SSC GD Constable 2026 Official Paper (Held On 18 May, 2026 Shift 3) (Previous Year Paper)

Pattern followed here is,

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 the set '(HW, KA, OF)':

For the set '(NU, QY, UD)':

Applying the same logic to the option '(JK, MO, QT)':

Hence, the correct answer is 'Option 3'.

We need to find the day on 1^st January 1678.

This is the first day of the year 1678, which means we must calculate the odd days for 1677 completed years plus the 1^st day of 1678.

Number of odd days in 1600 years = 0 (since 1600 is a multiple of 400).

Now, we calculate odd days for the remaining 77 years (from 1601 to 1677):

Number of leap years in 77 years = 77/4 = 19 (quotient).

Number of ordinary years in 77 years = 77 − 19 = 58.

Odd days in 77 years = (19 × 2) + (58 × 1)

= 38 + 58 = 96 odd days

96 days converted to weeks = 96/7 = 13 weeks and 5 odd days.

Next, we add the odd days for the current year up to 1^st January 1678:

Odd days = 1 (for 1^st January).

Total odd days = 0 (from 1600 years) + 5 (from 77 years) + 1 (for 1^st Jan) = 6 odd days.

Day code mapping:

0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday.

Since the total number of odd days is 6, the day was Saturday.

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 3”.

TT250 : QQ204

MS444 : PJ398

Similarly,

For JP354: ?

Hence, the correct answer is 'Option 2'.

ACK320 : FFB420 → 

PSJ180 : EVQ280 → 

DLM140 : ? →

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: Second Number = First Number + 42

For the third pair 2034 : 2076

⇒ 2034 + 42 = 2076

For the second pair 4146 : 4188

⇒ 4146 + 42 = 4188

Applying the same logic to the first pair

? : 5011

⇒ First Number + 42 = 5011

⇒ First Number = 5011 − 42

⇒ First Number = 4969

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: First Number = (Second Number × 3) − 6

For the first pair 2655 : 887

⇒ (887 × 3) − 6

⇒ 2661 − 6 = 2655.

For the third pair 2694 : 900

⇒ (900 × 3) − 6

⇒ 2700 − 6 = 2694.

Applying the same logic to the second pair

? : 461

⇒ (461 × 3) − 6

⇒ 1383 − 6 = 1377.

Hence, the correct answer is 'Option 1'.

The pattern observed is: (Sum of reverse positional values of letters) + 1.

SHARE is coded as 85 →

Sum of reverse positional values = 8 + 19 + 26 + 9 + 22 = 84

Code = 84 + 1 = 85

PAID is coded as 79 →

Sum of reverse positional values = 11 + 26 + 18 + 23 = 78

Code = 78 + 1 = 79

Similarly, let us find the code for GEAR:

Sum of reverse positional values = 20 + 22 + 26 + 9 = 77

Code = 77 + 1 = 78

Hence, the correct answer is “Option 4”.

Pattern followed here,

Hence, the correct answer is “Option 1”.

Pattern followed here,

Hence, the correct answer is “Option 3”.

We need to find the time between 3 AM and 4 AM when the angle is 120°.

Here, H = 3 and Angle = 120.

Substituting these values into the formula:

120 = |30 × 3 − 5.5M|

120 = |90 − 5.5M|

To find the time between 3 and 4, we consider the case where the minute hand has moved past the hour hand to create the 120° gap:

120 = 5.5M − 90

5.5M = 120 + 90

5.5M = 210

M = 210 / 5.5 = 420 / 11

M ≈ 38.18 minutes

The time is approximately 3:38 AM.

Hence, the correct answer is 3:38

Alternate Method

The angle between the hour hand and minute hand is given by: $\theta = |{60H - 11M \over 2}|$

Given H = 3 and θ = 120°:

120 = $|{60 \times 3 - 11M \over 2}|$

240 = |180 − 11M|

Since 11M > 180 for the hands to be 120° apart in this segment:

240 = 11M − 180

11M = 240 + 180

11M = 420

M = 420 / 11

M ≈ 38.18 minutes

Thus, the time is approximately 3:38 AM.

Hence, the correct answer is 3:38

At 2 AM, the position of the hands is:

Minute hand = 0° (at 12)

Hour hand = 2 × 30° = 60° (at 2)

Initial angle between hands = 60°

To be opposite, the minute hand must cover the initial 60° gap and gain another 180° relative to the hour hand.

Total angular distance to be covered = 60° + 180° = 240°

Time taken = Distance ÷ Relative speed

Time = 240 ÷ 5.5 = 480 ÷ 11 minutes

Time ≈ 43.636 minutes

Approximating to the nearest minute, we get 44 minutes.

Therefore, the time is approximately 2:44 AM.

Alternate Method

The angle θ between the hour hand and minute hand is given by the formula:

$\theta = | \frac{60H - 11M}{2} |$

Where H = hours and M = minutes.

Given H = 2 and θ = 180° (for opposite hands):

180 = | (60 × 2 − 11 × M) ÷ 2 |

360 = | 120 − 11M |

Since the minute hand must pass the hour hand to be opposite, we take the case where 11M > 120:

360 = 11M − 120

480 = 11M

M = 480 ÷ 11 ≈ 43.64 minutes

Hence, the correct answer is 2:44

Important Points ​The hour hand of a clock covers 360° in 12 hours.

Angular distance covered in 1 hour = 360 ÷ 12 = 30°

Angular distance covered in 1 minute = 30 ÷ 60 = 0.5°

The minute hand covers 360° in 60 minutes.

Angular distance covered in 1 minute = 360 ÷ 60 = 6°

The relative speed of the minute hand with respect to the hour hand = 6° − 0.5° = 5.5° per minute.

Two hands are opposite to each other when the angle between them is 180°.

Pattern followed here,

Hence, the correct answer is “Option 2”.

Pattern followed here,

Hence, the correct answer is “Option 2”.

Pattern followed here,

Hence, the correct answer is “Option 1”.

The logic followed here is based on the ratio and ages calculation.

Let the present age of S be 5x and the present age of T be 3x.

Ages after 2 years:

Age of S = 5x + 2

Age of T = 3x + 2

According to the question, the ratio of their ages after 2 years will be 7 : 5.

(5x + 2) / (3x + 2) = 7 / 5

By cross-multiplication:

5 × (5x + 2) = 7 × (3x + 2)

25x + 10 = 21x + 14

25x − 21x = 14 − 10

4x = 4

x = 1

Now, we find the present age of S:

Present age of S = 5x = 5 × 1 = 5 years

The question asks for the age of S after 3 years from the present:

Age after 3 years = Present age + 3

Age after 3 years = 5 + 3 = 8 years

Hence, the correct answer is “Option 1”.

The correct answer is 331 m/s.

Key Points

• Sound is a mechanical longitudinal wave that requires a material medium like air, water, or steel for its propagation.
• The speed of sound in a gas is primarily dependent on the temperature and the density of the medium.
• At a standard temperature of 0°C (equivalent to 273.15 K), the speed of sound in dry air is measured to be approximately 331 m/s.
• This value is derived using the Laplace correction to Newton's formula, which considers the propagation of sound as an adiabatic process. The formula is expressed as v = √(γRT/M), where γ is the adiabatic index, R is the universal gas constant, T is the absolute temperature, and M is the molar mass of the gas.
• In air, which consists mainly of nitrogen and oxygen, the speed is relatively low compared to solids and liquids because gases have much lower elasticity and higher compressibility.

 Additional Information

• Impact of Temperature:
• The speed of sound is directly proportional to the square root of absolute temperature.
• For every 1°C rise in temperature, the speed of sound increases by approximately 0.61 m/s.
• At 20°C (standard room temperature), the speed of sound increases to approximately 343 m/s or 344 m/s.
• At 25°C, the speed further reaches approximately 346 m/s.
• Humidity and Density:
• Humidity increases the speed of sound because moist air is less dense than dry air. Since speed is inversely proportional to the square root of density, lower density results in higher velocity.
• Changes in atmospheric pressure do not affect the speed of sound provided the temperature remains constant, as the density changes proportionally to the pressure.
• Speed in Different Media:
• Sound travels fastest in solids (e.g., approximately 5960 m/s in steel) due to high bulk modulus.
• Sound travels at an intermediate speed in liquids (e.g., approximately 1480 m/s in water at 20°C).

The correct answer is Ladakh Plateau.

Key Points

• The Ladakh Plateau is widely recognized as the Roof of the World in the context of Indian geography because it is the highest plateau in India, acting as a southward extension of the Tibetan Plateau.
• It is a trans-Himalayan landmass situated at an average elevation of more than 3,000 meters (approximately 9,800 feet), with some areas exceeding 5,000 meters.
• Geographically, it is located between the Karakoram Range in the north and the Great Himalayan Range in the south, forming a high-altitude cold desert.
• The plateau covers a vast area of approximately 59,146 square kilometers and is characterized by its high-altitude plains, such as the Depsang Plains and the Aksai Chin region.
• Due to the rain-shadow effect of the Himalayas, the region receives very little rainfall, averaging around 100 mm annually, leading to its unique arid and barren landscape.

 Additional Information

• Deccan Plateau:
• A large volcanic plateau covering most of South India, formed by basaltic lava flows during the Cretaceous period.
• It is bounded by the Satpura Range in the north and the Western and Eastern Ghats on the sides.
• Chotanagpur Plateau:
• Located in Eastern India, primarily in Jharkhand, it is a continental plateau composed of ancient Archean rocks.
• Known as the Ruhr of India due to its immense wealth of minerals like coal, iron ore, and bauxite.
• Malwa Plateau:
• Situated in central-western India, it forms a part of the Central Highlands and is drained by the Chambal River system.
• It consists of black soil, which is highly suitable for growing cotton and oilseeds.

The correct answer is Goa, India.

Key Points

• The 8^th BRICS Summit was held in Benaulim, Goa, India, on 15 and 16 October 2016. This marked the second time India hosted the summit, following the 4^th BRICS Summit in New Delhi in 2012.
• The theme for the 2016 summit was Building Responsive, Inclusive and Collective Solutions. The event focused on enhancing cooperation in areas such as trade, investment, security, and sustainable development.
• The summit was attended by the heads of state/government of the five member nations: Michel Temer (Brazil), Vladimir Putin (Russia), Narendra Modi (India), Xi Jinping (China), and Jacob Zuma (South Africa).
• The meeting concluded with the adoption of the Goa Declaration, which strongly condemned terrorism in all its forms and manifestations, stressing that there can be no ideological, religious, or political justification for such acts.
• A major highlight was the BRICS-BIMSTEC Outreach Summit held on the sidelines, where leaders from BIMSTEC countries (Bangladesh, Bhutan, Myanmar, Nepal, Sri Lanka, and Thailand) were invited to strengthen regional integration.

 Additional Information

• Ufa, Russia:
• Hosted the 7^th BRICS Summit in July 2015.
• It was significant for the official operationalization of the New Development Bank (NDB) and the Contingent Reserve Arrangement (CRA).
• Johannesburg, South Africa:
• The city hosted the 10^th BRICS Summit in 2018 and the 15^th BRICS Summit in August 2023.
• The 2023 summit was historic for announcing the expansion of the group to include new member nations.
• Beijing, China:
• China hosted the 14^th BRICS Summit in 2022 via video link.
• Other Chinese cities that hosted summits include Sanya (2011) and Xiamen (2017).
• BRICS Formation:
• The acronym BRIC was originally coined by Jim O'Neill in 2001.
• The group was formally constituted in 2006, and South Africa joined the group in 2010.

The correct answer is Access to advanced technology and larger markets.

Key Points

• The New Economic Policy (NEP) introduced in 1991 was a response to the severe Balance of Payments (BoP) crisis, shifting India from a closed economy to a more integrated, market-oriented one.
• Liberalization involved the dismantling of the License Raj, allowing Indian firms to expand production capacities and import modern machinery without the previous bureaucratic hurdles.
• Globalization facilitated the inflow of Foreign Direct Investment (FDI), which acted as a vehicle for the transfer of cutting-edge technology and superior managerial practices from developed economies.
• Indian industries gained access to larger markets through the reduction of tariff and non-tariff barriers, enabling domestic brands to compete on a global scale and improve their export performance.
• Integration with the world economy encouraged Indian entrepreneurs to innovate, leading to a significant increase in the quality and diversity of goods available in the domestic market.

 Additional Information

• LPG Reforms (1991):
• Liberalization: It aimed to promote free-market competition by removing government controls over prices and production in several industrial sectors.
• Privatization: Involved the disinvestment of public sector undertakings (PSUs) to improve operational efficiency through private ownership.
• Globalization: Encouraged the free flow of capital, goods, and services across international borders, aligned with the principles of the World Trade Organization (WTO).
• Industrial Efficiency:
• Contrary to a decline, competition from Multinational Corporations (MNCs) forced Indian firms to adopt cost-effective production and improve research and development (R&D).
• Role of the State:
• The government did not completely withdraw from infrastructure but shifted its role from a direct provider to a facilitator and regulator, utilizing models like Public-Private Partnership (PPP).

The correct answer is Heavy industry, steel, energy.

Key Points

• The term commanding heights was used to describe the strategic sectors of the economy that were intended to remain under State control to ensure social justice and rapid economic development.
• During the period of 1950-1980, India followed a socialist-inspired economic model where the Public Sector was assigned the lead role in industrialization.
• The Industrial Policy Resolution of 1956 (IPR 1956) explicitly categorized heavy industries, iron and steel, atomic energy, and heavy machinery as sectors reserved exclusively for the government.
• These industries were considered strategic because they provided the basic infrastructure and raw materials required for the growth of all other sectors, including the private sector.
• The Second Five-Year Plan, formulated by P.C. Mahalanobis, prioritized these capital-intensive industries to build a foundation for long-term self-reliance and to reduce dependence on foreign imports for basic industrial goods.

 Additional Information

• The Mahalanobis Model:
• This economic strategy focused on the development of capital goods rather than consumer goods to accelerate the rate of capital formation.
• It was based on the premise that a strong industrial base in steel and energy would automatically pull the rest of the economy forward through linkage effects.
• Reason for State Dominance:
• High Investment: Heavy industries required massive financial outlays that the Indian private sector lacked during the post-independence era.
• Long Gestation Periods: These projects took a long time to become profitable, making them unattractive to private entrepreneurs seeking quick returns.
• Other Sectors during 1950-1980:
• Agriculture: Though it contributed the most to GDP and employment, it was not classified as the commanding heights as it was largely in the private hands of millions of farmers.
• Textiles and Handicrafts: These were classified as consumer goods or small-scale industries and did not possess the strategic control over the economy that steel and energy did.

The correct answer is Structural.

Key Points

• Structural unemployment is a form of involuntary unemployment caused by a mismatch between the skills that workers in the economy can offer and the skills demanded of workers by employers.
• Technological progress is a primary driver of this phenomenon; as industries adopt automation, robotics, and artificial intelligence, traditional roles involving manual or routine labor become obsolete.
• This type of unemployment is considered long-term and chronic because it requires the displaced workforce to undergo significant reskilling or vocational training to fit into new sectors.
• Economic theories, such as Creative Destruction, suggest that while technology destroys old jobs, it creates new ones that require a different set of technical competencies.
• According to reports by the World Economic Forum, the rapid pace of the Fourth Industrial Revolution is expected to displace millions of roles, making structural unemployment a critical challenge for labor market policy.

 Additional Information

• Seasonal Unemployment:
• This occurs when demand for labor changes across different periods of the year. It is highly prevalent in the agricultural sector (during harvest/sowing) and the tourism industry.
• Disguised Unemployment:
• Refers to a situation where more people are working than necessary. In this case, the marginal productivity of the extra labor is zero. It is a common feature of overpopulated developing economies.
• Frictional Unemployment:
• A temporary phase where individuals are between jobs or are looking for their first job. It is often voluntary and reflects the time needed to match a worker with the right employer in a dynamic economy.

The correct answer is Rs. 15000 crores.

Key Points

• The Union Budget 2025 introduced the SWAMIH Fund-2 (Special Window for Affordable and Mid-Income Housing) to provide continued support to the real estate sector and ensure the delivery of homes to stuck buyers.
• A dedicated corpus of Rs. 15000 crores has been allocated for this second iteration of the fund, aiming to bridge the funding gap for stalled residential projects across India.
• The primary objective of SWAMIH Fund-2 is to offer priority debt financing for the completion of stressed, brownfield projects that fall under the affordable and middle-income housing categories.
• This initiative is part of the government’s broader strategy to revive the construction industry, protect the financial interests of homebuyers, and boost the overall GDP by stimulating demand in ancillary sectors.
• The fund focuses on projects that are net-worth positive, providing the final leg of capital required to achieve occupancy certificates and handover units to residents.

 Additional Information

• Background of SWAMIH Fund:
• SWAMIH Investment Fund I was launched in November 2019 with a target corpus of Rs. 25000 crores.
• It is a Category-II Alternative Investment Fund (AIF) registered with SEBI (Securities and Exchange Board of India).
• Management and Eligibility:
• The fund is managed by SBICAP Ventures Limited, a wholly-owned subsidiary of the State Bank of India.
• To qualify for funding, projects must be registered under the Real Estate (Regulation and Development) Act (RERA).
• Even projects categorized as Non-Performing Assets (NPA) or those facing NCLT proceedings are eligible if they meet the viability criteria.
• Strategic Importance:
• The real estate sector is the second-largest employer in India after agriculture; hence, the SWAMIH Fund plays a crucial role in maintaining economic stability.
• By providing last-mile funding, the government ensures that capital locked in incomplete structures is recovered through final sales.

The correct answer is 9 October 2024.

Key Points

• On 9 October 2024, the Union Cabinet, chaired by Prime Minister Narendra Modi, approved the continuation of the universal supply of Fortified Rice under all schemes, including the Pradhan Mantri Garib Kalyan Anna Yojana (PMGKAY).
• The rice fortification initiative will continue from July 2024 till December 2028, functioning as a central sector initiative aimed at enhancing nutritional security across the nation.
• This decision is aligned with the goal of addressing anemia and micronutrient deficiencies among the vulnerable population by providing essential nutrients through the Public Distribution System (PDS).
• The initiative was originally announced by the Prime Minister during the 75^th Independence Day speech in 2021, with the aim of supplying fortified rice to every government scheme by 2024.
• The Cabinet's approval ensures that the supply remains consistent for the next four years, covering approximately 80 crore people under the National Food Security Act (NFSA).

 Additional Information

• Nutritional Composition and Process:
• Fortified rice is produced by blending Fortified Rice Kernels (FRK) with regular rice in a ratio of 1:100.
• These kernels are enriched with essential micronutrients including Iron, Folic Acid, and Vitamin B12, which are critical for blood formation and neurological health.
• Financial and Structural Impact:
• The total financial outlay for the rice fortification ecosystem is estimated at Rs 17,082 crore, which will be 100% funded by the Central Government.
• The initiative is implemented through a robust supply chain involving over 21,000 rice mills equipped with blending machinery across India.
• The program covers various schemes including the Integrated Child Development Services (ICDS) and PM POSHAN (formerly Mid-Day Meal) to ensure health benefits for pregnant women, lactating mothers, and school-going children.

The correct answer is Alvars.

Key Points

• The Alvars were Tamil poet-saints of South India who lived between the 6^th and 9^th centuries CE and propagated the Bhakti movement through their intense devotion to Lord Vishnu.
• The word Alvar means one who is immersed in the love and experience of the Divine, signifying their complete surrender to Vaishnavism.
• There were twelve Alvars in total, coming from diverse social backgrounds, which highlighted the inclusive nature of the Bhakti tradition in medieval India.
• Their collective hymns, totaling 4,000 verses, were compiled by Nathamuni in the 10^th century into a sacred canon known as the Nalayira Divya Prabandham.
• Prominent members included Periyalvar, Nammalvar, and Andal, the only female saint among the twelve, who is celebrated for her poetic works like Thiruppavai.

 Additional Information

• Nayanars:
• These were a group of 63 saints devoted to Lord Shiva who lived during the same period as the Alvars.
• Their lives and works were documented in the Periyapuranam, and their hymns form the Tirumurai, which is central to Shaiva Siddhanta.
• Tirthankara:
• In Jainism, a Tirthankara is a savior and spiritual teacher of the Dharma who has conquered the Samsara (cycle of rebirth).
• There are 24 Tirthankaras in the present cosmic age, beginning with Rishabhanatha and ending with Mahavira.
• Yogi:
• A general term used in Hinduism, Buddhism, and Jainism to describe a practitioner of Yoga or an ascetic who seeks spiritual liberation through disciplined meditation.

The correct answer is Sikkim.

Key Points

• The Lepcha tribe is considered the indigenous community of Sikkim, and their folk dances are deeply intertwined with their reverence for the natural world and Himalayan landscapes.
• One of the most significant Lepcha dances is the Chu Faat dance, which is performed specifically to honor Mount Khangchendzonga and its five snowy peaks, which are believed to be repositories of five sacred treasures.
• The dance movements often mimic the grace of birds and the agility of wild animals, showcasing the community's ancestral bond with the flora and fauna of the Eastern Himalayas.
• Performers typically wear traditional costumes such as the Thokro-Dum (for men) and Dumvum (for women) while dancing to the tunes of traditional instruments like the Sanga (drum) and Palit (bamboo flute).

 Additional Information

• Sikkim:
• Other notable folk dances include the Singhi Chham (Snow Lion Dance), which symbolizes the mythical snow lion, and the Yak Chham, which pays tribute to the high-altitude animal essential for survival.
• The cultural fabric of the state is a unique blend of Lepcha, Bhutia, and Nepali traditions.
• Tripura:
• Famous for the Hojagiri dance, a balance-oriented folk dance performed by the Reang community during the Laxmi Puja festival.
• Telangana:
• Renowned for Perini Sivatandavam, a powerful ancient dance form that originated during the Kakatiya dynasty, often referred to as the 'Dance of Warriors'.
• West Bengal:
• While Lepchas also reside in the Darjeeling and Kalimpong regions, the state is more widely recognized for the Chhau dance (Purulia style) and the Gambhira mask dance.

The correct answer is Jammu and Kashmir.

Key Points

• The administration of the Union Territory of Jammu and Kashmir has initiated the geo-tagging of Chinar trees to ensure their preservation and long-term monitoring.
• This heritage conservation project is primarily executed by the Department of Floriculture, which is tasked with conducting a comprehensive census of these iconic trees across the Kashmir Valley.
• Each tree is assigned a unique identification number and its precise Geographic Information System (GIS) coordinates are recorded to create a digital database.
• The primary objective of geo-tagging is to prevent illegal felling, encroachment, and to keep a record of the health and age of the trees, which are protected under the Jammu and Kashmir Preservation of Specified Trees Act.

 Additional Information

• Chinar Tree (Platanus orientalis):
• Known locally as Booune, it is a massive deciduous tree that has been a part of the Kashmiri landscape for centuries.
• The tree is deeply integrated into the Mughal heritage of India, with many planted during the reigns of Emperors Akbar, Jehangir, and Shah Jahan in famous sites like Shalimar Bagh and Nishat Bagh.
• Chinar leaves are a symbol of the region and are frequently used as motifs in Kashmiri handicrafts, such as wood carving and Pashmina shawls.
• The oldest known Chinar in the region is located in Chattergam, Budgam district, and is estimated to be over 600 years old, purportedly planted by the Sufi saint Syed Qasim Shah.

The correct answer is 183.

Key Points

• In the Census of India, the population is divided into workers and non-workers based on their participation in economically productive activities.
• A Main Worker is defined as a person who has worked for the major part of the reference year, which is specifically at least six months or 183 days.
• This classification was prominently established during the 1981 Census to differentiate between steady employment and seasonal or temporary work.
• The duration of work includes both physical and mental activities and involves not only actual work but also effective supervision and direction of work.
• The identification of Main Workers helps the government calculate the Workforce Participation Rate (WPR) and understand the core economic stability of the country.

 Additional Information

• Marginal Worker:
• A person who worked for less than 183 days (or six months) in the reference year is categorized as a Marginal Worker.
• This group often includes seasonal laborers in the agricultural sector or individuals in the informal economy.
• Industrial Categories of Workers:
• Cultivators: Individuals engaged in cultivation on land owned or leased from the government or private institutions.
• Agricultural Labourers: Those who work on another person's land for wages without any right of lease or contract.
• Household Industry Workers: Persons working in industries such as processing, servicing, or manufacturing conducted by household members within the home or village.
• Other Workers: A broad category including government employees, factory workers, teachers, and those in the service sector.
• Census Administration:
• The census is conducted decennially by the Office of the Registrar General and Census Commissioner under the Ministry of Home Affairs.
• The Census Act, 1948 provides the legal framework for conducting these surveys in India.

The correct answer is Eid-ul-Fitr.

Key Points

• Eid-ul-Fitr, also known as the Festival of Breaking the Fast, is a major religious holiday celebrated by Muslims worldwide to conclude the holy month of Ramadan (Ramazan).
• Ramadan is the ninth month of the Islamic Hijri calendar, during which believers observe Sawm (fasting) from dawn to sunset, abstaining from food and drink.
• The celebration begins on the first day of Shawwal, the month following Ramadan, and its timing is determined by the specific sighting of the crescent moon (Hilal).
• A mandatory charitable contribution known as Zakat al-Fitr is given to the poor before the special Eid prayer (Salat al-Eid), ensuring that all members of the community can celebrate the occasion.
• The day is marked by communal prayers, family gatherings, feasting, and the giving of gifts, symbolizing spiritual renewal and gratitude to Allah for the strength provided during the fasting month.

 Additional Information

• Bakrid (Eid-al-Adha):
• Known as the Feast of Sacrifice, it honors the willingness of Prophet Ibrahim (Abraham) to sacrifice his son as an act of obedience to God.
• It falls on the 10^th day of Dhu al-Hijjah, the final month of the Islamic calendar, and marks the end of the Hajj pilgrimage.
• Muharram:
• This is the first month of the Islamic calendar; the 10^th day is known as Ashura.
• For Shia Muslims, it is a day of intense mourning to commemorate the martyrdom of Imam Hussain, the grandson of Prophet Muhammad, at the Battle of Karbala in 680 AD.
• Shab-e-Barat:
• Often referred to as the Night of Fortune or Night of Records, it is observed on the night between the 14^th and 15^th of the month of Sha'ban.
• It is a night of prayer and seeking forgiveness, as it is believed that Allah determines the destiny and provides for all creatures for the year ahead during this night.

The correct answer is Chottanagpur.

Key Points

• Birsa Munda was a charismatic tribal leader, folk hero, and freedom fighter born on November 15, 1875, in the Chottanagpur plateau region of what is now the state of Jharkhand.
• The Munda tribe is a prominent Adivasi group primarily concentrated in the Chottanagpur region, known for their traditional communal landholding system called Khuntkatti.
• During the late 19^th century, the Chottanagpur region witnessed the Ulgulan (The Great Tumult), a massive tribal rebellion led by Birsa against the British colonial authorities and the exploitative dikus (outsiders like moneylenders and landlords).
• Birsa aimed to reform tribal society, urging his followers to give up alcohol, clean their villages, and stop believing in witchcraft, while simultaneously fighting to restore the Munda Raj.
• His movement was so influential that it forced the British government to introduce the Chota Nagpur Tenancy Act in 1908, which prohibited the illegal transfer of tribal land to non-tribals.

 Additional Information

• Geographical Context of Other Regions:
• Dhar and Jhabua: These districts are located in the state of Madhya Pradesh and are historically associated with the Bhil and Bhilala tribes, who also participated in various anti-colonial struggles.
• Valsad: This is a district in Gujarat, inhabited by tribal communities like the Dhodiya, Dubla, and Kukna, but it was not the center of the Munda uprising.
• Legacy: Birsa Munda is revered as Dharti Aba (Father of the Earth). In his honor, the state of Jharkhand was officially created on his birth anniversary in the year 2000.

The correct answer is Both I and II.

Key Points

• Chemical-based industries utilize various raw materials, including those derived from mineral and petroleum sources, to manufacture a wide range of products. Synthetic fibres such as nylon, polyester, and acrylic are classic examples of this sector as they are produced through the chemical synthesis of polymers derived primarily from petrochemicals. Hence, statement I is correct.
• Many chemical industries rely heavily on natural minerals extracted from the earth or sea. Salts, sulphur, and potash are essential mineral inputs used to produce chemicals like sulphuric acid, fertilizers, and industrial salts. These minerals undergo intensive chemical processing to be converted into usable industrial goods. Hence, statement II is correct.

 Additional Information

• The chemical industry is broadly categorized into Organic and Inorganic sectors:
• Organic Chemicals:
• Includes petrochemicals, which are utilized for manufacturing synthetic fibres, synthetic rubber, plastics, and dye-stuffs.
• These plants are usually located near oil refineries or petrochemical complexes.
• Inorganic Chemicals:
• Includes sulphuric acid (used for fertilizers, plastics, paints), nitric acid, alkalis, soda ash (used for glass, soaps, detergents), and caustic soda.
• These industries utilize natural minerals like rock phosphate, sulphur, and magnesium as their primary raw materials.

The correct answer is 2012.

Key Points

• Sachin Tendulkar achieved the historic milestone of scoring his 100^th international century on March 16, 2012.
• The landmark century was reached during a match in the Asia Cup against Bangladesh.
• The match was hosted at the Sher-e-Bangla National Stadium in Mirpur, Dhaka, where Tendulkar scored 114 runs off 147 balls.
• This feat made him the first and only cricketer to score 100 centuries in international cricket, consisting of 51 Test centuries and 49 One Day International (ODI) centuries.
• The 100^th century came 369 days after he had scored his 99^th international century against South Africa during the 2011 ICC Cricket World Cup.

 Additional Information

• Sachin Tendulkar:
• Widely known as the Master Blaster, he began his international career in 1989 at the age of 16 against Pakistan.
• He remains the leading run-scorer in the history of both Test and ODI cricket, with 15,921 runs and 18,426 runs respectively.
• Tendulkar was the first player to record a double century in ODI cricket, achieved against South Africa in Gwalior in 2010.
• In 2014, he became the youngest recipient and the first sportsperson to be conferred with the Bharat Ratna, India's highest civilian award.
• He officially announced his retirement from all forms of international cricket in November 2013, following his 200^th Test match at Wankhede Stadium.

The correct answer is Both I and II.

Key Points

• During the 2008 Beijing Olympics, Sushil Kumar competed in the men's 66 kg freestyle wrestling category and won the Bronze Medal. He became the first Indian wrestler to win an Olympic medal since Khashaba Dadasaheb Jadhav in 1952. He secured the medal by defeating Leonid Spiridonov in the repechage round. Hence, statement I is correct.
• At the 2012 London Olympics, he improved his previous record by winning the Silver Medal in the 66 kg freestyle event. He reached the final after a series of intense bouts, including a semi-final victory over Akzhurek Tanatarov, but lost the gold medal match to Japan's Tatsuhiro Yonemitsu. Hence, statement II is correct.
• By winning medals in both 2008 and 2012, Sushil Kumar became the first individual athlete from independent India to win two individual Olympic medals, a record he held solely until it was matched by other athletes in later years.

 Additional Information

• Sushil Kumar career highlights and honors:
• He served as the Flag Bearer for the Indian contingent during the opening ceremony of the 2012 London Olympics.
• In 2010, he made history by becoming the first Indian wrestler to win a Gold Medal at the World Wrestling Championships held in Moscow.
• He is a dominant force in the Commonwealth Games, having secured Gold Medals in three consecutive editions: 2010 (Delhi), 2014 (Glasgow), and 2018 (Gold Coast).
• In recognition of his sporting excellence, the Government of India conferred upon him the Major Dhyan Chand Khel Ratna (formerly Rajiv Gandhi Khel Ratna) in 2009 and the Padma Shri in 2011.

The correct answer is Gymnastics.

Key Points

• Gymnastics is a foundational Olympic sport that comprises various disciplines requiring a combination of physical strength, flexibility, power, agility, and coordination.
• The Roman Rings, officially known as Still Rings in modern competition, is an apparatus exclusively used in Men's Artistic Gymnastics. It features two circular rings suspended by cables, demanding extreme upper-body stability and muscular control.
• The Vaulting Table is the standard equipment used for the Vault event in both men's and women's categories. It features a flat, cushioned surface that gymnasts strike with their hands to launch themselves into aerial maneuvers.
• In 2001, the International Gymnastics Federation (FIG) replaced the traditional Vaulting Horse with the Vaulting Table to provide a larger push-off area, significantly improving athlete safety and allowing for higher difficulty rotations.

 Additional Information

• Other Artistic Gymnastics Apparatus:
• Pommel Horse: A rectangular apparatus with two handles used by men for continuous circular leg movements.
• Balance Beam: A 10-centimeter-wide beam used by women for jumps, turns, and acrobatic skills.
• Parallel Bars: Two horizontal wooden bars used by male gymnasts for swinging and flight elements.
• Uneven Bars: An apparatus consisting of two bars set at different heights used in Women's Artistic Gymnastics.
• Terminology for Other Sports:
• Hockey: Key terms include Penalty Corner, Dribbling, Scoop, Bully, and AstroTurf.
• Long Jump: Involves technical terms like Take-off Board, Approach Run, Landing Pit, and Foul Jump.
• Pole Vault: Uses specialized terms such as Planting Box, Crossbar, Fiberglass Pole, and Bar Clearance.

The correct answer is 27.3.

Key Points

• In the 2024 Global Hunger Index (GHI), India has been assigned a score of 27.3, which places it in the 'serious' category on the hunger severity scale.
• The Global Hunger Index is a peer-reviewed annual report jointly published by Concern Worldwide of Ireland and Welthungerhilfe of Germany to track hunger at global, regional, and national levels.
• India was ranked 105^th out of 127 countries evaluated in the 2024 report, which is the 19^th edition of the index.
• The GHI score is calculated based on four indicators: Undernourishment, Child Stunting (low height for age), Child Wasting (low weight for height), and Child Mortality.
• According to the 2024 report, India's child wasting rate is 18.7%, which is identified as the highest in the world, indicating significant acute malnutrition among children under five.
• Other indicator values for India include a child stunting rate of 34.4%, an undernourishment rate of 13.7%, and an under-five mortality rate of 2.9%.

 Additional Information

• GHI Scoring and Severity Scale:
• The GHI score is measured on a 100-point scale where 0 represents no hunger and 100 is the worst possible score.
• Scores are categorized as Low (≤ 9.9), Moderate (10.0–19.9), Serious (20.0–34.9), Alarming (35.0–49.9), and Extremely Alarming (≥ 50.0).
• Historical and Comparative Context:
• In the previous year, 2023, India was ranked 111^th out of 125 countries with a score of 28.7.
• India's scores have shown long-term improvement from 38.4 in 2000 and 35.2 in 2008, although the progress has slowed down in recent years.
• Compared to neighboring countries in 2024, Sri Lanka (rank 56), Nepal (rank 68), and Bangladesh (rank 84) are ranked significantly higher than India, while Pakistan (rank 109) is ranked lower.

The correct answer is 156^th.

Key Points

• The Environmental Performance Index (EPI) is a prestigious biennial report produced by researchers at Yale University and Columbia University in collaboration with the World Economic Forum.
• In the 2024 EPI, China is positioned at the 156^th rank out of 180 countries, indicating significant challenges in balancing its rapid industrial output with environmental sustainability goals.
• The 2024 index uses a data-driven approach to rank nations based on their environmental health and ecosystem vitality, utilizing 58 performance indicators across 11 issue categories.
• China's ranking is particularly affected by its high volume of greenhouse gas emissions and poor air quality metrics, despite being a global leader in the manufacturing of renewable energy technologies like solar panels and wind turbines.
• The EPI 2024 report emphasizes that while China is investing heavily in green technology, its current coal-dependent infrastructure continues to impact its overall environmental score.

 Additional Information

• Global Leaders and Laggards:
• Estonia secured the 1^st rank in the 2024 index, followed by Luxembourg and Germany, which were praised for their aggressive decarbonization strategies.
• The bottom of the index is occupied by countries like Vietnam (180^th), Pakistan (177^th), and India (176^th), reflecting severe environmental crises in parts of Asia.
• Pillars of Assessment:
• Environmental Health: This pillar tracks metrics related to air quality, safe drinking water, and sanitation, directly measuring the impact of environment on human health.
• Ecosystem Vitality: This evaluates the management of natural resources, including biodiversity, forest cover, and fisheries.
• Climate Change: This is a critical component that assesses GHG emission trends and the projected ability of nations to meet net-zero targets by 2050.

Shortcut Trick

Perform the bracket calculation first: (43 + 12) = 55.

Apply multiplication next: 55 × 2 = 110.

Complete the remaining addition and subtraction from left to right: 79 + 88 − 54 + 110 − 89 = 134.

∴ The correct answer is 134.

Alternate Method

Given: 79 + 88 − 54 + (43 + 12) × 2 − 89

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

⇒ 79 + 88 − 54 + (55) × 2 − 89

⇒ 79 + 88 − 54 + 110 − 89

⇒ 167 − 54 + 110 − 89

⇒ 113 + 110 − 89

⇒ 223 − 89

⇒ 134

∴ The correct answer is 134.

Additional Information

BODMAS Rule

The rule defines the order of precedence: Brackets first, then Orders (exponents), followed by Division and Multiplication (same priority), and finally Addition and Subtraction (same priority).

Bracket Hierarchy

Calculations should always start from the innermost Parentheses (), then Curly braces {}, and then Square brackets [].

Sign Rules

When multiplying signs, (+) × (−) results in (−), while (−) × (−) results in (+).

Shortcut Trick

Solve multiplication and division first: 14 × 2 = 28 and 33 ÷ 3 = 11.

Expression becomes: 68 + 28 − 22 + 11 − 19 + 28.

Group positive and negative terms separately: (68 + 28 + 11 + 28) − (22 + 19).

Perform final calculation: 135 − 41 = 94.

∴ The correct answer is 94.

Alternate Method

Given:

68 + (14 × 2) − 22 + 33 ÷ 3 − 19 + 28

Method Used:

The BODMAS rule dictates the sequence of operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

⇒ 68 + 28 − 22 + 33 ÷ 3 − 19 + 28 (Solved bracket: 14 × 2 = 28)

⇒ 68 + 28 − 22 + 11 − 19 + 28 (Solved division: 33 ÷ 3 = 11)

⇒ 96 − 22 + 11 − 19 + 28 (Addition: 68 + 28 = 96)

⇒ 74 + 11 − 19 + 28 (Subtraction: 96 − 22 = 74)

⇒ 85 − 19 + 28 (Addition: 74 + 11 = 85)

⇒ 66 + 28 (Subtraction: 85 − 19 = 66)

⇒ 94 (Final Addition: 66 + 28 = 94)

∴ The correct answer is 94.

Additional Information

BODMAS / VBODMAS Rule

It ensures unique results for expressions; V stands for Vinculum (bar), which is solved before brackets.

Operator Precedence

Multiplication and division hold higher priority than addition and subtraction. Addition and subtraction can be solved left-to-right as they share the same priority level.

Grouping Strategy

To minimize calculation errors, sum all positive values and all negative values independently before finding the final difference.

Shortcut Trick

Memorize perfect cubes and perfect squares for speed.

Cube root: √³{2.197} = 1.3 (since 13³ = 2197).

Square root: √{1.21} = 1.1 (since 11² = 121).

Calculation: 1.3 × 1.1 = 1.43.

∴ The correct answer is 1.43.

Alternate Method

Given:

Expression: √³{2.197} × √{1.21}

Method Used:

Fractional conversion and prime factorization.

Calculations:

⇒ √³{2197 ÷ 1000} × √{121 ÷ 100}

⇒ (√³{2197} ÷ √³{1000}) × (√{121} ÷ √{100})

⇒ (13 ÷ 10) × (11 ÷ 10)

⇒ 1.3 × 1.1

⇒ 1.43

∴ The correct answer is 1.43.

Additional Information

Cubes and Cube Roots

A cube root of a number x is a number y such that y³ = x. For decimals, if the number has 3n decimal places, the cube root has n decimal places.

Squares and Square Roots

A square root of a number x is a number y such that y² = x. For decimals, if the number has 2n decimal places, the square root has n decimal places.

BODMAS Rule

Always solve Brackets, Orders (roots/powers), Division, Multiplication, Addition, and Subtraction in this specific sequence during simplification.

Shortcut Trick

Solve for square roots first: √225 = 15, √25 = 5, and √81 = 9.

Apply BODMAS logic: x = (15 ÷ 5) + 9 ⇒ x = 3 + 9 = 12.

Multiply the result by 2 to find 2x: 2 × 12 = 24.

∴ The correct answer is 24.

Alternate Method

Given:

x = √225 ÷ √25 + √81

Formula Used:

To solve mathematical expressions, we use the BODMAS rule which stands for Brackets, Orders (Powers and Roots), Division, Multiplication, Addition, and Subtraction.

Calculations:

⇒ x = 15 ÷ 5 + 9

⇒ x = 3 + 9

⇒ x = 12

We need to find the value of 2x:

⇒ 2x = 2 × 12

⇒ 2x = 24

∴ The correct answer is 24.

Additional Information

BODMAS Rule

The BODMAS rule ensures a standard order of operations: Brackets, Orders (roots/indices), Division, Multiplication, Addition, and Subtraction.

Perfect Square Roots

A perfect square is a number whose square root is a whole number. Knowing roots like √225 = 15, √25 = 5, and √81 = 9 is essential for fast simplification.

Linear Expressions

In expressions involving a variable x, ensure the entire term is simplified before multiplying by the coefficient (like the 2 in 2x).

Shortcut Trick

Area of a square is calculated by squaring its side length.

Area = (Side)²

Area = 6² = 36 cm².

∴ The correct answer is 36 cm².

Alternate Method

Given:

Side of the square (s) = 6 cm

Formula Used:

Area of Square = Side × Side = s²

Calculations:

⇒ Area = 6 cm × 6 cm

⇒ Area = 36 cm²

∴ The correct answer is 36 cm².

Additional Information

Perimeter of a Square

The total boundary length of a square is 4 × side.

Diagonal of a Square

The distance between opposite corners is given by the formula: Diagonal = √2 × Side.

Properties of a Square

All sides are equal, and all internal angles are exactly 90°.

Shortcut Trick

The diagonal of a square is always √2 times its side.

Given the side = 7 cm.

∴ Diagonal = 7 × √2 = 7√2 cm.

∴ The correct answer is 7√2 cm.

Alternate Method

Given:

Side (a) of the square = 7 cm

Formula Used:

In a square, the diagonal (d), side (a), and side (a) form an isosceles right-angled triangle.

According to Pythagoras Theorem: d² = a² + a² = 2a²

⇒ Diagonal (d) = a√2

Calculations:

⇒ Diagonal = side × √2

⇒ Diagonal = 7 × √2

⇒ Diagonal = 7√2 cm

∴ The correct answer is 7√2 cm.

Additional Information

Area of a Square

The area can be calculated as side² or using the diagonal as (diagonal²) ÷ 2.

Perimeter of a Square

The total boundary length is 4 × side.

Diagonal Relation

The diagonals of a square are equal, bisect each other at 90°, and also bisect the vertex angles into 45° each.

Shortcut Trick

Quickly check the sum of digits for divisibility by 3: 9999 (36), 10032 (6), and 9042 (15) are all multiples of 3.

Only 10019 has a sum of digits = 11, which is not divisible by 3.

Check 10019 for 11: (1 + 0 + 9) − (0 + 1) = 9, which is not divisible by 11.

∴ The correct answer is 10019.

Alternate Method

Given: Numbers are 10019, 9999, 10032, and 9042.

Formula: Divisibility by 3 (Sum of digits) and Divisibility by 11 (Alternating sum of digits).

Checking for 3:

⇒ 10019: 1 + 0 + 0 + 1 + 9 = 11 (Not divisible by 3)

⇒ 9999: 9 + 9 + 9 + 9 = 36 (Divisible by 3)

⇒ 10032: 1 + 0 + 0 + 3 + 2 = 6 (Divisible by 3)

⇒ 9042: 9 + 0 + 4 + 2 = 15 (Divisible by 3)

Checking for 11:

⇒ 10019: (Sum of digits at odd places) − (Sum of digits at even places)

⇒ (1 + 0 + 9) − (0 + 1) = 10 − 1 = 9 (Not divisible by 11)

Since 10019 fails both tests, it is the required number.

∴ The correct answer is 10019.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if the sum of all its digits is divisible by 3.

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a multiple of 11.

Divisibility by 33

If a number is divisible by both 3 and 11, it is also divisible by 33 (e.g., 9999, 10032, and 9042).

Shortcut Trick

A number is divisible by 6 if it is divisible by both 2 and 3.

The last digit of 36P2 is 2, so it is already divisible by 2.

For divisibility by 3, the sum of digits 3 + 6 + P + 2 = 11 + P must be divisible by 3.

Testing option (3): 11 + 7 = 18. Since 18 is divisible by 3, P = 7 is correct.

∴ The correct answer is 7.

Alternate Method

Given number: 36P2

Condition: The number must be divisible by 6.

⇒ Divisibility by 2: A number is divisible by 2 if it is even. 36P2 ends in 2, so it is even.

⇒ Divisibility by 3: The sum of the digits must be a multiple of 3.

⇒ Sum of digits = 3 + 6 + P + 2 = 11 + P

⇒ For divisibility by 3, (11 + P) ÷ 3 must leave a remainder of 0.

⇒ If P = 0: 11 + 0 = 11 (Not divisible by 3)

⇒ If P = 5: 11 + 5 = 16 (Not divisible by 3)

⇒ If P = 7: 11 + 7 = 18 (Divisible by 3, as 18 = 3 × 6)

⇒ If P = 2: 11 + 2 = 13 (Not divisible by 3)

∴ The correct answer is 7.

Additional Information

Divisibility by 2

A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.

Divisibility by 3

A number is divisible by 3 if the sum of all its digits is divisible by 3.

Composite Divisibility (Rule of 6)

To check divisibility by a composite number like 6, check divisibility by its co-prime factors (2 and 3).

Shortcut Trick

Solve the innermost square roots first: √400 = 20 and √25 = 5.

Add the values inside the outer radical: 20 + 5 = 25.

Calculate the final square root: √25 = 5.

∴ The correct answer is 5.

Alternate Method

Given:

Expression = √(√400 + √25)

Calculations:

⇒ √400 = 20

⇒ √25 = 5

⇒ √(20 + 5)

⇒ √25

⇒ 5

∴ The correct answer is 5.

Additional Information

Perfect Squares

A perfect square is a number that can be expressed as the product of an integer with itself. For example, 400 is 20² and 25 is 5².

Simplification Rule

For nested radicals, always simplify the innermost expression first according to standard mathematical precedence rules.

Square Root Properties

The operation √x × √x = x. However, √(a + b) is not equal to √a + √b; the addition must be performed before the outer root.

Shortcut Trick

Net change in Average = 34 − 28 = 6 units.

Total change in Sum = 6 × 4 = 24.

New Number = Replaced Number + Total Change.

New Number = 24 + 24 = 48.

∴ The correct answer is 48.

Alternate Method

Given:

Initial count (n) = 4 | Initial Average = 28 | Replaced number = 24 | New Average = 34.

Formula Used:

Sum = Average × Total Numbers

New Number = Old Number + (New Sum − Old Sum)

Calculations:

⇒ Initial Sum of 4 numbers = 28 × 4 = 112

⇒ New Sum of 4 numbers = 34 × 4 = 136

⇒ Difference in total sum = 136 − 112 = 24

⇒ Since 24 was replaced, the New Number must be 24 higher than the old one.

⇒ New Number = 24 + 24 = 48

∴ The correct answer is 48.

Additional Information

Average Replacement Rule

When one value is replaced: New Value = Replaced Value + (n × Change in Average), where n is the total number of observations.

Net Deviation

The sum of deviations from the average is always zero. If the average increases, the new entry must be greater than the replaced entry by the product of the count and the average increase.

Average Formula

Average = Sum of observations ÷ Total number of observations.

Shortcut Trick

The number B must be in the form LCM(3, 4, 5) × k + 1.

⇒ LCM(3, 4, 5) = 60, so B = 60k + 1.

Since B = 700 − A and A is small (from options), B is close to 700.

The largest multiple of 60 less than 700 is 660 (where k = 11).

⇒ B = 660 + 1 = 661.

⇒ A = 700 − 661 = 39.

∴ The correct answer is 39.

Alternate Method

Given:

⇒ B = 700 − A

⇒ B ÷ 3, B ÷ 4, and B ÷ 5 all leave a remainder of 1.

Formula Used:

⇒ Number = LCM(Divisors) × k + Remainder

Calculations:

⇒ LCM(3, 4, 5):

⇒ 3 × 4 × 5 = 60

⇒ B = 60k + 1

⇒ Substituting B in the first equation:

⇒ 60k + 1 = 700 − A

⇒ A = 699 − 60k

⇒ Since A must be a positive integer and looking at the options (around 40):

⇒ Try k = 11:

⇒ A = 699 − 60 × 11

⇒ A = 699 − 660

⇒ A = 39

∴ The correct answer is 39.

Additional Information

General Form of Remainder Problems

If a number N leaves the same remainder r when divided by x, y, and z, then N = LCM(x, y, z) × k + r.

Least Common Multiple (LCM)

LCM is the smallest quantity that is exactly divisible by each of two or more given quantities. For prime or co-prime numbers, it is simply their product.

Division Algorithm

Dividend = (Divisor × Quotient) + Remainder. This relationship helps in verifying the consistency of the result.

Shortcut Trick

To find the maximum number of boys, calculate the HCF of 156 and 234.

HCF(156, 234) = 78 (Since 156 = 78 × 2 and 234 = 78 × 3).

Number of chips each boy gets = Total Chips ÷ Maximum Boys.

Chips per boy = 156 ÷ 78 = 2.

∴ The correct answer is 2.

Alternate Method

Given:

Total Chips = 156

Total Toffees = 234

Condition: Maximum number of boys with equal distribution.

Step 1: Calculate HCF using Prime Factorization

⇒ 156 = 2 × 2 × 3 × 13 = 2² × 3¹ × 13¹

⇒ 234 = 2 × 3 × 3 × 13 = 2¹ × 3² × 13¹

⇒ HCF = 2¹ × 3¹ × 13¹ = 2 × 3 × 13 = 78

Step 2: Find chips per boy

⇒ Maximum boys = 78

⇒ Chips per boy = 156 ÷ 78

⇒ Chips per boy = 2

∴ The correct answer is 2.

Additional Information

Highest Common Factor (HCF)

The HCF of two or more numbers is the largest number that divides each of them without leaving a remainder. It is used to find the maximum size or maximum number in distribution problems.

HCF and LCM Relation

For any two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

Division Method for HCF

Divide the larger number by the smaller one. If there is a remainder, divide the previous divisor by this remainder. Repeat until the remainder is zero; the last divisor is the HCF.

Shortcut Trick

Ratio of Cost Price (CP) to Selling Price (SP) = 2 : 5.

Profit units = SP − CP = 5 − 2 = 3 units.

Given 3 units = ₹210 ⇒ 1 unit = ₹70.

Selling Price (SP) = 5 units = 5 × 70 = ₹350.

∴ The correct answer is ₹350.

Alternate Method

Given:

Ratio of CP : SP = 2 : 5

Total Profit = ₹210

Formula Used:

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

Let the Cost Price be 2x and the Selling Price be 5x.

⇒ Profit = SP − CP

⇒ 210 = 5x − 2x

⇒ 210 = 3x

⇒ x = 210 ÷ 3 = 70

⇒ Selling Price (SP) = 5x

⇒ SP = 5 × 70 = ₹350

∴ The correct answer is ₹350.

Additional Information

Profit Percentage

It is the percentage of profit earned on the cost price: Profit% = (Profit ÷ CP) × 100.

Loss Percentage

It is the percentage of loss incurred on the cost price: Loss% = (Loss ÷ CP) × 100.

Relation between CP and SP

Selling price can be calculated directly using: SP = [CP × (100 + Profit%)] ÷ 100 or SP = [CP × (100 − Loss%)] ÷ 100.

Shortcut Trick

If A is n times more than B, then A = (n + 1)B.

Here, n = 4, so A = 5B.

The percentage less formula is: [n ÷ (n + 1)] × 100.

Percentage less = (4 ÷ 5) × 100 = 80%.

∴ The correct answer is 80 percent.

Alternate Method

Given:

A is 4 times more than B.

Formula Used:

Percentage less = [(Higher Value − Lower Value) ÷ Higher Value] × 100

Calculations:

⇒ Let the value of B = 100.

⇒ A = B + (4 × B) = 100 + 400 = 500.

⇒ Difference between A and B = 500 − 100 = 400.

⇒ Percentage less = (Difference ÷ A) × 100

⇒ Percentage less = (400 ÷ 500) × 100

⇒ Percentage less = (4 ÷ 5) × 100 = 80%.

∴ The correct answer is 80 percent.

Additional Information

Times As vs Times More

x times as much means A = x × B. x times more than means A = B + (x × B) = (x + 1)B.

Base for Percentage Calculation

When calculating % less than A, A is the base (denominator). When calculating % more than B, B is the base.

Percentage Change Formula

Percentage Change = [(Final − Initial) ÷ Initial] × 100. Always ensure the denominator is the value being compared to.

Shortcut Trick

Profit = ₹200 and Selling Price (SP) = ₹4200.

Cost Price (CP) = SP − Profit = 4200 − 200 = ₹4000.

Profit fraction = Profit ÷ CP = 200 ÷ 4000 = 1/20.

Conversion: 1/20 × 100 = 5%.

∴ The correct answer is 5%.

Alternate Method

Given: Selling Price (SP) = ₹4200, Profit = ₹200.

Formula Used: Cost Price (CP) = Selling Price − Profit; Profit Percentage = (Profit ÷ Cost Price) × 100.

⇒ Cost Price (CP) = 4200 − 200

⇒ Cost Price (CP) = ₹4000

⇒ Profit Percentage = (200 ÷ 4000) × 100

⇒ Profit Percentage = (1 ÷ 20) × 100

⇒ Profit Percentage = 5%

∴ The correct answer is 5%.

Additional Information

Loss Percentage

When the Cost Price is greater than the Selling Price, the result is a loss. Loss % = (Loss ÷ CP) × 100, where Loss = CP − SP.

Calculation Base

Unless specified otherwise, both Profit Percentage and Loss Percentage are always calculated on the Cost Price (CP).

Selling Price from Profit %

If Profit % and CP are known, SP = CP × (100 + Profit %) ÷ 100.

Shortcut Trick

Ratio of Income : Expenditure : Savings = 100 : 50 : 50 = 2 : 1 : 1.

New Income = 2 × 140% = 2.8 units.

New Expenditure = 1 × 130% = 1.3 units.

New Savings = 2.8 − 1.3 = 1.5 units.

1.5 units = Rs. 7500 ⇒ 1 unit = Rs. 5000.

Initial Income = 2 units = 2 × 5000 = Rs. 10000.

∴ The correct answer is Rs. 10000.

Alternate Method

Given: Expenditure = 50% of Income, Income Increase = 40%, Expenditure Increase = 30%, Final Saving = Rs. 7500.

Formula Used: Income = Expenditure + Savings

⇒ Let Initial Income = 100 units.

⇒ Initial Expenditure = 50% of 100 = 50 units.

⇒ Initial Savings = 100 − 50 = 50 units.

⇒ New Income = 100 + 40% = 140 units.

⇒ New Expenditure = 50 + 30% of 50 = 50 + 15 = 65 units.

⇒ New Savings = 140 − 65 = 75 units.

⇒ Given New Savings = Rs. 7500.

⇒ 75 units = Rs. 7500 ⇒ 1 unit = Rs. 100.

⇒ Initial Income = 100 units = 100 × 100 = Rs. 10000.

∴ The correct answer is Rs. 10000.

Additional Information

Income-Expenditure Relationship

Total Income is always the sum of Expenditure and Savings (I = E + S). Any change in one affects the balance of the others.

Percentage Increase Calculation

New Value = Old Value × (1 + Rate/100). For example, a 40% increase means multiplying by 1.40.

Unitary Method in Savings

When values are given in percentages, assuming a base of 100 units for the original quantity simplifies the comparison with actual monetary values.

Shortcut Trick

Total work = LCM(40, 80) = 80 units.

Efficiency of M = 2 and N = 1 → Combined efficiency = 3 units/day.

Work done in 8 days = 3 × 8 = 24 units.

Percent work completed = (24 ÷ 80) × 100 = 30%.

∴ The correct answer is 30%.

Alternate Method

Given: M alone = 40 days, N alone = 80 days, Time worked together = 8 days.

Formula Used: Efficiency = Total Work ÷ Time | Percentage = (Part ÷ Whole) × 100

⇒ Combined efficiency of (M + N) = 2 + 1 = 3 units/day.

⇒ Work completed in 8 days = 3 × 8 = 24 units.

⇒ Percentage of work completed = (24 ÷ 80) × 100

⇒ Percentage = (3 ÷ 10) × 100 = 30%.

∴ The correct answer is 30%.

Additional Information

Combined Efficiency Formula

If two people complete work in A and B days, their combined 1-day work is 1/A + 1/B.

Work & Time Relation

Time taken to complete the whole work is the inverse of efficiency (Total Work ÷ Combined Efficiency).

Remaining Work

Remaining work percentage = 100% − Completed work percentage.

Shortcut Trick

Assume Total Work = LCM(9, 18) = 18 units.

Efficiency of (P + Q) = 18 ÷ 9 = 2 units/day and Efficiency of R = 18 ÷ 18 = 1 unit/day.

Total Efficiency of (P + Q + R) = 2 + 1 = 3 units/day.

Time for 1/6 part of work = (1/6 × 18) ÷ 3 = 3 ÷ 3 = 1 day.

∴ The correct answer is 1 day.

Alternate Method

Given: Time taken by (P + Q) = 9 days, Time taken by R = 18 days.

Formula: Total Work = Efficiency × Time

⇒ Combined Efficiency (P + Q + R) = 2 + 1 = 3 units/day.

⇒ Target Work = 1/6 × Total Work = 1/6 × 18 = 3 units.

⇒ Time Taken = Target Work ÷ Combined Efficiency

⇒ Time Taken = 3 ÷ 3 = 1 day.

∴ The correct answer is 1 day.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If A can do a work in x days, A_Efficiency = 1/x.

Fractional Work

To find the time for a fraction (n) of work, multiply the total time required for the full work by n: Time_fraction = n × Total Time.

Work and Wages

Wages are usually distributed in the ratio of the work done by each person, which is the same as the ratio of their efficiencies if they work for the same duration.

Shortcut Trick

Convert Speed of B to km/hr: 30 × (18 ÷ 5) = 108 km/hr.

When time is constant (1 hour), the ratio of distances is equal to the ratio of speeds.

Required Ratio = Speed of A : Speed of B = 50 : 108

Divide by 2: 25 : 54

∴ The correct answer is 25 : 54.

Alternate Method

Given:

Speed of A = 50 km/hr

Speed of B = 30 m/s

Time = 1 hour

Formula Used:

Distance = Speed × Time

1 m/s = 18 ÷ 5 km/hr

Calculations:

⇒ Speed of A = 50 km/hr

⇒ Distance covered by A in 1 hour = 50 × 1 = 50 km

⇒ Speed of B in km/hr = 30 × (18 ÷ 5) = 6 × 18 = 108 km/hr

⇒ Distance covered by B in 1 hour = 108 × 1 = 108 km

⇒ Respective ratio = Distance A : Distance B

⇒ Ratio = 50 : 108

⇒ Ratio = 25 : 54

∴ The correct answer is 25 : 54.

Additional Information

Unit Conversion

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

Constant Time Property

If time (t) is constant, the distance (d) traveled is directly proportional to the speed (s). Thus, d₁/d₂ = s₁/s₂.

Relative Speed

When two objects move in the same direction, relative speed = s₁ − s₂. In opposite directions, relative speed = s₁ + s₂.

Shortcut Trick

Extra time taken to cross the platform = 22 − 12 = 10 seconds.

In these 10 seconds, the train covers only the platform length (550 m).

Speed of the train = 550 m ÷ 10 s = 55 m/s.

Length of the train = Speed × Time to cross pole = 55 × 12 = 660 m.

∴ The correct answer is 660 m, 55 m/s.

Alternate Method

Given:

Time to cross pole (t₁) = 12 sec

Time to cross platform (t₂) = 22 sec

Length of platform (P) = 550 m

Formula Used:

Speed = Distance ÷ Time

Calculations:

Let the length of the train be L and its speed be S.

When crossing a pole: S = L ÷ 12 → (Eq 1)

When crossing a platform: S = (L + 550) ÷ 22 → (Eq 2)

Equating (Eq 1) and (Eq 2):

⇒ L ÷ 12 = (L + 550) ÷ 22

⇒ L ÷ 6 = (L + 550) ÷ 11

⇒ 11L = 6(L + 550)

⇒ 11L = 6L + 3300

⇒ 5L = 3300

⇒ L = 660 m

Now, calculate speed S:

⇒ S = 660 ÷ 12

⇒ S = 55 m/s

∴ The correct answer is 660 m, 55 m/s.

Additional Information

Crossing Stationary Objects

When a train crosses a pole or a standing person, the distance covered equals the length of the train. When it crosses a bridge or platform, the distance is (Length of Train + Length of Platform).

Unit Conversion

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

Relative Speed

For two objects moving in the opposite direction, relative speed = S₁ + S₂. For the same direction, relative speed = |S₁ − S₂|.

The correct answer is: Well heeled.

Key Points

• The phrase 'Wealthy or rich' refers to a person having a great deal of money, resources, or assets. (धनी या अमीर)
• Example: After years of hard work in the tech industry, he finally became wealthy enough to retire early.
• 'Well heeled' is an idiom used to describe someone who is wealthy or has a lot of money. The term originally referred to people who could afford to keep their shoes in good repair with new heels. (संपन्न/मालदार)
• Example: The charity event was attended by many well-heeled donors from the city.
• Hence, we can infer that the idiom for 'wealthy or rich' is 'well heeled'.

Therefore, the correct answer is: Well heeled.

Additional Information

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

• Well healed (पूरी तरह से ठीक हुआ): This refers to a wound or injury that has recovered or closed up completely. It is also often a common misspelling of 'well-heeled'.
• Example: The doctor confirmed that his surgical scar was well healed and he could resume sports.
• Well groomed (सजा-धजा/साफ-सुथरा): Describing a person who has a neat and tidy appearance, often regarding their hair, clothes, and hygiene.
• Example: As a professional model, she is always well groomed and presentable.
• Well brought up (अच्छी तरह से पाला-पोसा हुआ): Having been taught good manners and behavior by one's parents while growing up.
• Example: He is such a polite young man; it is clear that he was very well brought up.

The correct answer is: The whole nine yards.

Key Points

• The phrase 'The entirety of what's possible or available; all the related elements of something' refers to the complete range of something, including every single detail or component involved. (किसी चीज़ का संपूर्ण विस्तार या सब कुछ उपलब्ध होना)
• Example: To win the contract, we need to present the entirety of what's possible within our current infrastructure.
• 'The whole nine yards' is an idiom used to mean everything, the whole lot, or going to the full extent of a situation or task. (पूरी तरह से या सब कुछ)
• Example: When they renovated their house, they did the whole nine yards, including the landscaping and the pool.
• Hence, we can infer that the idiom 'the whole nine yards' correctly matches the given meaning.

Therefore, the correct answer is: The whole nine yards.

Additional Information

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

• All wool and yard wide (पूरी तरह से ईमानदार और विश्वसनीय): This idiom describes a person who is genuine, reliable, and honest.
• Example: You can trust his business advice; he is all wool and a yard wide.
• Thousand yard stare (शून्यता भरी दृष्टि): A blank, unfocused gaze often seen in people who have experienced severe emotional trauma or combat.
• Example: After the traumatic accident, the survivor sat on the curb with a thousand-yard stare.
• Hard yard (कठिन परिश्रम): Refers to the difficult and tedious work or effort required to achieve a goal.
• Example: If you want to reach the top of your profession, you have to put in the hard yards early in your career.

The correct answer is: Apropos.

Key Points

• The word 'Apropos' means very appropriate to a particular situation; relevant or pertinent. (उपयुक्त)
• Example: His comments were apropos of the current situation we are facing.
• 'Apropos' refers to the correct spelling of the term used to describe something that is opportune or relevant to the subject at hand. (सही वर्तनी)
• Example: The timing of his arrival was very apropos for the celebration.
• Hence, we can infer that 'Apropos' is the correctly spelled word among the options.

Therefore, the correct answer is: Apropos.

Additional Information

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

• Abrogate (रद्द करना): This is the correct spelling of the misspelled option 'Abrogatte' (which incorrectly has two 't's). It means to formally repeal, abolish, or do away with a law, right, or formal agreement.
• Example: The government has the power to abrogate the treaty if terms are not met.
• Alacrity (तत्परता): This is the correct spelling of the misspelled option 'Allacrity' (which incorrectly has two 'l's). It means brisk and cheerful readiness.
• Example: She accepted the invitation to the gala with alacrity.
• Avarice (लोभ): This is the correct spelling of the misspelled option 'Avarise' (which incorrectly ends in 'ise'). It refers to extreme greed for wealth or material gain.
• Example: The main character's downfall in the story was caused by his blind avarice.

The correct answer is: Deadly.

Key Points

• The word 'fatal' refers to something that causes death or leads to a disastrous end. (घातक)
• Example: The pilot made a fatal error during the landing, resulting in a tragic accident.
• 'Deadly' describes something that is capable of causing death or is extremely lethal; it is the most appropriate synonym for the word 'fatal'. (प्राणघातक)
• Example: Some species of spiders carry a deadly venom that can be fatal to humans.
• Hence, we can infer that the correct synonym of 'fatal' is 'deadly'.

Therefore, the correct answer is: Deadly.

Additional Information

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

• Harmless (हानिरहित): Not likely to cause any physical or mental injury.
• Example: Although the dog looks intimidating, it is actually quite harmless and friendly.
• Safe (सुरक्षित): Protected from or not exposed to danger or risk.
• Example: It is always important to keep your valuable documents in a safe place.
• Weak (कमजोर): Lacking physical strength, energy, or power.
• Example: He felt very weak and exhausted after recovering from the fever.

The correct answer is Option (4) i.e. Restuarant.

Key Points

• The word 'Restuarant' is the misspelt version of 'Restaurant'. It refers to a place where people pay to sit and eat meals that are cooked and served on the premises. (भोजनालय)
• Example: We decided to dine at a local restaurant to celebrate the occasion.
• 'Restaurant' is the correct spelling, characterized by the sequence of vowels 'a-u' before the 'r' and 'a' before 'nt'. (रेस्तरां)
• Example: The Italian restaurant around the corner serves the best lasagna in the city.
• Hence, we can infer that 'Restuarant' is the word with the incorrect spelling.

Therefore, the correct answer is- Restuarant.

Additional Information

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

• Disastrous (विनाशकारी): Something that causes great damage, failure, or a sudden catastrophe.
• Example: The disastrous fire destroyed several historic buildings in the town center.
• Pungent (तीखा/कटु): Having a sharply strong taste or smell that is often overpowering.
• Example: The pungent smell of onions always makes my eyes water while cooking.
• Benign (सौम्य/दयालु): Gentle and kindly in nature; or in a medical context, not harmful in effect.
• Example: The professor had a benign smile that immediately put the nervous students at ease.

The correct answer is: Exposed.

Key Points

• The word 'Enveloped' means to wrap up, cover, or surround something completely so as to hide or protect it. (ढका हुआ)
• Example: The mountain peak was enveloped in a thick blanket of clouds, making it invisible from the valley.
• 'Exposed' refers to something that is left uncovered, unprotected, or made visible to observation; it is the state of being revealed rather than hidden. (खुला हुआ)
• Example: The old foundations of the building were exposed during the excavation process.
• Hence, we can infer that the opposite of 'Enveloped' is 'Exposed'.

Therefore, the correct answer is: Exposed.

Additional Information

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

• Covered (ढका हुआ): To place something over or upon an object to protect, shut, or conceal it.
• Example: The ground was covered with fallen leaves after the autumn storm.
• Wrapped (लपेटा हुआ): To enclose something in a covering such as paper or fabric.
• Example: He wrapped the fragile gift carefully in silk cloth before placing it in the box.
• Surrounded (घिरा हुआ): To be present all around someone or something; encircled.
• Example: The peaceful cottage was surrounded by ancient oak trees and a small stream.

The correct answer is Option (3) i.e. Lexicographer.

Key Points

• The phrase 'A person who compiles dictionaries' refers to an individual who is responsible for collecting, defining, and organizing words for a dictionary. (शब्दकोश संकलक)
• Example: The project required a person who compiles dictionaries to document the unique technical terms of the medical field.
• 'Lexicographer' is the specific one-word substitution for a person whose professional job involves compiling or writing dictionaries. (कोशकार)
• Example: As a dedicated lexicographer, he spent years researching the etymology of ancient words for the new encyclopedia.
• Hence, we can infer that the most suitable one-word substitution for 'A person who compiles dictionaries' is 'Lexicographer'.

Therefore, the correct answer is- Lexicographer.

Additional Information

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

• Linguist (भाषाविद): A person who specializes in the study of language and its structure or is proficient in many languages.
• Example: The linguist compared the grammatical structures of several European languages.
• Grammarian (व्याकरण शास्त्री): A person who studies or writes about the rules and systems of a language.
• Example: The grammarian argued that the usage of the word had changed significantly over the last century.
• Calligrapher (सुलेखक): A person who excels in the art of producing beautiful and decorative handwriting.
• Example: The invitation cards were hand-lettered by a professional calligrapher to give them an elegant look.

The correct answer is: Circumlocution.

Key Points

• The phrase 'the use of too many words to say something simple' refers to a style of communication that is unnecessarily long, indirect, or roundabout. (गोल-मोल बात)
• Example: The politician was accused of using too much circumlocution to avoid giving a direct answer about the new tax policy.
• 'Circumlocution' is the specific term for the act of using more words than necessary to express an idea, often used to be vague or evasive. (शब्दबाहुल्य)
• Example: His speech was filled with circumlocution, making it difficult for the audience to grasp his main point.
• Hence, we can infer that the one-word substitution for the given phrase is 'circumlocution'.

Therefore, the correct answer is: Circumlocution.

Additional Information

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

• Rhetoric (वक्रपटुता / भाषणकला): The art of effective or persuasive speaking or writing, especially the exploitation of figures of speech.
• Example: The candidate’s powerful rhetoric helped him win the support of the youth.
• Hyperbole (अतिशयोक्ति): Exaggerated statements or claims that are not meant to be taken literally.
• Example: When he said he was so hungry he could eat a horse, it was clearly a hyperbole.
• Eloquence (सुवक्ता / वाक्पटुता): Fluent or persuasive speaking or writing that is clear and effective.
• Example: The lawyer’s eloquence in the courtroom had a significant impact on the jury’s decision.

The correct answer is 'in breach of'.

 

Key Points

• The phrase 'in breach of' means to fail to do something that is required by a law, rule, or agreement.
• In the context of the sentence, Deepika Padukone failed to fulfill her professional obligation by not attending the shooting, which constitutes a violation of her contract.
• The other options do not fit the context of violating a formal agreement.

Therefore, the correct answer is Option 4.

 

Complete Sentence: 'Deepika Padukone is in breach of her contract because she did not come to the shooting.'

 

Additional Information

• Option 1: 'against' is a preposition used to show opposition or contact, but it is not the standard legal term for violating a contract.
• Option 2: 'in accordance with' means following or obeying a rule/agreement. This is the opposite of what the sentence implies, as she missed the shooting.
• Option 3: 'by force of' means using the strength or power of something (e.g., by force of habit), which is irrelevant to a contractual violation.

The correct answer is Were the fields being tilled by the farmers when the storm hit?.

Key Points

• The sentence Were the farmers tilling the fields when the storm hit? is in the Active Voice and follows the Past Continuous Tense.
• The structure of an interrogative sentence in the Past Continuous active voice is: Was/Were + Subject + Verb-ing + Object?
• To convert this into Passive Voice, the object of the active sentence (the fields) becomes the new subject. Since the fields is a plural noun, the auxiliary verb Were is placed at the beginning of the sentence.
• The rule for Past Continuous passive conversion requires the addition of being followed by the Past Participle (V3) form of the main verb. Therefore, tilling changes to being tilled.
• The agent (original subject) the farmers is introduced by the preposition by.
• The subordinate clause when the storm hit is an adverbial of time and remains unchanged in the passive transformation.
• The final passive structure becomes: Were (Auxiliary) + the fields (Subject) + being + tilled (V3) + by the farmers (Agent) + when the storm hit?

 Additional Information

• Tense Mismatch Analysis:
• Simple Past Passive: Uses Was/Were + V3 without being. This represents a completed action rather than an ongoing one, making it unsuitable for translating a continuous active verb.
• Past Perfect Passive: Uses Had + been + V3. This denotes an action completed before another point in the past, which changes the original meaning of the sentence.
• Present Continuous Passive: Uses Am/Is/Are + being + V3. This shifts the timeframe from the past to the present, violating the rules of voice conversion where the tense must remain consistent.
• In English grammar, Voice describes the relationship between the action and the participants. The Passive Voice is typically used when the focus is on the action or the recipient rather than the performer.

The correct answer is Will the partners have signed the legal documents before the deal is officially announced?.

Key Points

• The provided sentence is in the Passive Voice of the Future Perfect Tense, which is characterized by the auxiliary verb structure will + have been + past participle (V3).
• To transform this into the Active Voice, the agent of the action (the partners), which follows the preposition by, must be moved to the subject position at the beginning of the clause.
• The object of the passive sentence (the legal documents) is moved to the position following the main verb in the active construction.
• The verb phrase will have been signed is converted to the active form will have signed, following the standard Future Perfect Active formula: Subject + will have + V3 + Object.
• Since the sentence is an interrogative (question), the auxiliary verb Will must remain at the start of the sentence, followed immediately by the new subject the partners.
• The secondary clause, before the deal is officially announced, remains unchanged as it serves as a time-defining subordinate clause that does not affect the primary voice conversion.

 Additional Information

• Voice and Tense Consistency:
• Active Voice: Focuses on the subject performing the action. For the Future Perfect Tense, this always uses will have + past participle.
• Passive Voice: Focuses on the object receiving the action. It always includes the auxiliary been between have and the past participle.
• Evaluation of Tense Mismatches:
• Present Continuous: Phrases like Are the partners signing imply an action currently in progress, which fails to represent the completion aspect of the Perfect Tense.
• Simple Past: Using Did the partners sign shifts the timeline to a completed event in the past, losing the future probability indicated by will.
• Present Perfect: The form Have the partners signed indicates an action completed at an unspecified time before now, which does not match the future deadline context of the original sentence.

The correct answer is Please send us a copy of your passport..

Key Points

• The given sentence 'You are requested to send us a copy of your passport' is in the Passive Voice. It follows the structure of an imperative sentence expressing a request.
• When converting passive voice sentences that begin with 'You are requested to' into active voice, the phrase is replaced with the word 'Please' to maintain the same polite tone and mood.
• The verb that follows the infinitive marker 'to' (which is 'send') becomes the main verb of the active voice sentence.
• The structure for an Active Imperative request is: Please + Verb (Base Form) + Object/Remaining predicate. Applying this rule, the sentence becomes 'Please send us a copy of your passport.'
• The subject 'You' is implied in imperative sentences, which is why it is omitted in the active form.

 Additional Information

• Imperative Sentences:
• These sentences are used to express orders, requests, suggestions, or advice.
• In Active Voice, they usually begin with a verb or 'Please'/'Kindly'.
• In Passive Voice, requests are transformed using 'You are requested to', while commands often use the 'Let + object + be + past participle' structure.
• Evaluation of Other Options:
• 'Let a copy of your passport be sent to us': This is a Passive Voice construction using the 'Let' format, which is typically used for orders rather than polite requests.
• 'Send us a copy of your passport': This is an active imperative, but it functions as a direct command and loses the request nuance provided by 'requested' in the original sentence.
• 'We request your passport copy': While grammatically active, it changes the syntactic structure of the original request and is less common as a direct conversion of an imperative request.

The correct answer is Option 1.

 

Key Points

• The error lies in the first part of the sentence: 'It was rude about the'.
• In English grammar, when we use an adjective to describe someone's behavior or character in the structure It + be + adjective + [person] + to-infinitive, the preposition 'of' must be used.
• Common adjectives used in this pattern include kind, polite, rude, generous, clever, and silly.
• Therefore, the preposition 'about' should be replaced with 'of' to make the sentence grammatically correct.
• The correct phrase is 'It was rude of the'.

Therefore, the correct answer is Option 1.

 

Correct Sentence: 'It was rude of the professor's daughter to have rejected the red rose which was being given by the young student.'

 

Additional Information

• professor's daughter to have – This part is correct. The perfect infinitive ('to have rejected') is used to refer to an action that occurred in the past.
• rejected the red rose which was – This part is grammatically sound, using the relative pronoun 'which' to refer back to the rose.
• being given by the young student – This part correctly uses the past continuous passive voice ('was being given') to describe the action performed by the student.

The correct answer is 'after'.

 

Key Points

• The phrasal verb 'take after' means to resemble an older relative in appearance or character.
• In the given sentence, the comparison is between Namrata and her mother regarding their physical resemblance (specifically their height).
• The preposition 'after' correctly completes the phrasal verb to show that Namrata looks like her mother.

Therefore, the correct answer is Option 2.

 

Complete Sentence: 'Namrata takes after her mother, even with the same height.'

 

Additional Information

• 'Take by' is generally used in phrases like 'take by surprise' or 'take by the hand'.
• 'Take for' means to believe someone or something to be a particular person or thing, often wrongly (e.g., 'I took him for a doctor').
• 'Take with' usually implies carrying something or accompanying someone.