Explanation : 

A has some coins

Let’s solve this step by step:

1. Initial Condition:
– A has x coins
– A gives half of coins plus 2 to B

2. After first transfer (A to B):
– A has: x/2 – 2 coins
– B has: x/2 + 2 coins

3. After second transfer (B to C):
– B gives half plus 2 to C
– B has: (x/2 + 2)/2 – 2 = x/4 – 1 coins
– C has: (x/2 + 2)/2 + 2 = x/4 + 3 coins

4. After third transfer (C to D):
– C gives half plus 2 to D
– C has: (x/4 + 3)/2 – 2 = x/8 – 1/2 coins
– D has: (x/4 + 3)/2 + 2 = x/8 + 7/2 coins

5. Given condition:
– D has smallest two-digit number (10)
– Therefore: x/8 + 7/2 = 10

6. Solve for x:
– x/8 + 7/2 = 10
– x/8 = 10 – 7/2
– x/8 = 6.5
– x = 52

Verification:
– A starts with 52 coins
– B gets 28 coins (26 + 2), A keeps 24
– C gets 16 coins (14 + 2), B keeps 12
– D gets 10 coins (8 + 2), C keeps 6

Answer: A had 52 coins initially

Explanation : 

101 plants on a 1.01 km road

Given information:
– Road length: 1.01 km = 1010 meters
– Total plants: 101
– Plants are equally spaced
– First plant at 0 meters
– Last plant at 1010 meters

Solution steps:

1. Find total gaps between plants:
– Total gaps = Total plants – 1
– Total gaps = 101 – 1 = 100 gaps

2. Find distance between consecutive plants:
– Distance = Total length ÷ Number of gaps
– Distance = 1010 ÷ 100 = 10.1 meters

3. Find distance for 5 consecutive plants:
– Number of gaps = Number of plants – 1
– Number of gaps = 5 – 1 = 4 gaps
– Total distance = Distance per gap × Number of gaps
– Total distance = 10.1 × 4 = 40.4 meters

Answer: The distance between 5 consecutive plants is 40.4 meters

Explanation : 

How many 3 digit natural numbers ??

Given conditions:
– Must be a 3-digit number
– All digits must be odd
– No repetition of digits allowed
– Number must be divisible by 5

Solution steps:

1. For divisibility by 5:
– Last digit must be either 0 or 5
– Since only odd digits allowed, last digit must be 5

2. Available odd digits: 1, 3, 5, 7, 9
– 5 is already used in units place
– Remaining digits for other positions: 1, 3, 7, 9

3. Filling other positions:
– Hundreds place: 4 choices (1, 3, 7, 9)
– Tens place: 3 choices (remaining digits after hundreds place)

4. Total possible numbers:
– Using multiplication principle
– 4 × 3 = 12 different numbers

Answer: 12 three-digit numbers possible

Explanation : 

Is x an integer?

Statement-1: x/3 is not an integer

– This tells us x cannot be evenly divided by 3
– Examples: x could be 2/3 (not an integer) or 4 (integer)
– Statement-1 alone is not sufficient

Statement-2: 3x is an integer

– This means x could be an integer or a fraction multiple of 1/3
– Examples: if 3x = 6, then x = 2 (integer)
if 3x = 2, then x = 2/3 (not integer)
– Statement-2 alone is not sufficient

Combined Analysis:
– Statement-1: x cannot be evenly divided by 3
– Statement-2: 3x is an integer
– Together they tell us x must be a fraction multiple of 1/3
– Still cannot determine if x is definitely an integer

Answer: Both Statement-1 and Statement-2 are not sufficient to answer the Question.

Explanation : 

A man completes 7/8 of a job in 21 days ….

Given:
– Man completes 7/8 of work in 21 days
– Work increases by 50%

Step 1: Find Rate of Work
– Total work = W
– Rate = (7/8)W ÷ 21 = W/24 per day

Step 2: Calculate New Work
– Increased work = 1.5W
– Already completed = 7/8W
– Remaining = 1.5W – 7/8W = 5/8W

Step 3: Calculate Days Required
– Time = Remaining work ÷ Rate
– = (5/8W) ÷ (W/24)
– = 15 days

Answer: 15 additional days required

Explanation : 

Q1: Correct Answer – (a) The central bank cannot work independently of the Government.

Explanation – (a) The central bank cannot work independently of the Government: This option suggests that the central bank and the government must work together in order to achieve their objectives. In the context of the passage, this means that monetary and fiscal policies must be coordinated in order to enhance the economic welfare of the people.

(b) Government should regulate financial markets and institutions closely: This option suggests that it is important for the government to closely monitor and regulate financial markets and institutions. While this may be a valid statement in general, it does not directly follow from the passage.

c) Market economy is not compatible with socialist policies of the Government: This option suggests that there is a conflict between a market economy and socialist policies implemented by the government. While this may be a topic for debate, it does not directly follow from the passage.

(d) Financial sector reforms are required for enhancing economic welfare of people: This option suggests that reforms in the financial sector are necessary in order to improve economic welfare. While this may be true, it does not directly follow from the passage which focuses on coordination between monetary and fiscal policies.

Explanation : 

Q1: Correct Answer – (d) Indian banking system requires structural reforms as a long-term solution for bad loans problem.

Explanation – The most logical, rational and practical suggestion implied by the passage given above is that the Indian banking system requires structural reforms as a long-term solution for bad loans problem (option d). The passage suggests that while resolution of bankruptcy cases and recapitalization of public sector banks can help in cleaning up bank books and increasing their capital cushion, they are only a part of the solution. Systemic reforms that address the problem of unsustainable lending are necessary to prevent future credit cycles from stressing the banking system.

Explanation : 

Q1: Correct Answer – (c) 2, 3 and 5 only

Explanation – 1. Too much globalization is not in the best interests of any country: This statement suggests that excessive globalization could have negative consequences for individual countries. However, this idea is not explicitly mentioned or implied in the passage.

2. Modern technologies are increasingly blurring the economic borders: This statement reflects the idea presented in the passage that new technologies such as driverless cars and custom-made biological products can create complex transnational issues that challenge traditional economic boundaries.

3. Innovation and capital have impinged on the domain of the state: This statement reflects the idea presented in the passage that new technologies and their associated capital flows can create complex issues that challenge traditional notions of state sovereignty and control.

4. Public policy of every country should focus on developing its own supply chains: This statement suggests that countries should prioritize developing their own supply chains to mitigate potential negative effects of globalization. However, this idea is not explicitly mentioned or implied in the passage.

5. Geopolitics will have to reconcile to many ambiguities and uncertainties: This statement reflects the idea presented in the passage that new technologies can create complex transnational issues with many ambiguities and uncertainties, which will require adaptation from geopolitical actors.

So based on these explanations, option © 2, 3 and 5 only remains as a correct answer.

Explanation : 

Q1: Correct Answer – (a) The conceptions of what is right or wrong exist due to the formation of a state.

Explanation –

(a) “The conceptions of what is right or wrong exist due to the formation of a state.” This option reflects the central idea of the passage that in a natural state, individuals determine what is good or bad according to their own fancy and sin cannot be conceived. It is only in a civil state where common consent decrees what is good or bad.

(b) “Unless a ruling authority decides as to what is right or wrong, no man would be morally right.” This option suggests that without a ruling authority to determine what is right or wrong, individuals would not be able to act morally. However, this idea is not explicitly stated in the passage.

(c) “Man is inherently immoral and selfish in a natural state.” This option suggests that individuals are inherently immoral and selfish when they are in a natural state. While the passage does mention that individuals consult only their own advantage in a natural state, it does not explicitly state that they are inherently immoral or selfish.

(d) “The idea of what is right or wrong is necessary for the survival of human species.” This option suggests that having an understanding of what is right and wrong is necessary for human survival. However, this idea is not mentioned in the passage.

Explanation : 

Q1: Correct Answer – (c) To maintain and develop our cities we need to adopt sustainability related interventions.

Explanation – The passage discusses the vulnerability of cities to climate change due to large populations and poor infrastructure. It highlights the need to address issues such as air quality and transport in order to identify sustainable solutions. The most logical and rational inference that can be made from this passage is option c) : “To maintain and develop our cities we need to adopt sustainability related interventions.”