SSC GD Constable 2026 Official Paper (Held On 27 May, 2026 Shift 3) (Previous Year Paper)

Logic followed here is,

−194 + 7 = −187

−187 + 7 = −180

−180 + 7 = −173

−173 + 7 = −166

−166 + 7 = −159 ≠ -160

−159 + 7 = −152

−152 + 7 = −145

Therefore, the wrong term in the series is −160.

Hence, the correct answer is “Option 4”.

Logic followed here is,

(−69 × 2) − 1 = −138 − 1 = −139

(−139 × 3) − 1 = −417 − 1 = −418

(−418 × 2) − 1 = −836 − 1 = −837

(−837 × 3) − 1 = −2511 − 1 = −2512

(−2512 × 2) − 1 = −5024 − 1 = −5025

(−5025 × 3) − 1 = −15075 − 1 = −15076

(−15076 × 2) − 1 = −30152 − 1 = −30153

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

For 'YA' related to 'CG':

For 'RL' related to 'VR':

Applying the same logic to find the missing cluster for 'TH':

The missing letter cluster is PB.

Hence, the correct answer is 'Option 4'.

For the set '(IY, KA, PZ)':

For the set '(PS, RU, IF)':

Applying the same logic to '(EH, GJ, TQ)':

Thus, (EH, GJ, TQ) follows the same logic.

Hence, the correct answer is 'Option 3'.

Given that February 10 is a Monday.

Days remaining in February = 29 − 10 = 19 days.

To reach March 1, we add the remaining days of February plus 1 day for the start of March:

Total days from February 10 to March 1 = 19 + 1 = 20 days.

Now, divide the total days by 7 to find the number of odd days:

20 ÷ 7 = 2 weeks and 6 odd days.

Day on March 1 = Monday + 6 days = Sunday.

Since March 1 is a Sunday, we can list the Mondays and Thursdays in March:

Mondays in March:

March 2, March 9, March 16, March 23, and March 30.

Total Mondays = 5.

Thursdays in March:

If March 2 is Monday, then March 3 is Tuesday, March 4 is Wednesday, and March 5 is Thursday.

The Thursdays are: March 5, March 12, March 19, and March 26.

Total Thursdays = 4.

Total count of Mondays and Thursdays = 5 + 4 = 9.

Hence, the correct answer is “Option 3”.

5 boys L, M, N, P and A are sitting in a row facing north (not necessarily in the same order).

1. N is second to the right of L.
2. A is fourth to the right of L.
3. P is not the immediate neighbour of L.

Only one boy is sitting to the right of P.

Hence, the correct answer is “Option 2”.

7 girls G1, G2, G3, G4, G5, G6 and G7 are sitting around a circular table facing opposite to the centre (not necessarily in the same order).

1. G4 is not next to G6.
2. G2 is not next to G1.
3. G6 is second to the left of G3.
4. G1 is third to the right of G3.
5. G7 is third to the right of G6.

G4 is sitting second to the left of G5.

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 4”.

CLR22 : GPW44 → 

ADJ55 : EHO110 →

Similarly,

TKU33 : ? →

Hence, the correct answer is 'Option 1'.

Dictionary order of given words:

1. Receipt
2. Receptacle 
3. Reception
4. Recess
5. Recessim

Correct order is: 12453

Hence, the correct answer is “Option 3”.

The logic followed here is:

Logic: Second Number = First Number − 55

For the first pair 2794 : 2739

⇒ 2794 − 55 = 2739

For the second pair 102 : 47

⇒ 102 − 55 = 47

Applying the same logic to the third pair

7618 : ?

⇒ 7618 − 55 = 7563

Hence, the correct answer is 'Option 2'.

The logic followed here is:

Logic: Second Number = (First Number − 2)²

For the first pair 13 : 121

⇒ (13 − 2)²

⇒ 11² = 121.

For the second pair 15 : 169

⇒ (15 − 2)²

⇒ 13² = 169.

Applying the same logic to the third pair

19 : ?

⇒ (19 − 2)²

⇒ 17² = 289.

Hence, the correct answer is 'Option 2'.

The pattern observed is: (Sum of positional values of letters) − 2.

PAID is coded as 28 →

Sum of positional values = 16 + 1 + 9 + 4 = 30

Code = 30 − 2 = 28

DEAR is coded as 26 →

Sum of positional values = 4 + 5 + 1 + 18 = 28

Code = 28 − 2 = 26

Similarly, let's find the code for PEAR:

Sum of positional values = 16 + 5 + 1 + 18 = 40

Code = 40 − 2 = 38

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

The correct answer is 1951.

Key Points

• The Constitution (First Amendment) Act, 1951, was the inaugural amendment to the Constitution of India, enacted shortly after the constitution came into force in 1950.
• It was introduced by the Provisional Parliament of India on May 10, 1951, and received presidential assent on June 18, 1951.
• The primary objective of this amendment was to overcome various judicial roadblocks regarding the Right to Property, enabling the implementation of land reform legislations and the abolition of the Zamindari system.
• It introduced the Ninth Schedule to the Constitution, which protects laws included in it from being challenged in courts on the grounds of violating Fundamental Rights.
• The amendment modified several articles, including Article 15, Article 19, Article 31, Article 85, Article 87, Article 174, Article 176, Article 341, Article 342, Article 372, and Article 376.
• It placed reasonable restrictions on the Freedom of Speech and Expression under Article 19(2), adding grounds such as public order, incitement to an offence, and friendly relations with foreign states.

 Additional Information

• Article 31A and 31B:
• These articles were inserted to shield land acquisition and reform laws from judicial scrutiny under Articles 14 and 19.
• While Article 31A protects specific classes of laws, Article 31B validates all acts and regulations listed in the Ninth Schedule.
• Social Justice Provisions:
• The amendment modified Article 15 by adding clause (4), empowering the state to make special provisions for the advancement of socially and educationally backward classes (SEBCs) or for the Scheduled Castes (SC) and Scheduled Tribes (ST).
• This was a direct response to the Supreme Court judgment in the State of Madras v. Champakam Dorairajan case.
• Sessions of Parliament:
• The amendment changed the provisions regarding the summoning and proroguing of Parliament and the State Legislatures, ensuring greater flexibility in legislative schedules.

The correct answer is Lok Sabha by majority resolution.

Key Points

• The Speaker of the Lok Sabha is the presiding officer of the lower house of the Indian Parliament, and their removal is strictly governed by the provisions of the Constitution of India.
• Under Article 94(c), the Speaker can be removed from office by a resolution passed by a majority of all the then members of the Lok Sabha, which is technically referred to as an Effective Majority.
• A mandatory requirement for moving such a resolution is that at least 14 days notice must be given to the Speaker expressing the intention to move the removal resolution.
• According to Article 96, while a resolution for the removal of the Speaker is under consideration, the Speaker cannot preside over the sitting of the House, although they have the right to be present and participate in the proceedings.
• During the voting on such a resolution, the Speaker is entitled to vote in the first instance but cannot exercise a casting vote in the event of an equality of votes.

 Additional Information

• Constitutional Framework
• Article 93: Mandates that the Lok Sabha shall choose two members of the House to be Speaker and Deputy Speaker respectively as soon as may be.
• Money Bill: Under Article 110, the Speaker possesses the final authority to certify whether a particular bill is a Money Bill, and this decision cannot be challenged in a court of law.
• Joint Sittings: The Speaker presides over the Joint Sitting of both Houses of Parliament, which is summoned by the President under Article 108 to resolve deadlocks on ordinary bills.
• Independence: To maintain the neutrality of the office, the Speaker's salary and allowances are charged on the Consolidated Fund of India and are not subject to the annual vote of Parliament.

The correct answer is Andhra Pradesh.

Key Points

• Kuchipudi is one of the eight principal Indian classical dance forms, recognized for its seamless blend of dance, music, and drama.
• The dance form originated in the village of Kuchipudi (also known as Kuchelapuram) located in the Krishna district of Andhra Pradesh.
• It was traditionally performed by Brahmins known as Bhagavathulu, who traveled across villages to perform Bhagavatha Mela, depicting stories from the Puranas.
• The modern framework of Kuchipudi was systematized in the 17^th century by Siddhendra Yogi, an ascetic and scholar who composed the iconic dance-drama Bhamakalapam.
• Originally a male-dominated art form where men played female roles, it evolved into a prominent solo and group performance style for both men and women during the 20^th century.
• The performance is characterized by fast-paced footwork, fluid body movements, and expressive eye movements accompanied by Carnatic music.

 Additional Information

• Geographical Origins of Other Classical Dances:
• Tamil Nadu: This state is the home of Bharatanatyam, the oldest classical dance form in India, traditionally associated with Devadasis in temples.
• Kerala: Known for two classical forms: Kathakali, a vigorous dance-drama reflecting the Tandava style, and Mohiniyattam, a graceful solo dance representing the Lasya style.
• Uttar Pradesh: The origin state for Kathak, which focus on intricate footwork and Chakkars (pirouettes).
• Special Features of Kuchipudi:
• Tarangam: A unique feat where the dancer performs on the rim of a brass plate, often while balancing a water pot on their head.
• Manduka Shabdam: A rhythmic sequence that tells the story of a frog, showcasing the mimetic skills of the performer.
• Famous Proponents: Legendary artists include Vempati Chinna Satyam, Raja and Radha Reddy, and Yamini Krishnamurthy.

The correct answer is Lactometer.

Key Points

• Archimedes' principle is a fundamental law in fluid mechanics stating that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
• A Lactometer is a specialized instrument used to check the purity of milk by measuring its density or specific gravity.
• The device operates based on the principle of buoyancy; when placed in a milk sample, it sinks to a specific level where the weight of the displaced milk equals the weight of the lactometer.
• If milk is pure, its density is higher (typically between 1.026 and 1.032 g/ml), causing the device to sink less; if water is added, the density decreases, and the device sinks further into the liquid.
• Other common applications of Archimedes' principle include the design of ships, submarines, and hydrometers used for testing various liquid densities.

 Additional Information

• Thermometer:
• Function: Used to measure temperature.
• Principle: Primarily works on the thermal expansion of substances (like mercury or alcohol) or changes in electrical resistance.
• Barometer:
• Function: Used to measure atmospheric pressure.
• Principle: Measures the pressure exerted by the atmosphere using mercury or a vacuum-sealed capsule (aneroid).
• Ammeter:
• Function: Used to measure the electric current in a circuit.
• Principle: Operates based on electromagnetism, where current passing through a coil creates a magnetic field that moves a needle.

The correct answer is Indian soldiers in World War I.

Key Points

• Across the Black Waters, published in 1939, is a landmark novel by Mulk Raj Anand, one of the founding fathers of the Indian English novel. It remains the only major Indian novel to depict the First World War from the perspective of an Indian soldier.
• The story follows the protagonist Lallu Singh (Lalu), a young peasant from the Punjab region who joins the British Indian Army to escape familial debt and the oppressive social structures of his village.
• The narrative focuses on the deployment of the Ludhiana Sikhs regiment to the Western Front in France and Belgium. It vividly describes the transition of rural Indians into the mechanized horror of trench warfare during World War I.
• The title refers to the Kala Pani (Black Waters) taboo, symbolizing the soldiers' journey across the ocean, which traditionally meant a loss of caste and a departure from their cultural roots.
• Anand emphasizes the humanitarian aspect and the alienation of these soldiers, who fought for the British Empire in a conflict they did not fully understand, highlighting themes of bravery, camaraderie, and the futility of war.

 Additional Information

• The Lalu Trilogy:
• This novel is the second part of a trilogy that tracks the life of Lallu Singh. The first part is The Village (1939), which deals with rural Punjab life, and the third is The Sword and the Sickle (1942), focusing on his return to India and involvement in peasant uprisings and political activism.
• Incorrect Themes Contextualized:
• Partition of India: This became a dominant theme in Indian literature post-1947. Notable works include Khushwant Singh's Train to Pakistan and Bapsi Sidhwa's Ice-Candy-Man.
• Urban Poverty: While Mulk Raj Anand is famous for addressing social injustice and poverty in works like Untouchable (1935) and Coolie (1936), Across the Black Waters specifically shifts focus to the military and international conflict.
• Tribal Life: This theme is more central to the works of authors like Gopinath Mohanty (e.g., Paraja) or Mahasweta Devi, rather than the primary focus of Anand's war novel.

The correct answer is 2007.

Key Points

• The inaugural ICC World Twenty20 (now known as the T20 World Cup) was hosted by South Africa in September 2007.
• India emerged as the champions of the first-ever edition by defeating their arch-rivals Pakistan in a high-voltage final held on September 24, 2007.
• The final match took place at the Wanderers Stadium in Johannesburg, where India won the toss and elected to bat first, setting a target of 158 runs.
• Under the leadership of the newly appointed captain Mahendra Singh Dhoni, India successfully defended the total, winning the match by a narrow margin of 5 runs.
• The victory was sealed in the final over when Joginder Sharma dismissed Misbah-ul-Haq, who was caught by S. Sreesanth at short fine-leg.

 Additional Information

• Tournament Highlights and Records:
• Gautam Gambhir played a stellar role in the final, scoring 75 runs off 54 balls, which anchored the Indian innings.
• Irfan Pathan was named the Player of the Match in the final for his exceptional bowling figures of 3/16 in four overs.
• Yuvraj Singh created a world record during a group stage match against England by hitting six sixes in a single over bowled by Stuart Broad.
• Pakistan's Shahid Afridi was declared the Player of the Tournament for his consistent all-round performance despite his team losing the final.
• Impact on Global Cricket:
• The massive success of the 2007 World Cup led to the conceptualization and launch of the Indian Premier League (IPL) in 2008.
• India's win popularized the T20 format globally, leading the ICC to make the tournament a biennial event to capitalize on the growing demand for short-format cricket.

The correct answer is Squamous epithelium.

Key Points

• Squamous epithelium is composed of extremely thin, flat cells that form a delicate lining, providing a smooth surface for transport and protection.
• In the oesophagus and the inner lining of the mouth, these cells are arranged in multiple layers (strata) to form stratified squamous epithelium.
• The primary function of this multilayered structure is to provide protection against mechanical stress, friction, and wear and tear encountered during the passage of food.
• Unlike the skin, the squamous epithelium in the mouth and oesophagus is usually non-keratinized, meaning it remains moist to facilitate the movement of the bolus.
• Because the outer layers can be easily replaced by new cells from the basal layer, this tissue is highly efficient at maintaining its integrity despite constant abrasion.

 Additional Information

• Columnar epithelium:
• Consists of tall, pillar-like cells found in the inner lining of the intestine and stomach.
• It is specialized for secretion of digestive enzymes and absorption of nutrients.
• Cuboidal epithelium:
• Composed of cube-shaped cells that form the lining of kidney tubules and ducts of salivary glands.
• Its main roles are providing mechanical support and facilitating secretion and absorption.
• Glandular epithelium:
• Formed when epithelial tissue folds inward to create multicellular glands.
• It is primarily involved in the secretion of substances like hormones, sweat, and mucus.

The correct answer is Abolishing the import licensing system for most goods.

Key Points

• The 1991 Economic Reforms, often referred to as the New Economic Policy (NEP), were launched under the leadership of Prime Minister P.V. Narasimha Rao and Finance Minister Dr. Manmohan Singh to address a severe Balance of Payments (BoP) crisis.
• Trade Liberalization was a core objective of these reforms, aiming to dismantle the restrictive License-Permit-Quota Raj that had isolated the Indian economy for decades.
• Before 1991, India maintained a rigorous Import Licensing System where almost all imports required government approval, leading to inefficiencies and a lack of technological growth.
• By abolishing the import licensing system for the majority of intermediate and capital goods, the government allowed domestic industries to freely procure global inputs, thereby enhancing productivity and competitiveness. Hence, the measure of abolishing the import licensing system for most goods is correct.
• This policy shift replaced administrative discretionary controls with a more transparent, market-driven mechanism, facilitating India's integration into the global market.

 Additional Information

• Tariff Rationalization: Contrary to imposing higher tariffs, the reforms focused on drastically reducing the peak customs duty to lower the cost of imports and encourage domestic industries to improve quality.
• Quantitative Restrictions (QRs): The 1991 reforms initiated the process of removing QRs on imports, which was fully completed by April 2001 to align with World Trade Organization (WTO) standards.
• Exchange Rate Reforms: To boost the external sector, the Indian Rupee was devalued by about 18-19 percent in July 1991, making Indian exports more attractive in the international market.
• Export Incentives: Instead of fixing quotas, the government introduced schemes like the Duty Entitlement Pass Book (DEPB) and ensured Current Account Convertibility by August 1994 to simplify trade-related foreign exchange transactions.

The correct answer is 3 points.

Key Points

• In American football, a field goal is a scoring maneuver worth 3 points that occurs when a team kicks the ball through the opponent's goalposts.
• The ball must be place-kicked or drop-kicked, usually from a scrimmage formation, and must pass between the uprights and over the crossbar.
• Teams generally attempt a field goal on fourth down when they are within the opponent's scoring range but are unable to secure a first down or a touchdown.
• A successful field goal requires a long snapper to deliver the ball to a holder, who secures it on the ground for the kicker.
• The distance of a field goal is calculated by adding 10 yards (the length of the end zone) to the distance between the line of scrimmage and the goal line, plus approximately 7 to 8 yards for the spot of the kick.

 Additional Information

• Touchdown:
• This is the most valuable scoring play, worth 6 points.
• It is achieved when a player carries the ball into or catches a pass within the opponent's end zone.
• Extra Point (PAT):
• Formally known as the Point After Touchdown, it is worth 1 point.
• It is awarded for a successful kick through the uprights immediately following a touchdown.
• Two-Point Conversion:
• An alternative to the extra point kick, where the team attempts to run or pass the ball into the end zone for 2 points.
• Safety:
• A rare scoring play worth 2 points awarded to the defensive team.
• It occurs when the offensive team is tackled in their own end zone or commits certain fouls there.

The correct answer is 1950-51.

Key Points

• The Economic Survey of India is a premier annual document released by the Ministry of Finance, Government of India, that provides a comprehensive overview of the national economy.
• The First Economic Survey of independent India was presented in the year 1950-51, establishing a formal tradition of reviewing the country's economic health and progress.
• In its initial years, the survey was not a standalone document but was presented as an integral part of the Union Budget documents.
• The tradition of presenting the survey along with the budget continued until 1964, after which the government decided to delink the two to allow for a more thorough analysis of economic trends before the budget announcement.
• Currently, the survey is typically presented in Parliament one day before the Union Budget is introduced by the Finance Minister.

 Additional Information

• Preparation and Supervision:
• The document is prepared by the Economics Division of the Department of Economic Affairs (DEA) within the Ministry of Finance.
• It is developed under the direct guidance and supervision of the Chief Economic Adviser (CEA) of India.
• Key Economic Indicators:
• The survey meticulously tracks and analyzes critical macroeconomic indicators such as Gross Domestic Product (GDP) growth rates, Inflation levels (CPI and WPI), and Foreign Exchange Reserves.
• It also evaluates sectoral performances in Agriculture, Manufacturing, and the Services Sector, providing a factual basis for future policy interventions.
• Policy Significance:
• While the survey is a descriptive and analytical report rather than a legally binding policy, it serves as an essential guide for policymakers, investors, and economists.
• It often contains a theme-based analysis focusing on specific challenges like Climate Change, Digital Infrastructure, or Social Welfare.

The correct answer is Digital services & microcredit expansion.

Key Points

• India Post serves as a vital engine for the rural economy by utilizing its extensive network of over 1,55,000 post offices, which constitutes one of the largest physical distribution networks in the world.
• The transformation of post offices into India Post Payments Bank (IPPB) branches has enabled digital financial inclusion, providing doorstep banking services through over 3,00,000 Postmen and Gramin Dak Sevaks.
• It acts as a catalyst for microcredit expansion by facilitating access to credit for small-scale farmers, artisans, and Self-Help Groups (SHGs), effectively bridging the gap between formal financial institutions and the unbanked rural population.
• The adoption of the Aadhaar Enabled Payment System (AePS) allows rural citizens to perform interoperable banking transactions, such as cash withdrawals and deposits, using only their biometric authentication.
• India Post is instrumental in the Direct Benefit Transfer (DBT) framework, ensuring that government subsidies, MGNREGA wages, and social security pensions are credited directly and transparently to beneficiaries.

 Additional Information

• Core Financial Services:
• Rural Postal Life Insurance (RPLI): Launched in 1995, it focuses on providing insurance cover to the rural public, particularly targeting weaker sections and women to provide financial security.
• Sukanya Samriddhi Yojana (SSY): This small deposit scheme, managed through post offices, encourages families to save for the education and marriage of the girl child, promoting long-term capital formation.
• Post Office Savings Bank (POSB): It manages billions in rural savings, fostering a culture of thrift and providing a safe avenue for capital accumulation in non-urban areas.
• Technological and Logistic Integration:
• The IT Modernization Project has networked all post offices, allowing for real-time tracking and electronic money orders, which are crucial for migrant workers sending remittances home.
• By providing e-commerce logistics, India Post connects rural entrepreneurs to a global marketplace, significantly boosting local production and employment.

The correct answer is Solar energy.

Key Points

• Non-conventional energy resources, also known as renewable energy, are derived from natural processes that are replenished constantly and are essentially inexhaustible.
• Solar energy is a primary non-conventional resource in India, harnessed through Photovoltaic (PV) cells or Solar Thermal systems to convert sunlight directly into electricity or heat.
• India is strategically located in the tropical zone, receiving abundant solar radiation for approximately 300 days a year, which provides a massive theoretical potential of 5,000 trillion kWh per year.
• The Government of India launched the Jawaharlal Nehru National Solar Mission (JNNSM) in 2010 to promote ecological sustainable growth and address energy security challenges.
• Unlike conventional fuels, solar energy is environmentally friendly as it produces no greenhouse gas emissions during operation, helping India meet its Nationally Determined Contributions (NDCs) under the Paris Agreement.

 Additional Information

• Conventional Energy Resources: These are traditional, finite sources that have been in use for a long time and contribute significantly to global warming.
• Coal: It is the most abundant fossil fuel in India and serves as the backbone of the thermal power industry, though it is highly polluting.
• Petroleum: Also known as crude oil, it is a vital source for transportation and petrochemical industries but faces rapid depletion and price volatility.
• Natural gas: Composed mainly of methane, it is considered the cleanest among fossil fuels but remains a non-renewable resource with limited reserves.
• Other Non-Conventional Sources:
• Wind Energy: Utilizes wind turbines to generate electricity, with India ranking among the top countries in installed capacity.
• Biomass: Derived from organic materials like agricultural waste, used primarily in rural areas for heating and power.
• Tidal and Geothermal Energy: These represent emerging sectors utilizing ocean tides and internal earth heat respectively.

The correct answer is 55.22.

Key Points

• The Pradhan Mantri Jan Dhan Yojana (PMJDY), launched on August 28, 2014, is the world's largest financial inclusion initiative, aimed at providing universal access to banking facilities.
• As of June 2025, the total number of Jan Dhan accounts in India has reached the milestone of 55.22 crore, signifying a massive expansion of the formal banking sector to the unbanked population.
• The growth trajectory shows a significant rise from the 50 crore mark achieved in August 2023, demonstrating the continued momentum of the National Mission for Financial Inclusion.
• Data indicates that approximately 55 percent of these account holders are women, and over 66 percent of the accounts are opened in rural and semi-urban areas, effectively reducing regional and gender disparities in banking.
• The total deposits in these accounts have also seen a substantial increase, providing a stable source of low-cost CASA (Current Account Savings Account) deposits for the Indian banking system.

 Additional Information

• Core Benefits of PMJDY:
• Accounts are zero-balance accounts, meaning there is no requirement to maintain a minimum balance.
• Every account holder is provided with a RuPay Debit Card, which includes a built-in Accident Insurance Cover of 2 lakh rupees for accounts opened after 2018.
• Eligible account holders can access an Overdraft (OD) facility of up to 10,000 rupees, acting as a micro-credit tool for the poor.
• The JAM Trinity:
• PMJDY is a crucial pillar of the JAM (Jan Dhan-Aadhaar-Mobile) trinity, which enables the government to facilitate Direct Benefit Transfer (DBT).
• This system ensures that subsidies and welfare payments from various schemes reach the beneficiaries directly, eliminating intermediaries and reducing fiscal leakages.

The correct answer is Buddhism.

Key Points

• Kanishka I, the most illustrious ruler of the Kushan Dynasty who reigned during the 2^nd century CE (c. 127−150 CE), is immortalized in history as a great patron of Buddhism.
• He played a critical role in organizing the Fourth Buddhist Council at Kundalvana in Kashmir, which was presided over by Vasumitra and co-presided by Ashvaghosha.
• Under his imperial support, Buddhism witnessed a monumental doctrinal shift and split into two major sects: Hinayana and Mahayana, with Kanishka largely championing the Mahayana tradition.
• His reign facilitated the flourishing of the Gandhara and Mathura schools of art, which produced the first anthropomorphic images of the Buddha, departing from the earlier tradition of using only symbols.
• Kanishka effectively utilized his vast empire, stretching from Central Asia to the Gangetic Valley, to spread Buddhist ideology along the Silk Road to China and other East Asian regions.

 Additional Information

• Eminent Figures at Court:
• Ashvaghosha: A renowned philosopher and poet who wrote the Buddhacharita, an epic poem on the life of the Buddha.
• Vasumitra: A prominent Buddhist scholar who played a leading role in compiling the Mahavibhasha, an extensive commentary on Buddhist philosophy.
• Charaka: The legendary physician often called the Father of Indian Medicine, who authored the Charaka Samhita under Kanishka's patronage.
• Nagarjuna: One of the most important Buddhist philosophers who founded the Madhyamaka (Middle Way) school.
• Context of Other Options:
• Jainism: Although it existed during this period, it received primary royal patronage from earlier rulers like Chandragupta Maurya and Kharavela of Kalinga.
• Zoroastrianism: This was a dominant Persian religion; while Kushan coins occasionally featured Zoroastrian deities like Miro and Mao, the state's primary historical legacy is tied to Buddhism.

The correct answer is 1013.

Key Points

• As of May 2025, India achieved a significant milestone in urban infrastructure by operationalizing 1013 kilometers of metro rail lines across the country.
• The expansion of the metro network is a core component of the National Urban Transport Policy, which aims to provide efficient, reliable, and sustainable public transport to the growing urban population.
• The Ministry of Housing and Urban Affairs (MoHUA) has been instrumental in overseeing these projects, ensuring that metro systems act as the backbone of Mass Rapid Transit Systems (MRTS) in major metropolitan areas.
• This milestone of 1013 km places India among the top nations globally with the largest operational metro networks, significantly enhancing inter-city connectivity and reducing the carbon footprint of urban travel.
• The operational lines have contributed to a shift from private vehicle usage to public transit, thereby mitigating traffic congestion and improving the overall quality of life for millions of citizens.
• The integration of various phases across cities like Delhi, Mumbai, Bengaluru, and Hyderabad has been pivotal in reaching this specific cumulative length by 2025.

 Additional Information

• Evolution of Indian Metro:
• Kolkata Metro: Established in 1984, it was the first underground metro system in India, marking the beginning of the metro era.
• Delhi Metro (DMRC): Starting in 2002, it revolutionized urban transport and remains the largest and busiest network in the country, contributing a massive share to the total 1013 km.
• Make in India: Under the Atmanirbhar Bharat initiative, a significant portion of metro rolling stock and components are now manufactured indigenously, reducing dependency on imports.
• Technological Advancements: India has introduced Driverless Train Operations (DTO) on specific corridors, such as the Magenta Line and Pink Line of the Delhi Metro, showcasing global technological standards.
• Future Targets: The government aims to expand the metro network to over 1500 km in the coming years, extending services to Tier-2 and Tier-3 cities through MetroLite and MetroNeo models.

The correct answer is USA.

Key Points

• Apollo-XI was the historic spaceflight mission that resulted in the first humans landing on the Moon, a feat achieved by the United States of America.
• The mission was launched on July 16, 1969, by the National Aeronautics and Space Administration (NASA) using the massive Saturn V rocket from Launch Complex 39A at the Kennedy Space Center in Florida.
• The crew consisted of three American astronauts: Commander Neil Armstrong, Lunar Module Pilot Edwin 'Buzz' Aldrin, and Command Module Pilot Michael Collins.
• On July 20, 1969, the Lunar Module, named Eagle, landed in the Sea of Tranquility, where Armstrong famously declared, 'That is one small step for [a] man, one giant leap for mankind.'
• This mission effectively concluded the Space Race between the USA and the Soviet Union, fulfilling the national goal proposed in 1961 by President John F. Kennedy.

 Additional Information

• USA (NASA):
• Founded in 1958, NASA has led numerous groundbreaking missions, including the Voyager probes, the Hubble Space Telescope, and the current Artemis program aiming to return humans to the Moon.
• India (ISRO):
• The Indian Space Research Organisation, established in 1969, is known for its Chandrayaan missions, with Chandrayaan-3 becoming the first to land near the lunar South Pole in 2023.
• China (CNSA):
• The China National Space Administration manages the Chang'e lunar missions and successfully performed the first soft landing on the far side of the Moon with Chang'e 4.
• France (CNES):
• The Centre National d'Études Spatiales is the French government space agency, a founding member of the European Space Agency (ESA) and a leader in the development of the Ariane launch vehicles.

The correct answer is 1856.

Key Points

• The Hindu Widows' Remarriage Act, also known as Act XV of 1856, was enacted on July 26, 1856, to legalize the remarriage of Hindu widows in all jurisdictions of the East India Company.
• The legislation was a major milestone in the social reform movement of the 19^th century, specifically targeting the harsh conditions and social exclusion faced by widows in Hindu society.
• Ishwar Chandra Vidyasagar, a prominent social reformer and educator, was the primary architect of this movement, providing scriptural evidence that Hinduism did not prohibit widow remarriage.
• The act was drafted and introduced during the tenure of Lord Dalhousie, though it was formally passed under the administration of Lord Canning.
• The law aimed to prevent the practice of Sati (which had been abolished in 1829) from being replaced by a life of perpetual misery and enforced asceticism for young widows.

 Additional Information

• Ishwar Chandra Vidyasagar:
• He was a polymath and the Father of Modern Bengali Prose who established numerous schools for girls and advocated for women's education.
• His persistent petitioning to the Legislative Council directly led to the passing of the 1856 Act.
• Lord Canning:
• He served as the Governor-General during the Revolt of 1857 and later became the first Viceroy of India in 1858.
• Significant Years in British India:
• 1833: Marks the Charter Act of 1833, which centralized the administration and redesignated the Governor-General of Bengal as the Governor-General of India.
• 1861: The year the Indian Councils Act was passed, introducing the Portfolio System and restructuring the Executive Council.
• 1885: The year the Indian National Congress was founded in Bombay by Allan Octavian Hume.

The correct answer is Both I and II.

Key Points

• The Demographic Transition Theory describes the process of population change from high birth and death rates to low rates as a society progresses through industrialization and economic development. The last stage (often Stage 4 or 5) represents a highly urbanized and technologically advanced society.
• Fertility (Statement I) decreases in the last stage because of social and economic shifts. Factors such as increased literacy, higher female labor force participation, the high cost of raising children in urban settings, and easy access to contraception lead families to prioritize smaller sizes, resulting in a low birth rate. Hence, statement I is correct.
• Mortality (Statement II) decreases and stabilizes at a low level due to major advancements in medical science, improved sanitation, and better nutritional standards. The elimination of large-scale epidemics and infectious diseases significantly increases life expectancy, making death rates very low and predictable. Hence, statement II is correct.

 Additional Information

• Stages of Demographic Transition:
• Stage 1 (High Stationary): High fertility and high mortality due to poor healthcare and famines, leading to slow population growth.
• Stage 2 (Early Expanding): Mortality drops due to better sanitation, but fertility stays high, causing a population explosion.
• Stage 3 (Late Expanding): Fertility begins to fall as industrialization spreads, and the population growth rate starts to slow down.
• Stage 4 (Low Stationary): Both fertility and mortality are low, leading to a stable or slowly growing population. Countries like Japan, Canada, and Germany are classic examples of this phase.
• Stage 5 (Declining): In some modern models, a fifth stage exists where fertility falls below the replacement level, leading to population contraction.

The correct answer is 6.

Key Points

• In standard professional tennis, a set is won by the first player or team to win at least six games. To win a set outright, a player must lead by a margin of at least two games, such as 6-0, 6-4, or 7-5.
• When both players win five games each, the score becomes 5-5. If the score then progresses to 6-6, neither player has achieved the required two-game lead to conclude the set, triggering a tiebreaker.
• The tiebreaker is a specialized game used to decide the winner of the set. During this phase, points are counted using ordinary numbers (1, 2, 3, etc.) instead of the standard tennis scoring of 15, 30, and 40.
• A standard tiebreaker is won by the first player to reach seven points, provided they lead by at least two points. The final score of such a set is recorded as 7-6.
• The introduction of the tiebreak system is credited to James Van Alen in 1965 and was officially adopted by the International Tennis Federation (ITF) to prevent excessively long matches and ensure broadcasting schedules are met.

 Additional Information

• Scoring Mechanics
• In a regular game, if both players reach a score of 40-40, it is called a Deuce. A player must then win an Advantage point and the following point to secure the game.
• Grand Slam Rules
• Starting from 2022, all four Grand Slam tournaments (Australian Open, French Open, Wimbledon, and US Open) implemented a unified 10-point tiebreaker when the score reaches 6-6 in the final set.
• ITF and Professional Tours
• The International Tennis Federation (ITF), ATP, and WTA enforce these rules to maintain global consistency in competitive play across different surfaces like clay, grass, and hard courts.

The correct answer is Kerala.

Key Points

• The state of Kerala has secured the first rank in the Urban Governance Index (UGI) 2024, demonstrating superior performance in local self-governance and administrative transparency.
• The Urban Governance Index is a comprehensive study released by the Praja Foundation, a Mumbai-based non-partisan organization that monitors the health of urban governance across India.
• The 2024 index highlights Kerala as the leading state due to its effective implementation of the 74^th Constitutional Amendment Act, which empowers Urban Local Bodies (ULBs).
• Kerala achieved a high score by excelling in the devolution of the 3 Fs: Functions, Funds, and Functionaries, ensuring that city governments have the autonomy to manage local affairs.
• The ranking evaluates states based on their ability to create empowered city administrations and foster citizen participation in urban decision-making processes.
• The state's success is largely attributed to its long-standing decentralization reforms and the institutionalization of Ward Committees in its Municipal Corporations and Municipalities.

 Additional Information

• Urban Governance Index (UGI) Pillars:
• Empowered City Elected Representatives: Evaluates the authority and fixed tenure of the Mayor and the power of the city council.
• Empowered City Administration: Assesses the recruitment and control of municipal staff and administrative efficiency.
• Empowered Citizens: Measures the effectiveness of grievance redressal systems and the formal role of citizens in planning.
• Fiscal Empowerment: Examines the financial autonomy of cities and their ability to generate independent revenue through property tax and other levies.
• Constitutional Foundation:
• The 74^th Constitutional Amendment Act of 1992 introduced Part IX-A to the Indian Constitution.
• It added the Twelfth Schedule, which lists 18 functional items like urban planning, water supply, and public health that should be managed by local bodies.
• Praja Foundation:
• A non-profit organization established in 1997 that aims to enable accountable governance through data-driven research and citizen reports.

Shortcut Trick

Solve the expression directly using the BODMAS rule (Bracket, Multiplication, Addition, Subtraction).

Step 1: Solve the bracket (32 + 18) = 50.

Step 2: Perform multiplication (27 × 2) = 54.

Step 3: Solve addition and subtraction: 121 − 50 + 54 = 125.

∴ The correct answer is 125.

Alternate Method

Given:

Expression: 45 + 76 − (32 + 18) + 27 × 2

Formula Used:

Apply the BODMAS order of operations: Brackets → Of → Division → Multiplication → Addition → Subtraction.

Calculations:

⇒ 45 + 76 − 50 + 27 × 2 (Solving the bracket 32 + 18)

⇒ 45 + 76 − 50 + 54 (Performing multiplication 27 × 2)

⇒ 121 − 50 + 54 (Performing addition 45 + 76)

⇒ 71 + 54 (Performing subtraction 121 − 50)

⇒ 125

∴ The correct answer is 125.

Additional Information

BODMAS Rule Hierarchy

Always prioritize Brackets (), then Of, then Division (÷) and Multiplication (×), and finally Addition (+) and Subtraction (−).

V-BODMAS Rule

In complex simplifications, a Vinculum (bar over numbers) is solved even before brackets.

Left-to-Right Rule

If an expression contains only addition and subtraction, solve strictly from left to right to avoid sign errors.

Shortcut Trick

Solve the expression using the BODMAS rule by prioritizing the bracket and multiplication.

Expression = 91 − 37 + (40) × 2 − 61 + 23

Expression = 91 − 37 + 80 − 61 + 23

Group positive and negative terms: (91 + 80 + 23) − (37 + 61) = 194 − 98

Expression = 96

∴ The correct answer is 96.

Alternate Method

Given: 91 − 37 + (26 + 14) × 2 − 61 + 23

Formula Used: BODMAS Rule (Bracket, Of, Division, Multiplication, Addition, Subtraction)

⇒ 91 − 37 + (40) × 2 − 61 + 23

⇒ 91 − 37 + 80 − 61 + 23

⇒ 54 + 80 − 61 + 23

⇒ 134 − 61 + 23

⇒ 73 + 23

⇒ 96

∴ The correct answer is 96.

Additional Information

BODMAS Rule

The rule determines the order of operations: Brackets, Of (Orders/Powers), Division, Multiplication, Addition, and Subtraction.

Left-to-Right Rule

For operations with the same priority level (like addition and subtraction), always calculate from the left to the right of the expression.

Grouping Positive Terms

To simplify complex additions/subtractions, sum all positive integers and all negative integers separately, then find the final difference.

Shortcut Trick

Rewrite the numerator as 8 × (2.5)³ + 1 = (2)³ × (2.5)³ + 1 = (2 × 2.5)³ + 1.

Therefore, Numerator = 5³ + 1 = 125 + 1 = 126.

Denominator = 5² − 4 = 25 − 4 = 21.

Final calculation: 126 ÷ 21 = 6.

∴ The correct answer is 6.

Alternate Method

Given: (8(2.5)³ + 1) ÷ (5² − 4)

Formula Used: BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

⇒ (8 × 15.625 + 1) ÷ (25 − 4)

⇒ (125 + 1) ÷ 21

⇒ 126 ÷ 21

⇒ 6

∴ The correct answer is 6.

Additional Information

BODMAS Rule

Simplification follows the BODMAS order: solve Brackets first, then Orders (indices/roots), followed by Division and Multiplication, and finally Addition and Subtraction.

Cube of Numbers

The cube of a decimal number is found by multiplying the number by itself twice (e.g., 2.5³ = 2.5 × 2.5 × 2.5 = 15.625).

Exponent Laws

Applying the law aⁿ × bⁿ = (a × b)ⁿ helps in simplifying calculations like 8 × (2.5)³ = (2 × 2.5)³ = 5³.

Shortcut Trick

Identify the relationship: number + √number = 42.

Since the sum is an integer (42), the number must be a perfect square.

Test the perfect square options: For 36, we get 36 + √36 = 36 + 6 = 42.

For 25, we get 25 + √25 = 25 + 5 = 30 (Incorrect).

∴ The correct answer is 36.

Alternate Method

Given: Sum of a number and its positive square root is 42.

Formula Used: Quadratic substitution where x + √x = k.

Let the positive square root of the number be a.

⇒ Number = a²

⇒ a² + a = 42

⇒ a² + a − 42 = 0

By splitting the middle term (factors of −42 that add up to 1 are 7 and −6):

⇒ a² + 7a − 6a − 42 = 0

⇒ a(a + 7) − 6(a + 7) = 0

⇒ (a + 7)(a − 6) = 0

⇒ a = 6 or a = −7

Since we need the positive square root, we take a = 6.

⇒ Number = a² = 6² = 36.

∴ The correct answer is 36.

Additional Information

Quadratic Formula

For any equation ax² + bx + c = 0, the roots can be found using the formula x = [−b ± √(b² − 4ac)] ÷ 2a.

Perfect Square Identification

A number is a perfect square if its prime factorization contains only even powers. Example: 36 = 2² × 3².

Nature of Roots

If the discriminant D = b² − 4ac is a perfect square, the roots of the quadratic equation are rational.

Shortcut Trick

Use the algebraic identity: (a + b)² + (a − b)² = 2(a² + b²)

Here, a = √6 and b = √2.

Numerator = 2[(√6)² + (√2)²] = 2(6 + 2) = 2 × 8 = 16.

Final Value = 16 ÷ 32 = 1/2.

∴ The correct answer is 1/2.

Alternate Method

Given Expression: [(√6 + √2)² + (√6 − √2)²] ÷ 32

Formula Used: (a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab

⇒ (√6 + √2)² = (√6)² + (√2)² + 2(√6 × √2) = 6 + 2 + 2√12 = 8 + 4√3

⇒ (√6 − √2)² = (√6)² + (√2)² − 2(√6 × √2) = 6 + 2 − 2√12 = 8 − 4√3

⇒ Numerator = (8 + 4√3) + (8 − 4√3)

⇒ Numerator = 8 + 8 = 16

⇒ Result = 16 ÷ 32 = 1/2

∴ The correct answer is 1/2.

Additional Information

Algebraic Identities for Squares

The sum of squares of sum and difference is (a + b)² + (a − b)² = 2(a² + b²), while the difference is (a + b)² − (a − b)² = 4ab.

Properties of Square Roots

For any non-negative number x, (√x)² = x. Also, √x × √y = √(xy).

Rationalization

When dealing with surds in the denominator, multiply both numerator and denominator by the conjugate (e.g., for a + √b, the conjugate is a − √b).

Shortcut Trick

Sum of an Arithmetic Progression (AP) = Average × Number of terms (n).

n = [(Last term − First term) ÷ Common difference] + 1 = [(138 − 24) ÷ 2] + 1 = 58.

Average = (First term + Last term) ÷ 2 = (24 + 138) ÷ 2 = 81.

Sum = 81 × 58 = 4698.

∴ The correct answer is 4698.

Alternate Method

Given: First term (a) = 24, Last term (l) = 138, Common difference (d) = 2.

Formula Used: l = a + (n − 1)d and S_n = (n ÷ 2)(a + l)

⇒ 138 = 24 + (n − 1) × 2

⇒ 138 − 24 = (n − 1) × 2

⇒ 114 = (n − 1) × 2

⇒ n − 1 = 114 ÷ 2

⇒ n − 1 = 57

⇒ n = 58

⇒ S₅₈ = (58 ÷ 2) × (24 + 138)

⇒ S₅₈ = 29 × 162

⇒ S₅₈ = 4698

∴ The correct answer is 4698.

Additional Information

Sum of First n Natural Numbers

The sum of the first n positive integers (1, 2, 3, ..., n) is given by: n(n + 1) ÷ 2.

Common Difference (d)

In an Arithmetic Progression, the common difference d is calculated as a_n − a_n−1.

nth Term Formula

The nth term of an AP is a_n = a + (n − 1)d, where 'a' is the first term and 'd' is the common difference.

Arithmetic Mean

The average of terms in any AP is equal to the mean of the first and last terms: (a + l) ÷ 2.

Shortcut Trick

Side (a) of the rhombus = Perimeter ÷ 4 = 60 ÷ 4 = 15 cm.

In a rhombus, half-diagonals and the side form a right-angled triangle.

Given half-diagonal (d₁/2) = 24 ÷ 2 = 12 cm.

Applying the Pythagorean triplet (9, 12, 15), the other half-diagonal (d₂/2) = 9 cm.

Full diagonal 2 (d₂) = 9 × 2 = 18 cm.

Ratio of diagonals = 24 : 18 = 4 : 3.

∴ The correct answer is 4:3.

Alternate Method

Given: Perimeter = 60 cm, Diagonal 1 (d₁) = 24 cm.

Formula Used: Perimeter = 4 × Side (a); Side² = (d₁/2)² + (d₂/2)²

⇒ 4 × a = 60

⇒ a = 15 cm

⇒ 15² = (24/2)² + (d₂/2)²

⇒ 225 = 12² + (d₂/2)²

⇒ 225 = 144 + (d₂/2)²

⇒ (d₂/2)² = 225 − 144 = 81

⇒ d₂/2 = √81 = 9 cm

⇒ Diagonal 2 (d₂) = 9 × 2 = 18 cm

⇒ Ratio of diagonals = 24 : 18 = 4 : 3

∴ The correct answer is 4:3.

Additional Information

Area of Rhombus

The area can be calculated using the product of its diagonals: Area = 1/2 × d₁ × d₂.

Side and Diagonal Relationship

The relationship between the side (a) and diagonals is given by: 4a² = d₁² + d₂².

Properties of Diagonals

The diagonals of a rhombus always bisect each other at right angles (90°) and also bisect the internal angles.

Shortcut Trick

The given series 4 + 8 + 12 + ... + 296 is a multiple of 4.

Taking 4 common: 4 × (1 + 2 + 3 + ... + 74), where 296 ÷ 4 = 74.

Number of terms n = 74.

Sum of first 74 natural numbers = [74 × (74 + 1)] ÷ 2 = 37 × 75 = 2775.

Total Sum = 4 × 2775 = 11100.

∴ The correct answer is 11100.

Alternate Method

Given:

First term (a) = 4

Common difference (d) = 8 − 4 = 4

Last term (l) = 296

Formula Used:

n-th term (l) = a + (n − 1)d

Sum of n terms (S_n) = (n/2) × (a + l)

Calculations:

⇒ 296 = 4 + (n − 1) × 4

⇒ 296 − 4 = 4(n − 1)

⇒ 292 = 4(n − 1)

⇒ n − 1 = 292 ÷ 4 = 73

⇒ n = 74

⇒ S₇₄ = (74 ÷ 2) × (4 + 296)

⇒ S₇₄ = 37 × 300

⇒ S₇₄ = 11100

∴ The correct answer is 11100.

Additional Information

Sum of Arithmetic Progression (AP)

The sum can also be calculated using the formula S_n = (n/2) × [2a + (n − 1)d].

Sum of first n Natural Numbers

The sum of the first n natural numbers is given by Σn = [n(n + 1)] ÷ 2.

Arithmetic Mean of an AP

The average or arithmetic mean of an AP series is simply (First term + Last term) ÷ 2.

Shortcut Trick

If every number in a data set is multiplied by a constant k, the average of that data set is also multiplied by the same constant k.

Original Average = 8

Multiplication Factor = 4

New Average = 8 × 4 = 32

∴ The correct answer is 32.

Alternate Method

Given:

⇒ Total numbers (n) = 11

⇒ Original average = 8

Formula Used:

⇒ Average = Sum of all observations ÷ Total number of observations

⇒ Sum = Average × Total number of observations

Calculations:

⇒ Original Sum = 11 × 8 = 88

⇒ When each of the 11 numbers is multiplied by 4, the sum is also multiplied by 4.

⇒ New Sum = 88 × 4 = 352

⇒ New Average = New Sum ÷ Total numbers

⇒ New Average = 352 ÷ 11 = 32

∴ The correct answer is 32.

Additional Information

Effect of basic operations on Average

If k is added to each observation, the new average becomes Old Average + k. If k is subtracted, it becomes Old Average − k.

Multiplication and Division Rule

If each observation is multiplied by k, the new average is Old Average × k. If divided by k (k not 0), the new average is Old Average ÷ k.

Constant Average Property

If all numbers in a set are identical (e.g., all are 8), the average of that set is simply that constant number (8).

Shortcut Trick

If every term in a series of consecutive natural numbers is increased by a constant value k, the average of the series also increases by exactly k.

The first series starts at a and the second series starts at a + 5.

Since both series contain 9 consecutive numbers, every term in the new series is exactly 5 more than the corresponding term in the old series.

Therefore, New Average = Old Average + 5 = x + 5.

∴ The correct answer is x + 5.

Alternate Method

Given: First term of first series = a, Number of terms (n) = 9, Average = x.

Formula Used: Average of n consecutive numbers = Middle term = ((n + 1) ÷ 2)^th term.

⇒ For 9 terms, the average is the 5^th term.

⇒ 5^th term of first series = a + (5 − 1) × 1 = a + 4.

⇒ Given, x = a + 4.

⇒ The second series starts with a + 5 and also has 9 terms.

⇒ 5^th term of second series = (a + 5) + 4 = a + 9.

⇒ New Average = (a + 4) + 5.

⇒ Substituting x for (a + 4), New Average = x + 5.

∴ The correct answer is x + 5.

Additional Information

Average of Arithmetic Progression (AP)

For any sequence in Arithmetic Progression, the average is calculated as (First term + Last term) ÷ 2.

Effect of Operations on Average

If every number in a data set is multiplied by k, the new average is k × (old average). If k is added, the new average is (old average) + k.

Middle Term Property

In a series with an odd number of terms (n) that are in AP, the average is always the exact middle term, which is the ((n + 1) ÷ 2)^th term.

Shortcut Trick

To find the HCF of numbers in prime factorization form, identify the common prime bases and pick the lowest power of each.

Common prime bases: 2, 3, and 5.

Lowest power of 2: 2³ | Lowest power of 3: 3⁴ | Lowest power of 5: 5¹.

HCF = 2³ × 3⁴ × 5.

∴ The correct answer is 2³ × 3⁴ × 5.

Alternate Method

Given:

Number 1 (N₁) = 2⁴ × 3⁶ × 5³ × 7⁴

Number 2 (N₂) = 2³ × 3⁴ × 5 × 11³

Formula Used:

Highest Common Factor (HCF) = Product of the smallest power of each common prime factor.

Calculations:

⇒ Prime base 2: Powers are 4 and 3. Smallest power is 2³.

⇒ Prime base 3: Powers are 6 and 4. Smallest power is 3⁴.

⇒ Prime base 5: Powers are 3 and 1. Smallest power is 5¹.

⇒ Prime bases 7 and 11 are not common to both numbers.

⇒ HCF = 2³ × 3⁴ × 5.

∴ The correct answer is 2³ × 3⁴ × 5.

Additional Information

Least Common Multiple (LCM)

For numbers in prime factorization form, LCM is the product of the highest power of every prime factor involved in the numbers.

Product Property

For any two positive integers A and B: A × B = HCF(A, B) × LCM(A, B).

HCF of Co-primes

If two numbers have no common prime factors, they are called co-prime and their HCF is 1.

Shortcut Trick

To find the maximum number of students for equal distribution, calculate the HCF of 165 and 385.

Difference between 385 and 165 = 220.

HCF must be a factor of 220. Check factors: 220 ÷ 4 = 55.

Since 55 divides both 165 (55 × 3) and 385 (55 × 7), it is the HCF.

∴ The correct answer is 55 students.

Alternate Method

Given:

Total Chips = 165

Total Toffees = 385

Formula:

Maximum number of recipients = HCF (Highest Common Factor) of the given quantities.

Prime Factorization:

⇒ 165 = 3 × 5 × 11

⇒ 385 = 5 × 7 × 11

Finding HCF:

⇒ Common prime factors = 5 and 11

⇒ HCF = 5 × 11

⇒ HCF = 55

∴ The correct answer is 55 students.

Additional Information

Highest Common Factor (HCF)

HCF is the largest positive integer that divides each of the integers without leaving a remainder. It is also known as the Greatest Common Divisor (GCD).

Difference Method for HCF

The HCF of two numbers is also a factor of their difference. HCF(a, b) = HCF(a − b, b) where a > b.

Relationship between HCF and LCM

For any two numbers a and b: HCF(a, b) × LCM(a, b) = a × b.

Shortcut Trick

Successive Percentage calculation: 40% of 50% is equal to 0.40 × 50% = 20%.

The problem states that 40% of 50% of the number is 160.

This means 20% of the number is 160.

Since the question asks for exactly 20 percent of that number, no further calculation is needed.

∴ The correct answer is 160.

Alternate Method

Given:

40% of 50% of a number = 160

Formula Used:

Percentage Value = (Percentage ÷ 100) × Total Value

Calculations:

⇒ Let the original number be x.

⇒ (40 ÷ 100) × (50 ÷ 100) × x = 160

⇒ (2 ÷ 5) × (1 ÷ 2) × x = 160

⇒ (1 ÷ 5) × x = 160

⇒ x = 160 × 5

⇒ x = 800

⇒ Required value = 20% of 800

⇒ Required value = (20 ÷ 100) × 800 = 160.

∴ The correct answer is 160.

Additional Information

Successive Percentage Rule

When calculating a% of b% of a number N, the effective percentage is (a × b) ÷ 100 % of N.

Percentage to Fraction Conversion

Standard fractions help in faster calculations: 50% = 1/2, 40% = 2/5, 20% = 1/5, and 25% = 1/4.

Interchangeability of Percentages

x% of y is always equal to y% of x. For example, 40% of 50 is the same as 50% of 40, which is 20.

Shortcut Trick

Ratio of Profit : Selling Price = 1 : 5

Cost Price = Selling Price − Profit = 5 − 1 = 4 units

Profit % = (Profit ÷ Cost Price) × 100

Profit % = (1 ÷ 4) × 100 = 25%

∴ The correct answer is 25 percent.

Alternate Method

Given: Ratio of Profit to Selling Price = 1 : 5

Formula Used: Profit % = (Profit ÷ Cost Price) × 100; where Cost Price = Selling Price − Profit

⇒ Let the Profit earned be 1x and the Selling Price be 5x.

⇒ Cost Price (CP) = Selling Price (SP) − Profit

⇒ CP = 5x − 1x = 4x

⇒ Profit % = (Profit ÷ CP) × 100

⇒ Profit % = (1x ÷ 4x) × 100

⇒ Profit % = 25%

∴ The correct answer is 25 percent.

Additional Information

Cost Price (CP)

The amount at which an article is purchased. CP = SP − Profit or CP = SP + Loss.

Profit Percentage

Unless otherwise stated, Profit % is always calculated on the Cost Price. Profit % = (Profit ÷ CP) × 100.

Selling Price (SP)

The amount at which an article is sold to a customer. SP = CP × (100 + Profit %) ÷ 100.

Loss Percentage

When CP > SP, a loss occurs. Loss % = (Loss ÷ CP) × 100, where Loss = CP − SP.

Shortcut Trick

Remaining work = Total Work × (1 − 4/7) × (1 − 2/5)

Remaining work = 70 × (3/7) × (3/5)

Remaining work = 10 × 3 × (3/5) = 2 × 9 = 18 units

∴ The correct answer is 18 units.

Alternate Method

Given: Total Work = 70 units; Work done on First Day = 4/7; Work done on Second Day = 2/5 of remaining.

⇒ Work done on First Day = 70 × (4/7) = 40 units

⇒ Remaining Work after First Day = 70 − 40 = 30 units

⇒ Work done on Second Day = 30 × (2/5) = 12 units

⇒ Final Remaining Work = 30 − 12 = 18 units

∴ The correct answer is 18 units.

Additional Information

Fractional Remainder Rule

To calculate the final quantity after multiple successive reductions, use the formula: Final = Initial × (1 − f₁) × (1 − f₂) × ... × (1 − f_n).

Work-Done Complement

If a person completes a/b part of the work, the part of work that remains incomplete is always (1 − a/b) = (b − a)/b.

Successive Percentage

Successive fraction reduction is equivalent to successive percentage decrease. For example, doing 2/5 of work is the same as completing 40% of the current remaining task.

Shortcut Trick

Work is equal (half part), so we use M₁ × D₁ = M₂ × D₂.

30 women × 10 days = M₂ × 2 days.

M₂ = 300 ÷ 2 = 150 women.

More women required = 150 − 30 = 120.

∴ The correct answer is 120 women.

Alternate Method

Given:

Initial women (M₁) = 30

Initial days (D₁) = 10 (for 1/2 work)

Remaining work (W₂) = 1/2

Target days (D₂) = 2

Formula Used:

Total Work = Number of Workers × Days (for full work)

Efficiency = Total Work ÷ Days

Calculations:

⇒ If 30 women take 10 days for half work, they take 20 days for full work.

⇒ If the new group takes 2 days for half work, they take 4 days for full work.

⇒ Efficiency of 30 women = 1 unit/day.

⇒ Efficiency of the new group required = 5 units/day.

⇒ If 1 efficiency → 30 women, then 5 efficiency → 30 × 5 = 150 women.

⇒ Additional women needed = Total required − Existing women = 150 − 30 = 120.

∴ The correct answer is 120 women.

Additional Information

General Man-Days Formula

For varying work, time, and men: (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where H is hours per day.

Work-Efficiency Relationship

Total Work = Men × Days × Efficiency. If work is constant, Men is inversely proportional to Days (M₁D₁ = M₂D₂).

Remaining Work Calculation

Remaining Work = Total Work (1) − Completed Work. If 1/2 is done, 1 − 1/2 = 1/2 remains.

Shortcut Trick

Total Relative Speed (km/hr) = [(Total Length) ÷ Time] × (18 ÷ 5)

Relative Speed = [(400 + 600) ÷ 36] × (18 ÷ 5) = [1000 ÷ 36] × (18 ÷ 5) = 100 km/hr

Since speeds are equal and trains move in opposite directions, 2 × Individual Speed = 100 km/hr

Individual Speed = 100 ÷ 2 = 50 km/hr

∴ The correct answer is 50 km/hr.

Alternate Method

Given:

Length of Train 1 (L₁) = 400 m

Length of Train 2 (L₂) = 600 m

Time (t) = 36 sec

Speed of both trains = S (same)

Formula:

Relative Speed (Opposite Direction) = S₁ + S₂

Speed = Distance ÷ Time

Calculations:

⇒ Relative Speed = (L₁ + L₂) ÷ t

⇒ S + S = (400 + 600) ÷ 36

⇒ 2S = 1000 ÷ 36

⇒ S = 1000 ÷ (36 × 2) = 1000 ÷ 72 m/s

⇒ To convert m/s to km/hr, multiply by 18 ÷ 5

⇒ S (in km/hr) = (1000 ÷ 72) × (18 ÷ 5)

⇒ S = (1000 ÷ 5) × (18 ÷ 72)

⇒ S = 200 × (1 ÷ 4)

⇒ S = 50 km/hr

∴ The correct answer is 50 km/hr.

Additional Information

Relative Speed Concepts

When two objects move in opposite directions, relative speed is the sum (S₁ + S₂). When they move in the same direction, relative speed is the difference |S₁ − S₂|.

Unit Conversion

To convert speed from m/s to km/hr, multiply the value by 18 ÷ 5. To convert from km/hr to m/s, multiply by 5 ÷ 18.

Total Crossing Distance

When a train crosses another train or a bridge/platform, the total distance covered is always the sum of their lengths (L₁ + L₂).

Shortcut Trick

Boat speed in still water = 30 ÷ 6 = 5 km/hr.

Condition: 72 ÷ (5 + v) + 18 ÷ (5 − v) = 26 hr, where v is stream speed.

Test options: If v = 4, then 72 ÷ (5 + 4) + 18 ÷ (5 − 4) = 72 ÷ 9 + 18 ÷ 1 = 8 + 18 = 26 hr.

The condition is satisfied for v = 4.

∴ The correct answer is 4 km/hr.

Alternate Method

Given:

Distance in still water = 30 km, Time = 6 hr.

Downstream distance = 72 km, Upstream distance = 18 km, Total time = 26 hr.

Formula Used:

Speed = Distance ÷ Time

Downstream Speed (d) = u + v

Upstream Speed (s) = u − v

Calculations:

⇒ Speed of boat in still water (u) = 30 ÷ 6 = 5 km/hr

⇒ Let stream speed be v km/hr

⇒ 72 ÷ (5 + v) + 18 ÷ (5 − v) = 26

⇒ [72(5 − v) + 18(5 + v)] ÷ [(5 + v)(5 − v)] = 26

⇒ [360 − 72v + 90 + 18v] ÷ (25 − v²) = 26

⇒ 450 − 54v = 26(25 − v²)

⇒ 450 − 54v = 650 − 26v²

⇒ 26v² − 54v − 200 = 0

⇒ 13v² − 27v − 100 = 0

⇒ 13v² − 52v + 25v − 100 = 0

⇒ 13v(v − 4) + 25(v − 4) = 0

⇒ (13v + 25)(v − 4) = 0

⇒ v = 4 (as speed cannot be negative)

∴ The correct answer is 4 km/hr.

Additional Information

Downstream and Upstream Speeds

Downstream speed (D) = u + v and Upstream speed (U) = u − v, where u is boat speed in still water and v is stream speed.

Speed of Boat and Stream

Boat speed in still water u = (D + U) ÷ 2 and Stream speed v = (D − U) ÷ 2.

Time, Speed and Distance Relation

Time = Distance ÷ Speed. When distance is constant, speed is inversely proportional to time.

Shortcut Trick

Profit = 40% ⇒ Ratio of SP : CP = 140 : 100 = 7 : 5

Given SP = 15/17 of MP ⇒ Ratio of MP : SP = 17 : 15

To find MP : CP, multiply the ratios: (MP/SP) × (SP/CP) = (17/15) × (7/5)

MP : CP = 119 : 75

∴ The correct answer is 119 : 75.

Alternate Method

Given:

Selling Price (SP) = (15/17) × Marked Price (MP)

Profit Percentage = 40%

Calculations:

⇒ Let Marked Price (MP) = 17 units

⇒ Selling Price (SP) = (15/17) × 17 = 15 units

⇒ We know that SP = CP × (100 + Profit%)/100

⇒ 15 = CP × (100 + 40)/100

⇒ 15 = CP × 140/100

⇒ 15 = CP × 7/5

⇒ CP = (15 × 5) / 7 = 75/7 units

⇒ Ratio of MP : CP = 17 : (75/7)

⇒ Multiply both sides by 7: (17 × 7) : 75

⇒ 119 : 75

∴ The correct answer is 119 : 75.

Additional Information

Relationship between MP and CP

The ratio of Marked Price to Cost Price can be directly found using the formula: MP/CP = (100 + Profit%) / (100 − Discount%).

Discount Percentage

Discount is always calculated on the Marked Price. Discount % = (MP − SP)/MP × 100.

Profit Percentage

Profit is always calculated on the Cost Price. Profit % = (SP − CP)/CP × 100.

Shortcut Trick

Selling Price (SP) = Marked Price (MP) × (100 − Discount)%

SP = 2000 × 72% = Rs. 1440

Profit = SP − Cost Price (CP) = 1440 − 1200 = Rs. 240

∴ The correct answer is Rs. 240.

Alternate Method

Given:

Marked Price (MP) = Rs. 2000

Cost Price (CP) = Rs. 1200

Discount Percentage = 28%

Formula Used:

1. Discount Value = (Discount% ÷ 100) × Marked Price
2. Selling Price (SP) = Marked Price − Discount Value
3. Profit = Selling Price − Cost Price

Calculations:

⇒ Discount Value = (28 ÷ 100) × 2000

⇒ Discount Value = 0.28 × 2000 = Rs. 560

⇒ Selling Price (SP) = 2000 − 560 = Rs. 1440

⇒ Profit = 1440 − 1200

⇒ Profit = Rs. 240

∴ The correct answer is Rs. 240.

Additional Information

Profit Percentage

Profit% = (Profit ÷ Cost Price) × 100. In this question, Profit% = (240 ÷ 1200) × 100 = 20%.

Markup Percentage

It is the percentage by which the Cost Price is increased to reach the Marked Price. Markup% = [(MP − CP) ÷ CP] × 100.

MP and CP Relationship

MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%). This ratio is useful for finding any one missing value when others are known.

The correct answer is: Option (3) i.e. Yoke.

Key Points

• The word 'Yoke' refers to a wooden crosspiece that is fastened over the necks of two animals (usually oxen) and attached to the plough or cart that they are to pull. (जुए का काठ / जुआ)
• Example: The farmer placed the yoke on the oxen to begin the days work in the fields.
• In the context of the given options, 'Yoke' is the only word that is spelt correctly. It is a noun that can also mean a burden or a state of being joined together. (बंधन)
• Example: Many nations struggled to free themselves from the yoke of colonial rule.
• Hence, we can infer that 'Yoke' is the correctly spelt word among the choices.

Therefore, the correct answer is: Yoke.

Additional Information

Here are the other options with their correct spellings, Hindi meanings, and example sentences:

• Yeild (Correct spelling is 'Yield') (पैदावार / समर्पण करना): To produce or provide a natural, agricultural, or industrial product; or to give way to arguments or pressure.
• Example: This fertile land yields a high tonnage of rice per acre.
• Yaern (Correct spelling is 'Yearn') (तड़पना / लालसा करना): To have an intense feeling of longing for something, typically something that one has lost or been separated from.
• Example: After years of living abroad, she began to yearn for her home country.
• Yiest (Correct spelling is 'Yeast') (खमीर): A microscopic fungus consisting of single oval cells that reproduce by budding, used for fermenting alcoholic beverages and leavening bread.
• Example: You must add yeast to the warm water and sugar to make the dough rise.

The correct answer is indispensable.

Key Points

• The word indispensable is the correct spelling, which is frequently misspelt as indispensible using an 'i' instead of an 'a' in the suffix.
• Etymologically, this term originates from the Medieval Latin word indispensabilis, which combines the negative prefix in- (meaning 'not') with dispensabilis (from the verb dispensare, meaning 'to distribute' or 'to weigh out').
• In modern English grammar, the word functions as an adjective meaning absolutely necessary, essential, or vital for a specific purpose, system, or outcome.

 Additional Information

• Transformative:
• An adjective indicating something that causes a profound, fundamental, or life-changing shift. It originates from the Latin verb transformare, meaning 'to change in shape'.
• Strategic:
• An adjective relating to the identification of long-term or overall goals and planning the specific means to achieve them. It is derived from the Greek noun strategos, meaning a general or military commander.
• Premature:
• An adjective used to describe something that occurs, is done, or is decided before the proper, standard, or expected time. Its etymological roots are found in the Latin term praematurus, combining prae- ('before') and maturus ('ripe').

The correct answer is: Refute.

Key Points

• The word confirm means to establish the truth or correctness of something that was previously believed, suspected, or feared. (पुष्टि करना)
• Example: The laboratory results helped to confirm the doctors initial diagnosis.
• Refute refers to the act of proving a statement, charge, or theory to be wrong or false; it is the direct opposite of confirming the truth. (खंडन करना)
• Example: The defense attorney was able to refute the allegations with clear video evidence.
• Hence, we can infer that the opposite of confirm is refute.

Therefore, the correct answer is: Refute.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Corroborate (पुष्टि करना/समर्थन करना): To support with evidence or authority; to make more certain.
• Example: Recent studies corroborate the idea that exercise improves mental health.
• Substantiate (प्रमाणित करना/पुष्टि करना): To provide evidence to support or prove the truth of something.
• Example: They were unable to substantiate the claims made against the company.
• Validate (मान्य करना/पुष्ट करना): To check or prove the validity or accuracy of something.
• Example: The data is used to validate the new software model.

The correct answer is New guidelines are issued by the health minister to improve public health every year.

Key Points

• The sentence 'The health minister issues new guidelines...' is in the Simple Present Tense (Indefinite), which is used to describe habitual actions or general truths, as indicated by the frequency phrase every year.
• In the transition from Active Voice to Passive Voice, the object of the active sentence, new guidelines, becomes the subject of the passive sentence to shift focus to the recipient of the action.
• The grammar rule for converting Simple Present to passive voice requires the formula: New Subject + is/am/are + Past Participle (V3) + by + Agent.
• Because the new subject new guidelines is plural, the auxiliary verb are must be used to ensure correct subject-verb agreement.
• The base verb issues is transformed into its past participle form, issued, which is mandatory for all passive constructions regardless of the original tense.
• The original subject, The health minister, is moved to the end of the clause as the agent and is introduced by the preposition by.
• The adverbial phrase 'to improve public health every year' remains intact to preserve the purpose and temporal context of the statement.

 Additional Information

• Evaluation of Tense Mismatches:
• Present Perfect Passive: Used in the phrase 'have been issued', this tense refers to actions that occurred at an indefinite time or have a present result, making it logically incompatible with the routine nature of the sentence.
• Present Continuous Passive: Represented by 'are being issued', this form indicates an ongoing action occurring at the exact moment of speaking, which does not reflect a yearly schedule.
• Simple Past Passive: The construction 'were issued' denotes a completed action in the past and fails to account for the regularity implied by the original present tense verb.

The correct answer is Her homework had been finished by her before dinner..

Key Points

• The original sentence is in the Past Perfect Tense, which follows the structural pattern: Subject + had + Past Participle (V3) + Object. In this case, She is the subject, had finished is the verb, and her homework is the object.
• To convert a sentence from Active Voice to Passive Voice in the Past Perfect Tense, the structure must be: Object + had been + Past Participle (V3) + by + Subject.
• The Object of the active sentence, her homework, becomes the Subject of the passive sentence.
• The auxiliary verb had is modified by adding been to indicate the Passive Voice state, resulting in had been finished.
• The Subject of the active sentence, She, which is a Nominative Pronoun, must be converted to its Objective Case, her, after the preposition by.
• The temporal phrase before dinner is an adjunct that remains at the end of the sentence to maintain the original meaning and context of the action's completion.

 Additional Information

• Tense Identification and Transformation:
• Past Perfect Passive: Requires the specific auxiliary had been. This differentiates it from the Simple Past Passive (was/were + V3) and the Present Perfect Passive (has/have been + V3).
• Consistency of Tense: One of the fundamental rules of Voice Conversion is that the tense of the sentence must not change. Since the active sentence uses had finished, the passive must retain the Past Perfect aspect.
• The Agent: In passive voice, the doer of the action (the agent) is introduced by the preposition by. While the agent can sometimes be omitted if it is obvious or unknown, the provided correct option includes by her to fully represent the original subject.
• Transitive Verbs: Only transitive verbs (verbs that take an object) like finish can be changed into the passive voice. The object homework provides the necessary component for this shift.

The correct answer is 'for'.

 

Key Points

• The preposition 'for' is used in the given sentence to complete the phrasal construction.
• In this context, the phrase 'put for' is utilized to denote accounting for, excusing, or standing in support of an action.
• Therefore, the sentence indicates that Harish could not tolerate or make allowances (put for with) the misbehaviour of his younger brother.

Therefore, the correct answer is Option 3.

 

Complete Sentence: 'Harish could not put for with the misbehaviour of his younger brother.'

 

Additional Information

• Option 1: 'in' is incorrect because 'put in' refers to spending time, submitting, or making an effort, which does not fit.
• Option 2: 'up' is a particle used in other phrasal contexts, but is not the appropriate choice for the correct option designated here.
• Option 4: 'out' is incorrect because 'put out' means to extinguish or cause inconvenience, which is contextually unsuitable.

The correct answer is held up for several hr.

Key Points

• The phrasal verb held up is the most suitable replacement because it specifically denotes a delay or a temporary stoppage of an activity or process caused by an obstacle or external force. In the provided sentence, the peace talks were interrupted for a duration of time by last-minute objections from the opposition.
• The original phrase held back is contextually different as it primarily means to restrain oneself, to suppress an emotion, or to withhold support or information. For example, one might hold back their feelings or hold back evidence. It is not the standard idiom used to describe a logistical delay in a formal meeting or conference.
• The structure of the sentence utilizes the passive voice (were held up), which correctly identifies that the negotiation process was the recipient of the action (the delay) performed by the opposing party, resulting in a setback of several hours.

 Additional Information

• Held on:
• This expression is frequently used to ask someone to wait for a brief moment, particularly during verbal communication or over a telephone call.
• It can also describe the act of clinging to an object or a belief with persistence, tenacity, or physical strength.
• Held behind:
• This is not a standard idiomatic phrasal verb for describing time-based delays in English.
• Related concepts usually involve the phrase falling behind, which refers to failing to keep up with a predetermined pace, schedule, or deadline.
• Other relevant Phrasal Verbs:
• Hold off: This means to delay starting an action or to keep someone at a distance (e.g., holding off an attack).
• Hold over: This refers to postponing an event to a future date or extending the duration of a show or engagement.

The correct answer is 'against'.

 

Key Points

• The verb appealed is typically followed by the preposition against when a person seeks to challenge or overturn a legal decision or a court sentence.
• In this context, the convict is requesting a higher authority to review and change the death sentence that has been imposed.
• The phrase appeal against is the standard legal expression used to describe the act of formal opposition to a verdict or penalty.

Therefore, the correct answer is Option 3.

 

Complete Sentence: 'The convict appealed against the death sentence.'

 

Additional Information

• Option 1: 'for' is used when someone is requesting something positive, such as appealing for mercy or appealing for help.
• Option 2: 'oy' is not a valid preposition in the English language and is likely a typographical error.
• Option 4: 'after' relates to time or sequence but does not correctly identify the object of the legal challenge in this phrasal structure.

The correct answer is eagerly looked forward to performing.

Key Points

• The sentence requires the correct usage of the phrasal verb look forward to, which expresses a feeling of excitement about something that is going to happen.
• In the phrase look forward to, the word to functions strictly as a preposition, not as part of an infinitive verb (to + verb).
• A fundamental rule of English grammar dictates that a preposition must be followed by a noun, a pronoun, or a gerund (the -ing form of a verb acting as a noun).
• Therefore, the verb perform must be converted into its gerund form, performing, to correctly follow the preposition to.
• The original underlined portion looked forward to perform is grammatically incorrect because it uses the base form of the verb instead of the required gerund.

 Additional Information

• Distinguishing Prepositional 'to' vs. Infinitive 'to':
• While to is often followed by the base verb (e.g., I want to eat), certain fixed expressions and phrasal verbs treat to as a preposition.
• Other common expressions that follow this gerund rule include:
• Accustomed to (e.g., He is accustomed to waking up early).
• With a view to (e.g., He studied hard with a view to passing the exam).
• Object to (e.g., They object to paying extra fees).
• Be used to (e.g., I am used to driving in traffic).
• Option Analysis:
• Eagerly looked forward for performing: This is incorrect because the standard prepositional phrase is look forward to, not look forward for.
• Was eagerly looking forward to perform: While the continuous tense is often used with this phrase, it fails to correct the primary error of using the infinitive instead of the gerund.

The correct answer is 'intricacy'.

Key Points

• The sentence refers to the astounding diversity of flowers as the epitome (a perfect example) of a specific quality of nature.
• The passage later discusses specialized mechanisms for pollination and symbiotic relationships, which imply a high level of detail and complexity.
• 'Intricacy' means the quality of being very detailed or complex, which perfectly fits the context of describing the sophisticated and diverse nature of flowers.
• Other options like 'simplicity' and 'uniformity' contradict the mention of astounding diversity and specialization.

Therefore, the correct answer is 'Option 1'.

Complete Passage: Flowers, in their astounding diversity, represent the epitome of nature's 1. intricacy. While some flowers bloom in wild, untamed environments, others are meticulously cultivated for aesthetic and 2. utilitarian purposes. The orchid, for instance, is not only admired for its exotic appearance but also for its highly specialized mechanisms for pollination. Orchids exhibit a symbiotic relationship with pollinators, especially bees and butterflies, who are attracted by the flower's scent and structure. There are over 25,000 species of orchids, each with its own unique traits. This diversity makes them a subject of fascination 3. among botanists and horticulturists alike. On the other hand, the lily known for its elegance and 4. symbolism thrives in temperate regions and boasts trumpet-shaped blossoms that often carry a strong, sweet fragrance. With species like the Easter lily and the tiger lily, they have captured the cultural imagination and are frequently used in religious and celebratory contexts. The lotus, revered in many ancient cultures, grows in aquatic environments and is 5. renowned for its ability to bloom unscathed through muddy waters. Its ability to remain pristine despite its environment symbolizes purity and enlightenment. Lastly, the carnation, once considered the flower of choice for corsages, has recently experienced a resurgence in popularity. Known for its ruffled petals, the carnation is often seen as a symbol of love and admiration.

Additional Information

• Simplicity: The state of being uncomplicated or easy to understand; the opposite of the complexity described in the text.
• Uniformity: The quality of being the same in all cases and at all times; this is the opposite of diversity.
• Fragility: The quality of being easily broken or damaged; while flowers can be fragile, it does not represent the epitome of their diversity in this context.

The correct answer is 'utilitarian'.

Key Points

• The sentence discusses the two main reasons for the cultivation of flowers: aesthetic and practical reasons.
• The term 'aesthetic' refers to the beauty or visual appeal of the flowers.
• The word 'utilitarian' relates to being useful or practical rather than just attractive. In the context of flowers, this refers to their use in medicine, food, perfumes, or other functional applications.
• Therefore, the word 'utilitarian' perfectly complements 'aesthetic' to cover the range of reasons why flowers are meticulously cultivated.

Therefore, the correct answer is 'Option 4'.

Complete Passage: Flowers, in their astounding diversity, represent the epitome of nature's 1. intricacy. While some flowers bloom in wild, untamed environments, others are meticulously cultivated for aesthetic and 2. utilitarian purposes. The orchid, for instance, is not only admired for its exotic appearance but also for its highly specialized mechanisms for pollination. Orchids exhibit a symbiotic relationship with pollinators, especially bees and butterflies, who are attracted by the flower's scent and structure. There are over 25,000 species of orchids, each with its own unique traits. This diversity makes them a subject of fascination 3. among botanists and horticulturists alike. On the other hand, the lily known for its elegance and 4. symbolism thrives in temperate regions and boasts trumpet-shaped blossoms that often carry a strong, sweet fragrance. With species like the Easter lily and the tiger lily, they have captured the cultural imagination and are frequently used in religious and celebratory contexts. The lotus, revered in many ancient cultures, grows in aquatic environments and is 5. renowned for its ability to bloom unscathed through muddy waters. Its ability to remain pristine despite its environment symbolizes purity and enlightenment. Lastly, the carnation, once considered the flower of choice for corsages, has recently experienced a resurgence in popularity. Known for its ruffled petals, the carnation is often seen as a symbol of love and admiration.

Additional Information

• Decorative: This means serving to make something look more attractive. Since 'aesthetic' is already mentioned, 'decorative' would be redundant in this context.
• Addictive: This relates to something that causes a strong habit or dependency, which is not a standard purpose for cultivating most flowers.
• Therapeutic: This refers specifically to healing or curing. While some flowers have therapeutic properties, 'utilitarian' is a broader term that encompasses all practical uses, including therapy.

The correct answer is 'among'.

Key Points

• The sentence describes how the vast diversity of orchids creates a shared interest or attraction within a specific group of people.
• The preposition 'among' is used when referring to something that is shared, occurring, or common within a specific group, class, or community.
• In this context, the fascination exists within the collective group of botanists and horticulturists.
• Using 'among' highlights that the interest is distributed throughout these professional communities.

Therefore, the correct answer is 'Option 3'.

Complete Passage: Flowers, in their astounding diversity, represent the epitome of nature's 1. intricacy. While some flowers bloom in wild, untamed environments, others are meticulously cultivated for aesthetic and 2. utilitarian purposes. The orchid, for instance, is not only admired for its exotic appearance but also for its highly specialized mechanisms for pollination. Orchids exhibit a symbiotic relationship with pollinators, especially bees and butterflies, who are attracted by the flower's scent and structure. There are over 25,000 species of orchids, each with its own unique traits. This diversity makes them a subject of fascination 3. among botanists and horticulturists alike. On the other hand, the lily known for its elegance and 4. symbolism thrives in temperate regions and boasts trumpet-shaped blossoms that often carry a strong, sweet fragrance. With species like the Easter lily and the tiger lily, they have captured the cultural imagination and are frequently used in religious and celebratory contexts. The lotus, revered in many ancient cultures, grows in aquatic environments and is 5. renowned for its ability to bloom unscathed through muddy waters. Its ability to remain pristine despite its environment symbolizes purity and enlightenment. Lastly, the carnation, once considered the flower of choice for corsages, has recently experienced a resurgence in popularity. Known for its ruffled petals, the carnation is often seen as a symbol of love and admiration.

Additional Information

• On: Usually refers to a position atop a surface or a specific day/date (e.g., on the table, on Monday).
• For: Often denotes a purpose, reason, or recipient (e.g., a gift for you), and while it can show attraction, 'among' is more appropriate for a collective group here.
• To: Typically indicates a direction, limit, or relationship (e.g., listening to music, travel to London).

The correct answer is 'Representation of ideas or qualities'.

Key Points

• The word symbolism refers to the practice of using symbols to represent ideas, qualities, or abstract concepts.
• In the context of the passage, the lily is described as being known for its elegance and the deeper meanings it carries in cultural, religious, and celebratory contexts.
• The text later clarifies this concept by stating that the lotus 'symbolizes purity and enlightenment,' which reinforces that the flowers represent specific values or qualities rather than just physical traits.
• Therefore, the most likely meaning of the word in parentheses is the representation of something beyond its literal or physical presence.

Therefore, the correct answer is 'Option 2'.

Complete Passage: Flowers, in their astounding diversity, represent the epitome of nature's 1. intricacy. While some flowers bloom in wild, untamed environments, others are meticulously cultivated for aesthetic and 2. utilitarian purposes. The orchid, for instance, is not only admired for its exotic appearance but also for its highly specialized mechanisms for pollination. Orchids exhibit a symbiotic relationship with pollinators, especially bees and butterflies, who are attracted by the flower's scent and structure. There are over 25,000 species of orchids, each with its own unique traits. This diversity makes them a subject of fascination 3. among botanists and horticulturists alike. On the other hand, the lily known for its elegance and 4. symbolism thrives in temperate regions and boasts trumpet-shaped blossoms that often carry a strong, sweet fragrance. With species like the Easter lily and the tiger lily, they have captured the cultural imagination and are frequently used in religious and celebratory contexts. The lotus, revered in many ancient cultures, grows in aquatic environments and is 5. renowned for its ability to bloom unscathed through muddy waters. Its ability to remain pristine despite its environment symbolizes purity and enlightenment. Lastly, the carnation, once considered the flower of choice for corsages, has recently experienced a resurgence in popularity. Known for its ruffled petals, the carnation is often seen as a symbol of love and admiration.

Additional Information

• Practical use: Refers to the functional or pragmatic application of an object (similar to utilitarianism).
• Physical appearance: Refers to the outward look, shape, or color of the flower.
• Scientific classification: Refers to the biological naming and categorization of organisms (Taxonomy).

The correct answer is 'Famous'.

Key Points

• The word 'renowned' is used in the passage to describe the lotus flower's reputation.
• 'Renowned' is an adjective that means widely known and celebrated; famous for a particular quality or achievement.
• In this context, the lotus is famous or renowned for its ability to bloom beautifully even in muddy waters, which makes it a symbol of purity.
• 'Famous' is the closest synonym among the given options.

Therefore, the correct answer is 'Option 3'.

Complete Passage: Flowers, in their astounding diversity, represent the epitome of nature's 1. intricacy. While some flowers bloom in wild, untamed environments, others are meticulously cultivated for aesthetic and 2. utilitarian purposes. The orchid, for instance, is not only admired for its exotic appearance but also for its highly specialized mechanisms for pollination. Orchids exhibit a symbiotic relationship with pollinators, especially bees and butterflies, who are attracted by the flower's scent and structure. There are over 25,000 species of orchids, each with its own unique traits. This diversity makes them a subject of fascination 3. among botanists and horticulturists alike. On the other hand, the lily known for its elegance and 4. symbolism thrives in temperate regions and boasts trumpet-shaped blossoms that often carry a strong, sweet fragrance. With species like the Easter lily and the tiger lily, they have captured the cultural imagination and are frequently used in religious and celebratory contexts. The lotus, revered in many ancient cultures, grows in aquatic environments and is 5. renowned for its ability to bloom unscathed through muddy waters. Its ability to remain pristine despite its environment symbolizes purity and enlightenment. Lastly, the carnation, once considered the flower of choice for corsages, has recently experienced a resurgence in popularity. Known for its ruffled petals, the carnation is often seen as a symbol of love and admiration.

Additional Information

• Ignored: Means to refuse to take notice of or acknowledge; this is the opposite of being renowned.
• Disputed: Means something that is argued about or questioned; it does not fit the context of the lotus's established reputation.
• Neglected: Means suffering a lack of proper care or attention; this refers to the state of maintenance rather than fame.