The correct answer is Agriculture contributed declining GDP share but absorbed majority employment.

Key Points

• The structural transformation of the Indian economy between 1950 and 1991 was unique and contradictory compared to global development patterns. In a typical developing economy, labor moves from Agriculture to Industry and then to Services.
• While the share of Agriculture in the Gross Domestic Product (GDP) declined significantly—from about 50% in 1950-51 to around 30% by 1990-91—the proportion of the population dependent on it for a livelihood did not decline proportionately.
• During this period, the Primary Sector (Agriculture) continued to absorb the majority of the workforce, accounting for approximately 67.4% of employment in 1991, despite its falling contribution to the national income. Hence, the statement regarding agriculture's declining GDP share vs. high employment absorption is correct.
• The Industrial Sector failed to grow at a pace rapid enough to absorb the surplus labor from the rural areas. Even though the Secondary Sector grew under various Five-Year Plans, its capacity for employment generation remained limited. Hence, the statement that manufacturing became the primary employment generator is incorrect.
• The Services Sector (Tertiary Sector) saw a faster growth in GDP share than the industrial sector, but this growth was not accompanied by an equivalent increase in employment opportunities during the pre-reform era. Hence, the statement that services led growth and employment equally is incorrect.

Additional Information

• Structural Composition of GDP:
• At the time of independence in 1947, India was a predominantly agrarian economy. The Planning Commission was established in 1950 to guide economic development.
• The Second Five-Year Plan (1956-1961), based on the Mahalanobis Model, focused heavily on heavy industries to modernize the economy, yet the workforce shift remained stagnant.
• Disguised Unemployment:
• The contradiction of high employment in Agriculture with low GDP contribution led to Disguised Unemployment. This is a phenomenon where more people are working in a sector than are actually required, and their marginal productivity is zero.
• By 1990, while Agriculture contributed only about one-third of the GDP, it still supported two-thirds of the Indian population.
• Role of the Secondary and Tertiary Sectors:
• The Secondary Sector includes Manufacturing, Electricity, and Construction. Its share in GDP increased from 13% in 1950 to about 24% in 1990.
• The Tertiary Sector (Trade, Transport, Banking, etc.) grew from 30% to approximately 40% of GDP in the same period, but the "jobless growth" in services became a point of concern for economists.
• Economic Reforms of 1991:
• Due to this structural imbalance and a Balance of Payments (BoP) crisis, India introduced Liberalization, Privatization, and Globalization (LPG) reforms in July 1991 under the leadership of P.V. Narasimha Rao and Finance Minister Dr. Manmohan Singh.
• Post-1991, the Services Sector became the main engine of GDP growth, though the challenge of shifting labor out of low-productivity agriculture remains a major theme in Indian economics today.

Shortcut Trick

SP of X = CP + Profit = 800 + 523 = 1323.

Remaining SP factor after 45% and 73% discounts = 0.55 × 0.27 = 0.1485.

Remaining SP factor after 89% discount = 0.11.

Ratio SP_X : SP_Y = 0.1485 : 0.11 = 135 : 100 = 27 : 20.

27 units = 1323 ⇒ 1 unit = 49 ⇒ SP_Y = 20 × 49 = 980.

Profit % on Y = (980 − 800) ÷ 800 × 100 = 180 ÷ 8 = 22.5%.

∴ Answer = 22.5%

Alternate Method 

Given:

CP of X = CP of Y = 800. MP of X = MP of Y. Profit on X = 523. Discounts on X = 45%, 73%. Discount on Y = 89%.

Formula used:

SP = CP + Profit; SP = MP × (1 − d₁/100) × (1 − d₂/100); Profit % = (Profit/CP) × 100

CP = 800 MP X: 45%, 73% disc. SP_X = 1323 Y: 89% disc. SP_Y = 980 Profit on Y = 980 − 800 = 180

Calculations:

For article X:

⇒ SP_X = 800 + 523 = 1323

⇒ SP_X = MP × (1 − 45/100) × (1 − 73/100)

⇒ 1323 = MP × 0.55 × 0.27

⇒ MP = 1323 ÷ (0.55 × 0.27) = 1323 ÷ 0.1485

For article Y:

⇒ SP_Y = MP × (1 − 89/100) = MP × 0.11

⇒ SP_Y = (1323 ÷ 0.1485) × 0.11 = 1323 × (1100 ÷ 1485)

⇒ SP_Y = 1323 × (20 ÷ 27) = 49 × 20 = 980

⇒ Profit on Y = 980 − 800 = 180

⇒ Profit % = (180 ÷ 800) × 100 = 22.5%

∴ The correct answer is 22.5% (Option 2).

Additional Information

Successive Discounts

Two successive discounts of a% and b% are equivalent to a single discount of [a + b − (a × b)/100]%.

Marked Price Formula

MP = CP × (100 + Profit%) ÷ (100 − Discount%). This relates CP and MP directly when profit and discount are known.

Effective Value

If an item is discounted by d%, its selling price becomes (100 − d)% of its marked price.

Calculation:

15% of 80 - (3/6) × $\sqrt[3]{216}$ × $\sqrt{36}$ = y

⇒ 3/20 × 80 - (1/2) × 6 × 6 = y

⇒ 3 × 4 - 3 × 6 = y

⇒ 12 - 18 = y

⇒ y = - 6

Hence, the correct answer is -6.

Shortcut Trick

Expression is of the form (a³ + b³) / (x² + y² − xy) where a = 10x and b = 10y.

Numerator = (10x)³ + (10y)³ = 1000(x³ + y³).

Expression reduces to 1000 × (x³ + y³) / (x² − xy + y²) = 1000(x + y).

Substitute x = 73.2 and y = 26.8: 1000 × (73.2 + 26.8) = 1000 × 100 = 100000.

∴ The correct answer is 100000.

Alternate Method

Given: Numerator = 732³ + 268³ and Denominator = 73.2² + 26.8² − 73.2 × 26.8

Formula Used: a³ + b³ = (a + b)(a² − ab + b²)

⇒ Let x = 73.2 and y = 26.8. Then 732 = 10x and 268 = 10y.

⇒ Expression = [(10x)³ + (10y)³] / [x² + y² − xy]

⇒ Expression = [1000x³ + 1000y³] / [x² − xy + y²]

⇒ Expression = 1000 × (x³ + y³) / (x² − xy + y²)

⇒ Expression = 1000 × [(x + y)(x² − xy + y²)] / (x² − xy + y²)

⇒ Expression = 1000 × (x + y)

⇒ Expression = 1000 × (73.2 + 26.8)

⇒ Expression = 1000 × 100 = 100000.

∴ The correct answer is 100000.

Additional Information

Algebraic Identity: Sum of Cubes

The formula a³ + b³ = (a + b)(a² − ab + b²) is a standard identity used to simplify expressions where a cubic sum is divided by a quadratic term.

Algebraic Identity: Difference of Cubes

Similarly, a³ − b³ = (a − b)(a² + ab + b²) is used for simplifying subtractions of cubes.

Decimal and Power Relationship

If a number is multiplied by 10, its square is multiplied by 100 (10²) and its cube is multiplied by 1000 (10³).

The correct answer is Cabinet Ministers – Ministers of State – Deputy Ministers.

Key Points

• The Council of Ministers in India consists of a three-tier hierarchy of ministers, which includes Cabinet Ministers, Ministers of State, and Deputy Ministers.
• Cabinet Ministers: These are the senior-most members of the Council of Ministers. They hold the charge of crucial ministries of the Central Government such as Home, Defense, Finance, and External Affairs. They are the primary policy-making body of the Government of India. Hence, this tier is correctly identified.
• Ministers of State: This is the second tier of the council. They can either be given independent charge of ministries/departments or can be attached to Cabinet Ministers. When attached, they assist the Cabinet Ministers in the discharge of their duties. Hence, this tier is correctly identified.
• Deputy Ministers: These are the third tier of the Council of Ministers. They are not given independent charge of any ministry and are always attached to Cabinet Ministers or Ministers of State. Their main function is to assist in administrative, parliamentary, and departmental work. Hence, this tier is correctly identified.
• The Prime Minister sits at the top of this entire structure as the head of the Council of Ministers, exercising supreme executive authority. Hence, the statement representing the tiers as Cabinet, Ministers of State, and Deputy Ministers is correct.

Additional Information

• Constitutional Basis: Article 74 of the Constitution of India provides for a Council of Ministers with the Prime Minister at the head to aid and advise the President. Article 75 deals with the appointment, tenure, responsibility, qualification, oath, and salaries of the ministers.
• Size of Council of Ministers: According to the 91^st Constitutional Amendment Act, 2003, the total number of ministers, including the Prime Minister, in the Central Council of Ministers shall not exceed 15% of the total strength of the Lok Sabha.
• Collective Responsibility: Under Article 75(3), the Council of Ministers is collectively responsible to the Lok Sabha (the Lower House of Parliament). This means that all ministers own joint responsibility to the Lok Sabha for all their acts of omission and commission.
• Cabinet vs. Council of Ministers: The Council of Ministers is a wider body consisting of 60 to 80 ministers, whereas the Cabinet is a smaller, more powerful core group consisting of about 15 to 20 ministers. The term "Cabinet" was inserted into Article 352 of the Constitution by the 44^th Amendment Act, 1978.
• Appointment: The Prime Minister is appointed by the President, and other ministers are appointed by the President on the recommendation of the Prime Minister. A person who is not a member of either House of Parliament can be appointed as a minister for a maximum period of 6 months, within which they must get elected to either house.

Important Points

• Individual Responsibility: Article 75 also contains the principle of individual responsibility, stating that the ministers hold office during the pleasure of the President.
• Council Hierarchy: While the Constitution does not classify the ministers into different ranks, this three-tier classification is based on British parliamentary conventions and has been followed in India since independence.
• Parliamentary Secretaries: Occasionally, a fourth category known as Parliamentary Secretaries is also appointed. They are senior members of the ruling party who assist the ministers in their parliamentary duties but are not technically part of the Council of Ministers.

Shortcut Trick

Time for P per round = 40 ÷ 5 = 8 min.

Time for R per round = (6 × 8) ÷ 7 = 48/7 min.

In same direction, Relative Speed = |1/8 − 7/48| = 1/48 rounds/min.

Initial gap = 1/2 round (diameter ends).

Time to meet = (1/2) ÷ (1/48) = 24 minutes.

∴ The correct answer is 24 minutes.

Alternate Method

Given:

Rounds by P = 5 in 40 min.

Relation: Time for 7 rounds of R = Time for 6 rounds of P.

Start position: Opposite ends of diameter (1/2 track apart).

Formula Used:

Speed = Distance ÷ Time

Relative Speed (Same Direction) = Speed₁ − Speed₂

Time of Meeting = Initial Distance ÷ Relative Speed

 P R  Initial Gap = 1/2 Round Same Direction Motion

Calculations:

⇒ Let track length = L

⇒ Speed of P (S_P) = (5 × L) ÷ 40 = L/8 per min

⇒ Time for 6 rounds of P = 6 × (L ÷ S_P) = 6 × 8 = 48 min

⇒ Speed of R (S_R) = (7 × L) ÷ 48 = 7L/48 per min

⇒ Initial separation distance = L/2 (Diameter ends)

⇒ Relative Speed = S_R − S_P = 7L/48 − L/8

⇒ Relative Speed = 7L/48 − 6L/48 = L/48 per min

⇒ Meeting Time = (L/2) ÷ (L/48)

⇒ Meeting Time = (1/2) × 48 = 24 minutes

∴ The correct answer is 24 minutes.

Additional Information

Meeting in Opposite Direction

When two people run in opposite directions, the relative speed is the sum of their individual speeds (S₁ + S₂).

Number of Meeting Points

If speeds are in ratio a:b (simplest form), they meet at (a−b) points in the same direction and (a+b) points in opposite directions.

Time for Subsequent Meetings

After the first meeting, each subsequent meeting occurs after a time interval of (Total Distance) ÷ (Relative Speed).

The logic followed here is:

Given: X, Y, Z, S, T and U live on six different floors of the same building.

The lowermost floor is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6.

Only Z lives above U.

T lives immediately below U.

Only Y lives below S.

 

Now, the person on floor number 4 is T.

Hence, the correct answer is Option 1.

Shortcut Trick

Recognize roots: √³2744 = 14 and √⁴256 = 4.

Substitute into expression: (14 ÷ 4) × (2 ÷ 42) × 72

Reduce ratios: (7 ÷ 2) × (1 ÷ 21) × 72

Combine: (7 ÷ 21) × (72 ÷ 2) = (1 ÷ 3) × 36 = 12

∴ Answer = 12

Alternate Method 

Given:

Expression: (√³2744 ÷ √⁴256) × (2 ÷ 42) × 72

Formula used:

Root property: √ⁿxⁿ = x

BODMAS rule: Simplify terms within brackets and roots first, then perform multiplication.

Term 1 Term 2 Term 3 14 / 4 2 / 42 72 Calculation: 3.5 × (1/21) × 72 = 12

Calculations:

Step 1: Simplify individual roots

⇒ √³2744 = √³(14 × 14 × 14) = 14

⇒ √⁴256 = √⁴(4 × 4 × 4 × 4) = 4

Step 2: Substitute and simplify fractions

⇒ (14 ÷ 4) × (2 ÷ 42) × 72

⇒ 3.5 × (1 ÷ 21) × 72

Step 3: Solve the multiplication

⇒ (3.5 ÷ 21) × 72

⇒ (1 ÷ 6) × 72

⇒ 72 ÷ 6 = 12

∴ The correct answer is 12 (Option 2).

Additional Information

Rules of Surds

The n-th root of a number can be expressed as an exponent: √ⁿx = x^(1/n). For example, √³x = x^(1/3).

Common Powers

Memorizing cubes up to 20 and fourth powers up to 10 helps in quick simplification. Note: 14³ = 2744 and 4⁴ = 256.

BODMAS / PEMDAS Rule

Always prioritize Roots/Exponents (Orders) and Brackets before performing Multiplication and Division from left to right.

The logic followed here is:

Logic: Middle term = (1^st term × last term)

(44, 968, 22)

⇒ (44 × 22) = 968

(26, 650, 25)

⇒ (26 × 25) = 650

Now, checking the options:

Option 1) (18, 108, 6)

⇒ 18 × 6 = 108 (True)

Option 2) (34, 173, 5)

⇒ 34 × 5 = 170 (false)

Option 3) (15, 348, 23)

⇒ 15 × 23 = 345 (false)

Option 4) (23, 210, 9)

⇒ 23 × 9 = 207 (false)

Hence, the correct answer is Option (1).

The correct answer is Creation of separate electorates.

Key Points

• The Indian Council Act of 1909, also famously known as the Morley-Minto Reforms, introduced the highly controversial system of separate electorates for Muslims. Under this provision, Muslim representatives were to be elected exclusively by Muslim voters.
• This move was criticized by the Indian National Congress and other nationalist leaders as it was perceived as a clear application of the "Divide and Rule" policy. By institutionalizing communalism in Indian politics, the British Government aimed to create a rift between Hindus and Muslims, thereby weakening the Nationalist Movement.
• The Act was named after Lord Morley, the then Secretary of State for India, and Lord Minto, the Viceroy of India. Due to his role in introducing communal representation, Lord Minto is often referred to as the "Father of Communal Electorate".
• The Creation of separate electorates is the correct answer because it directly targeted the unity of the Indian people by categorizing political interests based on religion, which eventually laid the groundwork for the Partition of India.

Additional Information

• Expansion of Legislative Councils: The Act increased the size of the Legislative Councils at both the Central and Provincial levels. The number of members in the Central Legislative Council was raised from 16 to 60. However, an official majority was retained at the Centre, while non-official majorities were allowed in the Provincial Councils.
• Inclusion of Indians in Executive Councils: For the first time, the Act provided for the association of Indians with the Executive Councils of the Viceroy and Governors. Satyendra Prasad Sinha became the first Indian to join the Viceroy’s Executive Council as the Law Member.
• Enhanced Deliberative Powers: The Legislative Councils were given the power to discuss the Budget and move resolutions. Members were also allowed to ask supplementary questions, although the executive still held the final authority and could reject resolutions without providing detailed reasons.
• Background of the Act: The reforms were enacted in the backdrop of the 1905 Partition of Bengal and the formation of the All India Muslim League in 1906. The Simla Deputation, led by Aga Khan in 1906, had specifically met Lord Minto to demand separate representation for Muslims to safeguard their political rights.

Important Points

• The Morley-Minto Reforms did not aim at establishing a parliamentary system in India; rather, they were intended to involve some Indians in the administration to placate the Moderate faction of the Congress while isolating the Extremists.
• The system of communal representation introduced in 1909 was further extended to Sikhs, Indian Christians, Anglo-Indians, and Europeans in the Government of India Act 1919 (Montagu-Chelmsford Reforms).
• Mahatma Gandhi later stated that "The Morley-Minto Reforms have been our undoing," emphasizing how the Creation of separate electorates sowed the seeds of communal disharmony that plagued the independence struggle for decades.
• Despite the increase in the number of members, the electorate remained very limited, based on property qualifications, education, or status, meaning only a tiny fraction of the Indian population had the Right to Vote.

The logic followed here is:

Logic: Sum of positions × 2

Checking the given codes:

For, VAJR

V(22) + A(1) + J(10) + R(18) = 51

⇒ 51 × 2 = 102 

For, DOTG

D(4) + O(15) + T(20) + G(7) = 46

⇒ 46 × 2 = 92 

Now, for ZELW:

Z(26) + E(5) + L(12) + W(23) = 66

⇒ 66 × 2 = 132

Hence, the correct answer is Option 2.

Given:

Vihaana walks 11 km North.

She turns left → 7 km West.

She turns left → 11 km South.

She turns right → 2 km West and reaches point R.

 

So, point R is 9 km to the West from the starting point.

Hence, the correct answer is Option 4.

The correct answer is Market-determined interest rates with reduced RBI intervention.

Key Points

• One of the most significant structural adjustments in India’s monetary policy following the 1991 Economic Reforms was the shift from an administered interest rate regime to a market-determined interest rate system. Prior to 1991, the Reserve Bank of India (RBI) strictly controlled interest rates for both deposits and loans.
• The Narasimham Committee (1991) on the Financial System recommended that interest rates should be allowed to be determined by market forces (demand and supply) to improve the efficiency of the banking sector and the allocation of capital. Hence, the statement regarding market-determined rates is correct.
• Post-reforms, the RBI gradually deregulated lending and deposit rates. By October 1994, the RBI abolished the minimum lending rate and allowed commercial banks to determine their own Prime Lending Rates (PLR).
• This shift allowed the RBI to move away from direct controls and instead use indirect instruments of monetary policy, such as the Repo Rate, Reverse Repo Rate, and Open Market Operations (OMO), to manage liquidity and inflation in the Indian economy.
• The structural adjustment also involved a significant reduction in the Statutory Liquidity Ratio (SLR) and Cash Reserve Ratio (CRR). The SLR, which was as high as 38.5% in 1991, was gradually brought down to increase the availability of funds for the private sector.

Additional Information

• 1991 Economic Crisis: India faced a severe Balance of Payments (BoP) crisis in 1991, with forex reserves dropping to a level barely enough to cover two weeks of imports. This led to the Liberalization, Privatization, and Globalization (LPG) reforms under the leadership of Prime Minister P.V. Narasimha Rao and Finance Minister Dr. Manmohan Singh.
• Monetary Policy Tools:
• Open Market Operations (OMO): Post-1991, OMOs became a vital regulatory tool. The RBI buys or sells Government Securities (G-Secs) to regulate the money supply. Statement 3 is incorrect because OMOs were strengthened, not eliminated.
• Deficit Financing: Before the reforms, the government relied heavily on automatic monetization of the fiscal deficit through Ad-hoc Treasury Bills. This was phased out by 1997 and eventually replaced by the Ways and Means Advances (WMA) system. Hence, statement 4 is incorrect as the goal was to curtail deficit financing.
• Priority Sector Lending (PSL): While the government still mandates 40% of Adjusted Net Bank Credit (ANBC) to the Priority Sector (including Agriculture and MSMEs), the overall structural trend moved away from general "controlled rates" toward market alignment, even within these sectors. Hence, statement 1 is partially true in practice but does not represent the "structural adjustment" of the reform era.

Important Points

• Liquidity Adjustment Facility (LAF): Introduced in June 2000 following the Narasimham Committee II (1998) recommendations, LAF allowed banks to manage their day-to-day liquidity mismatches through repo and reverse repo auctions.
• MCLR and EBLR: To ensure better transmission of monetary policy, the RBI transitioned from the Base Rate system to the Marginal Cost of Funds Based Lending Rate (MCLR) in 2016, and subsequently to External Benchmark Lending Rates (EBLR) in 2019 for retail and MSME loans.
• FRBM Act (2003): The Fiscal Responsibility and Budget Management Act was enacted to institutionalize fiscal discipline and reduce the fiscal deficit, further separating monetary policy from the government’s fiscal deficit requirements.

The logic followed here is:

Given: J, K, L, R, S and T live on six different floors of the same building.

The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. 

Only two people live between J and T.

Only two people live between S and K.

Only one person lives between L and K.

L lives on floor number 1.

J lives above K.

 

Now, people between R and S : 1 person.

Hence, the correct answer is Option 4.

The logic followed here is:

thus, "48" will replace the question mark in the given series.

Hence, the correct option is "Option 4".

Shortcut Trick

Total Work = LCM(12, 36) = 36 units

Efficiency of Reema = 36 ÷ 12 = 3 units/day; Efficiency of Juhi = 36 ÷ 36 = 1 unit/day

Work done in 1 cycle (2 days: Reema + Juhi) = 3 + 1 = 4 units

Number of cycles required = 36 ÷ 4 = 9 cycles

Total time = 9 cycles × 2 days/cycle = 18 days

∴ The correct answer is 18.

Alternate Method

Given: Reema = 12 days, Juhi = 36 days

Total work = LCM of 12 and 36 = 36 units

⇒ Total Efficiency (Reema + Juhi) = 3 + 1 = 4 units

⇒ According to the problem, they work on alternate days starting with Reema.

⇒ Work on Day 1 (Reema) = 3 units

⇒ Work on Day 2 (Juhi) = 1 unit

⇒ Total work done in 2 days = 3 + 1 = 4 units

⇒ Number of such 2-day cycles needed = Total work ÷ Work per cycle

⇒ Number of cycles = 36 ÷ 4 = 9 cycles

⇒ Total time taken = 9 × 2 days = 18 days

∴ The correct answer is 18.

Additional Information

Alternate Day Work

In alternate day problems, calculate the work done in one full cycle (all participants working once) and divide the total work by this cycle's output.

Remaining Work Calculation

If the total work is not perfectly divisible by the cycle's output, calculate the remaining work and assign it to the next person in sequence.

Work and Wages

Wages are always distributed in the ratio of the total work actually done by each individual, not just their efficiency ratio.

BODMAS Table: 

Given equation: 156 × 12 − 13 ÷ 8 + 71 = ?

Now, if + and − are interchanged and × and ÷ are interchanged, then:

⇒ 156 ÷ 12 + 13 × 8 − 71

⇒ 156 ÷ 12 = 13

⇒ 13 × 8 = 104

⇒ 13 + 104 − 71

⇒ 117 − 71

⇒ 46

Hence, the correct answer is Option 1.

The correct answer is Feudal lords.

Key Points

• The term Samanta refers to big landlords or warrior chiefs in different regions of the Indian subcontinent during the post-Gupta period (specifically between the 6^th and 12^th centuries CE). Hence, the option identifying them as Feudal lords is correct.
• These individuals were expected to bring gifts or tributes for their kings or overlords and provide them with military support during times of war.
• As Samantas gained power and wealth, they often declared themselves to be Mahasamanta or Mahamandaleshvara (the great lord of a circle or region), indicating an increase in their social and political status.
• The Samanta system led to the decentralization of political power, where the central monarch's authority became dependent on the loyalty of these subordinate feudal lords.
• If a Samanta became powerful enough, he could assert independence from his overlord. A famous example is Dantidurga, a Rashtrakuta chief who overthrew his Chalikya overlord in the mid-8^th century.

Additional Information

• Farmers: In the ancient and medieval periods, farmers were known as Krishakas or Halikas. While they provided the revenue that supported the Samantas, they did not hold administrative or military titles. Hence, this statement is incorrect.
• Religious heads: Religious leaders or priests (Brahmins) often received land grants known as Agrahara or Brahmadeya. While they managed land, their primary identity was spiritual and ritualistic rather than the military-administrative role associated with Samantas. Hence, this statement is incorrect.
• Architects: Professional builders and designers in ancient India were referred to as Shilpis or Sutradharas. They were responsible for the temple architecture of the era, such as the Khajuraho or Chola temples, but held no feudal authority. Hence, this statement is incorrect.
• Origin of the System: The practice of granting land to officers in lieu of cash salaries began during the Gupta Empire and became a dominant feature under King Harshavardhana in the 7^th Century CE.
• Economic Impact: The rise of the Samantas led to a manorial economy where the peasantry was often tied to the land, and local self-sufficiency became more prominent than long-distance trade.

Important Points

• Administrative Structure: The Samantas were responsible for maintaining law and order within their territories and collecting taxes, a portion of which was sent to the king.
• Military Obligation: One of the primary duties of a Samanta was to maintain a specific number of infantry and cavalry units to be placed at the king's disposal whenever required.
• Geographical Spread: This system was prevalent across North India under the Pratiharas and Palas, and in South India under the Rashtrakutas and Pallavas.
• Social Hierarchy: The Samanta occupied a middle position in the social hierarchy, acting as a bridge between the monarch and the common people (peasants and artisans).
• End of the System: The Samanta system began to decline with the advent of the Delhi Sultanate, which introduced a more centralized Iqta system of administration.

The correct answer is Every two years.

Key Points

• Biennial Update Reports (BURs) are specialized reports submitted by Non-Annex I parties (developing countries like India) to the United Nations Framework Convention on Climate Change (UNFCCC).
• According to the guidelines established during the Conference of Parties (COP 16) in Cancun (2010) and COP 17 in Durban (2011), these reports must be submitted every two years.
• The primary objective of the BUR is to provide an update on the information presented in the National Communications (NATCOM), specifically focusing on national greenhouse gas (GHG) inventories, mitigation actions and their effects, and the support needed and received.
• India submitted its First BUR to the UNFCCC in January 2016, the Second BUR in December 2018, and the Third BUR in February 2021.
• The Third BUR highlighted that India has successfully reduced the emission intensity of its Gross Domestic Product (GDP) by 24% between 2005 and 2016, showcasing significant progress toward its Paris Agreement goals.

Additional Information

• UNFCCC (United Nations Framework Convention on Climate Change):
• It was adopted in 1992 at the Rio Earth Summit and entered into force on March 21, 1994.
• Its ultimate objective is to stabilize greenhouse gas concentrations in the atmosphere at a level that prevents dangerous human interference with the climate system.
• It categorizes countries into Annex I (developed nations), Annex II (developed nations providing financial support), and Non-Annex I (mostly developing nations).
• National Communications (NATCOM):
• These are comprehensive reports that India is required to submit periodically. India submitted NATCOM-1 in 2004, NATCOM-2 in 2012, and NATCOM-3 in 2023.
• Unlike BURs which occur every two years, NATCOMs have a longer and more flexible reporting cycle depending on COP decisions.
• Enhanced Transparency Framework (ETF):
• Under the Paris Agreement (signed in 2015), the reporting system is transitioning from BURs to Biennial Transparency Reports (BTRs).
• The first BTR for all parties is mandated to be submitted by December 31, 2024. This will provide a more rigorous and uniform tracking mechanism for Climate Action globally.
• India’s GHG Inventory Sectors:
• India reports emissions from five major sectors: Energy, Industrial Processes and Product Use (IPPU), Agriculture, Waste, and Land Use, Land-Use Change and Forestry (LULUCF).
• The Energy sector remains the largest contributor to emissions in India, accounting for approximately 75% of total emissions (excluding LULUCF).

Important Points

• Institutional Arrangement: In India, the Ministry of Environment, Forest and Climate Change (MoEFCC) is the nodal agency responsible for preparing and submitting these reports to the UNFCCC.
• Technical Analysis: Once a BUR is submitted, it undergoes a Technical Analysis by a team of international experts as part of the International Consultation and Analysis (ICA) process.
• Yearly Submissions: While the question asks about BURs (which are every two years), developed countries (Annex I) are required to submit their GHG inventories every year.
• Global Context: The BUR helps in the Global Stocktake process, which assesses the collective progress of the world toward achieving the long-term goals of the Paris Agreement.

The correct answer is Proteins.

Key Points

• Proteins are known as the building blocks of the human body. Their primary function is the growth, maintenance, and repair of all body tissues, including muscles, organs, skin, and hair.
• Chemically, proteins are macromolecules composed of smaller units called amino acids. There are 20 different amino acids that combine in various sequences to form different proteins. Unlike carbohydrates and fats, proteins contain nitrogen in addition to carbon, hydrogen, and oxygen.
• Proteins act as enzymes, which are biological catalysts that speed up chemical reactions in the body. For example, digestive enzymes like pepsin and trypsin are essential for breaking down food.
• They also serve as hormones, such as insulin, which regulates blood sugar levels. Furthermore, antibodies are specialized proteins that are critical to the immune system for defending the body against viruses and bacteria.
• When the body lacks sufficient carbohydrates or fats, it can break down proteins to provide energy, yielding approximately 4 kcal per 1 gram of protein.

Additional Information

• Carbohydrates:
• The primary function of carbohydrates is to provide immediate energy to the body. They are broken down into glucose, which is the preferred fuel for the brain and muscles.
• Sources include cereals, fruits, and vegetables. They provide 4 kcal per gram.
• Fats:
• Fats serve as a concentrated source of energy, providing 9 kcal per gram, which is more than double the energy provided by proteins or carbs.
• They are essential for the absorption of fat-soluble vitamins like Vitamin A, D, E, and K. They also provide insulation and protect internal organs.
• Vitamins:
• Vitamins are micronutrients required in small quantities for various metabolic processes. They do not provide energy but are crucial for bone health, vision, and blood clotting.
• Examples include Vitamin C (for immunity) and Vitamin D (for calcium absorption).
• Minerals:
• Inorganic elements like Calcium, Iron, and Potassium are necessary for bone density, oxygen transport in the blood (via hemoglobin), and nerve signaling.

Important Points

• Essential Amino Acids: Out of the 20 amino acids, 9 are considered essential because the human body cannot synthesize them; they must be obtained through diet.
• Dietary Requirements: According to health guidelines, the Recommended Dietary Allowance (RDA) for an adult is approximately 0.8 grams of protein per kilogram of body weight. This requirement increases for infants, pregnant women, and athletes.
• Deficiency Diseases: Severe protein deficiency leads to conditions like Kwashiorkor (characterized by edema and a swollen abdomen) and Marasmus (characterized by stunted growth and tissue wasting), commonly seen in children in developing countries.
• Structural Proteins: Collagen is the most abundant protein in the human body, providing structure to connective tissues, while Keratin is the primary component of nails and hair.

Shortcut Trick

When a : b :: b : c, then b is the mean proportional where b² = ac.

Given b = 6 and c = 4a → a = c ÷ 4.

Substitute in formula: 6² = (c ÷ 4) × c

36 = c² ÷ 4 → c² = 144

c = √144 = 12

∴ Answer = 12

Alternate Method 

Given:

a : b :: b : c

c = 4a

b = 6

Formula used:

In a continued proportion a : b :: b : c, the relation is b² = ac

a = 3 b = 6 c = 12 Ratio 1:2 Ratio 1:2 Relation: 6² = 3 × 12 c = 4 × a = 4 × 3 = 12

Calculations:

From the proportion a : b :: b : c, we have:

⇒ b² = a × c

⇒ 6² = a × (4a)

⇒ 36 = 4a²

⇒ a² = 36 ÷ 4 = 9

⇒ a = √9 = 3

⇒ c = 4 × a = 4 × 3 = 12

∴ The correct answer is 12.

Additional Information

Mean Proportional

If a, b, c are in continued proportion, then b is the mean proportional such that b = √(ac).

Third Proportional

In the proportion a : b :: b : c, c is called the third proportional and is calculated as c = b² ÷ a.

Fourth Proportional

In the proportion a : b :: c : d, d is the fourth proportional and is given by d = (b × c) ÷ a.

Continued Proportion

Quantities a, b, c, d... are in continued proportion if a/b = b/c = c/d and so on.

The logic followed here is:

Given numbers: 547, 589, 652, 598, 637

Here, Highest and lowest numbers:

Highest number = 652

Lowest number = 547

Required digits:

Second digit of highest number (652) = 5

Second digit of lowest number (547) = 4

Sum: 5 + 4 = 9

Hence, the correct answer is Option 3.

Shortcut Trick

Product of two numbers = HCF × LCM

Other number = (HCF × LCM) ÷ First number

Other number = (186 × 1116) ÷ 372

Other number = 1116 ÷ 2 = 558

∴ Answer = 558

Alternate Method 

Given:

LCM of two numbers = 1116

HCF of two numbers = 186

One number = 372

Formula used:

First number × Second number = LCM × HCF

HCF (186) × LCM (1116) = Num 1 (372) × Num 2 (?)

Calculations:

Let the other number be x.

⇒ 372 × x = 1116 × 186

⇒ x = (1116 × 186) ÷ 372

⇒ x = 1116 × (186 ÷ 372)

⇒ x = 1116 × (1 ÷ 2)

⇒ x = 558

∴ The correct answer is 558.

Additional Information

Fundamental Relation

The product of any two numbers is always equal to the product of their HCF and LCM: Product = HCF × LCM.

HCF and LCM of Fractions

HCF of fractions = HCF(Numerators) ÷ LCM(Denominators) and LCM of fractions = LCM(Numerators) ÷ HCF(Denominators).

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is equal to the product of the two numbers.

HCF and Division

HCF is the largest number that divides the given numbers without leaving a remainder.

The correct answer is Promoting cottage industries in rural areas.

Key Points

• Directive Principles of State Policy (DPSP) are enumerated in Part IV of the Indian Constitution, spanning from Article 36 to 51. These principles are classified into Socialistic, Gandhian, and Liberal-Intellectual categories based on their ideology.
• Article 43 of the Constitution directs the State to endeavor to promote cottage industries on an individual or co-operative basis in rural areas. This reflects Mahatma Gandhi’s vision of self-sufficient village economies and rural upliftment. Hence, statement 3 is correct.
• Raising the standard of living and public health is mentioned under Article 47. While it aligns with the overall welfare state, it is primarily categorized as a Socialistic Principle rather than a specific Gandhian ideal in the classification of the Constitution. Hence, statement 1 is incorrect.
• Securing suitable employment for all is part of the "Right to Work" under Article 41. This directive is a Socialistic Principle aimed at ensuring economic security for citizens. Hence, statement 2 is incorrect.
• Safeguarding children against exploitation and providing them with opportunities for healthy development is covered under Article 39(f). This is classified as a Socialistic Principle added or emphasized to ensure social justice. Hence, statement 4 is incorrect.

Additional Information

• Gandhian Principles in DPSP: These principles are based on the ideology of Mahatma Gandhi and represent the program of reconstruction enunciated by him during the National Movement.
• Article 40: To organize village panchayats and endow them with such powers and authority as may be necessary to enable them to function as units of self-government.
• Article 43B: To promote voluntary formation, autonomous functioning, democratic control, and professional management of co-operative societies (Added by the 97^th Amendment Act, 2011).
• Article 46: To promote the educational and economic interests of Scheduled Castes (SCs), Scheduled Tribes (STs), and other weaker sections of the society and to protect them from social injustice and all forms of exploitation.
• Article 47: To prohibit the consumption of intoxicating drinks and drugs that are injurious to health.
• Article 48: To prohibit the slaughter of cows, calves, and other milch and draught cattle and to improve their breeds.
• Socialistic Principles: These aim at establishing social and economic justice and paving the way for a welfare state. Examples include Article 38 (promoting social order), Article 39 (equitable distribution of resources), and Article 42 (humane conditions of work and maternity relief).
• Liberal-Intellectual Principles: These reflect the ideology of liberalism. Examples include Article 44 (Uniform Civil Code), Article 50 (Separation of judiciary from executive), and Article 51 (Promotion of international peace and security).

Important Points

• The DPSP are borrowed from the Irish Constitution of 1937, which had copied them from the Spanish Constitution.
• Unlike Fundamental Rights, DPSPs are non-justiciable in nature, meaning they are not legally enforceable by the courts for their violation (as per Article 37). However, they are fundamental in the governance of the country.
• The Sapru Committee in 1945 suggested two categories of individual rights: one being justiciable (Fundamental Rights) and the other being non-justiciable (Directive Principles).
• In the Minerva Mills Case (1980), the Supreme Court held that the Indian Constitution is founded on the bedrock of the balance between Fundamental Rights and the Directive Principles.

The correct answer is Kopili River.

Key Points

• The National Waterway 57 (NW-57) is developed on the Kopili River, located in the state of Assam. Hence, the option Kopili River is correct.
• The stretch of NW-57 spans a length of approximately 48 kilometers, extending from the confluence of the Kopili River with the Brahmaputra River to the Teliagaon Railway Bridge.
• This waterway was officially designated under the National Waterways Act, 2016, which aimed to promote inland water transport as a fuel-efficient and cost-effective mode of logistics in India.
• The Kopili River is a significant south-bank tributary of the Brahmaputra River, flowing through the states of Meghalaya and Assam.
• The development of NW-57 is managed by the Inland Waterways Authority of India (IWAI), which is the statutory authority in charge of the waterways in the country.

Additional Information

• National Waterways Act, 2016:
• This Act came into force on April 12, 2016, and declared 111 inland waterways as National Waterways (NWs) across India.
• Before this Act, there were only 5 designated National Waterways in the country.
• The objective of the Act is to reduce logistics costs and carbon emissions by utilizing the vast network of rivers, canals, and creeks.
• Other Rivers and their National Waterway Designations:
• Zuari River: This river is located in Goa and is designated as National Waterway 111 (NW-111). It is one of the most important rivers for the transportation of iron ore.
• Kali River: Located in the state of Karnataka, the Kali River is designated as National Waterway 52 (NW-52).
• Gandak River: This river flows through Nepal and the Indian states of Bihar and Uttar Pradesh. It is designated as National Waterway 37 (NW-37).
• Inland Waterways Authority of India (IWAI):
• Established on October 27, 1986, under the Inland Waterways Authority of India Act, 1985.
• It is headquartered in Noida, Uttar Pradesh.
• The IWAI primarily undertakes projects for the development and maintenance of Inland Waterway Transport (IWT) infrastructure on national waterways through grants from the Ministry of Ports, Shipping and Waterways.

Important Points

• The Kopili River originates in the Borail range in Meghalaya at an altitude of about 1,600 meters.
• The river has a total length of 290 kilometers and a catchment area of about 16,420 square kilometers.
• The Kopili Hydro Electric Project, operated by NEEPCO (North Eastern Electric Power Corporation Limited), is a major power generation facility situated on this river.
• National Waterway 1 (NW-1), the longest in India, runs from Prayagraj to Haldia on the Ganga-Bhagirathi-Hooghly river system, covering 1,620 kilometers.
• The development of North Eastern waterways, like NW-57, is critical for enhancing connectivity and trade with neighboring countries like Bangladesh and Myanmar.

The correct answer is Cabinet committee on parliamentary affairs.

Key Points

• The Cabinet Committee on Parliamentary Affairs is the only major cabinet committee that is NOT headed by the Prime Minister; instead, it is typically chaired by the Union Home Minister.
• The primary function of this committee is to look after the progress of government business in the Parliament of India and ensure smooth coordination between the two houses, Lok Sabha and Rajya Sabha.
• The Cabinet Committee on Economic Affairs (CCEA) is chaired by the Prime Minister. It is responsible for reviewing economic trends and evolving an integrated strategy for policies like Minimum Support Price (MSP) and various developmental projects.
• The Cabinet Committee on Investment and Growth was newly constituted in June 2019 and is headed by the Prime Minister to identify key projects for implementation on a time-bound basis.
• The Cabinet Committee on Employment and Skill Development, also created in 2019, is headed by the Prime Minister and focuses on providing a direction to various initiatives for skill development and increasing employability in the country.

Additional Information

• Nature of Cabinet Committees: These are extra-constitutional bodies, meaning they are not mentioned in the Constitution of India. They are established under the Government of India Transaction of Business Rules, 1961.
• Types: There are two types of committees: Standing Committees, which are of a permanent nature, and Ad-hoc Committees, which are temporary and formed for specific tasks.
• Appointments Committee of the Cabinet: This committee is headed by the Prime Minister and includes the Home Minister. It decides on all higher-level appointments in the Central Secretariat, Public Sector Undertakings, and Banks.
• Cabinet Committee on Security (CCS): Chaired by the Prime Minister, it deals with issues of national security, defense expenditure, and external affairs that impact India's security.
• Cabinet Committee on Political Affairs: This is often described as a "Super-Cabinet" because it deals with all policy matters pertaining to domestic and foreign affairs. It is chaired by the Prime Minister.

Important Points

• Membership: While the number of members in these committees can vary from 3 to 8, they usually include Cabinet Ministers. Non-cabinet ministers can sometimes be invited as special invitees.
• Cabinet Committee on Accommodation: Like the Parliamentary Affairs committee, this committee is also usually headed by the Union Home Minister. It deals with the allotment of government accommodation to Members of Parliament and other officials.
• Role in Governance: These committees serve as an organizational device to reduce the enormous workload of the Cabinet and facilitate in-depth examination of policy issues and effective coordination.
• Evolution: The number and nomenclature of these committees change with the change in Government. For instance, in 2019, the NDA government re-constituted 8 committees, emphasizing Investment and Employment.

The logic followed here is:

thus, "108" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

Given: (Left) B * £ J E % $* V € G * D H @ A £ O V$ T Y (Right)

Now,

Letters, which are immediately preceded by a symbol and also immediately followed by a symbol.

So, Needed pattern is: Symbol – Letter – Symbol

(Left) B * £ J E % $ *** V € G *** D H @ A £ O V $ T Y (Right)

Only three letters satisfy the condition.

Hence, the correct answer is 'Option 3'.

The correct answer is Sikandra Fort.

Key Points

• Sikandra Fort: This monument is located in Agra, Uttar Pradesh, and serves as the final resting place (mausoleum) of the Mughal Emperor Akbar. It was completed in 1613. Since it is situated in North India and not in Maharashtra, it is not part of the Daulatabad complex. Hence, statement 1 is the correct answer.
• Chand Minar: Also known as the Tower of the Moon, this massive tower is located within the Daulatabad Fort in Maharashtra. It was built in 1445 by Ala-ud-din Bahmani to celebrate his capture of the fort. It stands at a height of about 63 meters. Hence, statement 2 is incorrect as it is an important monument inside the fort.
• Bharatmata Mandir: This is a significant temple located inside the Daulatabad Fort. The structure has a complex history, originally being a Hindu temple dedicated to Goddess Durga, which was later modified during the Delhi Sultanate rule and eventually dedicated to Mother India. Hence, statement 3 is incorrect as it is an important monument inside the fort.
• Jami Masjid: This mosque is one of the oldest surviving structures within the Daulatabad Fort premises, built in 1318 by Qutub-ud-din Mubarak Khilji. It is notable for its 106 pillars that were salvaged from earlier Hindu and Jain temples. Hence, statement 4 is incorrect as it is an important monument inside the fort.

Additional Information

• Daulatabad Fort (Devagiri): It is a 14^th-century fort city located in the Aurangabad (now Chhatrapati Sambhajinagar) district of Maharashtra. It was originally founded around 1187 by the first Yadava king, Bhillama V.
• Strategic Significance: The fort is famous for its invincible defense mechanisms, including a moat filled with crocodiles and the Andhari, a dark, winding subterranean passage designed to mislead and trap invading enemies.
• Capital Shift: In 1327, Sultan Muhammad bin Tughlaq of the Delhi Sultanate famously ordered the entire population of Delhi to move to Devagiri, renaming it Daulatabad (the City of Fortune), intended to be his new capital due to its central location in the Indian subcontinent.
• Sikandra Fort Architecture: The tomb of Akbar in Sikandra is a Mughal architectural masterpiece. It is unique because it lacks a traditional dome and is built primarily of red sandstone with white marble inlay work. The construction was started by Akbar himself and finished by his son Jahangir.
• Historical Occupancy: Over the centuries, the Daulatabad fort has been under the control of various dynasties, including the Yadavas, the Khiljis, the Tughlaqs, the Bahmani Sultans, the Nizam Shahis of Ahmadnagar, and finally the Mughals.

Important Points

• Chand Minar is the second tallest minaret in India, surpassed only by the Qutub Minar in Delhi. It shows a distinct Persian influence in its architectural style.
• The Yadava Dynasty, which built the original fort, was a prominent Indian dynasty that ruled a kingdom stretching from the Narmada River to the Tungabhadra River.
• Daulatabad is often referred to as one of the seven wonders of Maharashtra and remains a major archaeological site protected by the Archaeological Survey of India (ASI).
• The Mughal influence in Daulatabad was strengthened when Aurangzeb used it as a base for his Deccan campaigns during the 17^th century.

Shortcut Trick

Convert ratios to approximate decimals for instant comparison:

5 ÷ 12 ≈ 0.417

14 ÷ 31 ≈ 0.452

8 ÷ 33 ≈ 0.242

17 ÷ 39 ≈ 0.436

Comparing decimals: 0.452 > 0.436 > 0.417 > 0.242

∴ Answer = 14 : 31

Alternate Method 

Given:

Ratios to compare: 5 : 12, 14 : 31, 8 : 33, and 17 : 39

Formula used:

Ratio a : b can be written as fraction a/b. To compare two fractions a/b and c/d, check if a × d > b × c.

  0.2 0.3 0.4 0.5  8:33  5:12  17:39  14:31 (Largest) Comparison on Decimal Scale

Calculations:

Compare 14/31 with 5/12:

⇒ 14 × 12 = 168 and 31 × 5 = 155. Since 168 > 155, 14 : 31 > 5 : 12.

Compare 14/31 with 17/39:

⇒ 14 × 39 = 546 and 31 × 17 = 527. Since 546 > 527, 14 : 31 > 17 : 39.

Compare 14/31 with 8/33:

⇒ 14 × 33 = 462 and 31 × 8 = 248. Since 462 > 248, 14 : 31 > 8 : 33.

Comparing all values, 14 : 31 is the largest ratio.

∴ The correct answer is 14 : 31 (Option 2).

Additional Information

Cross-Multiplication Rule

For any two ratios a/b and c/d, if (a × d) > (b × c), then a/b > c/d. This is the most accurate method to compare fractions without decimals.

Percentage Conversion Method

Convert ratios to percentages by multiplying by 100. For example, 5 : 12 ≈ 41.67% and 14 : 31 ≈ 45.16%.

Common Denominator Method

Find the LCM of all denominators and convert all fractions to have this common denominator. The fraction with the largest numerator will be the largest ratio.

The correct answer is Himachal Pradesh.

Key Points

• In July 2023, the state of Himachal Pradesh witnessed unprecedented rainfall and cloudbursts, leading to catastrophic flash floods and landslides that severely crippled the power generation infrastructure. Hence, the statement that flash floods in Himachal Pradesh disrupted power stations in July 2023 is correct.
• The heavy rains caused a massive increase in the silt content (turbidity) of the Satluj and Beas rivers, forcing the immediate shutdown of several major Hydroelectric Projects (HEPs) to prevent damage to the turbine blades.
• Key power stations affected included the 1,500 MW Nathpa Jhakri Hydro Power Station, which is India’s largest underground hydroelectric project, and the 412 MW Rampur Hydro Power Station.
• The silt levels in the rivers reportedly crossed 10,000 parts per million (ppm), far exceeding the permissible limit of 2,000 to 3,000 ppm required for safe operation.
• This disruption led to a significant shortfall in the Northern Grid, affecting the power supply to several states including Punjab, Haryana, and Delhi.

Additional Information

• Geography and Vulnerability: Himachal Pradesh is a mountainous state in North India characterized by steep slopes and fragile ecosystems. In 2023, the combination of the Southwest Monsoon and a Western Disturbance led to extreme precipitation events in districts like Kullu, Mandi, and Shimla.
• Economic Impact: The state government estimated the total economic loss due to the floods at over 10,000 crore rupees, involving the destruction of over 40 bridges, several National Highways (NH-3 and NH-5), and hundreds of small water supply schemes.
• SJVN Limited: The Satluj Jal Vidyut Nigam (SJVN), a Mini Ratna public sector undertaking, manages the Nathpa Jhakri and Rampur projects. They had to halt operations for several days during the July 7–11, 2023 peak flood period.
• Comparison with Other States: While Sikkim faced a major glacial lake outburst flood (GLOF) affecting the Teesta III dam, that event occurred in October 2023, not July. Uttarakhand and Arunachal Pradesh also have high hydropower potential but did not report power station shutdowns of this specific scale during the July 2023 window.
• Hydropower Significance: Himachal Pradesh is often referred to as the "Power State" of India, with an estimated hydropower potential of about 27,436 MW, accounting for approximately 25% of the national potential.

Important Points

• The Role of Turbidity: High silt or turbidity acts like sandpaper on the metallic parts of the turbines. If the projects are not shut down, the abrasive action of quartz and other minerals in the silt can lead to erosion of the runners and guide vanes, requiring expensive and time-consuming repairs.
• Disaster Management: The National Disaster Response Force (NDRF) and the Indian Air Force (IAF) were deployed to rescue thousands of tourists and locals stranded in the Lahaul-Spiti and Kullu valleys during this period.
• Climate Change: Experts suggest that the increasing frequency of such flash floods in the Himalayas is a direct consequence of climate change and global warming, leading to unpredictable rainfall patterns in high-altitude regions.

Shortcut Trick

Linear pair at M: 5x + (3x + 2y) = 180 ⇒ 8x + 2y = 180 ⇒ 4x + y = 90

Since AB || CD, ∠PMB = corresponding ∠MND = 5x

Linear pair at N: ∠MND + ∠DNQ = 5x + (x + 3y) = 180 ⇒ 6x + 3y = 180 ⇒ 2x + y = 60

Solving: (4x + y) − (2x + y) = 90 − 60 ⇒ 2x = 30 ⇒ x = 15

Substituting x = 15 in 2x + y = 60 gives y = 30

∠BMN = 3(15) + 2(30) = 45 + 60 = 105°

∴ Answer = 105°

Alternate Method 

Given:

Line AB || Line CD with transversal PQ intersecting at M and N.

∠PMB = 5x°, ∠BMN = (3x + 2y)°, and ∠DNQ = (x + 3y)°

Formula used:

1. Sum of angles in a linear pair = 180°

2. Corresponding angles of parallel lines are equal.

   A B C D P Q M N 5x 3x + 2y x + 3y AB || CD

Calculations:

∠PMB and ∠BMN form a linear pair on transversal PQ at intersection M.

⇒ ∠PMB + ∠BMN = 180°

⇒ 5x + 3x + 2y = 180 ⇒ 8x + 2y = 180 ⇒ 4x + y = 90 --- (Eq. 1)

Since AB || CD, the corresponding angles ∠PMB and ∠MND are equal.

⇒ ∠MND = ∠PMB = 5x

∠MND and ∠DNQ form a linear pair on transversal PQ at intersection N.

⇒ ∠MND + ∠DNQ = 180°

⇒ 5x + x + 3y = 180 ⇒ 6x + 3y = 180 ⇒ 2x + y = 60 --- (Eq. 2)

Subtracting (Eq. 2) from (Eq. 1):

⇒ (4x + y) − (2x + y) = 90 − 60 ⇒ 2x = 30 ⇒ x = 15

Putting x = 15 in (Eq. 2):

⇒ 2(15) + y = 60 ⇒ 30 + y = 60 ⇒ y = 30

Now, finding the value of ∠BMN:

⇒ ∠BMN = 3x + 2y = 3(15) + 2(30) = 45 + 60 = 105°

∴ The correct answer is 105°, which is option (4).

Additional Information

Linear Pair of Angles

When two angles are adjacent and their non-common sides form a straight line, they are supplementary, i.e., Sum = 180°.

Parallel Lines and Transversal

When a transversal intersects two parallel lines, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum = 180°).

Vertically Opposite Angles

When two lines intersect, the angles opposite to each other at the vertex are always equal.

The correct answer is 1020 MW Punatsangchhu-II HEP.

Key Points

• The 1020 MW Punatsangchhu-II Hydroelectric Project (HEP) is a major bilateral cooperation project between India and Bhutan, situated on the Punatsangchhu River in the Wangdue Phodrang district of Bhutan. Hence, statement 4 is correct.
• During the high-level diplomatic engagements and the State Visit of Prime Minister Narendra Modi, the focus remained on the completion and joint inauguration of this mega project, which is a centerpiece of the India-Bhutan energy partnership for the year 2024 and 2025.
• The project is a run-of-the-river scheme designed to generate approximately 4,357 million units of electricity annually, significantly boosting Bhutan's GDP and providing clean energy to India.
• The financing for the Punatsangchhu-II project was provided by the Government of India, consisting of a 70% loan and a 30% grant, reflecting the deep economic ties between the two nations.
• The 1200 MW Punatsangchhu-I HEP is another project on the same river, but it has faced geological challenges and delays; therefore, it was not the project inaugurated during this specific visit. Hence, statement 1 is incorrect.

Additional Information

• 336 MW Chukha HEP:
• This was the first "mega" hydroelectric project built with Indian assistance in Bhutan.
• It was commissioned in the year 1986 and is located on the Wong Chhu River.
• It played a foundational role in Bhutan's economic development by generating export revenue from surplus power sold to India. Hence, statement 2 is incorrect.
• 720 MW Mangdechhu HEP:
• This project was jointly inaugurated by Prime Minister Narendra Modi and the then Bhutanese PM Lotay Tshering in August 2019.
• Located in the Trongsa district on the Mangdechhu River, it was awarded the prestigious Brunel Medal by the Institution of Civil Engineers (London) in 2021 for its excellence in civil engineering.
• It was formally handed over to Bhutan in December 2022. Hence, statement 3 is incorrect.
• Punatsangchhu-I HEP:
• With a capacity of 1200 MW, it is the largest of the projects currently under construction in Bhutan.
• It is located upstream of the Punatsangchhu-II project but has been delayed due to technical issues related to the right bank subsidence.
• Kholongchhu HEP:
• This is a 600 MW project and holds the distinction of being the first Joint Venture (JV) project between the two countries, involving DGPC of Bhutan and SJVN of India.

Important Points

• Strategic Cooperation: The cooperation in the hydro-power sector is a vital component of the India-Bhutan bilateral relationship, guided by the 2006 Agreement on Cooperation in Hydropower.
• Target Capacity: The two nations originally aimed to develop 10,000 MW of hydropower capacity in Bhutan for export to India, contributing to regional energy security.
• Economic Impact: Hydropower contributes nearly 14% to Bhutan's GDP and accounts for a significant portion of its total export earnings.
• Diplomatic Context: Prime Minister Narendra Modi's visit in March 2024 (and subsequent engagements through 2025) emphasized the "Neighborhood First" policy and strengthened the Bharat-Bhutan friendship through infrastructure and energy milestones.

The logic followed here is:

So, 'GYB 30' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Given: Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

Only four people have exams after V.

Only four people have exams before S.

P has the exam after R but before V.

T has the exam on some day after Q but not on Sunday.

Now, people between Q and U: 2 people

Hence, the correct answer is Option 3.

The correct answer is Shillong.

Key Points

• The National Air Quality Index (NAQI) released for the year 2025 indicates that Shillong, the capital of Meghalaya, has emerged as the city with the cleanest air among major Indian urban centers.
• The report, typically compiled by the Central Pollution Control Board (CPCB), monitors the air quality across various states and union territories using a real-time monitoring system.
• Shillong consistently records an AQI (Air Quality Index) value within the 'Good' category (0-50), primarily due to its geographical elevation, extensive forest cover, and relatively lower industrial density compared to metropolitan hubs.
• While cities like Mumbai and Kolkata struggle with vehicular emissions and construction dust, the North-Eastern region, particularly Shillong, benefits from favorable meteorological conditions and effective local environmental policies.
• The 2025 data highlights that Shillong maintained an average PM2.5 concentration well within the World Health Organization (WHO) guidelines, making it a benchmark for the National Clean Air Programme (NCAP).

Additional Information

• National Air Quality Index (NAQI):
• Launched in October 2014, the AQI is a tool to communicate the status of air quality to the people in terms that are easy to understand. It transforms complex air quality data of various pollutants into a single number, nomenclature, and colour.
• The Index considers eight pollutants: Particulate Matter (PM10), Particulate Matter (PM2.5), Nitrogen Dioxide (NO2), Sulphur Dioxide (SO2), Carbon Monoxide (CO), Ozone (O3), Ammonia (NH3), and Lead (Pb).
• AQI Categories:
• There are six AQI categories, namely Good (0-50), Satisfactory (51-100), Moderately Polluted (101-200), Poor (201-300), Very Poor (301-400), and Severe (401-500).
• Each category is associated with different health impacts, ranging from minimal impact in the 'Good' category to respiratory effects even on healthy people in the 'Severe' category.
• Performance of other Cities:
• Mumbai: Being a coastal city, it usually benefits from land and sea breezes, but 2025 reports show increased AQI levels due to massive infrastructure projects and metro construction.
• Kolkata: Faces challenges during winter months due to temperature inversion and transboundary pollution, often placing it in the 'Moderate' or 'Poor' category.
• Ranchi: As an industrial-mining belt capital, Ranchi often sees fluctuations in PM10 levels, though it generally fares better than the National Capital Region (NCR).

Important Points

• The Central Pollution Control Board (CPCB), a statutory organization under the Ministry of Environment, Forest and Climate Change, was established in 1974 under the Water (Prevention and Control of Pollution) Act.
• The National Clean Air Programme (NCAP) aims for a 20% to 30% reduction in Particulate Matter concentration by 2024/2025, taking 2017 as the base year for comparison.
• Shillong's success in 2025 is also attributed to the Meghalaya State Pollution Control Board's strict monitoring of cement plant emissions and coal mining regulations in nearby districts.
• The Safar (System of Air Quality and Weather Forecasting And Research) is another initiative by the Ministry of Earth Sciences to provide location-specific information on air quality in metropolitan cities like Delhi, Pune, Mumbai, and Ahmedabad.

The correct answer is Tuvalu.

Key Points

• The 90^th State Member of the International Union for Conservation of Nature (IUCN) is Tuvalu
• The government of the Pacific island nation officially joined the union on October 14, 2025, during the IUCN World Conservation Congress held in Abu Dhabi, United Arab Emirates.
• Tuvalu is the 11^th State Member from the Oceania region to join the IUCN.
• Tuvalu is one of the world's smallest and most climate-vulnerable nations.

Additional Information

• International Union for Conservation of Nature (IUCN):
• Established on 5 October 1948 in Fontainebleau, France, it is the world’s oldest and largest global environmental organization.
• The organization is headquartered in Gland, Switzerland and is composed of more than 1,400 member organizations and 15,000 experts.
• It is best known for the IUCN Red List, which assesses the extinction risk of thousands of species and subspecies worldwide.
• Geography and Location of Kiribati:
• Kiribati is a central Pacific nation comprising 33 atolls and reef islands, spanning all four hemispheres (North, South, East, and West).
• It is home to the Phoenix Islands Protected Area (PIPA), one of the largest marine protected areas in the world and a UNESCO World Heritage site.
• The capital and largest center is South Tarawa, which faces extreme challenges from overcrowding and environmental degradation.
• Context of Other Options:
• Maldives: Located in the Indian Ocean, it was one of the first countries to join IUCN among island nations and is a leader in climate advocacy.
• Nauru: The world's smallest island nation located in Micronesia, known for its history of phosphate mining and ongoing efforts toward land rehabilitation.

Important Points

• Functions of State Membership: Being a State Member allows a country to participate in the World Conservation Congress, held every four years, where members define the global conservation agenda.
• Climate Vulnerability: Most of Kiribati’s land sits less than 2 meters above sea level, making the IUCN’s expertise in Nature-based Solutions (NbS) vital for its survival.
• Biodiversity Focus: Kiribati manages over 3.5 million square kilometers of ocean, a territory vital for tuna migration and coral reef biodiversity.
• International Relations: This move signals Kiribati’s intent to use multilateralism to seek funding and technical support for biodiversity conservation under the Kunming-Montreal Global Biodiversity Framework.

Shortcut Trick

Convert fractions into decimals for faster calculation.

4/5 = 0.8 and 8/20 = 0.4

Expression = [3.75 + 0.8] − [3.5 − 0.4]

Expression = 4.55 − 3.1 = 1.45

∴ Answer = 1.45

Alternate Method

 

Given:

Expression: [3.75 + 4/5] − [3.5 − 8/20]

Formula used:

Decimal conversion of fractions: Numerator ÷ Denominator

Bracket 1: [3.75 + 0.8] = 4.55 Bracket 2: [3.5 − 0.4] = 3.10 Final Result: 4.55 − 3.10 = 1.45

Calculations:

⇒ Convert fractions to decimals: 4/5 = 0.8 and 8/20 = 0.4

⇒ Solve first bracket: [3.75 + 0.8] = 4.55

⇒ Solve second bracket: [3.5 − 0.4] = 3.10

⇒ Subtract the results: 4.55 − 3.10 = 1.45

∴ The correct answer is 1.45 (Option 4).

Additional Information

BODMAS Rule

Always follow the order: Brackets, Orders (powers), Division, Multiplication, Addition, and Subtraction.

Fraction Simplification

Reducing fractions like 8/20 to 2/5 by dividing by the HCF (4) simplifies calculations significantly.

Decimal Alignment

When adding or subtracting decimals, ensure decimal points are vertically aligned to avoid place-value errors.

The correct answer is Ctrl+A.

Key Points

• Ctrl+A: This keyboard shortcut is universally used to select all content within a document, folder, or window. Whether you are using Microsoft Word, Notepad, or a web browser, pressing these keys simultaneously highlights every element, including text, images, and objects. Hence, this option is correct.
• Ctrl+E: In applications like Microsoft Word and Google Docs, this shortcut is used for Center Alignment. It moves the cursor or the highlighted paragraph to the center of the page. It does not select content. Hence, this option is incorrect.
• Ctrl+R: This shortcut has dual primary functions depending on the software. In word processors, it is used for Right Alignment of text. In web browsers like Google Chrome or Microsoft Edge, it is used to Refresh or reload the current page. Hence, this option is incorrect.
• Ctrl+S: This is one of the most critical shortcuts used to Save the current progress of a file or document. It ensures that the data is written to the hard drive or cloud storage to prevent data loss. Hence, this option is incorrect.

Additional Information

• History of Keyboard Shortcuts: Many modern shortcuts, including Select All, Copy, and Paste, were popularized by the Xerox PARC researchers in the 1970s and later adopted by Apple and Microsoft in the 1980s.
• Platform Variations: While Windows and Linux users utilize the Control (Ctrl) key, macOS users utilize the Command (Cmd) key. Therefore, Cmd+A is the equivalent for Apple computers.
• Productivity Impact: Using keyboard shortcuts significantly increases efficiency. Research suggests that relying on shortcuts can save a professional several hours of work over a year by reducing the need to switch between the keyboard and the mouse.
• Common Text Editing Shortcuts:
• Ctrl+X: Used to Cut selected content.
• Ctrl+C: Used to Copy selected content to the clipboard.
• Ctrl+V: Used to Paste content from the clipboard.
• Ctrl+Z: Used to Undo the last action performed.

Important Points

• Formatting Shortcuts: Beyond alignment and selection, users frequently use Ctrl+B for Bold, Ctrl+I for Italic, and Ctrl+U for Underline to enhance document readability.
• Selection Alternatives: While Ctrl+A selects everything, users can use Shift + Arrow Keys to select specific portions of text or Shift + Click to select a range of files in a File Explorer.
• System Wide Utility: The Select All function is not limited to text; in the Windows File Explorer, Ctrl+A is the standard method to select 100% of the files and folders within a specific directory for bulk actions like moving or deleting.
• Navigation Shortcuts: Ctrl+Home moves the cursor to the start of a document, while Ctrl+End moves it to the very bottom, which are often used in conjunction with selection shortcuts.

Shortcut Trick

In a cyclic quadrilateral, the exterior angle is always equal to the interior opposite angle.

Side PQ is produced to point T, so the exterior angle at vertex Q is angle RQT.

The interior opposite angle to vertex Q is angle PSR.

Logic: angle PSR = angle RQT = 58°

∴ Answer = 58°

Alternate Method 

Given:

PQRS is a cyclic quadrilateral. Side PQ is produced to point T. Exterior angle RQT = 58°.

Formula used:

Sum of opposite angles of a cyclic quadrilateral = 180°

Linear pair sum = 180° (Angles on a straight line)

P Q R S T 58° ?

Calculations:

Since PQT is a straight line, angle PQR + angle RQT = 180°

⇒ angle PQR + 58° = 180°

⇒ angle PQR = 180° − 58° = 122°

In cyclic quadrilateral PQRS, the sum of opposite angles is 180°:

⇒ angle PSR + angle PQR = 180°

⇒ angle PSR + 122° = 180°

⇒ angle PSR = 180° − 122° = 58°

∴ The correct answer is option (2).

Additional Information

Cyclic Quadrilateral Opposite Angles

The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.

Exterior Angle Property

The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

Brahmagupta's Formula

Area of a cyclic quadrilateral = √((s−a)(s−b)(s−c)(s−d)), where s is the semi-perimeter (a+b+c+d)/2.

Ptolemy's Theorem

For a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides: d₁ × d₂ = (a × c) + (b × d).

The correct answer is Transport.

Key Points

• The Delhi Women & Child Development (WCD) Department has formulated the Women Safety Policy 2025 to provide a robust security framework for female employees across various sectors in the National Capital Territory (NCT) of Delhi.
• One of the primary mandates of this policy is the provision of safe transport facilities for women staff who are required to work during late hours, typically defined as shifts ending after 7:00 PM or 8:00 PM.
• The policy stipulates that employers are responsible for ensuring door-to-door pick-and-drop services to minimize the risks associated with commuting in the dark, thereby preventing harassment and ensuring physical safety.
• This mandatory arrangement is applicable to both government offices and private organizations, including BPOs, IT firms, and healthcare institutions operating within the city.
• The WCD Department emphasizes that the transportation must be monitored, preferably with GPS tracking and the presence of a security guard if the employee is the only woman in the vehicle.

Additional Information

• Delhi Women & Child Development (WCD) Department: This department is the nodal agency in Delhi responsible for the welfare, protection, and empowerment of women and children. It oversees the implementation of various state and central schemes like Ladli and Anganwadi services.
• POSH Act, 2013: The Sexual Harassment of Women at Workplace (Prevention, Prohibition and Redressal) Act, 2013, serves as the legal foundation for the Women Safety Policy 2025. It mandates the creation of an Internal Complaints Committee (ICC) in every organization with 10 or more employees.
• CCTV and Surveillance: Beyond transport, the 2025 Policy mandates the installation of high-definition CCTV cameras in all common areas, entry/exit points, and office cabs to ensure continuous monitoring and deterrence of criminal activities.
• Safety Audits: The policy introduces the concept of mandatory annual safety audits. Organizations must evaluate their infrastructure, lighting, and emergency response systems to identify potential "dark spots" or security loopholes.
• Gender Sensitization: It is compulsory for organizations to conduct gender sensitization workshops at least twice a year for all staff, including contractual workers, security personnel, and drivers, to foster a respectful work environment.

Important Points

• Verified Personnel: Under the new guidelines, all drivers and security guards employed for women’s transport must undergo mandatory police verification to ensure they have no prior criminal record.
• SOS Integration: Modern transport solutions provided by employers are encouraged to have SOS buttons integrated into mobile applications, directly linked to the Delhi Police helpline (112) or the office security desk.
• Legal Compliance: Non-compliance with the transport and safety norms can lead to heavy penalties, cancellation of trade licenses, or legal action under the relevant provisions of the Indian Justice Code (BNS).
• Workplace Infrastructure: The policy also suggests that for women staying late, there should be dedicated rest areas and separate washrooms with sanitary pad vending machines to ensure a dignified and healthy work environment.

The correct answer is Mg.

Key Points

• Chlorophyll is the green pigment found in the chloroplasts of plants, algae, and cyanobacteria, which is essential for the process of photosynthesis.
• The central component of the chlorophyll molecule is a Magnesium (Mg) ion, which is held within a large heterocyclic ring known as a porphyrin (or chlorin) ring. Hence, the statement regarding Mg is correct.
• Magnesium acts as the coordination center for the tetrapyrrole ring; its presence is vital because it helps in the absorption of light energy, specifically in the blue and red regions of the electromagnetic spectrum.
• Without the Mg ion, the pigment would be called pheophytin, which lacks the efficiency to capture solar energy for driving the light-dependent reactions of photosynthesis.
• In plants, Magnesium deficiency often leads to a condition called chlorosis, where the leaves turn yellow due to the breakdown of chlorophyll, significantly reducing the plant's ability to produce food.

Additional Information

• Calcium (Ca): This element is primarily used by plants for cell wall synthesis and maintaining the structural integrity of membranes. It exists as calcium pectate in the middle lamella. While it is a crucial macronutrient, it does not play a direct role as a central ion in light absorption within chlorophyll. Hence, the statement regarding Ca is incorrect.
• Sodium (Na): Although it is essential for certain C4 plants and CAM plants to help in the regeneration of phosphoenolpyruvate (PEP), it is not a part of the chlorophyll structure. In most C3 plants, it is not considered an essential nutrient for light absorption. Hence, the statement regarding Na is incorrect.
• Carbon (C): Carbon is the fundamental building block of all organic molecules, including the skeleton of chlorophyll. However, in the context of this question, Carbon is an element forming the structure rather than an "ion" that specifically aids the absorption of light in the coordination center. Hence, the statement regarding C is incorrect.
• The primary types of chlorophyll found in terrestrial plants are Chlorophyll a and Chlorophyll b. Chlorophyll a is the primary electron donor in the reaction center, while Chlorophyll b acts as an accessory pigment to broaden the spectrum of light absorbed.

Important Points

• Structural Composition: The porphyrin ring of chlorophyll is chemically similar to the heme group in hemoglobin found in human blood, with the primary difference being that chlorophyll contains Magnesium at its center, whereas hemoglobin contains Iron (Fe).
• Functionality: The Mg++ ion is coordinated to four nitrogen atoms within the ring. This specific electronic configuration allows the molecule to enter an excited state when struck by photons, initiating the electron transport chain.
• Discovery: The chemical structure of chlorophyll was elucidated by Richard Willstätter and Arthur Stoll in 1913, a feat for which Willstätter was awarded the Nobel Prize in Chemistry in 1915.
• Applications: Understanding the role of Magnesium in chlorophyll is vital for agriculture. Farmers use Epsom salts (magnesium sulfate) to treat Magnesium deficiency in soil to boost crop yields and ensure healthy green foliage.

The logic followed here is:

Given: Seven people K, L, M, N, P, Q and R are sitting around a circular table facing the centre.

Only two people sit between N and Q when counted from the right of N.

Only two people sit between Q and M.

Only three people sit between N and P.

L sits to the immediate left of R.

So, third to the left of K is R.

Hence, the correct answer is "Option 2".

The logic followed here is:

Given codes:

ALIT → 2159

HILT → 6912

Hence, code for H = 6

Hence, the correct answer is Option 2.

Shortcut Trick

Recognize the Pythagorean triplet (7, 24, 25) for radius, height, and slant height.

Slant height l = 25 m.

Curved Surface Area = πrl = (22/7) × 7 × 25 = 550 m².

Total cost = 550 × 40 = 22,000.

∴ Answer = ₹22,000

Alternate Method 

Given:

Radius of the base (r) = 7 m

Height of the tent (h) = 24 m

Cost of cloth = ₹40 per m²

Formula used:

Slant height (l) = √(r² + h²)

Curved Surface Area (CSA) = πrl

Total Cost = CSA × Rate

  h = 24m r = 7m l = 25m

Calculations:

Step 1: Calculate the slant height (l)

⇒ l = √(7² + 24²)

⇒ l = √(49 + 576) = √625 = 25 m

Step 2: Calculate the Curved Surface Area (CSA)

⇒ CSA = (22/7) × 7 × 25 = 550 m²

Step 3: Calculate the Total Cost

⇒ Total Cost = 550 × 40 = 22,000

∴ The correct answer is ₹22,000 (Option 2).

Additional Information

Total Surface Area (TSA) of a Cone

The TSA includes the curved area and the circular base: TSA = πr(l + r).

Volume of a Cone

The capacity of a conical tent is given by Volume = (1/3)πr²h.

Pythagorean Triplets

Common triplets for (r, h, l) include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Slant Height

The distance from the apex to any point on the base circumference is l = √(r² + h²).

The correct answer is ₹15,000.

Key Points

• The Employment Linked Incentive (ELI) Scheme was introduced as part of the Union Budget presented in July 2024 (often referred to in the context of the 2024-25 fiscal cycle/implementation through 2025) to boost job creation and skilling in India.
• Under Scheme A of the ELI initiative, first-time employees entering the formal workforce are provided a direct benefit of one month's wage.
• The maximum limit for this one-month wage incentive is set at ₹15,000, which is disbursed to the eligible individuals. Hence, the option ₹15,000 is correct.
• This benefit is specifically targeted at youth who are newly registered with the Employees' Provident Fund Organisation (EPFO).
• To be eligible for this scheme, the employee's monthly salary or wage must not exceed ₹1,00,000 per month.
• The incentive of ₹15,000 is not paid in a single lump sum but is released in three installments directly into the EPFO account of the employee.

Additional Information

• Structure of ELI Schemes: The government launched three distinct Employment Linked Incentive schemes (Scheme A, B, and C) to address different sectors of the economy.
• Scheme B (Job Creation in Manufacturing): This scheme focuses on the manufacturing sector, providing incentives to both employees and employers regarding their EPFO contributions during the first 4 years of employment.
• Scheme C (Support to Employers): This is designed to support employers across all sectors by reimbursing them up to ₹3,000 per month for 2 years for every additional employee hired.
• Budgetary Allocation: The Union Finance Minister Nirmala Sitharaman announced a total outlay of ₹2 lakh crore for five schemes aimed at employment and skilling over a period of 5 years.
• EPFO Integration: All these incentives are strictly linked to EPFO registration, ensuring that the benefits promote formalization of the Indian labor market and provide social security to workers.
• Target Impact: The ELI schemes are projected to benefit approximately 2.1 crore youth and first-time employees across the country, facilitating their transition into organized sector jobs.
• Mandatory Training: Along with the financial incentives, the government has emphasized skilling programs to ensure that the workforce meets the evolving demands of the industry.

Important Points

• Eligibility and Conditions: The primary condition for Scheme A is that the employee must be a first-timer in the formal sector, as identified by their Universal Account Number (UAN) registration date.
• Payment Mechanism: The Direct Benefit Transfer (DBT) mode is used to ensure transparency, where the ₹15,000 incentive is credited to the EPF account, encouraging long-term savings for the youth.
• Objective: The fundamental goal of the Employment Linked Incentive is to reduce the financial burden on first-time earners and incentivize companies to hire more freshers.
• Economic Context: Launched in July 2024, these schemes are a response to the need for job-rich growth and were a central pillar of the 2024-25 Budget strategy to tackle unemployment.

Shortcut Trick

A right triangle (3, 4, 5) revolved about side 3 cm forms a cone with height h = 3 and radius r = 4.

Volume = (1/3) × 3.14 × r² × h

Since h = 3, Volume = 3.14 × r² = 3.14 × 16

Volume = 50.24 cubic cm.

∴ Answer = 50.24 cubic cm

Alternate Method 

Given:

Sides of the triangle = 3 cm, 4 cm, and 5 cm (Note: 3² + 4² = 5², so it is a right-angled triangle).

The triangle is revolved about the side 3 cm.

Formula used:

Volume of Cone = (1/3) × 3.14 × r² × h

 h = 3 cm r = 4 cm l = 5 cm Solid: Cone (Volume = 50.24 cubic cm)

Calculations:

⇒ Height of the cone (h) = Side about which it revolves = 3 cm

⇒ Radius of the cone (r) = Perpendicular side = 4 cm

⇒ Volume = (1/3) × 3.14 × 4² × 3

⇒ Volume = 3.14 × 16 = 50.24 cubic cm

∴ The correct answer is (1).

Additional Information

Slant Height

The slant height (l) of a cone is given by the formula l = √(r² + h²).

Curved Surface Area

The Curved Surface Area (CSA) of a cone is calculated as π × r × l.

Total Surface Area

The Total Surface Area (TSA) of a cone is π × r × (r + l).

Revolution about Hypotenuse

Revolving a right triangle about its hypotenuse results in a double cone with a common base, where the radius is the altitude to the hypotenuse.

The logic followed here is based on the alphabetical position pattern:

Option 1: DF → EG

Option 2: HJ → IK

Option 3: LN → MO

Option 4: KM → NP

Thus, KM–NP does not follow the same pattern.

Hence, the odd one out is Option 4.

The correct answer is UN Department of Economic and Social Affairs (UN DESA).

Key Points

• The World Urbanization Prospects (WUP) is a flagship publication produced by the Population Division of the United Nations Department of Economic and Social Affairs (UN DESA).
• The 2025 Revision of this report represents a landmark shift as it is the first edition to fully implement the Degree of Urbanization (DegUrba) methodology for global comparative analysis.
• The Degree of Urbanization is a hierarchical classification that distinguishes the entire territory of a country into three main types of areas: Cities, Towns and semi-dense areas, and Rural areas.
• This methodology was formally endorsed by the United Nations Statistical Commission in March 2020 during its 51^st session to harmonize the diverse and often incomparable national definitions of "urban" and "rural" areas.
• By using population density and grid-based data (typically 1 km² cells), UN DESA aims to provide more consistent and accurate data on global urban trends, which is vital for international comparisons.

Additional Information

• UN Department of Economic and Social Affairs (UN DESA): Established in 1948 and headquartered in New York, USA, it acts as a vital interface between global policies and national action. The Population Division within UN DESA provides the international community with up-to-date estimates and projections of population age, location, and growth.
• World Urbanization Prospects (WUP): This series has been published since 1988. It provides a comprehensive set of estimates and projections of the urban and rural populations of all countries in the world and of their major urban agglomerations.
• UN-Habitat: Based in Nairobi, Kenya, the United Nations Human Settlements Programme focuses on sustainable urban development and the implementation of the New Urban Agenda. While they collaborate on data, the primary statistical responsibility for the WUP report lies with UN DESA.
• Global Urbanization Trends: According to previous reports, 55% of the world’s population lived in urban areas in 2018, a figure that is projected to increase to 68% by the year 2050. Most of this growth is expected to take place in Asia and Africa.
• Statistical Commission: This is the highest body of the global statistical system, bringing together Chief Statisticians from Member States. It oversees the work of the United Nations Statistics Division (UNSD) and ensures that international standards like the Degree of Urbanization are adopted.

Important Points

• Significance of DegUrba: Before the adoption of this methodology, countries used their own criteria (such as administrative boundaries, population size, or economic functions) to define urban areas, making it difficult to compare a city in India with a city in France or Brazil.
• SDG Monitoring: The use of standardized urbanization data by UN DESA is crucial for monitoring Sustainable Development Goal 11 (SDG 11), which seeks to make cities and human settlements inclusive, safe, resilient, and sustainable by 2030.
• Leading Contributors to Growth: It is estimated that just three countries—India, China, and Nigeria—will account for 35% of the total growth in the world’s urban population between 2018 and 2050. India is projected to add 416 million urban dwellers.
• Data Sources: The report relies on national census data, satellite imagery, and geospatial information to refine the application of the Degree of Urbanization methodology across different countries and continents.

The correct answer is Agraharam.

Key Points

• During the Chola Empire, which flourished between the 9^th and 13^th century in South India, the practice of donating tax-free lands to Brahmins was highly prevalent. These settlements were widely known as Agraharam or Brahmadeya.
• An Agraharam served as a residential quarter or a village where Brahmins settled to perform religious duties, Vedic education, and rituals. These lands were often situated near temples or fertile river banks.
• These land grants were exempted from the usual land revenue and other taxes, making them economically self-sufficient units. The primary function of these grants was to promote learning and sustain the priestly class.
• The internal governance of an Agraharam was managed by an assembly of Brahmin landowners known as the Mahasabha. This body looked after irrigation, taxation (if any), and the overall administration of the settlement.
• The Chola kings like Rajaraja I and Rajendra I frequently established these settlements to consolidate their political influence and propagate Hinduism throughout the country.

Additional Information

• Garbhagriha: This is a prominent architectural feature of Hindu temples, referring to the innermost sanctum or "womb chamber" where the primary deity is installed. It was never a term used for land grants.
• Valanadu: In the Chola administrative system, the empire was divided into provinces called Mandalam, which were further divided into Valanadu. A Valanadu was a large administrative unit consisting of several Nadu (districts).
• Mahasabha: While often associated with Agraharams, the Mahasabha was the assembly or the organisation that governed the Brahmin settlements. It was the administrative body rather than the land itself.
• Land Categories: The Chola inscriptions mention several types of land holdings, such as Vellanvagai (land for non-Brahmin peasants), Shalabhoga (land for maintenance of schools), Devadana (land gifted to temples), and Pallichchhandam (land donated to Jain institutions).

Important Points

• Uttaramerur Inscription: A famous inscription dated around 920 AD during the reign of Parantaka I provides detailed data and facts about the election process of the Sabha. It highlights the use of the Kuda-olai (pot-ticket) system for choosing representatives.
• Economic Impact: These grants led to the expansion of agriculture in South India as Brahmins introduced new irrigation techniques and management practices to the donated wastelands or forest areas.
• Role of the King: The donation of Agraharams was a political tool used by the Chola dynasty to gain legitimacy and to create a loyal class of intellectuals who would record the king's achievements in Sanskrit and Tamil epigraphs.
• Social Structure: These settlements were exclusive locations for Brahmins, which occasionally led to a stratified social hierarchy in the villages, though they remained centers of great cultural and intellectual activity.

The correct answer is Andaman and Nicobar Islands.

Key Points

• Barren Island is located in the Andaman Sea and is the only confirmed active volcano in South Asia. It is a part of the Indian Union Territory of the Andaman and Nicobar Islands.
• The island is situated approximately 138 kilometers (86 miles) northeast of Port Blair, the capital of the islands.
• The first recorded eruption of the volcano occurred in 1787. After remaining dormant for about 150 years, the volcano erupted again in 1991, with the eruption lasting for six months.
• Recent volcanic activity on the island has been observed in 2005-07, 2017, and minor ash emissions were reported as recently as 2021.
• The island is approximately 3 kilometers wide, with a 2-kilometer-wide caldera created during prehistoric explosive eruptions.

Additional Information

• Andaman and Nicobar Islands:
• This archipelago consists of about 572 islands, divided into the Andaman group in the north and the Nicobar group in the south, separated by the Ten Degree Channel.
• The highest point in the islands is Saddle Peak, which stands at an elevation of 732 meters in North Andaman.
• The islands are home to Particularly Vulnerable Tribal Groups (PVTGs) such as the Jarawa, Sentinelese, Onge, and Great Andamanese.
• Lakshadweep Islands:
• Located in the Arabian Sea, this is India's smallest Union Territory, consisting of 36 islands with a total area of 32 square kilometers.
• Unlike the volcanic Andaman islands, these are coral islands formed as atolls.
• The administrative headquarters is located at Kavaratti.
• Narcondam Island:
• Also located in the Andaman Sea, it is home to another volcano in India, which is currently classified as dormant or extinct.
• It is famous for the endemic Narcondam Hornbill, a bird species found nowhere else on Earth.
• Minicoy and Rameswaram Islands:
• Minicoy Island is the southernmost island of Lakshadweep, separated from the rest of the archipelago by the Nine Degree Channel.
• Rameswaram Island (also known as Pamban Island) is located between mainland India and Sri Lanka in the Gulf of Mannar and is connected to the mainland by the famous Pamban Bridge.

Important Points

• Tectonic Setting: The volcanic activity in the Andaman Sea is a result of the subduction of the Indian Plate beneath the Burmese Plate (part of the Eurasian Plate) along the Andaman Trench.
• Strategic Significance: The Andaman and Nicobar Command (ANC), established in 2001, is India's first and only tri-service theater command, highlighting the region's immense strategic importance in the Indian Ocean.
• Judicial Jurisdiction: The Andaman and Nicobar Islands fall under the legal jurisdiction of the Calcutta High Court, specifically the Circuit Bench at Port Blair.
• Biodiversity: The islands are part of the Indo-Burma biodiversity hotspot, featuring tropical rainforests and extensive mangrove ecosystems that support diverse marine and terrestrial life.

Given: # : ZJR :: PZH : %

Option 1) # = TDL , % = VFN

For # (TDL) to ZJR

For % (VFN) to PZH

Since, both transformations follow a consistent shift pattern, Option 1 is correct.

Option 2) # = UDL , % = VFN

For # (UDL) to ZJR

For % (VFN) to PZH

Since, the patterns do not match, Option 2 is incorrect.

Option 3) # = TDL , % = VCN

For # (TDL) to ZJR

For % (VCN) to PZH

Since, the patterns do not match, Option 3 is incorrect.

Option 4) # = TDM , % = VFN

For # (TDM) to ZJR

For % (VFN) to PZH

Since, the patterns do not match, Option 4 is incorrect.

Hence, the correct answer is "Option 1".

The correct answer is (i) False, (ii) True.

Key Points

• Statement (i): When a file is deleted and moved to the Recycle Bin in Windows 11, its contents are not immediately erased. Instead, the file is simply moved to a hidden system folder, usually located at $Recycle.Bin on the root of each drive. The data remains physically present on the storage disk until the user chooses to Empty the Recycle Bin or the system automatically overwrites the space if it becomes critically low. Hence, statement (i) is False.
• Statement (ii): The file path (e.g., C: > Users > Documents > file.txt) represents a hierarchical structure used by the NTFS (New Technology File System). This organization resembles an inverted tree where the Root Directory (like C:) branches into Subdirectories (folders), and each individual file has a unique absolute path that defines its exact logical location within that hierarchy. Hence, statement (ii) is True.
• The Recycle Bin acts as a safety buffer, allowing users to restore accidentally deleted items to their original location. This feature has been a staple of the Windows Operating System since Windows 95.
• In Windows 11, the File Explorer manages these paths and provides a visual interface for navigating the hierarchical data. While a user can create a Shortcut to a file in multiple locations, the source file itself maintains only one primary hierarchical path on the disk.

Additional Information

• Windows 11 File Management:
• Windows 11, released in October 2021, introduced a redesigned File Explorer with Tabs and a simplified context menu to enhance productivity.
• The NTFS file system supports a maximum path length of 260 characters by default, though this can be extended via Registry edits.
• Metadata such as creation date, file size, and author name are stored alongside the file in the Master File Table (MFT).
• Permanent Deletion:
• To bypass the Recycle Bin and remove a file immediately, users can use the keyboard shortcut Shift + Delete.
• Even after permanent deletion, data recovery software can sometimes retrieve files unless the storage blocks have been overwritten by new data.
• On modern Solid State Drives (SSDs), the TRIM command helps the operating system wipe data blocks more efficiently after permanent deletion to maintain performance.
• Hierarchical vs. Flat File Systems:
• A Hierarchical file system organizes data in a parent-child relationship, which is the standard for Windows, macOS, and Linux.
• Conversely, Cloud Storage (like Amazon S3) often uses a Flat File System where files (objects) are stored in a single layer and identified by unique keys rather than a nested folder path.

Important Points

• File Extensions: In Windows 11, the extension (e.g., .txt, .docx, .exe) tells the operating system which application should be used to open the file. By default, File Explorer may hide these extensions for known file types.
• Logical vs. Physical Deletion: Moving to the Recycle Bin is a logical move. The physical data remains on the sectors of the Hard Disk Drive (HDD) or SSD until the logical link is severed and the space is reused.
• Storage Drive Letters: In India and globally, most PCs assign C: as the system drive where Windows 11 is installed, while additional partitions or external drives are assigned letters like D:, E:, or F:$.

Shortcut Trick

Identify the Modal Class (highest frequency): Class 70-80 with frequency 38.

Apply Mode Formula: l + [ (f₁ − f₀) ÷ (2f₁ − f₀ − f₂) ] × h

Mode = 70 + [ (38 − 18) ÷ (2 × 38 − 18 − 26) ] × 10

Mode = 70 + [ 20 ÷ 32 ] × 10 = 70 + 6.25

∴ Answer = 76.25

Alternate Method 

Given:

Class intervals (Age) and their respective frequencies (No. of patients).

Maximum frequency = 38, which lies in the class 70-80.

Formula used:

Mode = l + [ (f₁ − f₀) ÷ (2f₁ − f₀ − f₂) ] × h

Where: l = lower limit of modal class, f₁ = frequency of modal class, f₀ = frequency of preceding class, f₂ = frequency of succeeding class, h = class width.

f0=18f1=38f2=26Modal Class: 70-80Result Mode ≈ 76.25

Calculations:

From the table, Modal Class = 70-80

⇒ l = 70, h = 10

⇒ f₁ = 38 (frequency of class 70-80)

⇒ f₀ = 18 (frequency of class 60-70)

⇒ f₂ = 26 (frequency of class 80-90)

⇒ Mode = 70 + [ (38 − 18) ÷ (2 × 38 − 18 − 26) ] × 10

⇒ Mode = 70 + [ 20 ÷ (76 − 44) ] × 10

⇒ Mode = 70 + [ 20 ÷ 32 ] × 10

⇒ Mode = 70 + 0.625 × 10 = 70 + 6.25

⇒ Mode = 76.25

∴ The correct answer is 76.25.

Additional Information

Empirical Formula

Relationship between Mean, Median, and Mode: Mode = 3 × Median − 2 × Mean.

Median for Grouped Data

Median = l + [ (N/2 − cf) ÷ f ] × h, where cf is cumulative frequency and N is total frequency.

Mean for Grouped Data

Direct Method: Mean = Σf_ix_i ÷ Σf_i, where x_i is the class mark (midpoint).

Modal Class Definition

The class interval that has the highest frequency in a grouped frequency distribution.

The correct answer is Article 6.

Key Points

• Article 6 of the Constitution of India deals specifically with the rights of citizenship for persons who migrated to India from Pakistan. It provides that a person who migrated before the commencement of the Constitution shall be deemed a citizen if they or their parents/grandparents were born in undivided India. Hence, this is the correct option.
• Article 5 outlines citizenship at the commencement of the Constitution (January 26, 1950) for individuals who had their domicile in India and were born in India, or whose parents were born in India, or who had been ordinarily resident for at least five years. Hence, this statement is incorrect.
• Article 8 addresses the citizenship rights of certain persons of Indian origin residing outside India. It allows such individuals to become citizens if they are registered by the diplomatic or consular representative of India in the country where they are residing. Hence, this statement is incorrect.
• Article 10 ensures the continuance of the rights of citizenship. It states that every person who is considered a citizen under any of the preceding articles shall continue to be a citizen, subject to the provisions of any law made by the Parliament. Hence, this statement is incorrect.

Additional Information

• Constitutional Provisions: Part II of the Indian Constitution, spanning from Article 5 to Article 11, defines who was eligible for Indian citizenship at the time of the Constitution's adoption.
• Single Citizenship: Unlike federal structures like the USA, India provides for Single Citizenship, meaning there is no separate state citizenship; all citizens owe allegiance only to the Union of India.
• The Citizenship Act, 1955: Since the constitutional provisions only dealt with citizenship at the time of commencement, the Parliament enacted the Citizenship Act in 1955 to regulate the acquisition and loss of citizenship after 1950.
• Acquisition Methods: Under the 1955 Act, citizenship can be acquired by Birth, Descent, Registration, Naturalization, and Incorporation of Territory.
• Loss of Citizenship: The Act also mentions three ways to lose citizenship: Renunciation, Termination, and Deprivation.

Important Points

• The Cut-off Date: For Article 6, the significant date is July 19, 1948. Individuals migrating before this date needed to be ordinarily resident in India since their migration to be deemed citizens.
• Registration Requirement: Those migrating from Pakistan on or after July 19, 1948, had to be registered as a citizen by an officer appointed by the Government of the Dominion of India, provided they had resided in India for at least six months prior to their application.
• Article 7 (Migration to Pakistan): This article deals with persons who migrated to Pakistan after March 1, 1947, but later returned to India under a permit for resettlement or permanent return; they could acquire citizenship similarly to those migrating after the 1948 cut-off.
• Article 11 Power: It gives exclusive power to the Parliament of India to make any law regarding citizenship. This ensures that the Constitution does not permanently limit the legislative scope of the government regarding who qualifies as an Indian national.
• Ministry Involvement: The Ministry of Home Affairs is the primary government organization responsible for overseeing citizenship, naturalization, and the Overseas Citizenship of India (OCI) scheme.

The correct answer is Article 87.

Key Points

• Article 87 of the Constitution of India provides for the Special Address by the President to both Houses of Parliament.
• Under Article 87(1), the President must address both the Lok Sabha and Rajya Sabha assembled together at the commencement of the first session after each general election to the House of the People.
• Additionally, the President delivers this address at the commencement of the first session of every year, which is typically the Budget Session.
• The primary purpose of this address is for the President to inform Parliament of the causes of its summons, outlining the government’s policy goals and legislative agenda for the coming year.
• Article 87(2) specifies that rules shall be made for the allotment of time for discussion of the matters referred to in such address, which leads to the Motion of Thanks.

Additional Information

• Article 85:
• This article deals with the Sessions of Parliament, their prorogation, and dissolution.
• It empowers the President to summon each House of Parliament to meet at such time and place as he thinks fit, ensuring that 6 months shall not intervene between its last sitting in one session and the date appointed for its first sitting in the next session.
• It also provides the authority to the President to dissolve the Lok Sabha.
• Article 86:
• This article grants the President the right to address and send messages to either House of Parliament or both Houses assembled together.
• Unlike Article 87, the address under Article 86 is discretionary and can be delivered at any time, not just at the start of a session or year.
• It also ensures the attendance of members for such an address.
• Article 88:
• This article mentions the Rights of Ministers and the Attorney-General of India in respect of the Houses.
• Every Minister and the Attorney-General has the right to speak in, and otherwise to take part in the proceedings of, either House, any joint sitting of the Houses, and any Committee of Parliament of which he may be named a member.
• However, they are not entitled to vote by virtue of this article unless they are a member of that specific House.

Important Points

• Historical Context: The provision for the Presidential address is borrowed from the British Constitution, specifically the "Speech from the Throne."
• Nature of Address: The speech is drafted by the Government (the Cabinet) and not the President personally; it reflects the policies and programs of the Executive.
• Motion of Thanks: After the address, a Motion of Thanks is moved in both Houses. It is a constitutional convention that if this motion is defeated in the Lok Sabha, it amounts to a vote of no-confidence in the government, leading to its resignation.
• Amendment: Originally, the Constitution (First Amendment) Act, 1951, modified Article 87 to require the address only at the first session of the year instead of every session.

Shortcut Trick

Profit Ratio = Investment Ratio (since time is constant for all).

Ratio of Capitals (Suman : Kunal : Pooja) = 1050 : 1510 : 1280 = 105 : 151 : 128.

Total Ratio parts = 105 + 151 + 128 = 384 units.

Pooja's share = (128 ÷ 384) × Total Profit = 1/3 × 1650.

Pooja's share = 550.

∴ Answer = 550

Alternate Method 

Given:

Investment of Suman = ₹1050

Investment of Kunal = ₹1510

Investment of Pooja = ₹1280

Total Profit at the end of 1 year = ₹1650

Formula used:

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂) : (Capital₃ × Time₃)

Investment Comparison ₹1050 Suman ₹1510 Kunal ₹1280 Pooja Total Profit = ₹1650

Calculations:

Ratio of Profit of Suman, Kunal, and Pooja = 1050 × 1 : 1510 × 1 : 1280 × 1

⇒ Profit Ratio = 105 : 151 : 128

⇒ Total ratio units = 105 + 151 + 128 = 384

⇒ Pooja's share in profit = (Ratio of Pooja ÷ Total Ratio) × Total Profit

⇒ Pooja's share = (128 ÷ 384) × 1650

⇒ Pooja's share = (1 ÷ 3) × 1650

⇒ Pooja's share = 550

∴ The correct answer is ₹550.

Additional Information

Ratio of Investment and Time

If profits and times are given, the ratio of capitals is C₁ : C₂ = (P₁ ÷ T₁) : (P₂ ÷ T₂).

Compound Partnership

When partners invest different amounts for different time periods, profit is distributed in the ratio of the product of capital and time.

Working and Sleeping Partner

A working partner manages the business and may receive a salary or fixed percentage of profit before the remaining profit is divided according to the investment ratio.

The correct answer is A computer generates incorrect output because the initial data entered was flawed..

Key Points

• Diligence is a core characteristic of a computer system that allows it to perform repetitive tasks for long periods without becoming tired, bored, or losing concentration. Unlike humans, who may suffer from physical or mental fatigue after working for a few hours, a computer remains consistent in its performance.
• Despite being diligent, a computer suffers from a significant limitation known as Lack of IQ (Intelligence Quotient). A computer is a machine that follows instructions and cannot think, reason, or make judgments on its own; it requires a human-defined program to function.
• The scenario where a computer generates incorrect output due to flawed data refers to the GIGO (Garbage In, Garbage Out) principle. This highlights that while the computer is diligent enough to process the data, it lacks the common sense to identify that the input is incorrect. Hence, statement 2 is correct.
• A computer performing trillions of calculations per second refers to the characteristic of Speed, which is measured in units like MIPS (Million Instructions Per Second) or FLOPS (Floating Point Operations Per Second). Hence, statement 1 is incorrect.
• The ability of a computer to continue processing for 72 hours straight without losing attention is the definition of Diligence itself, rather than a limitation that diligence cannot overcome. Hence, statement 3 is incorrect.
• Using a computer for different tasks like booking flights and writing code highlights the characteristic of Versatility. This means the computer can be used in various locations such as offices, airports, and schools for diverse applications. Hence, statement 4 is incorrect.

Additional Information

• Speed: Computers are capable of executing millions of instructions in a fraction of a second. Modern Supercomputers can perform quadrillions of calculations per second. This feature makes them indispensable for scientific research and weather forecasting.
• Accuracy: If the algorithms and input data are correct, a computer provides 100% error-free results. Errors usually occur due to human intervention or incorrect programming, not the machine's internal logic.
• Storage (Versatility of Memory): Computer systems have huge storage capacities. Data is stored in bits and bytes on devices like Hard Disk Drives (HDD), Solid State Drives (SSD), and Cloud storage. This allows for the retention of vast amounts of information for an indefinite period.
• No Feelings: Computers do not have emotions, tastes, or intuition. They cannot make subjective decisions based on experience or feelings, which is a major limitation compared to the human brain.
• Dependency: A computer is a dependent machine. It requires a power source and a user to provide input. Without software (instructions) and hardware (physical parts), the system is non-functional.

Important Points

• GIGO (Garbage In, Garbage Out): This term is fundamental in Computer Science. It emphasizes that the reliability of the output is strictly dependent on the integrity of the input data. For organizations, this means data validation is a critical step in data processing.
• Evolution of Intelligence: While traditional computers have Zero IQ, the year 1956 marked the formal beginning of Artificial Intelligence (AI). Modern AI aims to overcome the "No IQ" limitation by using Machine Learning and Neural Networks to mimic human decision-making.
• Reliability: Because computers are diligent and accurate, they are considered highly reliable. They are used in critical functions like space exploration (NASA/ISRO), medical surgeries, and global banking systems where consistency is vital.

Given Statements:

All tea is a snack.

All tea is brunch.

All brunches are dinner.

The least possible Venn diagram for the given statement is:

Conclusions:

I. All tea is dinner – True (Because tea ⊂ brunch and brunch ⊂ dinner, so tea ⊂ dinner).

II. Some brunches are snacks – True (Because tea is common to both brunch and snack, so at least some brunches are snacks).

So, both conclusion I and II follow.

Hence, the correct answer is "Option 2".

The correct answer is Government of India Act, 1919.

Key Points

• The Government of India Act, 1919, also known as the Montagu-Chelmsford Reforms, introduced a system called Dyarchy in the provinces of British India.
• Under this system of Dyarchy, the provincial subjects of administration were divided into two distinct categories: Reserved Subjects and Transferred Subjects.
• Reserved Subjects: These included vital departments such as Law and Order, Finance, Land Revenue, and Police. These subjects were administered by the Governor with the help of his Executive Council, without being responsible to the Legislative Council.
• Transferred Subjects: These included departments like Education, Public Health, Local Self-Government, and Agriculture. These were administered by the Governor with the aid of Ministers who were responsible to the Legislative Council.
• This Act marked the first time that the British Government officially declared its objective of gradual introduction of responsible government in India.
• The Act also introduced Bicameralism at the center for the first time, consisting of an Upper House (Council of State) and a Lower House (Legislative Assembly).

Additional Information

• Indian Councils Act, 1892:
• This Act increased the number of additional (non-official) members in the Central and Provincial Legislative Councils.
• It increased the functions of Legislative Councils and gave them the power of discussing the budget and addressing questions to the executive.
• It provided for the nomination of some non-official members, introducing a limited and indirect use of election in filling up some of the non-official seats.
• Government of India Act, 1909 (Morley-Minto Reforms):
• This Act is significantly known for introducing Separate Electorates for Muslims, thereby legalizing communalism in Indian politics.
• It considerably increased the size of the Legislative Councils at both the Central and Provincial levels.
• For the first time, it provided for the association of Indians with the Executive Councils of the Viceroy and Governors; Satyendra Prasad Sinha became the first Indian to join the Viceroy’s Executive Council as a Law Member.
• Government of India Act, 1935:
• This Act abolished Dyarchy in the provinces and introduced Provincial Autonomy in its place.
• However, it provided for the adoption of Dyarchy at the Centre, dividing federal subjects into Reserved and Transferred (though this provision never came into operation).
• It provided for the establishment of an All-India Federation consisting of provinces and princely states as units.
• It also led to the establishment of the Reserve Bank of India (RBI) in 1935 and a Federal Court in 1937.

Important Points

• The 1919 Act was based on the report submitted by Edwin Montagu, the then Secretary of State for India, and Lord Chelmsford, the Viceroy of India.
• It mandated that three of the six members of the Viceroy’s Executive Council (other than the Commander-in-Chief) were to be Indians.
• The Act extended the principle of communal representation by providing separate electorates for Sikhs, Indian Christians, Anglo-Indians, and Europeans.
• It granted a limited franchise to people on the basis of property, tax, or education.
• It also provided for the establishment of a Public Service Commission, leading to the setting up of a Central Public Service Commission in 1926 for recruiting civil servants.
• The Simon Commission was appointed in November 1927 (two years ahead of schedule) to report on the working of the reforms introduced by the Act of 1919.

The logic followed here is:

Given: Seven people B, C, O, P, Q, R and S are sitting around a circular table facing the centre.

Only two people sit between P and B when counted from the right of P.

Only S sits between O and P.

Q sits to the immediate left of B.

C is not an immediate neighbour of P.

Now, Third to the left of R is O.

Hence, the correct answer is "Option 4".

Shortcut Trick

Men ratio = 100 : 50 = 2 : 1

Days ratio = 1 : 2 (Inverse of Men ratio because Total Provision is constant)

1 unit = 26 days

2 units = 26 × 2 = 52 days

∴ Answer = 52

Alternate Method 

Given:

Initial number of men (M₁) = 100

Initial number of days (D₁) = 26

Number of men who left = 50

Remaining men (M₂) = 100 − 50 = 50

Formula used:

M₁ × D₁ = M₂ × D₂ (Chain Rule when work/provision is constant)

Initial: 100 Men D1 = 26 Days Final: 50 Men (Left 50) D2 = 52 Days Inverse Relation Men ÷ 2 → Days × 2 Total Provision = 2600 units

Calculations:

Total provision = M₁ × D₁ = 100 × 26 = 2600 man-days

⇒ 2600 = M₂ × D₂

⇒ 2600 = 50 × D₂

⇒ D₂ = 2600 ÷ 50

⇒ D₂ = 52

∴ The correct answer is 52.

Additional Information

General Chain Rule (MDH Rule)

The relationship between men (M), days (D), hours (H), and work (W) is given by (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂.

Inverse Proportion

In provision problems, the number of men is inversely proportional to the number of days the food lasts, provided the consumption per man remains constant.

Provision Addition Case

If more men join, the provisions will last for fewer days. New Days = (Initial Men × Initial Days) ÷ (Initial Men + New Men).