text{Combined rate} = \frac{1}{20} + \frac{1}{30}.
$$

Step 2: Simplify the combined rate

Find the least common denominator (LCD) of 20 and 30:
$$
\text{LCD of 20 and 30} = 60.
$$

Convert the fractions:
$$
\frac{1}{20} = \frac{3}{60}, \quad \frac{1}{30} = \frac{2}{60}.
$$

Add the rates:
$$
\text{Combined rate} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60}.
$$

Simplify:
$$
\text{Combined rate} = \frac{1}{12}.
$$

This means the two pipes together can fill $\frac{1}{12}$ of the tank per minute.

Step 3: Calculate the total time

The total time taken to fill the tank completely is the reciprocal of the combined rate:
$$
\text{Time taken} = \frac{1}{\text{Combined rate}} = \frac{1}{\frac{1}{12}} = 12 \, \text{minutes}.
$$

Final Answer:

The total time required to fill the tank is:
$$
\boxed{(b) 12 \text{minutes}}
$$

Explanation:

Problem Analysis

We are tasked with finding the number of pairs of brown socks in the original order. Let’s denote:

– The number of pairs of black socks as $5$ (given).
– The number of pairs of brown socks as $x$ (unknown, to be determined).
– The price of one pair of brown socks as $b$.
– The price of one pair of black socks as $3b$ (since black socks are thrice as expensive as brown socks).

Step 1: Calculate the original bill

The total cost of the original order is:
$$
\text{Original Bill = 5} \cdot \text{(3b) + x} \cdot \text{b = 15b + xb}.
$$

Step 2: Calculate the incorrect bill

When the clerk interchanges the number of black and brown socks, the bill is calculated as:
$$
\text{Incorrect Bill = x} \cdot \text{(3b) + 5} \cdot \text{b = 3xb + 5b.}
$$

Step 3: Analyze the given condition

We are told that the incorrect bill is 100% more than the original bill. This means the incorrect bill is double the original bill:
$$
\text{Incorrect Bill = 2} \cdot \text{Original Bill}.
$$

Substitute the values of the bills:
$$
\text{3xb + 5b = 2} \cdot \text{ (15b + xb).}
$$

Simplify the equation:
$$
\text{3xb + 5b = 30b + 2xb.}
$$

Combine like terms:
$$
\text{3xb – 2xb = 30b – 5b.}
$$

$$
\text{xb = 25b.}
$$

Cancel $b$ (since $b \neq 0$):
$$
x = 25.
$$

Step 4: Verify the result

If $x = 25$, then:

1. Original Bill:
$$
\text{15b + 25b = 40b.}
$$

2. Incorrect Bill:
$$
3 \cdot \text{25b + 5b = 75b + 5b = 80b.}
$$

The incorrect bill is indeed double the original bill:
$$
\text{80b = 2} \cdot \text{40b.}
$$

Thus, the calculation is correct.

Final Answer:

The number of pairs of brown socks in the original order is:
$$
\boxed{\text{(d) 25}}
$$

Explanation:

Problem Analysis

A student has to select 2 subjects out of 5 available subjects: Commerce (C), Economics (E), Statistics (S), Mathematics I (M1), and Mathematics II (M2). However, there is a restriction:

– Mathematics II (M2) can only be selected if Mathematics I (M1) is also selected.

We need to calculate the number of valid combinations of 2 subjects under this condition.

Step 1: List all possible combinations

Without the restriction, the total number of combinations of 2 subjects from 5 is:
$$
\binom{5}{2} = \frac{5 \cdot 4}{2} = 10.
$$

However, the restriction eliminates certain combinations. Specifically:
– M2 cannot be selected without M1, meaning any combination involving M2 but not M1 is invalid.

Step 2: Identify valid combinations

Let us evaluate the valid combinations manually:

1. Combinations not involving M2:

These are all combinations of the remaining 4 subjects (C, E, S, and M1):
$$
\{C, E\}, \{C, S\}, \{C, M1\}, \{E, S\}, \{E, M1\}, \{S, M1\}.
$$
There are 6 such combinations.

2. Combinations involving M2:

Since M2 can only be chosen if M1 is also chosen, the only valid combinations with M2 are:
$$
\{M1, M2\}.
$$
There is 1 such combination.

Step 3: Total valid combinations

Adding these:
$$
\text{Total valid combinations} = 6 + 1 = 7.
$$

Final Answer:

The number of valid combinations is:
$$
\boxed{\text{(c) 7}}
$$

Explanation:

1. Understanding the passage:
   • The passage discusses the need for governments to sometimes infringe on individual rights for larger public interest, but emphasizes that such actions must be authorized and regulated by rules and safeguards.
   • It highlights the risks of discretionary powers being misused and stresses the importance of conducting government work within a framework of rules and principles to ensure consistency and predictability.
2. Analyzing the options:
   • (a) Government should always be given wide discretionary power in all matters of administration:
     Incorrect. The passage explicitly argues against wide discretionary powers and calls for limits, rules, and safeguards to minimize abuse.
   • (b) The supremacy of rules and safeguards should prevail as opposed to the influence of exclusive discretion of authority:
     Correct. This aligns with the passage’s core argument that discretion must be limited and subject to rules and safeguards to prevent misuse.
   • (c) Parliamentary democracy is possible only if the Government has wider discretionary power:
     Incorrect. The passage does not suggest that wide discretionary powers are essential for parliamentary democracy; rather, it emphasizes minimizing discretion and ensuring decisions are rule-based.
   • (d) None of the above statements is a logical assumption that can be made from this passage:
     Incorrect. Statement (b) logically follows from the passage.
3. Conclusion:

   The correct answer is: (b) The supremacy of rules and safeguards should prevail as opposed to the influence of exclusive discretion of authority.

Explanation:

Problem Analysis

We are tasked with selecting:

1. One Principal from two eligible candidates.

2. Two Vice-Principal from six candidates(since all six are eligible for the Vice-Principal posts).

We need to determine the total number of possible combinations.

Step 1: Selection of the Principal

There are 2 eligible candidates for the post of Principal. The number of ways to select one Principal is:
$$
\binom{2}{1} = 2
$$

Step 2: Selection of the Vice-Principals

After the Principal is selected, there are still 5 remaining candidates eligible for the two Vice-Principal posts. The number of ways to select two Vice-Principals from the remaining 5 candidates is:
$$
\binom{5}{2} = \frac{5 \cdot 4}{2} = 10
$$

Step 3: Total Number of Combinations

The total number of combinations is the product of the ways to select the Principal and the ways to select the Vice-Principals:
$$
\text{Total combinations} = \binom{2}{1} \cdot \binom{5}{2} = 2 \cdot 10 = 20
$$

Step 4: Verify the options

The problem specifies the number of combinations, but the correct answer does not appear in the provided options (the closest match is “None of the above”).

Final Answer:

The correct number of combinations is: None of the above

Explanation:

1. Understanding the passage:
   • The passage emphasizes the importance of formal financial institutions in mobilizing savings, particularly in rural areas of developing countries like India.
   • It states that access to safe, reliable financial institutions and appropriate financial instruments is limited for rural households. Without such access, poor households are more likely to spend their savings due to immediate spending temptations.
2. Analyzing the statements:
   • Statement 1: “Indian financial institutions do not offer any financial instruments to rural households to mobilize their savings.”
     Incorrect. The passage mentions that access to financial institutions and instruments is limited, particularly in rural areas, but it does not claim that no financial instruments are offered to rural households.
   • Statement 2: “Poor households tend to spend their earnings/savings due to lack of access to appropriate financial instruments.”
     Correct. The passage explicitly states that poor households without access to formal savings mechanisms are prone to immediate spending temptations.
3. Conclusion: Only Statement 2 is correct. Therefore, the correct answer is (b) 2 only.

Explanation:

1. Understanding the passage:
   • The passage highlights the lack of access to safe and reliable financial institutions and instruments, especially in rural areas of developing countries like India.
   • It emphasizes the role of formal financial institutions in mobilizing savings, managing cash flow volatility, and helping poor households avoid spending temptations.
   • The central theme revolves around the importance of providing equitable access to financial services, which is the essence of financial inclusion.
2. Analyzing the options:
   • (a) Establish more banks:
     While establishing more banks might help, the passage does not focus solely on increasing the number of banks but rather on improving access to financial services, which is broader than this option.
   • (b) Increase the Gross Domestic Product (GDP) growth rate:
     Incorrect. The passage does not discuss GDP growth or its relationship to financial inclusion or savings.
   • (c) Increase the interest rate of bank deposits:
     Incorrect. The passage emphasizes access to financial services and instruments, not changes to interest rates as a mechanism to mobilize savings.
   • (d) Promote financial inclusion:
     Correct. The passage directly emphasizes the need to provide access to safe, reliable financial institutions and instruments for all, especially rural and poor households, which is the core of financial inclusion.
3. Conclusion: The crucial message conveyed in the passage is (d) Promote financial inclusion.

Explanation:

1. Understanding the passage:
   • The passage critiques the practice of favoring people based on caste, community, or religion rather than merit. It argues that this favoritism undermines democracy, making it “phoney.”
   • It emphasizes the need to respect individuals as humans and extend opportunities for development based on merit, which is essential for establishing true democracy.
2. Analyzing the options:
   • (a) Our country has a lot of diversity with its many castes, communities, and religions:
     Incorrect. While the passage acknowledges diversity, its focus is on favoritism and its impact on democracy, not simply diversity.
   • (b) True democracy could be established by providing equal opportunities to all:
     Correct. This aligns with the passage’s core argument that favoritism erodes democracy and that equality in opportunities is essential for a true democracy.
   • (c) So far none of us have actually understood the meaning of democracy:
     Incorrect. The passage critiques specific practices within democracy, not the understanding of its meaning.
   • (d) It will never be possible for us to establish truly democratic governance in our country:
     Incorrect. The passage does not suggest that true democracy is impossible but highlights the need for addressing favoritism to achieve it.
3. Conclusion:

   The correct answer is: (b) True democracy could be established by providing equal opportunities to all.

Explanation:

1. Understanding the passage:
   • The passage emphasizes the negative health impacts of open defecation, including the spread of diseases, malnutrition, stunted growth, and cognitive development issues.
   • These health problems contribute to a reduction in physical and cognitive capacity, ultimately affecting the human capital and productivity of the workforce.
2. Analyzing the options:
   • (a) The Central and State governments in India do not have enough resources to afford a latrine for each household:
     Incorrect. The passage does not discuss the affordability of latrines or the resource constraints of governments.
   • (b) Open defecation is the most important public health problem of India:
     Incorrect. While open defecation is presented as a significant issue, the passage does not label it as the “most important” public health problem.
   • (c) Open defecation reduces the human capital of India’s workforce:
     Correct. The passage links open defecation to malnutrition, stunted growth, reduced cognitive development, and health problems, which directly reduce the productivity and potential of the workforce.
   • (d) Open defecation is a public health problem in all developing countries:
     Incorrect. The passage specifically focuses on India and does not generalize the problem to all developing countries.
3. Conclusion:The correct answer is: (c) Open defecation reduces the human capital of India’s workforce.

Explanation:

1. Understanding the statement:
   • The statement emphasizes creating an environment where individuals have the opportunity to become their “best selves.”
   • This implies that liberty is not merely the absence of restrictions or laws but the presence of conditions that enable personal growth and self-realization.
2. Analyzing the options:
   • (a) Liberty is the absence of restraint on human action:
     Incorrect. While the absence of restraint may be a component of liberty, the statement focuses on maintaining an atmosphere that fosters self-growth, not just the absence of restrictions.
   • (b) Liberty is what law permits people to perform:
     Incorrect. This view ties liberty strictly to legal permissions, which is narrower than the concept described in the statement.
   • (c) Liberty is the ability to do what one desires:
     Incorrect. Liberty as described in the statement is not about unbridled freedom or fulfilling desires but about creating conditions for individuals to achieve their potential.
   • (d) Liberty is the maintenance of conditions for the growth of human personality:
     Correct. The statement aligns with this view, as it emphasizes fostering an atmosphere for individuals to develop their best selves.
3. Conclusion:

   The correct answer is: (d) Liberty is the maintenance of conditions for the growth of human personality.

Explanation:

1. Understanding the passage:
   • The passage highlights the increasing share of portfolio investments from advanced economies in emerging economies, including India.
   • It flags this trend as a potential threat to global financial stability, particularly in the context of the United States Federal Reserve’s potential reversal of its “Quantitative Easing” policy, which could trigger a chain reaction affecting emerging economies.
2. Analyzing the options:
   • (a) Foreign portfolio investments are not good for emerging economies:
     Incorrect. The passage does not say foreign portfolio investments are inherently bad for emerging economies. It highlights the associated risks if global policies change suddenly.
   • (b) Advanced economies undermine the global financial stability:
     Incorrect. The passage does not suggest advanced economies deliberately undermine global stability. It focuses on potential risks stemming from their policy changes.
   • (c) India should desist from accepting foreign portfolio investments in the future:
     Incorrect. The passage does not recommend India or other emerging economies to stop accepting foreign investments. It only highlights the risks of over-reliance.
   • (d) Emerging economies are at a risk of shock from advanced economies:
     Correct. The passage specifically discusses the potential vulnerability of emerging economies like India to shocks caused by policy changes in advanced economies, such as the US Federal Reserve’s reversal of “Quantitative Easing.”
3. Conclusion:

   The correct answer is: (d) Emerging economies are at a risk of shock from advanced economies.

Explanation:

1. Understanding the passage:
   • The passage highlights a feedback loop where climate change worsens poverty by disrupting crops and increasing hunger, while poverty exacerbates climate change through unsustainable resource use.
   • This interdependence calls for systemic changes to address both issues simultaneously.
2. Analyzing the options:
   • (a) Government should allocate more funds to poverty alleviation programmes and increase food subsidies to the poor communities:
     While this might help in the short term, it does not address the systemic relationship between poverty and climate change mentioned in the passage.
   • (b) Poverty and climate impacts reinforce each other and therefore we have to re-imagine our food systems:
     Correct. This directly captures the idea of the cyclical relationship between poverty and climate change and suggests systemic changes to food systems to break this cycle.
   • (c) All the countries of the world must unite in fighting poverty and malnutrition and treat poverty as a global problem:
     While this is true in a broader sense, the passage specifically focuses on the interplay between poverty and climate change, not on treating poverty as a solely global problem.
   • (d) We must stop unsustainable agricultural practices immediately and control food prices:
     While important, this option addresses only part of the issue and does not encompass the broader systemic relationship between poverty and climate impacts.
3. Conclusion:

   The correct answer is: (b) Poverty and climate impacts reinforce each other and therefore we have to re-imagine our food systems

Explanation:

1. Understanding the statement:
   • The passage describes how mangroves contribute to coastal food chains by shedding leaves, which are broken down and consumed by fungi and bacteria. This process creates a cascading food chain that supports various marine and terrestrial species.
2. Analyzing the options:
   • (a) Coastal areas cannot have food chains without mangroves:
     Incorrect. The passage highlights the importance of mangroves in some food chains but does not imply that all coastal areas or food chains depend on mangroves.
   • (b) Mangroves are an essential component of all marine ecosystems:
     Incorrect. The passage does not generalize mangroves as essential to all marine ecosystems, only to specific coastal food chains.
   • (c) Mangroves have a crucial role in some of the coastal food chains:
     Correct. The passage explicitly describes how mangroves are vital to certain coastal food chains by providing a base for nutrient cycling and energy flow.
   • (d) The composition of marine flora and fauna is largely determined by mangroves:
     Incorrect. The passage does not claim that mangroves dictate the overall composition of marine life; it focuses on their role in specific food chains.
3. Conclusion:

   The correct answer is: (c) Mangroves have a crucial role in some of the coastal food chains.

Explanation:

Variables:

1. Let the number of cars (four-wheelers) = $x$.
2. Let the number of scooters/motorbikes (two-wheelers) = y.

Given:

1. Total number of vehicles = x + y.
2. Total number of wheels = 4x + 2y.
3. The total number of wheels is 100 more than twice the number of parked vehicles: 4x + 2y = 2(x + y) + 100

Step 1: Simplify the equation

Expand and simplify the equation:

4x + 2y = 2x + 2y + 100

4x − 2x = 100

2x = 100

x = 50

Step 2: Verify the solution

• The number of cars is x = 50.
• The total number of vehicles is x + y.
• Total wheels = 4x + 2y = 2(x + y) + 100, which holds true.

Final Answer:

The number of cars parked is (c) 50.

Explanation:

Problem Analysis

Two glasses of the same type are partially filled with milk, and the remaining space is filled with water. The glasses are then mixed into a pot. We are tasked to find the ratio of milk to water in the pot.

Step 1: Understand the problem

– Each glass is of equal volume. Let the volume of each glass be $V$.
– The first glass is $\frac{1}{3}$ full of milk, so the volume of milk in the first glass is:
$$
\text{Milk in first glass} = \frac{1}{3}V.
$$
The remaining $\frac{2}{3}$ of the first glass is filled with water:
$$
\text{Water in first glass} = \frac{2}{3}V.
$$

– The second glass is $\frac{1}{4}$ full of milk, so the volume of milk in the second glass is:
$$
\text{Milk in second glass} = \frac{1}{4}V.
$$
The remaining $\frac{3}{4}$ of the second glass is filled with water:
$$
\text{Water in second glass} = \frac{3}{4}V.
$$

Step 2: Combine the contents of both glasses

When both glasses are mixed in the pot:
– The total volume of milk is:
$$
\text{Total milk} = \frac{1}{3}V + \frac{1}{4}V.
$$
Find a common denominator to simplify:
$$
\text{Total milk} = \frac{4}{12}V + \frac{3}{12}V = \frac{7}{12}V.
$$

– The total volume of water is:
$$
\text{Total water} = \frac{2}{3}V + \frac{3}{4}V.
$$
Find a common denominator to simplify:
$$
\text{Total water} = \frac{8}{12}V + \frac{9}{12}V = \frac{17}{12}V.
$$

Step 3: Calculate the ratio of milk to water

The ratio of milk to water is:
$$
\text{Ratio of milk to water} = \frac{\text{Total milk}}{\text{Total water}} = \frac{\frac{7}{12}V}{\frac{17}{12}V}.
$$
Cancel $V$ and $\frac{1}{12}$:
$$
\text{Ratio of milk to water} = \frac{7}{17}.
$$

Final Answer:

The ratio of milk to water in the pot is:
$$
\boxed{7 : 17}
$$

Explanation:

Given:

• Total number of students = 130
• Students who failed in English = 62
• Students who failed in Mathematics = 52
• Students who failed in both English and Mathematics = 24

Step 1: Number of students who failed in at least one subject

The total number of students who failed in at least one subject is given by:

Students failing in at least one subject=(Failed in English)+(Failed in Mathematics)−(Failed in both English and Mathematics)

Substitute the values:

Students failing in at least one subject=62+52−24=90

Step 2: Number of students who passed

The students who passed are those who did not fail in any subject:

Students who passed = Total students − Students failing in at least one subject

Substitute the values:

Students who passed = 130 − 90 = 40

Final Answer:

The number of students who passed is (a) 40.

Explanation:

Problem Analysis

In a 500-meter race:

– B starts $45$ meters ahead of A.
– By the time A finishes the race, B is still $35$ meters behind A.
– We are to find the ratio of the speed of A to the speed of B.

Step 1: Understand the scenario

– The total distance covered by A is $500$ meters.
– Since B is $35$ meters behind A when A finishes, the total distance covered by B is:
$$
500 – 35 = 465 \, \text{meters}.
$$

Let the time taken by both A and B to complete their respective distances be $t$ (since they started at the same time).
Let the speed of A be $v_A$ and the speed of B be $v_B$.

Using the formula for speed:
$$
v_A = \frac{\text{Distance covered by A}}{\text{Time taken}} = \frac{500}{t}
$$
$$
v_B = \frac{\text{Distance covered by B}}{\text{Time taken}} = \frac{465}{t}.
$$

Step 2: Calculate the ratio of speeds

The ratio of the speed of A to B is:
$$
\frac{v_A}{v_B} = \frac{\frac{500}{t}}{\frac{465}{t}} = \frac{500}{465}.
$$

Simplify:
$$
\frac{v_A}{v_B} = \frac{500}{465} = \frac{100}{93}.
$$

Step 3: Final Ratio

The ratio of the speed of A to B is:
$$
\boxed{25 : 21}
$$

Final Answer:

The correct option is: $\boxed{\text{(a) 25 : 21}}$

Explanation:

Problem Analysis

We are tasked with finding the percentage of people in a town who do not read any magazine, given the percentage of people reading magazines $A$, $B$, and $C$, and their overlaps.

Step 1: Represent the given data

– $P(A) = 45%$: People who read magazine $A$.
– $P(B) = 55%$: People who read magazine $B$.
– $P(C) = 40%$: People who read magazine $C$.
– $P(A \cap B) = 30%$: People who read both $A$ and $B$.
– $P(B \cap C) = 15%$: People who read both $B$ and $C$.
– $P(A \cap C) = 25%$: People who read both $A$ and $C$.
– $P(A \cap B \cap C) = 10%$: People who read all three magazines.

Step 2: Use the inclusion-exclusion principle

The formula for the union of three sets $A$, $B$, and $C$ is:
$$
P(A \cup B \cup C) = P(A) + P(B) + P(C) – P(A \cap B) – P(B \cap C) – P(A \cap C) + P(A \cap B \cap C)
$$

Substitute the given values:
$$
P(A \cup B \cup C) = 45 + 55 + 40 – 30 – 15 – 25 + 10
$$

Simplify:
$$
P(A \cup B \cup C) = 80%
$$

Step 3: Calculate the percentage of people who do not read any magazine

The total population is $100%$. The percentage of people who do not read any magazine is:
$$
100% – P(A \cup B \cup C) = 100% – 80% = 20%
$$

Final Answer:

The percentage of people who do not read any magazine is: 20%

Explanation:

Let’s calculate the final amounts of money each individual has after the transactions to determine which statement is not correct.

Initial amounts:

• Each of A, B, C, and D has Rs. 100.

Transactions:

1. A pays Rs. 20 to B:
   • A=100−20=80
   • B=100+20=120
2. B pays Rs. 10 to C:
   • B=120−10=110
   • C=100+10=110
3. D pays Rs. 30 to C:
   • D=100−30=70
   • C=110+30=140

Final amounts:

• A=80
• B=110
• C=140
• D=70

Evaluating the options:

1. (a) C is the richest:
   • Correct, as C=140, which is the highest amount.
2. (b) D is the poorest:
   • Correct, as D=70, which is the lowest amount.
3. (c) C has more than what A and D have together:
   • A + D = 80 + 70 = 150.
   • C = 140.
   • Incorrect, because $C$ does not have more than A+D.
4. (d) B is richer than D:
   • Correct, as B=110B and D=70.

Conclusion:

The statement that is not correct is (c) C has more than what A and D have together.

Explanation:

1. Analyzing the assumptions:
   • Assumption 1: “Higher economic growth is essential to ensure reduction in economic disparity.”
     This assumption is not valid, as the passage explicitly states that focusing exclusively on economic growth is problematic and often leads to adverse distributional effects (which can increase disparities). The passage suggests that economic growth alone does not necessarily reduce economic disparity and emphasizes the importance of balanced approaches.
   • Assumption 2: “Environmental degradation is sometimes a consequence of economic growth.”
     This assumption is valid. The passage mentions that an unbalanced emphasis on economic growth is often associated with negative environmental consequences, thereby supporting this assumption.
2. Conclusion:
   • Only Assumption 2 is valid. Therefore, the correct answer is (b) 2 only.

Explanation:

1. Context of the passage:
   • The passage emphasizes that human development cannot rely solely on economic growth, as growth is not always positively correlated with human development and may lead to negative environmental and distributional effects.
   • It also highlights the importance of balanced approaches that include investments in non-income aspects of human development, such as health and education.
2. Analyzing the statements:
   • Statement 1: “In developing countries, a strong institutional framework is the only requirement for human development and policy options.”
     This is incorrect. The passage mentions institutional, structural, and political constraints, but it does not state that a strong institutional framework is the only requirement for human development. Other factors, like balanced approaches and investments in non-income areas, are also crucial.
   • Statement 2: “Human development and economic growth are not always positively inter-related.”
     This is correct. The passage explicitly states that focusing exclusively on economic growth is problematic and that the relationship between human development and economic growth is not straightforward.
   • Statement 3: “Focusing only on human development should be the goal.”
     This is incorrect. The passage argues for a balanced approach that integrates both income and non-income aspects of human development, rather than focusing solely on one.
3. Conclusion:
   • Only Statement 2 is correct. Therefore, the correct answer is (c) 2 only.

Explanation:

1. Context of the passage:
   • The passage highlights challenges faced by rural citizens in transitioning to electronic wage payments under MGNREGS.
   • Despite having bank accounts, many recipients lack the financial and technological literacy needed to manage the process independently and still rely on village leaders, as they did under the paper-based system.
2. Analyzing the options:
   • (a) MGNREGS should be extended only to those who have a bank account: This is not implied in the passage, as the issue is not merely the presence of a bank account but the lack of financial literacy to use it effectively.
   • (b) The paper-based system of payments is more efficient than electronic payment in the present scenario: The passage does not suggest this. The inefficiency arises from a lack of financial literacy, not from the electronic payment system itself.
   • (c) The goal of electronic wage payments was not to eliminate mediation by village leaders: This is incorrect. The goal of electronic payments is to eliminate mediation and ensure direct transfers, but the lack of literacy prevents recipients from utilizing the system properly.
   • (d) It is essential to provide financial literacy to the rural poor: This aligns with the core issue presented in the passage. The lack of financial and functional literacy is the root cause of continued dependence on village leaders despite the availability of electronic wage payments.

Conclusion:

The correct answer is: (d) It is essential to provide financial literacy to the rural poor.

Explanation:

1. Context of the passage:
   • The passage describes the social and loyal behavior of flamingos in large flocks, emphasizing their group activities such as mating dances and protective creches for chicks while searching for food.
   • These behaviors enhance the survival and protection of their offspring.
2. Analyzing the options:
   • (a) Mass nesting in all species of birds is essential to ensure complete survival of their offspring: The passage does not generalize to all bird species, nor does it claim mass nesting is essential for complete survival.
   • (b) Only birds have the capacity to develop social behaviour and thus can do mass nesting to raise their chicks in safety: The passage does not claim that only birds can develop social behavior or perform mass nesting.
   • (c) Social behaviour in some species of birds increases the odds of survival in an unsafe world: This is a logical corollary because the passage highlights how flamingos’ social behavior, such as group mating dances and creches, improves the survival odds of their chicks.
   • (d) All species of birds set up creches for their chicks to teach them social behaviour and loyalty: The passage specifically discusses flamingos and does not make a generalization about all bird species.

Conclusion:

The correct answer is: (c) Social behaviour in some species of birds increases the odds of survival in an unsafe world.

Explanation:

1. Context of the passage:
   • The passage emphasizes that the government should not rule by fear or demand obedience but instead aim to free individuals from fear.
   • It aims to provide security so that citizens can live freely and develop their minds and bodies without harm.
   • It rejects the idea of control or turning citizens into irrational beings or puppets, advocating for unshackled reasoning and personal development.
2. Analyzing the options:
   • (a) The true aim of government is to secure the citizens their social and political freedom: This aligns with the passage, which speaks of enabling individuals to live without fear, develop freely, and employ reason without restrictions. Social and political freedom inherently includes these aspects.
   • (b) The primary concern of government is to provide absolute social security to all its citizens: The passage does not prioritize “absolute social security” as the goal; instead, it focuses on freedom and security for development and rationality.
   • (c) The best government is the one that allows the citizens to enjoy absolute liberty in all matters of life: While the passage advocates for freedom, it does not suggest “absolute liberty in all matters,” which could lead to harm or disregard for the rights of others.
   • (d) The best government is the one that provides absolute physical security to the people of the country: The passage does not focus solely on physical security; it also emphasizes freedom, development, and unshackled reasoning.

Conclusion:

The most logical and rational inference is (a) because it encapsulates the government’s role in ensuring citizens’ freedom and security, as described in the passage.

Explanation:

1. Context of the passage:
   • The story revolves around the societal pressure to have a male heir, which is deeply rooted in a patriarchal mindset.
   • Manak’s mother orchestrates his second marriage without regard for Guleri’s feelings, showing the prioritization of family lineage over an individual’s emotions.
   • Guleri’s tragic response to the second marriage reflects the emotional toll of such societal norms on women.
   • The line “Take him away! He stinks of kerosene” shows Manak’s guilt and emotional devastation caused by the rigid societal structure.
2. Analyzing the options:
   • (a) Male chauvinism and infidelity: While Manak is passive, the story is less about male dominance or infidelity and more about societal pressure to conform to patriarchal expectations.
   • (b) Love and betrayal: Although love and heartbreak are present, the story’s core message is about societal norms rather than personal betrayal.
   • (c) Lack of legal safeguards for women: The story does not directly discuss legal aspects or safeguards for women.
   • (d) Influence of patriarchal mindset: The societal pressure to continue the family name and the devaluation of a childless woman are directly rooted in patriarchal traditions, making this the most appropriate answer.

Thus, the correct answer is: (d) influence of patriarchal mindset.

Explanation:

1. Context of the passage:
   • The passage highlights the inadequacies in municipal corporations, including understaffing, lack of skilled personnel, and insufficient recruitment frameworks.
   • It stresses that urban service delivery is complex and requires technical, managerial, and professional skills, which are currently not emphasized in hiring practices.
2. Analyzing the options:
   • (a) The task of providing urban services is a complex issue which requires the organisational expansion of municipal bodies all over the country: While the passage mentions complexity, it focuses more on the need for skilled personnel rather than organizational expansion. This option is too broad.
   • (b) Our cities can provide better quality of life if our local government bodies have adequate staff with required skills and competencies: This directly aligns with the core argument of the passage—that better staffing with the right skills and competencies can improve urban service delivery and infrastructure.
   • (c) Lack of skilled staff is due to the absence of institutions which offer the requisite skills in city management: The passage does not discuss the absence of training institutions as a cause of the problem.
   • (d) Our country is not taking advantage of the demographic dividend to manage the problems associated with rapid urbanization: The passage does not mention demographic dividend or rapid urbanization as a focus.

Conclusion:

The correct answer is: (b) Our cities can provide better quality of life if our local government bodies have adequate staff with required skills and competencies.

Explanation:

1. Premises given:
   • All good athletes want to win.
   • All athletes who want to win eat a well-balanced diet.
   • Therefore, all athletes who do not eat a well-balanced diet are bad athletes.
2. Logical flow of the argument:
   • If someone is a good athlete, they must want to win.
   • If they want to win, they must eat a well-balanced diet.
   • Hence, anyone who does not eat a well-balanced diet cannot be a good athlete (they are classified as bad athletes).
3. Analyzing the options:
   • (a) No bad athlete wants to win: This is incorrect because the argument does not say anything about bad athletes’ desire to win or not.
   • (b) No athlete who does not eat a well-balanced diet is a good athlete: This directly follows from the argument since eating a well-balanced diet is a condition for being a good athlete.
   • (c) Every athlete who eats a well-balanced diet is a good athlete: This is incorrect because eating a well-balanced diet is necessary but not sufficient to be a good athlete.
   • (d) All athletes who want to win are good athletes: This is incorrect because wanting to win does not automatically make someone a good athlete; it is just one condition.

Thus, the correct answer is (b). no athlete who does not eat a well-balanced diet is a good athlete.

Explanation:

1. Context of the passage:
   • The passage discusses the responsibility of richer states in promoting clean energy and reducing carbon emissions.
   • Richer states have better financial resources and are therefore more capable of adopting renewable energy solutions and even assisting poorer states.
   • The challenges, like financial losses in State Electricity Boards, are mentioned as hindrances to adopting renewable energy.
2. Analyzing the options:
   • (a) The richer States must lead in the production and adoption of renewable energy: This is a logical and rational assumption based on the passage. Since richer states have the resources, they should take the lead in reducing emissions and promoting renewable energy, as implied in the text.
   • (b) The poor States always have to depend on rich States for electricity: The passage mentions poorer states needing help with clean energy projects but does not imply they always depend on richer states for electricity.
   • (c) The State Electricity Boards can improve their finances by undertaking clean energy projects: This is not supported by the passage. In fact, it highlights that renewable energy is more expensive than fossil fuels, and State Electricity Boards are already in financial trouble.
   • (d) The high economic disparity between the rich and poor States is the major cause of high carbon emissions in India: The passage does not argue this point, nor does it focus on economic disparity as the major cause of carbon emissions.

Thus, the most logical and rational assumption is (a) The richer States must lead in the production and adoption of renewable energy.

Explanation:

Radha disagrees with Geeta’s statement that Naresh has become a better boxer since he started meditation. She argues that a boxer’s most important asset is aggressiveness, implying that meditation, in her view, reduces aggressiveness. This belief aligns with the idea that meditation may have a calming effect, which Radha perceives as detrimental to boxing performance. Therefore, her statement reflects the belief that meditation tends to make a person less aggressive.

Explanation:

To determine the son’s age, we analyze the problem step by step.

Step 1: Define the variables

Let the age of the son be $x$ years.

– The age of the father is $9x$ years (9 times the son’s age).
– The age of the mother is $8x$ years (8 times the son’s age).

The total of the father’s and mother’s ages is given as $51$ years:
$$
9x + 8x = 51
$$

Step 2: Solve for $x$

Simplify the equation:
$$
17x = 51
$$

Divide both sides by $17$:
$$
x = \frac{51}{17} = 3
$$

Step 3: Verify the solution

– If the son’s age is $3$ years, the father’s age is:
$$
9 \cdot 3 = 27 \, \text{years}
$$

– The mother’s age is:
$$
8 \cdot 3 = 24 \, \text{years}
$$

– The total age of the father and mother is:
$$
27 + 24 = 51 \, \text{years}
$$

This matches the given information, so the solution is correct.

Final Answer:

The age of the son is: $ \boxed{3 \, \text{years}} $

Explanation:

To determine the total number of questions in the test, we analyze the problem step by step.

Step 1: Understand the given data
– The candidate attempted $8$ questions.
– He secured $50%$ marks in each of the $8$ questions he attempted.
– The candidate’s total marks in the test were $40%$.
– All questions carried equal marks, and we need to find the total number of questions in the test.

Step 2: Represent the total marks in the test
Let the total number of questions in the test be $N$. Since all questions carry equal marks, let the marks for each question be $M$. Therefore, the total marks in the test are:
$$
\text{Total marks} = N \cdot M
$$

The candidate scored $40%$ of the total marks, which is:
$$
\text{Candidate’s marks} = 0.4 \cdot N \cdot M
$$

Step 3: Represent the candidate’s obtained marks
The candidate attempted $8$ questions and secured $50\%$ marks in each. Hence, the marks he obtained are:
$$
\text{Marks obtained} = 8 \cdot \left(0.5 \cdot M\right) = 4 \cdot M
$$

Step 4: Equate the two expressions for marks obtained
The candidate’s marks obtained, $4 \cdot M$, is equal to $40%$ of the total marks, $0.4 \cdot N \cdot M$. Equating the two:
$$
4 \cdot M = 0.4 \cdot N \cdot M
$$

Cancel $M$ (since $M \neq 0$):
$$
4 = 0.4 \cdot N
$$

Simplify:
$$
N = \frac{4}{0.4} = 10
$$

Step 5: Verify the result
If the total number of questions is $10$, the total marks are $10 \cdot M$. The candidate attempted $8$ questions and secured $50%$ marks in each, giving $4 \cdot M$ marks. This is exactly $40%$ of the total marks:
$$
\frac{4 \cdot M}{10 \cdot M} = 0.4 = 40%
$$

Thus, the calculation is correct.

Final Answer:

The total number of questions in the test is: $ \boxed{10} $

Explanation:

To find the missing number $X$ in the series $7, X, 21, 31, 43$, we need to identify the pattern in the sequence.

Step 1: Analyze the differences in the given series

The given series is:

$$
7, X, 21, 31, 43
$$

We calculate the differences between consecutive terms:

1. From $7$ to $X$: Difference = $X – 7$
2. From $X$ to $21$: Difference = $21 – X$
3. From $21$ to $31$: Difference = $31 – 21 = 10$
4. From $31$ to $43$: Difference = $43 – 31 = 12$

The differences in the later terms ($10$ and $12$) suggest that the series increases by a progressively larger step.

Step 2: Assume the differences follow an arithmetic progression

The differences are:

$$
X – 7, \, 21 – X, \, 10, \, 12
$$

Let us assume the differences follow an arithmetic progression with a common difference of $2$:

1. First difference: $X – 7$
2. Second difference: $21 – X$
3. Third difference: $10$
4. Fourth difference: $12$

From the arithmetic progression:
$$
21 – X = (X – 7) + 2
$$

Step 3: Solve for $X$

Simplify the equation:
$$
21 – X = X – 7 + 2
$$

$$
21 – X = X – 5
$$

$$
21 + 5 = 2X
$$

$$
26 = 2X \implies X = 13
$$

Step 4: Verify the series

Substitute $X = 13$ into the series:

$$
7, 13, 21, 31, 43
$$

Calculate the differences:
$$
13 – 7 = 6, \quad 21 – 13 = 8, \quad 31 – 21 = 10, \quad 43 – 31 = 12
$$

The differences are $6, 8, 10, 12$, which form an arithmetic progression with a common difference of $2$. Thus, the solution is verified.

Final Answer:

The missing number is: $ \boxed{13} $

Explanation:

To solve the problem, we analyze the given matrix:

$$
\begin{array}{|c|c|c|c|c|c|}
\hline
3 & 8 & 10 & 2 & ? & 1 \\
\hline
6 & 56 & 90 & 2 & 20 & 0 \\
\hline
\end{array}
$$

Step 1: Look for a relationship between Row 1 and Row 2
Let the numbers in Row 1 be $x$ and the corresponding numbers in Row 2 be $y$. Testing for a pattern between $x$ and $y$:

Column 1: $3 \to 6$
$$
y = x \times 2 \quad (3 \times 2 = 6)
$$

Column 2: $8 \to 56$
$$
y = x \times 7 \quad (8 \times 7 = 56)
$$

Column 3: $10 \to 90$
$$
y = x \times 9 \quad (10 \times 9 = 90)
$$

Column 4: $2 \to 2$
$$
y = x \times 1 \quad (2 \times 1 = 2)
$$

Column 5: $? \to 20$
From the pattern, $y = x \times 4$. Substituting $y = 20$:
$$
20 = x \times 4 \implies x = 5
$$

Column 6: $1 \to 0$
$$
y = x \times 0 \quad (1 \times 0 = 0)
$$

Step 2: Final Answer

The missing number in the matrix is:
$$
\boxed{5}
$$

Explanation:

The passage specifically mentions that “proneness to exaggerate, to suppress or modify the truth, wittingly or unwittingly, is a natural weakness of man, and silence is necessary in order to surmount it.” Here, the author highlights that silence helps overcome the tendency to overstate or exaggerate, which is a natural weakness in human communication.

Analysis of Options:

• (a) constitutional shyness:
  The author acknowledges their constitutional shyness, but silence is not mentioned as a means to overcome it. Instead, shyness is described as advantageous and has helped the author grow.
• (b) hesitancy in speech:
  Hesitancy in speech is mentioned as an aspect of the author’s shyness, but silence is not explicitly linked to overcoming this.
• (c) suppression of thoughts:
  The author emphasizes the importance of restraining thoughts, not suppressing them. Silence helps in being deliberate and truthful, not in suppressing thoughts.
• (d) tendency to overstate:
  This aligns directly with the passage, which states that silence is necessary to overcome exaggeration or modification of the truth.

Conclusion:

The author views silence as a tool to overcome the human weakness of exaggeration or overstating the truth. Therefore, the correct answer is (d) tendency to overstate.

Explanation:

The passage emphasizes that the author has developed habits of economy of words and restraining thoughts, which ensure that he rarely says or writes anything thoughtless. He explicitly states, “I do not recollect ever having had to regret anything in my speech or writing,” attributing this to his careful and deliberate communication style.

This discipline has spared him “many a mishap and waste of time.” Thus, the most appropriate reason is that he hardly utters or writes a thoughtless word.

Analysis of Options:

• (a) He hardly utters or writes a thoughtless word:
  This is explicitly stated in the passage and is the main reason for the author avoiding mishaps.
• (b) He is a man of immense patience:
  While patience is a virtue that might help in avoiding mishaps, the passage does not specifically highlight this as the reason for the author’s avoidance of mishaps.
• (c) He believes that he is a spiritual person:
  The author discusses silence as part of the “spiritual discipline of a votary of truth,” but this is a general observation about silence, not the primary reason for being spared mishaps.
• (d) He is a votary of truth:
  While the author mentions truth, being a “votary of truth” is not directly linked to why he avoids mishaps. The reason is his deliberate habit of avoiding thoughtless words.

Conclusion:

The author’s careful speech and writing—ensuring that a thoughtless word rarely escapes him—are the most appropriate reasons for being spared mishaps. Thus, the correct answer is (a) he hardly utters or writes a thoughtless word.

Explanation:

The passage discusses the high child mortality rate in India and highlights several causes, such as:

• Lack of basic health practices like breastfeeding and immunization.
• Absence of care during critical phases of pregnancy and post-delivery.
• Issues like child marriages, anaemia among young women, and poor adolescent sanitation.

The key idea is that these challenges can be addressed through better maternal and child health services, which would involve universalization (making services accessible to all) and integration (combining maternal and child health efforts).

Analysis of Options:

• (a) A lot of Indians are illiterate and hence do not recognize the value of basic health practices:
  While illiteracy may play a role in the lack of basic health practices, the passage doesn’t explicitly attribute child mortality to illiteracy. This is an assumption, not a direct inference.
• (b) India has a very huge population and the government alone cannot manage public health services:
  The passage mentions a large reproductive population, but it does not make a claim that the government alone is incapable of managing public health services. This statement is not directly inferred.
• (c) Universalization and integration of maternal health and child health services can effectively address the problem:
  This is the critical inference. The passage identifies various preventable issues (e.g., lack of immunization, breastfeeding, care during pregnancy, etc.) that impact child mortality. Addressing these through a unified and universal approach to maternal and child health is the most logical solution.
• (d) The nutrition of women in childbearing age does not affect child mortality rate:
  This contradicts the passage, which clearly mentions issues like anaemia among young women as a factor impacting child mortality. This option is incorrect.

Conclusion:

The passage emphasizes the importance of addressing child mortality through better health practices and care. Thus, (c) is the correct inference, as it aligns with the solution implied in the passage.

Explanation:

The passage discusses the environmental and societal problems caused by long-distance food transportation and food processing. It highlights two key issues:

1. Long-distance food transportation leads to pollution, food wastage, and increased demand for packaging and preservation. This implies that consuming locally grown food (regionally sourced) is more eco-friendly, as it reduces the environmental footprint. Thus, Statement 1 is true.
2. Food processing and preservation put a burden on natural resources, as they require energy, packaging materials, and sometimes lead to waste during processing. The passage specifically mentions the increased demand for preservation and packaging, making Statement 2 true as well.

Analysis of Options:

• (a) 1 only: While Statement 1 is true, it is incomplete because Statement 2 is also supported by the passage.
• (b) 2 only: This is incorrect because Statement 1 is also valid, as discussed.
• (c) Both 1 and 2: This is the correct choice, as both statements are supported by the passage’s discussion of environmental threats and burdens caused by long-distance food transportation and food processing.
• (d) Neither 1 nor 2: This is incorrect because both statements are true.

Conclusion:

The passage emphasizes that consuming regionally grown food helps the environment and that the food processing industry places strain on natural resources. Therefore, the correct answer is (c) Both 1 and 2.

Explanation:

The passage discusses the justification for restricting the right to govern to a select few and suggests that such exclusions are argued to benefit society and political stability. The essential parts of the argument are:

• (b) The idea of ‘super’ and ‘sub’ human beings supports the notion of segregation, which is directly relevant to the passage.
• (c) Systemic efficacy and exceptions to universal participation justify the exclusion mentioned in the passage.
• (d) Recognition of disparities in individual capacities ties to the argument about why some are deemed more fit to govern than others.

Explanation:

The passage outlines the challenges of ensuring food security for a growing population projected to reach nine billion by 2050. It highlights several factors that contribute to this issue:

• Global population growth (affecting all countries).
• Shifting consumption patterns and climate change, which are global challenges.
• Limited resources, such as arable land and potable water.
• The role of efficiency in farming, waste reduction, and resource management to address the problem.
• Collaboration between rich and poor countries to improve crop storage, reduce waste, and adjust food consumption.

Analysis of Options:

• (a) The population of the world is growing very fast: While this is true, it only describes part of the context (population growth) and doesn’t address the collective nature of food security challenges.
• (b) Food security is a perennial problem only in developing countries: This is incorrect because the passage discusses challenges that affect both developing (e.g., crop storage) and developed nations (e.g., cutting back on resource-intensive foods like meat).
• (c) The world does not have enough resources to meet the impending food scarcity: This is overly pessimistic and doesn’t reflect the solutions offered in the passage (e.g., higher yielding crops, waste reduction, etc.).
• (d) Food security is increasingly a collective challenge: This is the best answer as the passage emphasizes the global nature of the issue and the need for collaborative solutions, involving both rich and poor countries.

Thus correct answer is: (d) Food security is increasingly a collective challenge.