Search Previous Year Questions

The correct answer is Option 3.

 

Key Points

• Statement 1 is correct: The passage describes Hugh Grant's decision to nap as 'quietly radical' because it represents an act of mild surrender to the body's needs in a public setting, effectively acting against societal performance metrics and expectations of constant engagement.
• Statement 2 is correct: The author explicitly clarifies that this act of sleeping was a surrender 'not to laziness, but to limits.' It highlights that acknowledging the physical limitations caused by factors like age (noting he is a 64-year-old man) should not be mistaken for a lack of industry or laziness.
• Statement 3 is correct: The term 'leading man' typically denotes the protagonist or lead actor in a film; however, the author uses it metaphorically to suggest that by choosing to rest, Grant has become a figurehead or 'leading man' for the sleep-deprived, portraying a 'resting hero' rather than the typical 'action hero'.
• Since all three statements accurately reflect the themes and specific wording of the passage, the correct code is 1, 2 and 3.

Therefore, the correct answer is 1, 2 and 3.

 

Additional Information

• Context: The event took place at Wimbledon during the men's singles quarterfinals match between Flavio Cobolli and Novak Djokovic.
• Royal Box: This is a prestigious seating section at the Centre Court of Wimbledon, making the actor's nap even more noticeable and socially significant.
• Forty winks: A common English idiom meaning to take a short sleep or nap during the day.
• Unexpected ace: The author uses this tennis metaphor to describe the nap as a surprising yet successful move by Hugh Grant, subverting the high-intensity environment of the sports arena.

The correct answer is Option 2.

 

Key Points

• Statement 1 is incorrect: According to the passage, Hugh Grant was watching the men's singles quarterfinals, not the semifinal match.
• Statement 2 is incorrect: While the phrase 'unexpected ace' is a tennis term used to describe the nap, the passage does not view the act with opprobrium (harsh criticism). Instead, the author uses phrases like 'praise be to Grant' and 'elegant case for surrender,' showing a positive and empathetic perspective.
• Statement 3 is correct: The passage explicitly states that Grant made a case for surrender to the body's quiet wisdom over society's relentless performance metrics. This indicates he prioritized his physical needs over societal expectations.
• Since only the third statement aligns with the facts and tone of the passage, the correct code is 3 only.

Therefore, the correct answer is 3 only.

 

Additional Information

• Forty winks: This is an idiomatic expression meaning a short sleep or a nap during the day.
• Royal Box: An exclusive seating area at Wimbledon, typically reserved for the Royal Family and their guests.
• Radical Action: The author describes the nap as 'quietly radical' because it goes against the societal norm of constant engagement and performance, especially in a high-profile public setting.

The correct answer is Option 1.

 

Key Points

• According to the passage, in the fine-tuning phase, participants (both leaders and followers) attempt to extract remaining benefits from a technology that is increasingly exhausted. This results in both categories having similar per capita incomes. Therefore, statement 3 is correct.
• The passage outlines a chronological sequence of technological developments: scavenging (3 million years ago), followed by hunting (1 million years ago), followed by farming (12 thousand years ago), and finally industrial technology (over 200 years ago).
• Statement 4 accurately reflects this timeline: industrial technology appeared after scavenging; scavenging occurred before hunting; and hunting was followed by farming. Thus, statement 4 is correct.
• The convergence theory uses these phases to explain how the labour-productivity gap is narrowed over time.

Therefore, the correct answer is 3 and 4 only.

 

**Correct

Conclusion:

** The fine-tuning phase involves extracting leftover benefits from exhausted tech, and the historical progression moved from scavenging to hunting, farming, and then industrial technology.

 

Additional Information

• Statement 1: This is incorrect because the passage explicitly states that during the breakaway phase, the per capita income of technology followers is unchanged, rather than describing the progress as merely slow.
• Statement 2: This is incorrect because the passage says the catch-up phase involves followers adopting new technology to close the gap; it does not mention that technology leaders stagnate during this period.

The correct answer is Option 2.

 

Key Points

• The convergence theory is defined by the process through which countries work to close the labour-productivity gap existing between themselves and the technology leader. Statement 2 is considered correct as it identifies this gap as the central focus of the theory.
• The passage describes technology leaders as the entities that initiate a new technology (like industrial technology or farming), meaning they logically arrive at and define different economic eras earlier than the followers. Thus, statement 3 is correct.
• The model segments the process into three distinct phases: the breakaway phase, the catch-up phase, and the fine-tuning phase.
• Based on the passage analysis, only statements 2 and 3 accurately reflect the provided information.

Therefore, the correct answer is 2 and 3.

 

Additional Information

• Statement 1 is incorrect: The passage explicitly states that the convergence model divides economic eras (not nations) into three phases: breakaway, catch-up, and fine-tuning.
• Statement 4 is incorrect: The timeline mentioned begins 3 million years ago (scavenging). Statement 4 appears to be a random summation of the numbers mentioned in the text (3,000,000 + 1,000,000 + 12,000 + 200), which does not represent the actual time period covered by the theory.
• During the breakaway phase, the per capita income of leaders rises while that of followers remains unchanged.
• During the fine-tuning phase, technology becomes exhausted, and both leaders and followers reach similar income levels.

Shortcut Trick

Equal amounts of copper and zinc in Alloy R means copper is 50%.

Apply Alligation on Copper concentration:

Alloy P (20%) and Alloy Q (60%) mix to give Alloy R (50%).

Ratio P : Q = (60 − 50) : (50 − 20) = 10 : 30 = 1 : 3.

∴ The correct answer is 1 : 3.

Alternate Method

Given:

Alloy P: Copper = 20%, Zinc = 80%

Alloy Q: Copper = 60%, Zinc = 40%

Alloy R: Copper = 50%, Zinc = 50% (since they are in equal amounts)

Calculations:

⇒ Let the quantity of Alloy P be x and Alloy Q be y.

⇒ Quantity of Copper in R = (20% of x) + (60% of y)

⇒ Total quantity of R = x + y

⇒ Concentration of Copper in R = 50% = 1/2

⇒ [0.2x + 0.6y] / [x + y] = 0.5

⇒ 0.2x + 0.6y = 0.5x + 0.5y

⇒ 0.6y − 0.5y = 0.5x − 0.2x

⇒ 0.1y = 0.3x

⇒ x/y = 0.1 / 0.3 = 1/3

∴ The correct answer is 1 : 3.

Additional Information

Alligation Rule

It is used to find the ratio in which two ingredients at given prices/concentrations must be mixed to produce a mixture at a target price/concentration. Ratio = (Higher Value − Mean Value) : (Mean Value − Lower Value).

Concentration in Mixtures

When components are mixed, the weight of a specific element (like Copper) in the final mixture is the sum of its weights in the individual alloys.

Percentage to Ratio Conversion

Equal amounts of two components in a mixture always represent a 1 : 1 ratio or 50% concentration for each component.

Shortcut Trick
The difference between a 2-digit number and its reverse is always 9 × (Difference of its digits).
Let the digits be x and y. Then, A − B = 9(x − y).
Given A − B is a multiple of 27 ⇒ 9(x − y) = 27, 54, 81... ⇒ (x − y) must be 3, 6, or 9.
For (x − y) = 3: Pairs are (4,1), (5,2), (6,3), (7,4), (8,5), (9,6) → 6 numbers.
For (x − y) = 6: Pairs are (7,1), (8,2), (9,3) → 3 numbers. (x − y = 9 ⇒ 9,0 is excluded as B must be 2-digit).
∴ The correct answer is 9.

Alternate Method
Given: A is a 2-digit number (10x + y), B is its reverse (10y + x). A > B and B is also a 2-digit number (y ≠ 0).
Formula Used: A − B = (10x + y) − (10y + x) = 9(x − y).

⇒ x and y are digits where 1 ≤ x, y ≤ 9 and x ≠ y.
⇒ Since A − B is a multiple of 27, 9(x − y) = 27 × k.
⇒ (x − y) = (27 × k) ÷ 9 = 3k.
⇒ If k = 1: x − y = 3. Possible (x,y) pairs: (4,1), (5,2), (6,3), (7,4), (8,5), (9,6). Total = 6.
⇒ If k = 2: x − y = 6. Possible (x,y) pairs: (7,1), (8,2), (9,3). Total = 3.
⇒ If k = 3: x − y = 9. Possible (x,y) pairs: (9,0). But y ≠ 0 because B is a 2-digit number.
⇒ Total possible values of A = 6 + 3 = 9.
∴ The correct answer is 9.

Additional Information
Difference of Reversed Numbers
The difference between any 2-digit number and its reverse is always divisible by 9. The quotient is the difference of the digits.
Sum of Reversed Numbers
The sum of any 2-digit number and its reverse is always divisible by 11. (10x + y) + (10y + x) = 11(x + y).
2-Digit Number Constraints
For a number 10x + y to be a 2-digit number, the leading digit x must be from {1, 2, ..., 9}. If its reverse is also a 2-digit number, then y must also be from {1, 2, ..., 9}.

The logic followed here is**:** The letters of the word are shifted forward and backward alternatively by 1 position (+1, −1, +1, −1).

ZERO is coded as ADSN →

The pattern observed is a sequential shift of +1 and −1 applied to each letter.

 

Similarly, let's find the code for STOP:

Therefore, the code for STOP is TSPO.

Hence, the correct answer is "Option 2".

Shortcut Trick

Area width is common (3'), so solve for length 100' using tile lengths 3', 7', and 11'.

To maximize tiles (x), use the smallest tile: (31 × 3') + (1 × 7') = 100' ⇒ x = 31 + 1 = 32 tiles.

To minimize tiles (y), use the largest tile: (8 × 11') + (4 × 3') = 100' ⇒ y = 8 + 4 = 12 tiles.

Difference x − y = 32 − 12 = 20.

∴ The correct answer is 20.

Alternate Method

Given: Dimensions of rectangular area = 3' × 100'. Tile sizes = 3' × 3', 3' × 7', 3' × 11'.

Since one dimension (3') is common to the area and all tiles, we simplify the problem to a one-dimensional length of 100' to be covered by segments of 3', 7', and 11'.

Let a, b, and c be the number of tiles of length 3', 7', and 11' respectively.

Equation: 3a + 7b + 11c = 100

Step 1: Finding the maximum number of tiles (x)

To maximize the count, we use the smallest tile (3') as much as possible.

⇒ If we use only 3' tiles: 100 ÷ 3 = 33.33 (Not possible exactly).

⇒ If a = 31: 3 × 31 = 93. Remainder = 100 − 93 = 7.

⇒ We can use one 7' tile (b = 1).

⇒ Total tiles x = 31 (of 3') + 1 (of 7') = 32 tiles.

Step 2: Finding the minimum number of tiles (y)

To minimize the count, we use the largest tile (11') as much as possible.

⇒ If we use only 11' tiles: 100 ÷ 11 = 9.09 (Not possible exactly).

⇒ If c = 9: 11 × 9 = 99. Remainder = 1. (No tile fits).

⇒ If c = 8: 11 × 8 = 88. Remainder = 100 − 88 = 12.

⇒ We can cover 12' using four 3' tiles (a = 4).

⇒ Total tiles y = 8 (of 11') + 4 (of 3') = 12 tiles.

Step 3: Calculating x − y

⇒ x − y = 32 − 12 = 20.

∴ The correct answer is 20.

Additional Information

Linear Diophantine Equations

Equations like 3a + 7b + 11c = 100 require integer solutions. The minimum sum (a+b+c) occurs when the variable with the largest coefficient is maximized.

Optimization Strategy

To maximize the total number of items, prioritize the smallest unit; to minimize, prioritize the largest unit while ensuring the total sum is met exactly.

Constraints in Tiling

When a tile dimension matches the area dimension exactly, the problem effectively becomes 1D, simplifying 2D area coverage to a length-partitioning problem.

Shortcut Trick

Since the distance segments (0-200 km and 600-800 km) and their respective final speeds (V/8) are the same in both scenarios, the time difference depends only on the 400 km middle segment.

In Scenario 1, middle segment speed = V/2. In Scenario 2, middle segment speed = V/4.

Time difference ⇒ Distance ÷ (Speed₂) − Distance ÷ (Speed₁) = 4 hours.

400 ÷ (V/4) − 400 ÷ (V/2) = 4 ⇒ 1600/V − 800/V = 4.

800/V = 4 ⇒ V = 200 km/h.

∴ The correct answer is 200 kmph.

Alternate Method

Given:

Total Journey = 800 km. Let original Speed = V km/h.

Minor Accident: Speed becomes 1/2 of existing. Mechanical Defect: Speed becomes 1/4 of existing.

Calculations:

Total time for Scenario 1 (T₁):

⇒ T₁ = 200/V + 400/(V/2) + 200/(V/8)

⇒ T₁ = 200/V + 800/V + 1600/V = 2600/V

Total time for Scenario 2 (T₂):

⇒ T₂ = 200/V + 400/(V/4) + 200/(V/8)

⇒ T₂ = 200/V + 1600/V + 1600/V = 3400/V

According to the question, Scenario 2 takes 4 hours more:

⇒ T₂ − T₁ = 4

⇒ 3400/V − 2600/V = 4

⇒ 800/V = 4

⇒ V = 800/4 = 200 km/h.

∴ The correct answer is 200 kmph.

Additional Information

Relative Speed

When two objects move in the same direction, relative speed = V₁ − V₂. When they move in opposite directions, relative speed = V₁ + V₂.

Average Speed

Average Speed = Total Distance ÷ Total Time. If distances are equal for two speeds a and b, Average Speed = 2ab ÷ (a + b).

Time and Distance Relationship

For a constant distance, speed is inversely proportional to time (V ∝ 1/T). For a constant time, distance is directly proportional to speed (D ∝ V).

Shortcut Trick

Calculate weighted scores: (Score₁ × 0.2) + (Score₂ × 0.3) + (Score₃ × 0.5).

C1 = 5.2 | C2 = 5.1 | C3 = 5.2 | C4 = 4.5 | C5 = 5.0.

Ranking the scores in descending order: 5.2, 5.2, 5.1, 5.0, 4.5.

For exactly 3 selections, the 3^rd highest score is the cutoff.

∴ The correct answer is 5.1.

Alternate Method

Given: weightage w₁ = 0.2, w₂ = 0.3, w₃ = 0.5.

Formula Used: Total Weighted Score = Σ(Score_i × weight_i)

⇒ Candidate 1 Score: (5 × 0.2) + (4 × 0.3) + (6 × 0.5) = 1.0 + 1.2 + 3.0 = 5.2

⇒ Candidate 2 Score: (4 × 0.2) + (6 × 0.3) + (5 × 0.5) = 0.8 + 1.8 + 2.5 = 5.1

⇒ Candidate 3 Score: (3 × 0.2) + (2 × 0.3) + (8 × 0.5) = 0.6 + 0.6 + 4.0 = 5.2

⇒ Candidate 4 Score: (9 × 0.2) + (4 × 0.3) + (3 × 0.5) = 1.8 + 1.2 + 1.5 = 4.5

⇒ Candidate 5 Score: (8 × 0.2) + (8 × 0.3) + (2 × 0.5) = 1.6 + 2.4 + 1.0 = 5.0

⇒ Sorted Scores: 5.2 (C1), 5.2 (C3), 5.1 (C2), 5.0 (C5), 4.5 (C4)

⇒ For exactly 3 candidates, the cutoff is the 3^rd highest value.

∴ The correct answer is 5.1.

Additional Information

Weighted Average

It is calculated as Σ(x_i × w_i) / Σw_i. When the sum of weights equals 1, the formula simplifies to Σ(x_i × w_i).

Selection Cutoff

The cutoff score is the minimum score required to remain in the selection pool based on the number of vacancies available.

Weightage Impact

Components with higher weightages (like Component 3 with 0.5) have a greater impact on the final score than those with lower weightages.