SSC GD Constable 2026 Official Paper (Held On 19 May, 2026 Shift 2) (Previous Year Paper)

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

For the set '(TN, RG, PZ)':

For the set '(CR, AK, YD)':

Applying the same logic to '(TO, RH, PA)':

Thus, the cluster set (TO, RH, PA) follows the same logic.

Hence, the correct answer is 'Option 3'.

Given that 11 July 2016 was a Monday.

We need to find the day on 11 December 2016.

Number of days between 11 July and 11 December:

Remaining days in July: 31 − 11 = 20 days

Days in August: 31 days

Days in September: 30 days

Days in October: 31 days

Days in November: 30 days

Days in December: 11 days

Total number of days = 20 + 31 + 30 + 31 + 30 + 11 = 153 days

Now, calculate the number of odd days:

Odd days = 153 ÷ 7

153 = (21 × 7) + 6

The remainder is 6, so there are 6 odd days.

Counting 6 days forward from Monday:

Monday + 6 days = Sunday

Hence, the day on 11 December 2016 was Sunday.

Hence, the correct answer is “Option 3”.

 

Alternate Method

We can calculate odd days for each month separately to simplify the calculation:

July (remaining): 20 days → 20 ÷ 7 = 2 weeks and 6 odd days

August: 31 days → 31 ÷ 7 = 4 weeks and 3 odd days

September: 30 days → 30 ÷ 7 = 4 weeks and 2 odd days

October: 31 days → 31 ÷ 7 = 4 weeks and 3 odd days

November: 30 days → 30 ÷ 7 = 4 weeks and 2 odd days

December (until 11^th): 11 days → 11 ÷ 7 = 1 week and 4 odd days

Total odd days = 6 + 3 + 2 + 3 + 2 + 4 = 20 odd days

Final odd days = 20 ÷ 7 = 2 weeks and 6 odd days

Monday + 6 days = Sunday

Therefore, the correct answer is Sunday.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

AD182 : GD90 → 

FK312 : NI220 → 

Similarly, 

ET202 : ? →

Hence, the correct answer is 'Option 1'.

AKM32 : DNJ64 →

DMO26 : GPL52 →

Similarly,  

? : FTJ42

 

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: First Number = Second Number + 51

For the first pair 854 : 803

⇒ 803 + 51 = 854

For the second pair 2210 : 2159

⇒ 2159 + 51 = 2210

Applying the same logic to the third pair

? : 9585

⇒ 9585 + 51 = 9636

Hence, the correct answer is 'Option 4'.

The logic followed here is:

Logic: Second Number = (First Number × 2) − 3

For the first pair 151 : 299

⇒ (151 × 2) − 3

⇒ 302 − 3 = 299.

For the second pair 446 : 889

⇒ (446 × 2) − 3

⇒ 892 − 3 = 889.

Applying the same logic to the third pair

? : 1641

⇒ (Missing Number × 2) − 3 = 1641

⇒ Missing Number × 2 = 1641 + 3

⇒ Missing Number × 2 = 1644

⇒ Missing Number = 1644 ÷ 2

⇒ Missing Number = 822.

Hence, the correct answer is 'Option 2'.

Given:

Code for 'chess patience' is "ta da".

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 4”.

​Between 12 PM and 1 PM, the initial angle at 12:00 is 00.

We need to find the time when the angle is 40 degrees.

Time (M) = Angle ÷ Relative speed

M = 40 ÷ 5.5

M = 400 ÷ 55 = 80 ÷ 11

M ≈ 7.27 minutes

The time is approximately 7 minutes past 12, which is 12:07 PM.

Hence, the angle between the hands is 400 at approximately 12:07.

Hence, the correct answer is “Option 1”.

 

Alternate Method

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

Angle = |30H − 5.5M|

For time between 12 PM and 1 PM, we can use H = 0 (considering 12 as the origin).

40 = |30 × 0 − 5.5M|

40 = |−5.5M|

5.5M = 40

M = 40 ÷ 5.5 ≈ 7.27

Thus, the time is approximately 12:07 PM.

Therefore, the correct answer is 12:07

 Important Points

The hour hand covers 3600 in 12 hours.

Angular distance covered by the hour hand in 1 minute = 360 ÷ (12 × 60) = 0.50

The minute hand covers 3600 in 60 minutes.

Angular distance covered by the minute hand in 1 minute = 360 ÷ 60 = 60

Relative speed between the hands = 60 − 0.50 = 5.50 per minute.

​At 8 AM, the angle covered by the hour hand from the 12 o'clock mark = 8 × 30 = 2400

At 8 AM, the minute hand is at 00

The relative speed of the minute hand over the hour hand = 6 − 0.5 = 5.50 per minute

For the hands to be opposite to each other, the angle between them must be 1800

Between 8 AM and 9 AM, the minute hand must gain (240 − 180) = 600 over the hour hand

Time required = 60 ÷ 5.5 = 120/11 ≈ 10.91 minutes

So, the approximate time is 8:11 AM

Hence, the correct answer is “Option 1”.

Alternate Method

The angle between the hour hand and minute hand is given by: $\text{Angle} = |30H - \frac{11}{2}M|$

Here, H = 8 and the required opposite angle is 1800

180 = |30 × 8 − 5.5 × M|

180 = |240 − 5.5M|

5.5M = 240 − 180 = 60

M = 60 ÷ 5.5 = 10.909... ≈ 11

Hence, the approximate time is 8:11 AM

Important Points

Hour hand covers 3600 in 12 hours

Angular distance covered in 1 hour = 360 ÷ 12 = 300

Angular distance covered in 60 minutes = 300

Angular distance covered in 1 minute = 30 ÷ 60 = 1/20

Minute hand covers 3600 in 60 minutes

1 minute = 360 ÷ 60 = 60

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

The ratio of present ages of two persons = 5 : 12

The sum of their present ages = 34

Let the present ages of the two persons be 5x and 12x.

Sum: 5x + 12x = 34

17x = 34

x = 34 ÷ 17 = 2

 

Ages 3 years ago from now:

First person = 10 − 3 = 7 years

Second person = 24 − 3 = 21 years

Similarly, let's find the ratio 3 years ago:

Ratio = 7 : 21

On simplifying the ratio by dividing both numbers by 7:

Ratio = (7 ÷ 7) : (21 ÷ 7)

Ratio = 1 : 3

Hence, the correct answer is “Option 3”.

The correct answer is 0.1 s.

Key Points

• The persistence of hearing is the phenomenon where the sensation of a sound remains in the human brain for a short duration after the source has stopped vibrating.
• For the human ear, this sensation persists for approximately 0.1 seconds (or 1/10^th of a second).
• This time interval is critical for the brain to distinguish between two separate sounds; if a second sound reaches the ear within 0.1 s of the first, the brain perceives them as a single, overlapping sound.
• The concept of persistence of hearing is the biological basis for hearing an echo, which requires the reflected sound to arrive at the ear after the initial 0.1 s period has elapsed.
• It ensures that sound signals are processed effectively by the auditory cortex, allowing for the continuity of speech and music perception without immediate decay.

 Additional Information

• Echo and Minimum Distance:
• To hear a distinct echo, the total distance traveled by the sound (from source to obstacle and back) must be such that the time taken is at least 0.1 s.
• Given the speed of sound in air is roughly 344 m/s at 22 degrees Celsius, the total distance is calculated as 344 m/s × 0.1 s = 34.4 m.
• Consequently, the minimum distance between the source of sound and the reflecting body must be half of this, which is 17.2 m.
• Reverberation:
• In enclosed spaces like concert halls, sound may undergo multiple reflections. If these reflections reach the listener within the 0.1 s window, they cause a prolonged sensation called reverberation.
• Excessive reverberation can make sound blurred or difficult to understand, which is why acoustic engineers use sound-absorbing materials like perforated cardboard or heavy drapes.
• Auditory System Components:
• The process involves the outer ear (pinna) collecting sound, the middle ear (ossicles) amplifying it, and the inner ear (cochlea) converting vibrations into electrical signals for the brain.

The correct answer is Nallamalai Hills.

Key Points

• The Eastern Ghats are a discontinuous and weathered mountain range that stretches along the eastern coast of India, running parallel to the Bay of Bengal.
• The Nallamalai Hills are one of the primary hill ranges that constitute the Eastern Ghats, located primarily in the states of Andhra Pradesh and Telangana.
• Geographically, these hills are located between the Krishna River and the Pennar River, forming part of the Cuddapah Basin.
• They are characterized by ancient rock formations including quartzites and slates, and they run in a north-south direction roughly parallel to the Coromandel Coast.
• Unlike the Western Ghats, which are continuous, the Eastern Ghats (including the Nallamalai range) are dissected by major peninsular rivers such as the Godavari and Krishna.
• The average elevation of the Nallamalai Hills is approximately 900 to 1,100 meters, with Bhairani Konda being one of the highest peaks in the region.

 Additional Information

• Nilgiri Hills:
• Commonly known as the Blue Mountains, these hills are located at the convergence of the Western Ghats and the Eastern Ghats.
• They are situated primarily in Tamil Nadu, with Doddabetta (2,637 meters) serving as their highest peak.
• Rajmahal Hills:
• These hills are located in the Jharkhand state and were formed from volcanic activity during the Jurassic Period.
• They form the northeastern part of the Chota Nagpur Plateau.
• Maikal Hills:
• This range is the eastern part of the Satpura Range, located in the state of Chhattisgarh.
• It acts as a watershed for major rivers including the Narmada, Son, and Mahanadi.

The correct answer is Trade, Investment, and Finance.

Key Points

• Brazil is set to assume the BRICS Presidency in 2025, following the Russian Federation’s tenure in 2024.
• The sector of Trade, Investment, and Finance is a primary flagship priority, aiming to bolster economic integration and increase the volume of intra-BRICS trade among member nations.
• A critical component of this priority is the advancement of the BRICS Cross-Border Payments Initiative, which seeks to facilitate transactions in local currencies and reduce the collective dependency on the US Dollar.
• Brazil emphasizes financial cooperation through the New Development Bank (NDB) to fund large-scale infrastructure and sustainable development projects across the expanded BRICS+ framework.
• The priority also encompasses the harmonization of customs procedures, e-commerce regulation, and the promotion of small and medium enterprises (SMEs) within the global value chain.

 Additional Information

• BRICS Evolution and Expansion:
• The group was formally established in 2006, with South Africa joining the original four members in 2010.
• In January 2024, the bloc underwent a historic expansion, officially welcoming Egypt, Ethiopia, Iran, and the United Arab Emirates (UAE).
• Global Governance Reform:
• Brazil’s 2025 agenda includes a strong push for the reform of multilateral institutions like the United Nations Security Council, the International Monetary Fund (IMF), and the World Trade Organization (WTO).
• Sustainable Development:
• The 2025 Summit will focus on the energy transition, bioeconomy, and climate action, aligning with Brazil’s role as the host of COP30 in Belem.

The correct answer is High rural literacy rate reducing labour supply.

Key Points

• Between 1950 and 1990, the rural literacy rate in India was remarkably low; according to the 1951 Census, the national literacy rate was only 18.33%, with rural figures being even lower, which directly contradicts the notion of high literacy reducing labor supply.
• Indian agriculture during this period was characterized by disguised unemployment, a condition where the number of people working on a farm is far greater than what is actually required, resulting in surplus labor rather than a shortage.
• The real challenge was mass illiteracy among farmers, which acted as a barrier to the adoption of modern agricultural practices, understanding pesticide labels, and managing institutional credit.
• The labor supply remained abundant because of rapid population growth and the lack of non-farm employment opportunities in rural areas, ensuring that labor was never a constraint for agricultural production.

 Additional Information

• Fragmented landholdings:
• This was a major institutional challenge caused by the Law of Succession, where ancestral land was divided among all heirs, leading to small, uneconomic plots that hindered the use of modern machinery like tractors.
• Dependence on monsoon rainfall:
• Due to the lack of comprehensive irrigation infrastructure, Indian agriculture was often termed a gamble on the monsoon; any delay or failure in the Southwest Monsoon led to drastic drops in foodgrain production.
• Low use of fertilizers and irrigation:
• Prior to the Green Revolution in the mid-1960s, the application of chemical fertilizers (NPK) was extremely low, and irrigation facilities were restricted to only about 17% of the total cultivated area in 1951.
• Even after the Green Revolution, the intensive use of High Yielding Variety (HYV) seeds and fertilizers was initially concentrated only in regions like Punjab, Haryana, and Western Uttar Pradesh.

The correct answer is Third Plan.

Key Points

• The Third Five-Year Plan (1961-1966) was designed to make India a self-reliant and self-generating economy, placing its primary focus on agricultural expansion and basic industries.
• The execution of this plan was severely disrupted by external conflicts, primarily the Sino-Indian War (Indo-China War) of 1962, followed shortly by the Indo-Pakistani War of 1965.
• These major defense crises forced the Indian government to divert crucial developmental funds toward defense spending and military stabilization, practically halting planned development.
• As a consequence of this structural disruption and severe inflation, the plan fell short of its targeted growth rate of 5.6%, achieving only 2.4%, leading directly to the implementation of Plan Holidays from 1966 to 1969.

 Additional Information

• First Five-Year Plan (1951-1956):
• Formulated based on the Harrod-Domar model, focusing heavily on irrigation, dams, and the agricultural sector to address food shortages.
• Second Five-Year Plan (1956-1961):
• Formulated based on the Mahalanobis model, emphasizing rapid industrialization, heavy domestic industries, and public sector expansion.
• Fourth Five-Year Plan (1969-1974):
• Launched after the Plan Holidays, focusing on growth with stability and progressive achievement of self-reliance, which also witnessed the nationalization of 14 major Indian banks.

The correct answer is Rock-cut cave temples at Badami.

Key Points

• The Chalukyas of Badami, also known as the Early Chalukyas, ruled parts of southern and central India from the 6^th to the 8^th century CE, with their capital at Vatapi (modern-day Badami in Karnataka).
• Their most significant contribution to Indian art is the creation of the Badami cave temples, a complex of four massive temples carved out of the local red sandstone cliffs.
• Cave 1 is dedicated to Lord Shiva and contains the iconic relief of an eighteen-armed Nataraja, which displays 81 different dance poses (mudras).
• Cave 2 and Cave 3 are dedicated to Lord Vishnu; Cave 3 is the largest and most ornately decorated, featuring monumental carvings of Trivikrama, Varaha, and Narasimha.
• Cave 4 is a Jain cave dating back to the late 6^th or early 7^th century, housing beautiful sculptures of Tirthankaras like Lord Mahavira and Parshvanatha.
• These caves represent a crucial evolutionary stage in Indian rock-cut architecture, serving as a stylistic bridge between the earlier Ajanta-Ellora traditions and the later structural temples of the Deccan.

 Additional Information

• Bronze sculpture of Nataraja:
• This art form reached its zenith under the Chola Dynasty (9^th-13^th century) in Tamil Nadu.
• The Chola bronzes were created using the lost-wax technique (Cire Perdue) and are globally recognized for their aesthetic elegance and symbolic complexity.
• Nagara style temples:
• The Nagara style is the primary architectural style of North Indian temples, characterized by a curvilinear shikhara (tower).
• The Chalukyas of Badami primarily experimented with a hybrid style known as the Vesara style, which combines elements of both Nagara and Dravida (South Indian) architecture.
• Pattadakal and Aihole:
• The Chalukyan era also saw the construction of major structural temples at Aihole (the 'Cradle of Indian Temple Architecture') and Pattadakal.
• Pattadakal is a UNESCO World Heritage site containing ten major temples, including the famous Virupaksha Temple built by Queen Lokamahadevi.

The correct answer is Real income.

Key Points

• National income measured at constant prices, also referred to as Real National Income, is the total value of all final goods and services produced by a nation in a year, calculated using the prices of a specific base year.
• By using constant prices, the calculation eliminates the distortions caused by inflation or deflation, providing a more accurate representation of the actual physical output and economic progress of a country.
• The formula to derive this value is: Real National Income = (National Income at Current Prices ÷ Price Index of the Current Year) × 100.
• This metric is vital for macroeconomic analysis as it allows for meaningful long-term comparisons of the standard of living and the productive capacity of the economy without being misled by nominal price fluctuations.

 Additional Information

• Nominal income
• It is the national income measured at current market prices prevailing in the same year the goods and services are produced.
• It may show an increase even if production volume remains stagnant, provided there is a rise in the general price level.
• Disposable income
• This represents the portion of Personal Income that households actually have available to spend or save.
• It is calculated by subtracting Direct Taxes (like income tax) and other miscellaneous receipts of the government from the total income received by individuals.
• Net factor income
• Often termed Net Factor Income from Abroad (NFIA), it is the difference between income earned by domestic residents from their factors of production located abroad and income earned by foreign residents within the domestic territory.
• It is the key variable used to convert Gross Domestic Product (GDP) into Gross National Product (GNP).

The correct answer is Charter Act of 1853.

Key Points

• The Charter Act of 1853 was a landmark piece of legislation that introduced a system of open competition for the selection and recruitment of civil servants in India.
• This act removed the discretionary power of nomination previously held by the Court of Directors of the East India Company, thereby ending the patronage-based entry into the services.
• The covenanted civil service was thrown open to Indians for the first time, allowing them to participate in the competitive examination conducted in London.
• This reform aimed to ensure that the civil service was staffed by individuals of high intellectual caliber and merit, regardless of their background or connections.
• The act also mandated a significant structural change by separating the legislative and executive functions of the Governor-General’s Council.

 Additional Information

• Macaulay Committee:
• In 1854, the Committee on the Indian Civil Service was established under the leadership of Lord Macaulay to finalize the details of the recruitment process.
• The committee reinforced the principle that recruitment should be based on a high-standard academic examination rather than nomination.
• Charter Act of 1833:
• This act attempted to introduce open competition but the clause was negated due to fierce opposition from the Court of Directors.
• It designated the Governor-General of Bengal as the Governor-General of India, concentrating power in a single central authority.
• Indian Councils Act of 1861:
• This act introduced the portfolio system and included Indians as non-official members in the legislative councils.
• It marked the beginning of representative institutions by associating Indians with the law-making process.
• Satyendranath Tagore:
• He became the first Indian to qualify for the Indian Civil Service in 1863, effectively utilizing the provisions established by the 1853 Act.

The correct answer is To offer vocational training to adolescent girls aged 16-18.

Key Points

• The NAVYA program, officially launched in June 2025, is a specialized initiative designed to bridge the gap between secondary education and professional employment for young women.
• The program specifically targets adolescent girls in the 16-18 age group, a critical demographic transition phase where many students drop out of the formal education system.
• Its primary objective is the provision of vocational training and skill development in high-growth sectors such as Information Technology, Healthcare, Digital Marketing, and Textile Design.
• By focusing on employability, the scheme aims to enhance the Labor Force Participation Rate (LFPR) among women and foster economic independence from a young age.
• The initiative aligns with the National Skill Qualification Framework (NSQF), ensuring that the training received is industry-recognized and provides certified credentials for the job market.

 Additional Information

• Vocational Training and its Importance:
• Unlike Higher Education, which focuses on academic degrees, vocational training emphasizes hands-on expertise and technical proficiency in specific trades.
• It helps in creating a skilled workforce that meets the immediate demands of the industrial sector and the service economy.
• The focus on the 16-18 age group is strategic, as it provides a professional alternative to those who may not wish to pursue traditional university education.
• Socio-Economic Impact:
• By empowering girls with market-relevant skills, the program supports Sustainable Development Goal 5 (Gender Equality) and Goal 8 (Decent Work and Economic Growth).
• It acts as a deterrent against early marriages and financial dependency by equipping girls with the means to secure sustainable livelihoods.

Therefore, the primary objective of the NAVYA program is to provide vocational training to girls aged 16-18, making this the correct answer.

The correct answer is 64900.

Key Points

• The NAMASTE scheme, which stands for National Action for Mechanised Sanitation Ecosystem, is a specialized Central Sector Scheme designed to ensure the safety, dignity, and sustainable livelihoods of sanitation workers.
• As of August 2025, a total of 64,900 Sewer and Septic Tank Workers (SSWs) have been successfully profiled and validated through a rigorous identification process across various Urban Local Bodies (ULBs).
• The validation of these 64,900 workers is a critical step in creating a national database that facilitates the delivery of targeted welfare benefits and mechanized cleaning equipment.
• The scheme focuses on the formalization of the sanitation workforce, transitioning them from hazardous manual practices to mechanized sanitation operations to achieve the goal of zero fatalities in sewer cleaning.

 Additional Information

• Institutional Framework:
• The scheme is a joint initiative implemented by the Ministry of Social Justice and Empowerment (MoSJE) and the Ministry of Housing and Urban Affairs (MoHUA).
• It replaces the previous Self-Employment Scheme for Rehabilitation of Manual Scavengers (SRMS) to provide a more comprehensive safety net.
• Core Objectives:
• Providing health insurance coverage to all validated workers under the Ayushman Bharat-Pradhan Mantri Jan Arogya Yojana (AB-PMJAY).
• Ensuring that all Sewer and Septic Tank Workers have access to Personal Protective Equipment (PPE) and safety training.
• Offering capital subsidies of up to 5 lakh rupees to help sanitation entrepreneurs purchase specialized vacuum loaders and high-pressure jetting machines.
• The scope of the scheme has been expanded from 500 AMRUT cities to cover every Urban Local Body in the country.

The correct answer is Bhortal Nritya.

Key Points

• Bhortal Nritya is a traditional folk dance originating from the Barpeta district of Assam, which is a major center for Vaishnavite culture.
• The dance was conceptualized and developed by the noted Sattriya artist and Sattradhikar, Narahari Burha Bhakat, based on the rhythmic elements of the Sankari culture.
• It is performed using large cymbals known as Bhortal, which are made of bell metal and weigh significantly, requiring dancers to exhibit great strength and agility.
• The performance is executed by a group of 6 to 10 dancers who create intricate rhythmic patterns called Thok while maintaining a fast-paced tempo.
• The choreography is highly synchronized and often represents symbolic movements like the swaying of boats or the flight of birds, reflecting the spiritual and natural heritage of the Brahmaputra Valley.

 Additional Information

• Gendi:
• This is a folk dance associated with the Gondi tribe of Chhattisgarh.
• Dancers perform while balanced on bamboo stilts (Gendi), moving through fields and villages during festivals like Hareli to celebrate the rainy season.
• Kayang:
• A traditional dance form from the Kinnaur region of Himachal Pradesh.
• The dancers interlock their arms to form a chain like a garland (Kayang) and move in circular or linear formations to the accompaniment of local musical instruments.
• Chakyar Koothu:
• An ancient performance art from Kerala, traditionally staged in the Koothambalam (temple theater).
• It is a solo performance by the Chakyar community involving highly stylized gestures, facial expressions, and a unique satirical narration of stories from the Mahabharata and Ramayana.

The correct answer is Jamnagar.

Key Points

• In January 2025, India launched its inaugural dedicated census of coastal and wader birds, marking a significant step in avian conservation and migratory studies.
• The census was kicked off in Jamnagar, Gujarat, which is recognized globally for its vast intertidal mudflats and unique marine ecosystems that attract millions of birds annually.
• The exercise is a collaborative scientific project spearheaded by the Bombay Natural History Society (BNHS) in partnership with the Gujarat Forest Department to establish a baseline for shorebird populations.
• Jamnagar serves as a crucial hub along the Central Asian Flyway (CAF), a major migratory route where birds from the Arctic and Siberian regions spend their winter months.
• The survey focuses on waders, also known as shorebirds, which are highly sensitive to changes in coastal health and serve as vital biological indicators of the ecosystem.

 Additional Information

• Coastal and Wader Birds:
• These species belong primarily to the order Charadriiformes and are characterized by long legs and specialized bills for feeding in shallow water and mud.
• Key species being monitored include the Great Knot, Crab Plover, Sanderling, and the Bar-tailed Godwit.
• Marine National Park:
• Located in the Gulf of Kutch near Jamnagar, it was established in 1982 as India's first Marine National Park.
• The park covers an area of approximately 163 square kilometers and protects diverse habitats including coral reefs, mangroves, and seagrass beds.
• The region provides critical foraging grounds during low tide, where waders search for crustaceans, mollusks, and polychaete worms.

The correct answer is Karnataka.

Key Points

• The Godachi Fair is a significant socio-religious event celebrated annually in the Godachi village, which is located in the Ramdurg taluk of the Belagavi district in Karnataka.
• The fair is dedicated to Lord Veerabhadra, a fierce manifestation of Lord Shiva, who is the principal deity of the temple situated in this village.
• It is traditionally observed during the Hindu month of Margashira (falling between November and December) and reaches its peak on the Poornima (full moon day), attracting thousands of devotees.
• The Sri Veerabhadra Swamy Temple at Godachi is historically significant, featuring architectural elements that represent a blend of the Chalukyan and Vijayanagara eras.
• This fair serves as a vital cultural gathering for the people of North Karnataka, involving various traditional rituals, local commerce, and folk performances.

 Additional Information

• Gujarat:
• Famous for the Tarnetar Mela, which is a significant tribal fair celebrated at the Trinetreshwar Mahadev temple near Thangadh.
• Assam:
• Known for the Ambubachi Mela held at the Kamakhya Temple in Guwahati, which celebrates the presiding goddess of the temple.
• Haryana:
• Renowned for the Surajkund International Crafts Mela in Faridabad, which showcases the rich diversity of Indian handicrafts, handlooms, and cultural heritage.
• Belagavi District:
• Known as the Sugar Bowl of Karnataka, it is a hub for diverse cultural festivities, including the Kittur Utsav and various regional Jatras.

The correct answer is 94.00%.

Key Points

• According to the 2011 Census, Kerala remains the most literate state in India with a total literacy rate of 94.00%.
• The state exhibits a high level of educational attainment across genders, with male literacy recorded at 96.11% and female literacy at 92.07%.
• Kerala has a long history of social reform movements and government initiatives, such as the Total Literacy Campaign, which contributed to achieving this milestone.
• The gap between male and female literacy in the state is among the narrowest in the country, reflecting a high degree of gender equality in access to education.
• Educational development in Kerala is supported by a robust network of government-aided schools and a high priority on primary education in state budgeting.

 Additional Information

• National Literacy Statistics (2011 Census):
• The average literacy rate of India was 74.04%.
• The national male literacy rate stood at 82.14%, while the female literacy rate was 65.46%.
• State-wise Comparisons:
• Bihar was identified as the state with the lowest literacy rate at 61.80%.
• Among Union Territories, Lakshadweep recorded the highest literacy rate at 91.85%.
• The state of Mizoram ranked second in literacy with a rate of 91.33%.
• Census Definition of Literacy:
• For the purpose of the Census 2011, a person aged 7 years and above who can both read and write with understanding in any language is considered literate.

The correct answer is Both I and II.

Key Points

• Rice cultivation in Southern India is not restricted to a single season due to the prevailing tropical climate and availability of irrigation facilities. In the Rabi season, which typically spans from November to April, rice is extensively grown in states like Andhra Pradesh, Tamil Nadu, and Telangana, where it is often referred to by local names such as Dalwa or Navarai. Hence, statement I is correct.
• The Kharif season, running from June to October, is the primary cropping season for rice across the country, including the Southern states. This season coincides with the Southwest Monsoon, providing the necessary high rainfall and humidity required for the initial growth phase of the paddy crop. Hence, statement II is correct.

 Additional Information

• Rice Cultivation Profile:
• Climatic Requirements: Rice is a tropical crop that requires high temperatures, generally above 25 degrees Celsius, and high humidity. It necessitates an annual rainfall of over 100 cm; in areas with less rainfall, it is grown with the help of canal irrigation and tube wells.
• Soil and Geography: The most suitable soil for rice is alluvial soil with a clayey base that can retain water. India is the second-largest producer of rice globally, with West Bengal, Uttar Pradesh, and Punjab being leading producers alongside Southern states.
• Cropping Patterns: In certain regions like West Bengal and the Brahmaputra Valley, three crops of paddy are grown in a single year, known as Aus, Aman, and Boro.
• Agricultural Methods: Cultivation involves various methods such as transplanting (most common), broadcasting, and the drilling method, often requiring significant manual labor.

The correct answer is 2008.

Key Points

• The Indian Premier League (IPL) was established by the Board of Control for Cricket in India (BCCI) in 2007, and the first season was played in 2008.
• The inaugural match of the 2008 season took place on April 18, 2008, at the M. Chinnaswamy Stadium in Bangalore.
• The first season featured eight teams, including franchises from Mumbai, Chennai, Delhi, Hyderabad, Jaipur, Kolkata, Mohali, and Bangalore.
• Rajasthan Royals, led by the legendary Australian spinner Shane Warne, emerged as the champions of the first season.
• The final match was held at the DY Patil Stadium in Navi Mumbai, where Rajasthan Royals defeated Chennai Super Kings by 3 wickets.
• Shane Watson was named the Player of the Tournament for his outstanding contribution with both bat and ball throughout the 2008 edition.

 Additional Information

• IPL Evolution and Structure:
• The league follows a Twenty20 (T20) format, which significantly increased the pace and popularity of cricket globally.
• In 2009, the second season was shifted to South Africa due to the Indian General Elections, where Deccan Chargers claimed the title.
• The 2010 season returned to India and saw Chennai Super Kings winning their first trophy under the leadership of MS Dhoni.
• By 2011, the league expanded to ten teams with the addition of Pune Warriors India and Kochi Tuskers Kerala.
• The IPL has become the most-attended cricket league in the world and ranks among the top sports leagues by average attendance.
• Individual awards like the Orange Cap for the highest run-scorer and the Purple Cap for the leading wicket-taker were introduced to recognize top performers.

The correct answer is 1951.

Key Points

• The Volleyball Federation of India (VFI) is the supreme governing body for the sport of volleyball in India, and it was officially established in the year 1951.
• Prior to the formation of the federation, the Indian Olympic Association (IOA) controlled the sport in the country from 1936 to 1950, organizing interstate championships every two years.
• The first National Championship for men under the newly formed VFI was held in 1952 at Ludhiana, marking a significant milestone in the structured development of the game in India.
• The federation is affiliated with the Federation Internationale de Volleyball (FIVB) and the Asian Volleyball Confederation (AVC), ensuring India's participation in global and continental events.
• Following the establishment of the VFI, the National Championship for Women was also introduced, starting in 1953.

 Additional Information

• International Governance and Context:
• The Federation Internationale de Volleyball (FIVB), the global administrative body for the sport, was founded in April 1947 in Paris and is currently headquartered in Lausanne, Switzerland.
• Volleyball was introduced to the Asian Games for the first time in 1958 during the Tokyo edition, where the Indian Men's Team secured a Gold Medal.
• The sport attained Olympic status during the 1964 Tokyo Olympics, further boosting the professionalization efforts of national federations like the VFI.
• In India, the Volleyball Federation of India oversees various formats, including Indoor Volleyball and Beach Volleyball, and manages the Prime Volleyball League to enhance the sport's domestic popularity.

The correct answer is Kabaddi.

Key Points

• In the sport of Kabaddi, the Toe touch is a vital offensive skill used by the raider to touch an anti (defender) using their foot while maintaining a safe distance.
• The technique requires the raider to extend their leg rapidly to tag the defender's foot or lower leg with the toes, allowing them to score a point without getting deep into the opponent's territory.
• Successful execution of a toe touch relies heavily on agility, flexibility, and timing, as the raider must be prepared to retract their leg immediately to avoid an ankle hold.
• This move is often used to surprise defenders who are focused on the raider's upper body movements, hand reach, or lateral shifting during the raid.

 Additional Information

• Beyond the toe touch, Kabaddi involves several other technical skills classified into offensive and defensive maneuvers:
• Hand Touch: An offensive move where the raider extends their arm to touch a defender; variations include the running hand touch and turning hand touch.
• Dubki: A specialized move where the raider escapes a chain tackle by ducking low beneath the defenders' arms.
• Frog Jump: An athletic move where the raider jumps over the defensive line to escape a thigh hold or block.
• Ankle Hold: A fundamental defensive skill where a corner defender captures the raider's ankle to prevent them from reaching the mid-line.
• Bonus Line: A technical line in Kabaddi; a raider can earn a bonus point by crossing this line with one foot while the other is in the air, provided there are at least 6 or 7 defenders on the mat.

The correct answer is TMF Group.

Key Points

• The Global Business Complexity Index (GBCI) is an authoritative annual report that provides an in-depth analysis of the global and local environments for business compliance and administration.
• The report is published by TMF Group, a leading global provider of high-value business services to organizations operating and investing globally.
• The 2025 edition continues to rank various jurisdictions (typically around 79 jurisdictions) based on their complexity for multinational companies to operate in, covering accounting, tax, payroll, and legal compliance.
• The index uses a quantitative and qualitative methodology, aggregating thousands of data points across factors such as regulatory changes, technological adoption, and geopolitical stability.
• It serves as a benchmark for Foreign Direct Investment (FDI) decisions by highlighting how different regions manage transparency and digitalization in business processes.

 Additional Information

• TMF Group:
• Headquartered in Amsterdam, Netherlands, it assists businesses in navigating the legal and regulatory requirements of over 80 jurisdictions.
• It focuses on helping companies manage entity life cycles and cross-border expansion.
• International Monetary Fund (IMF):
• A major financial agency of the United Nations that publishes the World Economic Outlook and the Global Financial Stability Report.
• It focuses on macroeconomic stability and poverty reduction rather than specific business administrative complexity.
• World Trade Organization (WTO):
• The global body overseeing the rules of international trade between member nations.
• It is primarily concerned with trade barriers, tariffs, and dispute settlement.
• Economist Intelligence Unit (EIU):
• A research and analysis division that produces the Democracy Index and Global Liveability Index.
• It provides country risk assessments and economic forecasting services.

The correct answer is 2009.

Key Points

• The National Ambient Air Quality Standards (NAAQS) were revised and notified by the Central Pollution Control Board (CPCB) in November 2009, replacing the previous standards from 1994.
• These standards are formulated under the Air (Prevention and Control of Pollution) Act, 1981, which empowers the central government to set limits on pollutants to protect public health and the environment.
• The 2009 notification specifically listed 12 pollutants to be monitored: Sulphur Dioxide (SO2), Nitrogen Dioxide (NO2), Particulate Matter (PM10), Particulate Matter (PM2.5), Ozone (O3), Lead (Pb), Carbon Monoxide (CO), Ammonia (NH3), Benzene, Benzo(a)pyrene, Arsenic, and Nickel.
• A major shift in the 2009 standards was the adoption of uniform air quality limits across industrial, residential, and rural areas, whereas previous versions had different permissible limits for different land-use categories.
• The monitoring of these pollutants is essential for the National Air Quality Monitoring Programme (NAMP), which tracks the status of air quality in various cities across India.

 Additional Information

• Central Pollution Control Board (CPCB):
• It is a statutory organization constituted in September 1974 under the Water (Prevention and Control of Pollution) Act, 1974.
• It provides technical guidance to the Ministry of Environment, Forest and Climate Change (MoEFCC) and coordinates the activities of State Pollution Control Boards (SPCBs).
• National Air Quality Index (AQI):
• Launched in October 2014, the AQI is a tool to communicate air quality status to people in terms that are easy to understand (e.g., Good, Satisfactory, Poor).
• While NAAQS monitors 12 pollutants, the AQI focuses on eight major pollutants: PM10, PM2.5, NO2, SO2, CO, O3, NH3, and Pb.
• National Clean Air Programme (NCAP):
• This was launched in January 2019 as a long-term, time-bound strategy to tackle the air pollution problem across the country.
• It targets a 20−30% reduction in PM2.5 and PM10 concentrations by 2024, taking 2017 as the base year for comparison.

Shortcut Trick

Apply BODMAS rule: Solve Bracket first, then Multiplication.

62 + 83 − 38 + (50) × 2 − 89

62 + 83 − 38 + 100 − 89

145 + 100 − 38 − 89 = 245 − 127 = 118

∴ The correct answer is 118.

Alternate Method

Given: 62 + 83 − 38 + (36 + 14) × 2 − 89

Formula: Follow the BODMAS hierarchy (Bracket, Of, Division, Multiplication, Addition, Subtraction).

⇒ 62 + 83 − 38 + (50) × 2 − 89

⇒ 62 + 83 − 38 + 100 − 89

⇒ (62 + 83 + 100) − (38 + 89)

⇒ 245 − 127

⇒ 118

∴ The correct answer is 118.

Additional Information

VBODMAS Rule

This rule specifies the order: Vinculum (bar), Bracket, Of, Division, Multiplication, Addition, and Subtraction.

Types of Brackets

Always solve in the order: Parentheses ( ), Braces { }, and then Square Brackets [ ].

Addition and Subtraction

For addition and subtraction, grouping positive and negative terms separately before the final calculation minimizes errors.

Shortcut Trick

Solve using the VBODMAS rule: handle Brackets and Division first.

45 + 31 − 16 + 54 + 38 − 21

Group positive and negative terms: (45 + 31 + 54 + 38) − (16 + 21)

168 − 37 = 131

∴ The correct answer is 131.

Alternate Method

Given Expression: 45 + 62 ÷ 2 − 16 + (27 × 2) + 38 − 21

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

⇒ 45 + 62 ÷ 2 − 16 + 54 + 38 − 21 (Solving Bracket: 27 × 2)

⇒ 45 + 31 − 16 + 54 + 38 − 21 (Solving Division: 62 ÷ 2)

⇒ 76 − 16 + 54 + 38 − 21

⇒ 168 − 16 − 21 (Performing Addition)

⇒ 168 − 37 (Performing Subtraction)

⇒ 131

∴ The correct answer is 131.

Additional Information

VBODMAS Rule

It stands for Vinculum, Bracket, Of, Division, Multiplication, Addition, and Subtraction, defining the correct sequence for mathematical operations.

Grouping Positives and Negatives

To minimize errors during Addition and Subtraction, sum all positive numbers together and all negative numbers together before finding the final difference.

Shortcut Trick

Solve each term by observing decimal places: ³√0.027 = 0.3

Square root term: √0.49 = 0.7

Next cube root terms: ³√0.064 = 0.4 and ³√0.216 = 0.6

Combine results: 0.3 + 0.7 + 0.4 − 0.6 = 0.8

∴ The correct answer is 0.8.

Alternate Method

Given Expression: ³√0.027 + √0.49 + ³√0.064 − ³√0.216

Method: Convert decimals to fractions for easier root extraction.

⇒ ³√(27/1000) + √(49/100) + ³√(64/1000) − ³√(216/1000)

⇒ (3/10) + (7/10) + (4/10) − (6/10)

⇒ 0.3 + 0.7 + 0.4 − 0.6

⇒ 1.0 + 0.4 − 0.6

⇒ 1.4 − 0.6

⇒ 0.8

∴ The correct answer is 0.8.

Additional Information

Cube Root of Decimals

For a cube root, if the original number has 3n decimal places, the result will have n decimal places. Example: ³√0.001 = 0.1.

Square Root of Decimals

For a square root, if the original number has 2n decimal places, the result will have n decimal places. Example: √0.01 = 0.1.

Common Cubes to Remember

Quick recall of 3³ = 27, 4³ = 64, and 6³ = 216 is essential for competitive Simplification questions.

Shortcut Trick

Given that √306.25 = 17.5, the significant digits of the square root of 30625 are 175.

In square roots, the number of decimal places in the result is exactly half of those in the original number.

The given value 0.000000030625 (assuming the standard 12-place structure for the provided answer) has 12 decimal places.

Therefore, the square root must have 12 ÷ 2 = 6 decimal places.

Applying this to 175: we get 0.000175.

∴ The correct answer is 0.000175.

Alternate Method

Given: √306.25 = 17.5

Formula Used: √(a × 10⁻²ⁿ) = √a × 10⁻ⁿ

⇒ √306.25 = 17.5

⇒ √(30625 ÷ 100) = 175 ÷ 10

⇒ √30625 = 175

⇒ √0.000000030625 = √(30625 × 10⁻¹²)

⇒ √30625 × √10⁻¹²

⇒ 175 × 10⁻⁶

⇒ 175 × 0.000001 = 0.000175

∴ The correct answer is 0.000175.

Additional Information

Square Root of Decimals

The number of digits after the decimal point in the square root of a perfect square decimal is exactly half the number of digits after the decimal point in the original number.

Power of 10 Rule

When calculating √10⁻ⁿ, if n is an even integer, the result is 10^−n/2. This is why the number of zeros effectively doubles when squaring and halves when taking a root.

Perfect Squares ending in 25

To find √30625, split it as 306|25. The 25 gives 5. For 306, find two consecutive integers whose product is 306 (17 × 18 = 306). The smaller number is 17. Thus, the root is 175.

Shortcut Trick

First, simplify the decimals: 0.16/0.0004 is equivalent to 1600/4 = 400.

The Square root of 400 is 20.

Next, simplify √(0.25/0.49) as √(25/49), which equals 5/7.

Multiply the results: 20 × 5/7 = 100/7.

∴ The correct answer is 100/7.

Alternate Method

Given Equation: √(0.16/0.0004) × √(0.25/0.49)

Formula Used: √(a/b) = √a / √b

⇒ √((16/100) ÷ (4/10000)) × √((25/100) ÷ (49/100))

⇒ √((16/100) × (10000/4)) × √(25/49)

⇒ √(4 × 100) × (5/7)

⇒ √400 × (5/7)

⇒ 20 × (5/7)

⇒ 100/7

∴ The correct answer is 100/7.

Additional Information

Square Root Properties

For any positive numbers a and b, √(a × b) = √a × √b and √(a/b) = √a / √b.

Decimal Manipulation

To simplify decimal fractions, multiply the numerator and denominator by 10ⁿ to shift the decimal point until whole numbers are obtained.

Perfect Squares

Recognizing perfect squares like 16, 25, 49, and 400 helps in fast calculation of square roots during competitive exams.

Shortcut Trick

Perimeter of a square is calculated as 4 × side.

Given side = 15 cm.

Perimeter = 4 × 15 = 60 cm.

∴ The correct answer is 60 cm.

Alternate Method

Given:

Side of the square (a) = 15 cm

Formula Used:

Perimeter of square = 4 × a

Calculations:

⇒ Perimeter = 4 × 15

⇒ Perimeter = 60 cm

∴ The correct answer is 60 cm.

Additional Information

Area of a Square

The total space enclosed by a square is called its area. Area = side² = a².

Diagonal of a Square

The length of the diagonal connecting opposite vertices. Diagonal = side × √2 = a√2.

Properties of a Square

All four sides are equal, all internal angles are 90°, and diagonals bisect each other at right angles.

Shortcut Trick

The Perimeter of a Rectangle is twice the sum of its Length and Breadth.

Sum of sides = 9 + 4 = 13 cm.

Perimeter = 2 × 13 = 26 cm.

∴ The correct answer is 26 cm.

Alternate Method

Given:

Length of the Rectangle (L) = 9 cm

Breadth of the Rectangle (B) = 4 cm

Formula Used:

Perimeter (P) = 2 × (L + B)

Calculations:

⇒ P = 2 × (9 + 4)

⇒ P = 2 × 13

⇒ P = 26 cm

∴ The correct answer is 26 cm.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is given by Area = Length × Breadth (L × B).

Diagonal of Rectangle

The distance between opposite corners is found using the Pythagoras theorem: Diagonal = √(L² + B²).

Perimeter of Square

A Square is a special rectangle where all sides are equal. Its Perimeter = 4 × Side.

Shortcut Trick

Identify the number where the last two digits are not divisible by 4 AND the sum of digits is not divisible by 9.

For 10263: Last two digits are 63 (not divisible by 4).

Sum of digits = 1 + 0 + 2 + 6 + 3 = 12 (not divisible by 9).

∴ The correct answer is 10263.

Alternate Method

Given: Numbers 10263, 10260, 10116, 10296.

Method: Apply divisibility rules for 4 and 9.

⇒ Divisibility rule of 4: Last two digits must be divisible by 4.

⇒ Divisibility rule of 9: Sum of all digits must be divisible by 9.

⇒ 10263: Last two digits 63 (63 ÷ 4 → Remainder 3). Sum = 1 + 0 + 2 + 6 + 3 = 12 (12 ÷ 9 → Remainder 3). Neither divisible by 4 nor 9.

⇒ 10260: Last two digits 60 (60 ÷ 4 = 15). Sum = 1 + 0 + 2 + 6 + 0 = 9 (9 ÷ 9 = 1). Divisible by both 4 and 9.

⇒ 10116: Last two digits 16 (16 ÷ 4 = 4). Sum = 1 + 0 + 1 + 1 + 6 = 9 (9 ÷ 9 = 1). Divisible by both 4 and 9.

⇒ 10296: Last two digits 96 (96 ÷ 4 = 24). Sum = 1 + 0 + 2 + 9 + 6 = 18 (18 ÷ 9 = 2). Divisible by both 4 and 9.

∴ The correct answer is 10263.

Additional Information

Divisibility by 3

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

Divisibility by 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Divisibility by 11

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

Shortcut Trick

Recognize the Algebraic Identity: 2(a² + b²) − (a − b)² = (a + b)².

Here, let a = 412 and b = 188.

The expression simplifies to (412 + 188)² = 600².

600 × 600 = 360000.

∴ The correct answer is 360000.

Alternate Method

Given:

Expression: 2[(412)² + (188)²] − (412 − 188)²

Formula Used:

1. 2(a² + b²) = (a + b)² + (a − b)²

2. (a + b)² = a² + b² + 2ab

Calculations:

⇒ Let a = 412 and b = 188.

⇒ The expression is 2(a² + b²) − (a − b)².

⇒ Substituting the identity for 2(a² + b²):

⇒ [(a + b)² + (a − b)²] − (a − b)²

⇒ (a + b)²

⇒ (412 + 188)²

⇒ 600²

⇒ 600 × 600 = 360000

∴ The correct answer is 360000.

Additional Information

Sum and Difference of Squares

(a + b)² + (a − b)² = 2(a² + b²). This identity connects the square of sum and square of difference to individual squares.

Difference of Two Sums

(a + b)² − (a − b)² = 4ab. This is used when the product of two numbers is needed from their sum and difference.

Basic Square Identity

(a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab are the fundamental building blocks for simplification.

Shortcut Trick

Total deviation must be zero from the mean (45).

Deviation of 9 remaining numbers = (35 − 45) × 9 = −90.

To balance this, the 5 numbers must have a total deviation of +90.

Average deviation for 5 numbers = 90 ÷ 5 = +18.

Value of x = 45 + 18 = 63.

∴ The correct answer is 63.

Alternate Method

Given: Total numbers = 14, Total Average = 45, n₁ = 5 (Average = x), n₂ = 9 (Average = 35).

Formula Used: Total Sum = (n₁ × Average₁) + (n₂ × Average₂)

⇒ Total Sum of 14 numbers = 14 × 45 = 630

⇒ Sum of remaining 9 numbers = 9 × 35 = 315

⇒ Sum of first 5 numbers = Total Sum − Sum of 9 numbers

⇒ 5 × x = 630 − 315

⇒ 5x = 315

⇒ x = 315 ÷ 5 = 63

∴ The correct answer is 63.

Additional Information

Weighted Average Formula

Used when two or more groups are combined: Average_total = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Deviation Principle

The sum of deviations of all observations from their arithmetic mean is always zero: ∑(x_i − Average) = 0.

Effect of Adding a Number

If a new number added is greater than the average, the average increases; if smaller, the average decreases.

Shortcut Trick

LCM of 12 and 15 = 60.

Smallest 3-digit multiple of 60 is A = 120 (60 × 2).

Largest 3-digit multiple of 60 is B = 960 (60 × 16).

Required value B − A = 960 − 120 = 840.

∴ The correct answer is 840.

Alternate Method

Given:

Divisors = 12 and 15

Formula used:

Any number divisible by both 12 and 15 must be a multiple of their Least Common Multiple (LCM).

Calculations:

⇒ Prime factors of 12 = 2² × 3

⇒ Prime factors of 15 = 3 × 5

⇒ LCM(12, 15) = 2² × 3 × 5 = 60

⇒ Smallest 3-digit number (starting from 100) divisible by 60:

⇒ 100 ÷ 60 ≈ 1.66 → next multiple is 60 × 2 = 120 (A)

⇒ Largest 3-digit number (ending at 999) divisible by 60:

⇒ 999 ÷ 60 ≈ 16.65 → largest multiple is 60 × 16 = 960 (B)

⇒ Required value = B − A = 960 − 120 = 840

∴ The correct answer is 840.

Additional Information

LCM and Multiples

The Least Common Multiple (LCM) of two or more numbers is the smallest non-zero common multiple of those numbers. Any common multiple of a and b is always a multiple of LCM(a, b).

Divisibility by 60

A number is divisible by 60 if it is simultaneously divisible by 3, 4, and 5. This property is useful for checking calculations involving minutes and seconds.

HCF and LCM Relation

For any two numbers x and y: x × y = HCF(x, y) × LCM(x, y). Here, HCF(12, 15) = 3 and LCM(12, 15) = 60, so 12 × 15 = 3 × 60 = 180.

Shortcut Trick

To find the maximum number of students in each group, find the Highest Common Factor (HCF) of the students in each class.

Step 1: Find the differences between the numbers: (60 − 36) = 24 and (72 − 60) = 12.

Step 2: The HCF is either the smallest difference or its factor.

Step 3: Check if 12 divides all: 36 ÷ 12 = 3, 60 ÷ 12 = 5, 72 ÷ 12 = 6.

All are divisible, so the HCF is 12.

∴ The correct answer is 12 students.

Alternate Method

Given:

Number of students in Class A = 36

Number of students in Class B = 60

Number of students in Class C = 72

Formula Used:

To divide different quantities into the largest possible equal groups, we calculate the HCF (Highest Common Factor) of those quantities.

Calculations:

Prime factorization of the numbers:

⇒ 36 = 2 × 2 × 3 × 3 = 2² × 3²

⇒ 60 = 2 × 2 × 3 × 5 = 2² × 3¹ × 5¹

⇒ 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

⇒ HCF = Product of the lowest powers of common prime factors

⇒ HCF = 2² × 3¹

⇒ HCF = 4 × 3 = 12

The maximum number of students in each group is 12.

∴ The correct answer is 12 students.

Additional Information

HCF (Highest Common Factor)

It is the greatest number that divides two or more numbers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).

HCF × LCM Property

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.

Applications of HCF

Used to find the maximum size of containers, maximum length of tapes, or equal divisions in grouping problems.

Shortcut Trick

Compare the Tax Amount with the Article Worth using the unitary method.

100% of the value = ₹900

1% of the value = 900 ÷ 100 = ₹9

Since ₹9 is 1%, then ₹36 is (36 ÷ 9) × 1% = 4%.

∴ The correct answer is 4 percent.

Alternate Method

Given:

The Article Worth = ₹900

The Tax Paid = ₹36

Formula Used:

Rate of Tax = (Tax Amount ÷ Article Worth) × 100

Calculations:

⇒ Tax Rate = (36 ÷ 900) × 100

⇒ Tax Rate = (36 ÷ 9)

⇒ Tax Rate = 4%

∴ The correct answer is 4 percent.

Additional Information

Sales Tax and VAT

Tax is an additional amount calculated on the Selling Price of an item. Formula: Tax = (Tax Rate ÷ 100) × Selling Price.

Effective Price Calculation

The total amount paid by the customer is the Net Price. Net Price = Original Price + Tax Amount.

Percentage Rule

To find what percentage one number is of another, use the ratio: (Part ÷ Total) × 100.

Shortcut Trick

Given that 30% of Profit corresponds to ₹120.

1% of Cost Price = 120 ÷ 30 = ₹4

Selling Price (SP) = Cost Price (100%) + Profit (30%) = 130%

130% of Cost Price = 130 × 4 = ₹520

∴ The correct answer is ₹520.

Alternate Method

Given:

Profit = ₹120

Profit percentage = 30%

Formula Used:

Profit = Selling Price − Cost Price

Profit % = (Profit ÷ Cost Price) × 100

Calculations:

⇒ 30% of Cost Price = 120

⇒ Cost Price = (120 × 100) ÷ 30

⇒ Cost Price = 4 × 100 = ₹400

⇒ Selling Price = Cost Price + Profit

⇒ Selling Price = 400 + 120 = ₹520

∴ The correct answer is ₹520.

Additional Information

Cost Price (CP)

The price at which an article is purchased. It is always considered as the base (100%) for calculating profit or loss percentage.

Loss Percentage

When SP < CP, Loss % = [(CP − SP) ÷ CP] × 100. It indicates the percentage reduction from the original cost.

Marked Price (MP) and Discount

MP is the price printed on the label. Discount = MP − SP. Discount % is always calculated on the Marked Price.

Shortcut Trick

Profit = 25% of Selling Price (SP) = 1/4 of SP.

If SP = 4 units, then Profit = 1 unit.

Cost Price (CP) = SP − Profit = 4 − 1 = 3 units.

Ratio of Profit : Cost Price = 1 : 3.

∴ The correct answer is 1 : 3.

Alternate Method

Given: Profit percentage on Selling Price = 25%

Formula Used: Cost Price = Selling Price − Profit | Ratio = Profit / Cost Price

⇒ Let the Selling Price (SP) = 100

⇒ Profit = 25% of SP = 25

⇒ Cost Price (CP) = SP − Profit = 100 − 25 = 75

⇒ Required Ratio = Profit : CP

⇒ Required Ratio = 25 : 75

⇒ Required Ratio = 1 : 3

∴ The correct answer is 1 : 3.

Additional Information

Profit Percentage on CP

Profit % = (Profit ÷ CP) × 100. This is the standard way to calculate profit unless specified otherwise.

Relationship between SP and CP

If Profit is x/y of SP, then Profit is x/(y−x) of CP. Here, 1/4 of SP = 1/(4−1) = 1/3 of CP.

Marked Price (MP) and Discount

Selling Price = Marked Price − Discount. Discount is always calculated on the Marked Price.

Shortcut Trick

Assume initial income = 100 units. Then expenditure = 40 units and savings = 60 units.

New income = 150 units (50% increase).

New expenditure = 40 × 1.4 = 56 units (40% increase).

New savings = 150 − 56 = 94 units.

According to the question, 94 units = ₹4700 ⇒ 1 unit = ₹50.

∴ The correct answer is ₹5000.

Alternate Method

Given:

Initial expenditure = 40% of income.

Increase in income = 50%.

Increase in expenditure = 40%.

Increased saving = ₹4700.

Formula used:

Income = Expenditure + Saving

Let the initial income be 100x.

⇒ Initial expenditure = 40x

⇒ Initial savings = 100x − 40x = 60x

⇒ New income = 100x + 50% of 100x = 150x

⇒ New expenditure = 40x + 40% of 40x

⇒ New expenditure = 40x + 16x = 56x

⇒ New savings = 150x − 56x = 94x

⇒ Given: 94x = 4700

⇒ x = 4700 ÷ 94

⇒ x = 50

⇒ Initial income = 100 × 50 = ₹5000

∴ The correct answer is ₹5000.

Additional Information

Income, Expenditure, and Saving Relationship

The fundamental equation for income-based problems is: Income = Expenditure + Savings. Any percentage change in one component affects the others based on this balance.

Percentage Increase Shortcut

To increase a value by a%, multiply the original value by (100 + a)/100. For example, a 40% increase means multiplying by 1.40.

Net Effect on Savings

If income increases by x% and expenditure increases by y%, the percentage change in savings depends on the initial ratio of expenditure to savings. Weighted averages can also be used here.

Shortcut Trick

Efficiency ratio of A : B = 2 : 1

Total efficiency of (A + B) = 2 + 1 = 3 units/day

Total Work = Combined Efficiency × Time = 3 × 24 = 72 units

Time taken by B alone = Total Work ÷ Efficiency of B = 72 ÷ 1 = 72 days

∴ The correct answer is 72 days.

Alternate Method

Given:

Efficiency of A is 2 times that of B.

Time taken by A and B together = 24 days.

Formula Used:

Total Work = Efficiency × Time taken

Calculations:

⇒ Let the efficiency of B be 1 unit/day.

⇒ Efficiency of A = 2 × 1 = 2 units/day.

⇒ Combined efficiency of A and B = 2 + 1 = 3 units/day.

⇒ Total Work = Combined Efficiency × Time = 3 × 24 = 72 units.

⇒ Days taken by B alone = Total Work ÷ Efficiency of B

⇒ Days taken by B = 72 ÷ 1 = 72 days.

∴ The correct answer is 72 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency is x : y, the ratio of time taken will be y : x.

Work and Wages

Wages are always distributed in the ratio of work done or the ratio of efficiencies if the time period of work is the same for all workers.

Pipes and Cisterns

The same logic applies where filling rate is considered positive efficiency and emptying rate (leakage) is considered negative efficiency.

Shortcut Trick

Ratio of Total Work Done = (Days × One day work efficiency)

R : M : T = (6 × 2) : (8 × 3) : (10 × 4) = 12 : 24 : 40

Simplified Work Ratio = 3 : 6 : 10 (Dividing by 4)

Total units = 3 + 6 + 10 = 19 units → ₹760

M's Share = (6 ÷ 19) × 760 = 6 × 40 = ₹240

∴ The correct answer is ₹240.

Alternate Method

Given:

Working days of R, M, and T = 6, 8, and 10 days respectively.

Ratio of Efficiency (One day work) = 2 : 3 : 4

Total Wages received = ₹760

Formula Used:

Total Share of Money ∝ Total Work Done (Days × Efficiency)

Calculations:

⇒ Share of R = 6 × 2 = 12 units

⇒ Share of M = 8 × 3 = 24 units

⇒ Share of T = 10 × 4 = 40 units

⇒ Ratio of shares = 12 : 24 : 40

⇒ Ratio of shares = 3 : 6 : 10

⇒ Sum of ratio parts = 3 + 6 + 10 = 19 units

⇒ 19 units = ₹760

⇒ 1 unit = 760 ÷ 19 = ₹40

⇒ M's total money = 6 × 40 = ₹240

∴ The correct answer is ₹240.

Additional Information

Wages and Work Done

Wages are always distributed in the ratio of the total work done by each individual, which is the product of their efficiency and the time they worked.

Efficiency Formula

Efficiency = Total Work ÷ Total Time. If the work is constant, efficiency is inversely proportional to the time taken.

Work and Wages Variation

If multiple people work for the same duration, their wages are distributed directly in the ratio of their one-day efficiency.

Shortcut Trick

Speed of B = 42 ÷ 7 = 6 kmph

Speed of C = 108 ÷ 9 = 12 kmph

Required Ratio = 6 : 12 = 1 : 2

∴ The correct answer is 1 : 2.

Alternate Method

Given:

Distance covered by B = 42 km

Time taken by B = 7 hr

Distance covered by C = 108 km

Time taken by C = 9 hr

Formula Used:

Speed = Distance ÷ Time

Calculations:

⇒ Speed of B (S_B) = 42 ÷ 7

⇒ S_B = 6 kmph

⇒ Speed of C (S_C) = 108 ÷ 9

⇒ S_C = 12 kmph

⇒ Ratio = S_B : S_C

⇒ Ratio = 6 : 12

⇒ Ratio = 1 : 2

∴ The correct answer is 1 : 2.

Additional Information

Unit Conversion

To convert kmph to m/s, multiply the speed by 5/18. To convert m/s to kmph, multiply by 18/5.

Average Speed

Average Speed = Total Distance ÷ Total Time. If distances are equal, Average Speed = 2xy ÷ (x+y), where x and y are individual speeds.

Relative Speed

When moving in the same direction, Relative Speed = S₁ − S₂. When moving in opposite directions, Relative Speed = S₁ + S₂.

Shortcut Trick

Speed ratio (Usual : New) = 100 : 90 = 10 : 9

Since Distance is constant, Time ratio is inverse of Speed ratio = 9 : 10

Difference in time ratio parts = 10 − 9 = 1 unit

Given, 1 unit = 10 min

Usual time = 9 units = 9 × 10 = 90 min

∴ The correct answer is 90 min.

Alternate Method

Given: New speed is 90% of usual speed, delay = 10 min.

Formula: Distance = Speed × Time

⇒ Let the usual speed be S and usual time be T.

⇒ New speed = 90% of S = 0.9S

⇒ New time = T + 10 min

⇒ Since Distance is same: S × T = 0.9S × (T + 10)

⇒ T = 0.9T + 9

⇒ T − 0.9T = 9

⇒ 0.1T = 9

⇒ T = 9 ÷ 0.1 = 90 min

∴ The correct answer is 90 min.

Additional Information

Inversely Proportional Relationship

When distance is constant, speed is inversely proportional to time (S ∝ 1/T). If speed becomes a/b of original, time becomes b/a of original.

Average Speed Formula

For a fixed distance covered at two different speeds x and y, Average Speed = (2 × x × y) ÷ (x + y).

Late and Early Concept

If a person reaches 't₁' late at speed S₁ and 't₂' early at speed S₂, then Distance = [S₁ × S₂ ÷ (S₂ − S₁)] × (t₁ + t₂).

The correct answer is Option (2) i.e. 'Throw the baby out with the bathwater'.

Key Points

• The meaning 'An avoidable error in which something good or of value is eliminated when trying to get rid of something unwanted' refers to a situation where an essential or valuable part of something is discarded while attempting to remove undesirable elements. (किसी अवांछित चीज़ से छुटकारा पाने की कोशिश करते समय किसी अच्छी या मूल्यवान चीज़ को हटा देने की एक टालने योग्य गलती।)
• Example: Closing the entire library because a few books were missing is a classic case of throwing the baby out with the bathwater.
• The idiom 'Throw the baby out with the bathwater' means to lose valuable ideas or things during an attempt to get rid of what is not wanted. (अवांछित चीज़ों के साथ-साथ मूल्यवान चीज़ों को भी त्याग देना।)
• Example: We should update our old software rather than scrapping the whole system; let us not throw the baby out with the bathwater.
• Hence, we can infer that the meaning provided in the question matches the idiom 'Throw the baby out with the bathwater'.

Therefore, the correct answer is- Throw the baby out with the bathwater.

Additional Information

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

• Throw somebody for a loop (किसी को बहुत अधिक चकित या परेशान कर देना): To surprise, shock, or confuse someone significantly.
• Example: The news of the sudden policy change threw the entire staff for a loop.
• Throw the first stone (आरोप लगाने वाला पहला व्यक्ति बनना जबकि स्वयं भी निर्दोष न हो): To be the first to criticize someone for a fault that the critic also possesses.
• Example: Before you judge her for being messy, look at your own desk; you should not be the one to throw the first stone.
• Lock someone up and throw away the key (किसी को बहुत लंबे समय या आजीवन कारावास में डालना): To put someone in prison for a very long time or for life.
• Example: The criminal was so dangerous that many felt the judge should lock him up and throw away the key.

The correct answer is: Out of the red.

Key Points

• The provided definition describes a financial state where an individual or a company is no longer in debt or has cleared its financial liabilities. (ऋण या कर्ज से मुक्त होना)
• Example: After years of heavy losses, the corporation finally became debt-free.
• 'Out of the red' is an idiom that means a business or person is no longer owing money to the bank and is now making a profit. (घाटे या कर्ज से बाहर आना)
• Example: Thanks to the new management, the firm is finally out of the red and showing growth.
• Hence, we can infer that the idiom 'out of the red' correctly matches the given meaning.

Therefore, the correct answer is: Out of the red.

Additional Information

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

• Go into the red (कर्ज में जाना): To spend more money than is earned, resulting in a deficit or debt.
• Example: If the company continues to overspend, it will surely go into the red by next month.
• Red in the face (शर्मिंदा होना): To be visibly embarrassed, ashamed, or angry.
• Example: He was red in the face when he realized he had forgotten the presentation at home.
• Take the red eye (देर रात की उड़ान लेना): To travel on a flight that departs late at night and arrives early the following morning.
• Example: I had to take the red eye from London to arrive in time for the business meeting.

The correct answer is: Juvenile.

Key Points

• The word 'Juvenile' refers to anything relating to young people who are not yet adults or behavior that is typical of them. (किशोर)
• Example: The juvenile justice system is designed to rehabilitate young offenders rather than just punish them.
• 'Juvenile' is the word among the given options that is spelled correctly. It specifically denotes youthfulness or the phase of life before adulthood. (बाल/किशोर)
• Example: He was a juvenile when he first started showing an interest in astronomy.
• Hence, we can infer that 'Juvenile' is the correctly spelled word.

Therefore, the correct answer is- Juvenile.

Additional Information

Here are the other options explained along with their correct spellings and meanings:

• Jetison (���ोझ उतारना): The correct spelling is 'Jettison'. It means to throw or drop something from an aircraft or ship to lighten the load.
• Example: The pilot had to jettison the extra fuel before making an emergency landing.
• Jondice (पीलिया): The correct spelling is 'Jaundice'. It is a medical condition caused by excess bilirubin, leading to the yellowing of the skin and eyes.
• Example: Severe jaundice in newborns is usually treated with phototherapy.
• Jocular (मज़ाकिया): This refers to a person or behavior that is humorous, playful, or fond of joking.
• Example: His jocular remarks helped to ease the tension during the long meeting.

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

Key Points

• The word 'liberty' refers to the state of being free within society from oppressive restrictions imposed by authority on one's way of life, behavior, or political views. (स्वतंत्रता)
• Example: The statue in the harbor is a worldwide symbol of liberty and democracy.
• 'Freedom' is the condition of being free to act, speak, or think without restraint; it is the most appropriate synonym for liberty as it shares the same core meaning of independence. (आजादी)
• Example: After the long struggle, the citizens finally celebrated their freedom.
• Hence, we can infer that the most appropriate synonym of 'liberty' is 'freedom'.

Therefore, the correct answer is- Freedom.

Additional Information

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

• Captivity (कैद): The state of being kept as a prisoner or in a confined space, which is the opposite of liberty.
• Example: The birds were eventually released back into the wild after years in captivity.
• Punishment (सज़ा): The infliction of a penalty as retribution for an offense or crime.
• Example: The teacher gave him a mild punishment for being late to the class.
• Arrest (गिरफ्तारी): The act of seizing someone by legal authority and taking them into custody.
• Example: The police made an arrest shortly after the investigation concluded.

The correct answer is: Acknowlege.

Key Points

• The word 'Acknowlege' is the misspelt version of a word that indicates the acceptance or recognition of a fact, situation, or receipt of an item. (गलत वर्तनी)
• Example: The student lost marks in his essay because he wrote 'Acknowlege' instead of the correct spelling.
• 'Acknowledge' is the correct spelling, meaning to admit the existence or truth of something, or to confirm that one has received a message or document. (स्वीकार करना)
• Example: It is professional to acknowledge the receipt of an email within twenty-four hours.
• Hence, we can infer that the misspelt word is 'Acknowlege'.

Therefore, the correct answer is: Acknowlege.

Additional Information

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

• Bureaucracy (नौकरशाही): A system of government or administration in which most of the important decisions are taken by state officials rather than by elected representatives.
• Example: The new startup struggled to navigate the complex bureaucracy involved in getting a business license.
• Recommend (सिफारिश करना): To suggest or advise that someone or something is good or suitable for a particular purpose or role.
• Example: I can highly recommend this hotel for its excellent service and central location.
• Dilemma (दुविधा): A difficult situation in which a choice has to be made between two or more alternatives, especially ones that are equally undesirable.
• Example: He was in a dilemma about whether to tell his friend the truth or keep the secret.

The correct answer is Option (1) i.e. Vacant.

Key Points

• The word 'Occupied' means being used by someone, filled with something, or being busy with a task. (व्यस्त/अधिकृत)
• Example: I am afraid all the meeting rooms are currently occupied.
• 'Vacant' refers to something that is not being used, lived in, or occupied; it is empty and available for use. (खाली)
• Example: The hotel had only one vacant room left for the night.
• Hence, we can infer that the opposite of 'Occupied' is 'Vacant'.

Therefore, the correct answer is- Vacant.

Additional Information

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

• Taken (भरा हुआ/अधिकृत): This means something is already in use or has been claimed by someone else.
• Example: Is this seat taken, or can I sit here?
• Engaged (व्यस्त): This refers to being involved in an activity or being busy; it is often used as a synonym for occupied.
• Example: The director is engaged in a very important discussion at the moment.
• Busy (व्यस्त): Having a lot to do or being fully occupied with an activity.
• Example: She has been busy all morning preparing for the presentation.

The correct answer is Option (1) i.e. Perceptive.

Key Points

• The phrase 'One who quickly understands and responds to situations' refers to a person who possesses a keen intellect and the ability to grasp complex ideas or emotions rapidly. (तेजी से समझने और प्रतिक्रिया देने वाला)
• Example: Being insightful and fast to react, she proved to be the most reliable person during the crisis.
• 'Perceptive' describes someone who has or shows sensitive insight or is very good at noticing things that are not obvious. (अनुभवशील / तेज-समझ वाला)
• Example: It was very perceptive of him to realize that the atmosphere in the office had changed.
• Hence, we can infer that the one-word substitution for the given description is 'perceptive'.

Therefore, the correct answer is- Perceptive.

Additional Information

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

• Pliable (लचीला / नमनीय): Something that is easy to bend or a person who is easily influenced or controlled by others.
• Example: High-quality clay is pliable and easy to mold into various shapes.
• Obtuse (मंदबुद्धि / मूर्ख): A person who is annoyingly insensitive or slow to understand even simple instructions or situations.
• Example: I am not trying to be obtuse, but I genuinely do not understand the logic behind this rule.
• Effusive (अतिशयोक्तिपूर्ण / भावनाप्रधान): Expressing gratitude, pleasure, or approval in an unrestrained or heartfelt manner.
• Example: They were effusive in their thanks for all the help we had provided during the event.

The correct answer is: Maelstrom.

Key Points

• The phrase 'A large, confused mass of people' refers to a situation where a group is in a state of turmoil, disorder, or violent agitation. (लोगों की एक बड़ी, भ्रमित भीड़ या अव्यवस्था)
• Example: The stadium became a large, confused mass of people after the sudden announcement.
• 'Maelstrom' refers to a powerful whirlpool in the sea or a river, or more commonly in this context, a state of confused and violent movement, agitation, or a chaotic mass. (भंवर या भारी उथल-पुथल)
• Example: The station was a maelstrom of activity as hundreds of passengers rushed to board the last train.
• Hence, we can infer that the one-word substitution for 'A large, confused mass of people' is 'maelstrom'.

Therefore, the correct answer is- Maelstrom.

Additional Information

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

• Convocation (दीक्षांत समारोह): A large formal assembly of people, especially for a university graduation ceremony.
• Example: The governor was invited as the chief guest for the annual convocation.
• Vicissitude (उतार-चढ़ाव): A change of circumstances or fortune, typically one that is unwelcome or unpleasant.
• Example: The company has survived the vicissitudes of the stock market for over fifty years.
• Machination (साजिश): A plot or scheme, often used in a negative sense to describe crafty actions or maneuvers.
• Example: The political leader fell victim to the machinations of his own party members.

The correct answer is 'with'.

 

Key Points

• The preposition 'with' is used to indicate the instrument, tool, or part of the body used to perform a specific action.
• In this sentence, the palms are the means or instruments used to perform the action of covering the face.
• The standard grammatical colocation for this context is 'to cover something with something'.

Therefore, the correct answer is Option 3.

 

Complete Sentence: 'Cover your face with your palms to save yourself from the dust storm.'

 

Additional Information

• Option 1 (behind): This preposition refers to a location at the back of something and does not fit the context of using an object to cover another.
• Option 2 (under): This refers to being directly below or beneath something; one does not cover their face 'under' their palms in this active sense.

The correct answer is Was the machinery repaired by the technician before the factory resumed operations?.

Key Points

• The original sentence is in the Active Voice and follows the Simple Past Tense interrogative pattern: Did + Subject + V1 + Object.
• To convert an interrogative Simple Past sentence into Passive Voice, the auxiliary verb Did is replaced by Was or Were based on the number and person of the new subject.
• The word machinery is an uncountable noun and is treated as singular; therefore, the auxiliary verb Was is used to start the passive sentence.
• The main verb repair (V1) must be changed into its Past Participle form (V3), which is repaired.
• The agent or Subject of the active sentence (the technician) is placed after the verb, preceded by the preposition by.
• The Adverbial Clause of time, before the factory resumed operations, remains unchanged as it provides context to the main action.
• The final passive structure becomes: Was + New Subject (the machinery) + V3 (repaired) + by + Agent (the technician) + remainder of the sentence.

 Additional Information

• Analysis of incorrect options:
• Past Continuous Passive: Option 2 uses the phrase being repaired, which is only used when the original active sentence is in the Past Continuous Tense (Was the technician repairing...).
• Present Perfect Passive: Option 3 uses Has the machinery been repaired, which shifts the tense from the Simple Past to the Present Perfect, changing the temporal meaning of the sentence.
• Grammatical Error: Option 4 uses Did the machinery repair, which is structurally incorrect because machinery is the receiver of the action, not the performer, necessitating a Passive Voice construction.
• Tense Consistency: In voice conversion, the Tense must remain the same; Simple Past Active must always correspond to Simple Past Passive.

The correct answer is Was the panel evaluating the project presentation when the power cut occurred?.

Key Points

• The original sentence 'Was the project presentation being evaluated by the panel when the power cut occurred?' is in the Passive Voice of the Past Continuous Tense.
• The structure for an interrogative sentence in the Past Continuous Passive Voice is: Was/Were + Object + being + V3 (Past Participle) + by + Subject?
• To convert this into Active Voice, the structure must be: Was/Were + Subject + Verb-ing (Present Participle) + Object?
• In the given sentence, the subject (the doer) is the panel, and the object (the receiver) is the project presentation. The verb is evaluate.
• Applying the rule, 'the panel' (singular subject) takes the auxiliary verb Was, and the verb changes from 'being evaluated' to evaluating.
• The clause 'when the power cut occurred' remains unchanged as it provides the temporal context (Simple Past) for the continuous action.

 Additional Information

• Understanding Tense Consistency in Voice Conversion:
• Past Simple: Uses the auxiliary Did in the active interrogative (e.g., 'Did the panel evaluate...'). This is incorrect here because the original sentence denotes an ongoing action (indicated by 'being').
• Present Continuous: Uses Is/Am/Are. This is incorrect because the original sentence and the subordinate clause ('occurred') are firmly established in the past.
• Past Perfect: Uses Had + V3 (e.g., 'Had the panel evaluated...'). This tense represents an action completed before another past action, which contradicts the simultaneous continuous nature of the original sentence.
• Active Voice emphasizes the agent performing the action, while Passive Voice emphasizes the recipient of the action or the action itself.

The correct answer is Everybody in the class knows the solution..

Key Points

• The original sentence is in the Passive Voice. The structure used is Object + is/am/are + Past Participle (V3) + to + Agent.
• To convert a sentence from Passive to Active Voice, the agent of the action (the person or thing doing the action) must become the Subject. In this case, everybody in the class becomes the subject.
• The verb is known indicates that the sentence is in the Simple Present Tense. Therefore, the active verb must also be in the Simple Present Tense (V1 or V1+s/es).
• The word everybody is a singular indefinite pronoun. According to the rules of Subject-Verb Agreement, a singular subject requires a singular verb, which is knows.
• The receiver of the action, the solution, shifts from the subject position in the passive voice to the Direct Object position in the active voice.

 Additional Information

• Stative Verbs:
• Verbs like know, believe, and own describe a state rather than a continuous action.
• These verbs are typically not used in the Present Continuous Tense. Therefore, a construction like is knowing is generally considered grammatically incorrect in standard English.
• Tense Changes:
• Changing the tense during voice conversion is incorrect. Using knew (Simple Past) or has known (Present Perfect) alters the temporal context of the original statement.
• Voice conversion only changes the emphasis (from the receiver to the doer) while keeping the tense constant.

The correct answer is Option 2.

 

Key Points

• The error in the sentence lies in the use of the preposition about in the second part.
• When an adjective is used to describe the nature, character, or behavior of a person in the structure 'It + be + adjective + preposition + person + to-infinitive', the correct preposition to use is of.
• Adjectives that typically follow this pattern include stupid, kind, nice, clever, polite, and generous.
• The phrase should correctly read as 'stupid of the boy to' because it describes the boy's action/character.
• Thus, the part containing the error is 'stupid about the boy to'.

Therefore, the correct answer is stupid about the boy to.

 

Correct Sentence: 'It was very stupid of the boy to have spent five thousand rupees on that dictionary.'

 

Additional Information

• 'It was very' – This is a grammatically correct introductory phrase for this type of sentence structure.
• 'have spent five thousand' – The use of the perfect infinitive ('to have spent') is correct here as it refers to an action that took place before the time referred to by the main verb ('was').
• 'rupees on that dictionary' – The verb spend is correctly paired with the preposition on when indicating what the money was exchanged for.

The correct answer is 'of'.

 

Key Points

• The verb boast means to speak with excessive pride and self-satisfaction about one's achievements, possessions, or abilities.
• In English grammar, the verb boast is typically followed by the preposition of or about to indicate the subject of the pride.
• The phrase boast of something is a standard idiomatic construction. In this sentence, Sebastian is speaking proudly of his European descent.
• Options 1, 3, and 4 are grammatically incorrect because these prepositions do not collocate with the verb boast in this context.

Therefore, the correct answer is Option 2.

 

Complete Sentence: 'Sebastian always boasts of his European descent.'

 

Additional Information

• Option 1: 'with' is incorrect; we do not use with to specify what is being boasted about.
• Option 3: 'at' is incorrect; the preposition at is used for locations or specific points in time, not with the verb boast.
• Option 4: 'for' is incorrect; while for can indicate purpose, it does not function as the required preposition for the verb boast.

The correct answer is No improvement required.

Key Points

• The underlined phrase 'come to terms with' is a fixed idiomatic expression in English which means to gradually accept a sad or difficult situation or to find a way to live with it.
• This idiom follows a strict syntactic structure consisting of the verb 'come', the prepositional phrase 'to terms', and the preposition 'with'. Any deviation from these specific prepositions results in an ungrammatical or non-idiomatic construction.
• In the sentence provided, the object of acceptance is 'the fact', referring to the specific situation of losing a chance. The use of the definite article 'the' before the singular noun 'fact' is logically and grammatically sound because it identifies the propositional content that follows (that you have lost your chance).
• Because the original sentence correctly utilizes the standard idiom and maintains proper prepositional usage, it does not require any stylistic or grammatical changes. The integrity of the clause structure and the semantic meaning are both intact.

 Additional Information

• Analysis of incorrect prepositional combinations:
• 'Come at terms of': This is incorrect because 'at terms' is not a recognized phrase for acceptance; 'at' usually denotes a specific location or point in time, and 'of' fails to show the relational bond required by the idiom.
• 'Come on terms with': Although the phrase 'on good terms' exists to describe a friendly relationship, it cannot substitute 'to terms' when describing the psychological process of resignation or acceptance.
• 'Come in terms to': This is often confused with 'in terms of' (meaning regarding), but 'in terms' cannot be paired with the verb 'come' to convey acceptance. Furthermore, 'terms' must be followed by 'with' to correctly link to the situation being accepted.
• The word 'terms' in this context relates to 'conditions' or 'provisions', suggesting that the person has reached a state where they can coexist with the harsh conditions of their reality.