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Given:

There are 7 cubes. 6 cubes have equal weight and 1 cube is lighter.

We need to find the lightest cube using a balance.

First Attempt:

Divide the 7 cubes into:

1. 3 cubes on left side
2. 3 cubes on right side
3. 1 cube aside

Case 1: If both sides balance, then the remaining cube is the lightest.

Case 2: If one side is lighter, then the lightest cube is among those 3 cubes.

Second Attempt:

From the suspected 3 cubes, compare:

1 cube vs 1 cube

If one side is lighter, that cube is the answer. If both balance, then the third cube is the lightest.

Therefore, the minimum number of attempts required is 2.

Hence, the correct answer is "Option 1".

The correct answer is Option 3.

 

Key Points

• The passage discusses the evolution of customer-service technology, comparing current AI advancements with previous waves like email and voice menus.
• It emphasizes that while AI might indeed change the job landscape, its effects could be salutary (beneficial) for the workforce.
• The core argument is that human agents will be freed up from repetitive or stressful duties (like handling irate customers) to focus on more creative and rewarding tasks, such as using feedback to improve products.
• Therefore, the statement that reflects the redirection of human intervention toward fulfilling tasks most accurately captures the point of view of the passage.

Therefore, the correct answer is Option 3.

 

Additional Information

• Option 1 is incorrect because the passage suggests that human agents will have different, more rewarding work to do, rather than no work at all.
• Option 2 focuses on the degree of human redundancy, whereas the passage emphasizes the qualitative shift in the nature of human work.
• Option 4 is inaccurate because the passage explicitly mentions that previous waves of technology also stoked concerns about job losses; AI is not the first to raise such alarms.

The correct answer is Option 4.

 

Key Points

• Statement 1 is correct: The passage explicitly states that previous waves of customer-service technology, such as email and voice menus, consistently 'stoked concerns of job losses.'
• Statement 2 is correct: The author notes that instead of jobs simply disappearing, AI might allow human agents to be 'freed up' to focus on creative and rewarding tasks, such as improving products through feedback. This implies the discovery of alternative channels for engagement.
• Statement 3 is incorrect: The passage suggests that AI could actually lead to beneficial (salutary) outcomes by reducing the time employees spend dealing with irate customers, thereby making the work environment less stressful, not more.
• Therefore, both conclusions 1 and 2 are supported by the text.

Therefore, the correct answer is 1 and 2.

 

Additional Information

• The term salutary in the passage means producing good effects or being beneficial, which directly contradicts the idea that technology inevitably leads to stressful outcomes.
• The passage emphasizes a qualitative shift in labor, where automation handles repetitive tasks while humans pivot toward high-value, creative roles.
• The phrase fail to materialise regarding job losses from email and voice menus supports the idea that historical fears have often been misplaced.

The correct answer is Option 3.

 

Key Points

• Statement 3 is the only valid conclusion as the passage explicitly states that Rai Sahib held to old values and believed that a landlord who didn't look after his tenants was less than human. This directly connects traditional values with concern for tenants.
• Statement 1 is incorrect because the passage contrasts Rai Sahib with selfish Zamindars who would ignore the welfare of cattle to make money, implying that not all landlords possess such goodness.
• Statement 2 is not a generalized conclusion provided by the text; while the cattle from nearby villages used the ground, the focus of the passage is on Rai Sahib's personal decision to preserve it rather than the universal purpose of all such grounds.
• Statement 4 is incorrect because the passage mentions there was a cool freshness in the morning, but Hori anticipated scorching 'loo' winds for the rest of the day, indicating it would get hotter, not cooler.
• Therefore, the only correct conclusion based strictly on the text is 3.

Therefore, the correct answer is 3 only.

 

**Correct

Conclusion:

** "Landlords who believe in tradition (old values) tend to be more concerned about their tenants."

 

Additional Information

• The passage highlights the character of Rai Sahib as an exception to the typical selfish Zamindars of that era.
• The term 'loo' refers to the strong, dusty, gusty, hot, and dry summer afternoon wind from the west which blows over the western Indo-Gangetic Plain region of North India and Pakistan.
• The phrase 'less than human' emphasizes the moral weight Rai Sahib placed on the duty of a landlord toward his dependents.

The correct answer is Option 4.

 

Key Points

• Statement 1 is incorrect because the passage only refers to a specific bit of land reserved for grazing. It does not suggest that all of Rai Sahib’s landholdings were excluded from farming; in fact, as a Zamindar with tenants, his other lands were naturally used for cultivation.
• Statement 2 is incorrect because the text highlights that Rai Sahib held old values and cared for his tenants, explicitly distinguishing him from selfish or greedy landlords.
• Statement 3 is incorrect because the passage clearly states that farmers had offered a good price for the land. Therefore, it is easily ascertainable that he could have earned money by leasing it.
• Statement 4 is correct based on the passage, as it mentions Rai Sahib felt any landlord who did not look after his tenants was less than human, showing he valued their livelihood.
• Since statements 1, 2, and 3 are false according to the text, they are the not correct statements.

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

 

Additional Information

• The passage emphasizes the moral character of Rai Sahib, who prioritizes the common good (village grazing) over personal profit.
• The mention of the loo wind and the cool freshness of the morning provides the environmental context in which Hori is reflecting on the landlord's kindness.
• The term Zamindar refers to a landowner, and the passage explores the ethical responsibilities expected of that position according to traditional values.

Given:

Starts facing East

Travels 4 km straight

Turns right and travels 3 km

Turns left and travels 2 km

Turns left and travels 3 km

 

Step-by-step movement:

Minimum distance between initial and final point = 6 km

Final direction faced = North

Hence, the correct answer is "Option 4".

Logic followed here is.

Logic: Each number in the sequence, other than the first two, is the sum of the two immediately preceding numbers.

Given:

First number = 4

Second number = 7

Calculating the terms of the sequence:

3^rd number = 1^st number + 2^nd number = 4 + 7 = 11

4^th number = 2^nd number + 3^rd number = 7 + 11 = 18

5^th number = 3^rd number + 4^th number = 11 + 18 = 29

6^th number = 4^th number + 5^th number = 18 + 29 = 47

The sequence is summarized below:

Therefore, the sixth number in the sequence is 47.

Shortcut Trick

Company A ratio (M : F) = 13 : 10 (Total = 23 units)

Company B ratio (M : F) = 7 : 5

To make female workers equal, multiply Company B ratio by 2 → 14 : 10 (Total = 24 units)

Required Ratio (Total A : Total B) = 23 : 24

∴ The correct answer is 23 : 24.

Alternate Method

Given:

Ratio of Male to Female in Company A = 13 : 10

Ratio of Male to Female in Company B = 7 : 5

Formula Used:

Total workers = Male workers + Female workers

⇒ Let the number of female workers in both companies be 10x.

⇒ For Company A: Male = (13/10) × 10x = 13x

⇒ Total workers in Company A = 13x + 10x = 23x

⇒ For Company B: Male = (7/5) × 10x = 14x

⇒ Total workers in Company B = 14x + 10x = 24x

⇒ Ratio of Total A to Total B = 23x : 24x = 23 : 24

∴ The correct answer is 23 : 24.

Additional Information

Equating Ratios

When one component is common or equal in two ratios, multiply the entire ratio by a constant to make that component's numerical value the same in both sets.

Combined Ratio

If A : B = x : y and B : C = p : q, the combined ratio A : B : C is found by equating the value of B in both ratios.

Proportion Rule

If four quantities a, b, c, d are in proportion, then a/b = c/d, which implies a × d = b × c.

Shortcut Trick

Let the two distinct numbers be a and b.

We know: HCF × LCM = a × b.

Given: HCF × LCM = a³ ⇒ a × b = a³ ⇒ b = a².

Statement I: Difference = a² − a = a(a − 1). Product of two consecutive integers is always even.

Statement II: Since b = a², one number is clearly a perfect square.

∴ The correct answer is Both I and II.

Alternate Method

Given:

Two distinct numbers: n₁ and n₂.

Product of HCF and LCM = (n₁)³.

Formula Used:

HCF × LCM = Product of the numbers

Step-by-step Calculation:

⇒ Let the numbers be x and y.

⇒ x × y = x³

⇒ y = x³ ÷ x

⇒ y = x²

⇒ Since the numbers are distinct, x ≠ 1 (as 1² = 1).

Evaluating Statement I:

⇒ Difference = y − x = x² − x

⇒ Difference = x(x − 1)

⇒ For any integer x, one of x or (x − 1) must be even.

⇒ Even × Odd = Even. Thus, Statement I is correct.

Evaluating Statement II:

⇒ Since y = x², y is a perfect square.

⇒ Thus, Statement II is correct.

∴ The correct answer is Both I and II.

Additional Information

Fundamental Property of HCF and LCM

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b. This property holds only for two numbers.

Consecutive Integers Property

The product of n consecutive integers is always divisible by n! (n factorial). For 2 consecutive integers, the product is always divisible by 2! = 2 (i.e., it is even).

Perfect Squares

A number is a perfect square if it can be expressed as k² where k is an integer. Examples include 4, 9, 16, 25, etc.

Shortcut Trick

Divisibility rule of 11: Sum of digits at odd positions − Sum of digits at even positions = 0, 11, 22...

For the number 4x5y790: (4 + 5 + 7 + 0) − (x + y + 9) = 16 − (x + y + 9) = 7 − (x + y).

For divisibility by 11, 7 − (x + y) must be 0 or −11.

⇒ x + y = 7 or x + y = 18.

In both cases, (7 ÷ 11) or (18 ÷ 11) leaves a remainder of 7.

∴ The correct answer is 7.

Alternate Method

Given: The number is 4x5y790 and it is divisible by 11.

⇒ Sum of digits at odd positions = 4 + 5 + 7 + 0 = 16

⇒ Sum of digits at even positions = x + y + 9

⇒ Difference = |16 − (x + y + 9)| = |7 − (x + y)|

⇒ Since the number is divisible by 11, the difference must be a multiple of 11.

⇒ Case 1: 7 − (x + y) = 0 ⇒ x + y = 7

⇒ Case 2: 7 − (x + y) = −11 ⇒ x + y = 18 (since max sum of two digits is 9 + 9 = 18)

⇒ When x + y = 7 is divided by 11: 7 ÷ 11 → Remainder = 7

⇒ When x + y = 18 is divided by 11: 18 ÷ 11 → Remainder = 7

∴ The correct answer is 7.

Additional Information

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is 0 or a multiple of 11 (e.g., 11, 22, 33...).

Digit Sum Constraints

For any two single digits x and y, the minimum sum (x + y) is 0 and the maximum sum is 9 + 9 = 18.

Remainder Theorem Basics

If a number N is smaller than the divisor D, the remainder when N is divided by D is N itself (e.g., 7 ÷ 11 leaves remainder 7).