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The logic for determining the valid conclusions is based on a direct analysis of the statements provided in the passage.

**Analysis of

Conclusions:

**

Detailed Breakdown:

1. Conclusion 1: This is a direct paraphrase of the authors call to view sport as a way of life rather than just a competitive activity.
2. Conclusion 2: Seclusion refers to the state of being private and away from people. The passage addresses this by noting children rarely leave the house and suggesting sport as a solution to mitigate this behavior.
3. Conclusion 3: While the author argues sport is more than just medals and quotas, the inclusion of these terms confirms that securing a job via a sports quota is a recognized outcome of sporting achievement (laurels).
4. Conclusion 4: The passage lists several skills like time management and teamwork. These are essential corporate sector skills. Since the passage says they can be learned through sport, the statement that they cannot be learned is incorrect.

Therefore, the valid conclusions are 1, 2 and 3.

The correct answer is Option 2.

Key Points

• Statement 1 is incorrect. While the passage mentions that parents often say their children are inactive and rarely leave the house, it does not claim that the parents themselves are not encouraging. It only highlights their observations regarding their children's behavior.
• Statement 2 is correct. The passage explicitly mentions that from sport, one can learn time management, teamwork, and coordination. These are essential life skills that contribute to personal development.
• Statement 3 is correct. The text advocates for a culture where sport is seen as a way of life, describing it as a path to building a healthier, happier society. Improving the health and happiness of its members directly helps evolve the nature of society.
• Therefore, only statements 2 and 3 are supported by the passage.

Therefore, the correct answer is 2 and 3.

Additional Information

• Mental Health Benefits: The passage highlights that sport is a tool to tackle modern issues like depression and anxiety among the current generation.
• Beyond Competition: It emphasizes that the value of sport transcends traditional rewards like winning medals or securing jobs through a sports quota.
• Social Impact: By fostering coordination and teamwork, sport serves as a foundational element for a more integrated and functional community.

Let:

1. Number of forward jumps = F
2. Number of backward jumps = B

Given:

F + B = 31 ..........

(1) Each forward jump = +5 ft

Each backward jump = −2 ft

Net distance = 15 ft forward

So,

5F − 2B = 15 .......... (2) From (1):

B = 31 − F

Substitute in (2):

5F − 2(31 − F) = 15

5F − 62 + 2F = 15

7F = 77

F = 11

Then,

B = 31 − 11 = 20

Difference between forward and backward jumps:

20 − 11 = 9

Hence, the correct answer is "Option 4".

Solution

⇒ P and R are adjacent to Q. This means Q is seated between P and R.

⇒ T and R are adjacent to S. This means S is seated between T and R.

⇒ Combining these clues, we get a partial sequence: P - Q - R - S - T.

⇒ S and W are on opposite chairs. In an 8-seat circular arrangement, opposite means there are 3 persons between them on either side.

⇒ U and W are adjacent to V. This means V is seated between U and W.

⇒ The condition states that while going clockwise from P, one meets R before T. This confirms the clockwise order of the first sequence: P → Q → R → S → T.

⇒ Based on the clues, the final clockwise arrangement starting from Q is: Q → R → S → T → U → V → W → P.

⇒ Clockwise from P, R (2^nd seat) is met before T (4^th seat). This satisfies all conditions.

⇒ Now, moving clockwise from Q to meet W, we cross the following persons: R, S, T, U, and V.

⇒ Counting these persons: R(1), S(2), T(3), U(4), V(5).

∴ The correct answer is 5.

Given:

Table top dimensions = 6' × 10'

Two blue rectangles of dimensions = 2.5' × 8'

Each blue rectangle shares exactly two sides with the table edges.

Since each blue rectangle must touch two edges of the table, it can only be placed at a corner.

Possible corner placements are:

1. Top-left
2. Top-right
3. Bottom-left
4. Bottom-right

Now we count distinct visible patterns from above.

The two blue rectangles can form:

1. Both on top side corners
2. Both on bottom side corners
3. Both on left side corners
4. Both on right side corners

These give 4 different observable patterns.

Hence, the correct answer is "Option 2".

pThe correct answer is Neither 1 nor 2

Key Points

• Statement 1 is incorrect because it uses the term Real value in a general sense, whereas the passage specifically discusses Real Value Added (RVA). In economic accounting, these are distinct terms; Real Value Added is the difference between the real value of output and the real value of inputs. Furthermore, the statement uses the term output cost, but the passage refers to output prices. Price (what a seller receives) and Cost (what a producer spends) are not interchangeable in this context.
• Statement 2 is incorrect because the passage states that double deflation is a method used by most countries, but it is not universally adopted. The passage explicitly highlights India as an example of an economy that does not use this practice, instead deflating inputs and outputs using the same deflator (single deflation). The use of the word universally makes the statement factually incorrect based on the text.
• The passage explains that when input prices (like oil) fall while output prices and quantities remain the same, the actual physical contribution (the Real Value Added) should remain constant. However, if an economy uses a single deflator, it erroneously suggests an increase in productivity or real growth that did not actually occur.

Additional Information

• Double Deflation is an accounting technique where Gross Output is deflated by an output price index and Intermediate Consumption is deflated by an input price index to arrive at Real Gross Value Added (GVA).
• GVA is defined as: GVA = Value of Output − Value of Intermediate Consumption.
• In India, the reliance on Single Deflation, often using the Wholesale Price Index (WPI) as a proxy, has been a subject of debate among economists, especially when global commodity prices for raw materials fluctuate significantly compared to finished goods.
• The System of National Accounts (SNA), the international standard for GDP calculation, generally recommends the use of double deflation to provide a more accurate picture of an economy's manufacturing sector.

The correct answer is 1 only

Key Points

• Deflation strategies involve the process of converting Nominal Values (current prices) into Real Values (constant prices) to remove the impact of inflation. Statement 1 is valid because if an inappropriate or lower Deflator is used while actual input costs are rising sharply, the Real Value Added of manufacturers can be artificially inflated, making their performance look better than the actual physical growth suggests.
• Double Deflation is a method used in National Income Accounting to estimate the Real Gross Value Added (GVA). It requires deflating the value of Gross Output by an Output Price Index and separately deflating the Intermediate Consumption (inputs) by an Input Price Index.
• Statement 2 is invalid because deflating both input and output against a single price index is known as Single Deflation. Double deflation specifically mandates the use of two distinct indices to account for the different price movements of what a factory sells versus what it buys.
• In the manufacturing sector, if input prices (like raw materials) rise faster than output prices, using a single deflator can lead to a significant overestimation of Real GDP growth.

Additional Information

• The Gross Value Added (GVA) is calculated as: GVA = Gross Value of Output − Value of Intermediate Consumption.
• The Wholesale Price Index (WPI) is often used as a proxy deflator for the manufacturing sector in many developing economies, though experts argue that the Producer Price Index (PPI) provides a more accurate measure for Double Deflation.
• Real GDP is a better indicator of economic health than Nominal GDP because it reflects the actual volume of goods and services produced, excluding the 'noise' of price changes.
• Many economists have raised concerns about India's GDP calculation methods, specifically the shift to GVA at basic prices and the reliance on single deflation during periods of volatile commodity prices.

Logic followed here is.

Logic: The string is formed by the repetition of a specific sequence of characters a and b. By analyzing the fixed characters provided in the string, we can deduce the base pattern.

Step 1: Map the given characters and their positions

The provided string has a total of 15 positions. The known characters are distributed as follows:

Step 2: Identify the repeating pattern →

Since the string length is 15, let us test a 5-character repeating pattern. We divide the string into three equal segments:

• Segment 1 (Positions 1-5): x b x a x
• Segment 2 (Positions 6-10): a x x a x
• Segment 3 (Positions 11-15): a x b a b

By comparing the characters at corresponding positions across the three segments, we can deduce the base pattern:

• Position 1 of the pattern: From index 6 and index 11 → a
• Position 2 of the pattern: From index 2 → b
• Position 3 of the pattern: From index 13 → b
• Position 4 of the pattern: From index 4, 9, and 14 → a
• Position 5 of the pattern: From index 15 → b

The identified pattern is a b b a b.

Similarly, let us apply the pattern to the string →

By mapping the 7^th and 8^th positions to the second segment of the repeating pattern, we find:

7^th position = b

8^th position = b

Therefore, the characters x x at the 7^th and 8^th positions are bb.

Hence, the correct answer is "Option 4".

Shortcut Trick

The total exponent of 10 in the expression is the minimum of the exponents of 2 and 5.

Exponent of 5 → (2 × 25) + (2 × 32) = 50 + 64 = 114.

Exponent of 2 → (5 × 75) = 375.

Max power of 10 available = 114 ∴ 10^m+3 = 10¹¹⁴ (since 1000 = 10³).

m + 3 = 114 ⇒ m = 111.

∴ The correct answer is 111.

Alternate Method

Given: 10^m × 1000 × n = 75²⁵ × 25³² × 32⁷⁵

Formula: (a^b)^c = a^{b × c} and 10 = 2 × 5.

⇒ 10^m × 10³ × n = (3 × 5²)²⁵ × (5²)³² × (2⁵)⁷⁵

⇒ 10^m+3 × n = 3²⁵ × 5⁵⁰ × 5⁶⁴ × 2³⁷⁵

⇒ 10^m+3 × n = 3²⁵ × 5¹¹⁴ × 2³⁷⁵

⇒ 10^m+3 × n = 3²⁵ × 2^{375 − 114} × (2¹¹⁴ × 5¹¹⁴)

⇒ 10^m+3 × n = (3²⁵ × 2²⁶¹) × 10¹¹⁴

⇒ Since n is not divisible by 10, compare the powers of 10:

⇒ m + 3 = 114

⇒ m = 114 − 3 = 111

∴ The correct answer is 111.

Additional Information

Power of 10 in a Product

To find the number of trailing zeros or the highest power of 10 in an expression, calculate the powers of 2 and 5 in its prime factorization. The answer is always min(power of 2, power of 5).

Exponent Laws

Key rules used: (x^a)^b = x^a×b and x^a × x^b = x^a+b and (x × y)^a = x^a × y^a.

Divisibility by 10

A number is not divisible by 10 if its prime factorization does not contain at least one pair of (2 × 5). If it contains only 2s or only 5s (but not both), it is not divisible by 10.

Shortcut Trick

Relative speed (Same direction) = 100 − 4 = 96 kmph

Relative speed (Opposite direction) = 100 + 4 = 104 kmph

Since the length of train is constant: Time₁ × Speed₁ = Time₂ × Speed₂

⇒ 15 × 96 = Time₂ × 104

⇒ Time₂ = 1440 ÷ 104 ≈ 13.85 seconds

∴ The correct answer is 13.85 seconds.

Alternate Method

Given: Speed of Train (S_T) = 100 kmph, Speed of Person (S_P) = 4 kmph, Time (same direction) = 15 seconds.

Formula Used: Distance = Relative Speed × Time

⇒ Relative Speed (Same) = 100 − 4 = 96 kmph

⇒ Relative Speed (Same) in m/s = 96 × 5 ÷ 18 = 80 ÷ 3 m/s

⇒ Length of Train = (80 ÷ 3) × 15 = 400 m

⇒ Relative Speed (Opposite) = 100 + 4 = 104 kmph

⇒ Relative Speed (Opposite) in m/s = 104 × 5 ÷ 18 = 260 ÷ 9 m/s

⇒ Time taken (Opposite) = Distance ÷ Relative Speed

⇒ Time = 400 ÷ (260 ÷ 9) = (400 × 9) ÷ 260

⇒ Time = 3600 ÷ 260 = 180 ÷ 13 ≈ 13.846 seconds

∴ The correct answer is 13.85 seconds.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed = S₁ − S₂. When they move in opposite directions, relative speed = S₁ + S₂.

Unit Conversion

To convert speed from kmph to m/s, multiply by 5/18. To convert m/s to kmph, multiply by 18/5.

Train Crossing a Point Object

When a train crosses a person, pole, or signal, the distance traveled is equal to the length of the train itself.