SSC GD Constable 2026 Official Paper (Held On 29 May, 2026 Shift 3) (Previous Year Paper)

Logic followed here is,

−261 + 6 = −255

−255 + 6 = −249 ≠ -250

−249 + 6 = −243

−243 + 6 = −237

−237 + 6 = −231

−231 + 6 = −225

−225 + 6 = −219

Therefore, −250 is the wrong term in the series.

Hence, the correct answer is “Option 3”.

Logic: (Previous number × 2) − 4 = Next number

Following the pattern:

−59

(−59 × 2) − 4 = −118 − 4 = −122

(−122 × 2) − 4 = −244 − 4 = −248

(−248 × 2) − 4 = −496 − 4 = −500

(−500 × 2) − 4 = −1000 − 4 = −1004

(−1004 × 2) − 4 = −2008 − 4 = −2012

(−2012 × 2) − 4 = −4024 − 4 = −4028

(−4028 × 2) − 4 = −8056 − 4 = −8060

The missing number in the series is −122.

Hence, the correct answer is “Option 1”.

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Pattern followed here is,

Hence, the correct answer is “Option 2”.

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Pattern followed here is,

Hence, the correct answer is “Option 4”.

For 'YJ' related to 'UE':

For 'KB' related to 'GW':

Applying the same logic to find the cluster related to 'PX':

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Thus, TC is related to PX.

Hence, the correct answer is 'Option 3'.

For the set '(YB, WY, UV)':

For the set '(BO, ZL, XI)':

Applying the same logic to the options:

In Option 4, the group '(WE, UB, SY)' follows the same pattern:

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Hence, the correct answer is 'Option 4'.

Rules for a Leap Year:

1. A year is a leap year if it is divisible by 4.
2. However, for a century year (years ending in 00), it must be divisible by 400 to be a leap year.

Checking the year 1800:

1800 ÷ 4 = 450 (Divisible)

1800 ÷ 400 = 4.5 (Not divisible)

Since 1800 is a century year not divisible by 400, it is an ordinary year. Therefore, February in 1800 had 28 days.

Days in specified months:

• November: 30 days
• February: 28 days (Ordinary year)
• July: 31 days
• September: 30 days

Calculation:

Sum of days = Days in November + Days in February + Days in July + Days in September

Sum = 30 + 28 + 31 + 30

Sum = 58 + 31 + 30

Sum = 89 + 30

Sum = 119

Hence, the total sum of the number of days is 119.

Hence, the correct answer is “Option 4”.

5 boys A, B, C, D and E are sitting in a row facing north (not necessarily in the same order).

1. D is to the immediate left of C.
2. A is third to the left of B.
3. B is the immediate neighbour of E and C.

C is sitting in the middle of the row.

Hence, the correct answer is “Option 1”.

Given that the sales of 6 companies L, M, N, O, P and Q are all different.

From the clues, we can deduce the following relationships:

1. Sales of L is less than only O.

→ Only O has higher sales than L.

→ O > L > _ > _ > _ > _

2. Sales of P is more than only Q.

→ P is the second lowest and Q is the lowest.

→ _ > _ > _ > L > P > Q

3. Sales of N is more than M.

→ N > M

4. Since L is already fixed as the second highest, the remaining positions are occupied by O, N and M.

→ Final order becomes:

→ O > L > N > M > P > Q

Now check the conclusions:

I. M > Q  → True (M is above Q)

II. M > L  → False (L is above M)

Thus, only conclusion I is correct.

Hence, the correct answer is "Option 1".

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Similarly,

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Hence, the correct answer is “Option 3”.

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AKT82 : EOY164 → 

LMN61 : PQS122 → 

Similarly,

CJP93 : ? → 

Hence, the correct answer is 'Option 3'.

Dictionary order of given words,

3. Position
4. Positive
5. Pository
6. Positure
7. Possibility

Correct order is : 32514

Hence, the correct answer is “Option 3”.

The logic followed here is:

Logic: First Number − 47 = Second Number

For the first pair 4244 : 4197

⇒ 4244 − 47 = 4197.

For the second pair 6679 : 6632

⇒ 6679 − 47 = 6632.

Applying the same logic to the third pair

? : 2367

⇒ ? − 47 = 2367

⇒ ? = 2367 + 47 = 2414.

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: Second Number = (First Number × 2) − 10

For the first pair 198 : 386

⇒ (198 × 2) − 10

⇒ 396 − 10 = 386.

Applying the same logic to the second pair 502 : 994

⇒ (502 × 2) − 10

⇒ 1004 − 10 = 994.

Applying the same logic to find the missing number for ? : 1600

⇒ (Missing Number × 2) − 10 = 1600

⇒ Missing Number × 2 = 1600 + 10

⇒ Missing Number × 2 = 1610

⇒ Missing Number = 1610 ÷ 2 = 805.

Hence, the correct answer is 'Option 2'.

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SOAK is coded as TSWF →

PLAY is coded as QPWT →

Similarly,

let's find the code for RACY:

Hence, the correct answer is “Option 4”.

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Pattern followed here is,

Hence, the correct answer is “Option 3”.

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Pattern followed here is,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

The correct answer is President of India.

Key Points

• According to Article 216 of the Constitution of India, every High Court shall consist of a Chief Justice and such other Judges as the President may from time to time deem it necessary to appoint.
• The Constitution does not fix the maximum strength of a High Court; instead, it leaves it to the discretion of the President of India to determine the number of judges based on the workload and the volume of pending cases in a particular court.
• The President periodically reviews the sanctioned strength of judges for each High Court to ensure the efficient delivery of justice and to manage the judicial backlog.
• While the President decides the number of judges, the actual appointment process involves a collegium system and consultation with the Chief Justice of India and the Governor of the respective state under Article 217.

 Additional Information

• Parliament:
• Unlike the High Courts, the strength of the Supreme Court of India is decided by the Parliament through legislation.
• Under Article 124(1), Parliament has the power to prescribe the number of judges in the Supreme Court.
• Chief Justice of India:
• The Chief Justice of India (CJI) is the head of the Judiciary of India and leads the collegium that recommends names for judicial appointments.
• The CJI does not have the constitutional authority to unilaterally decide the sanctioned strength of a High Court.
• Governor of the State:
• The Governor is consulted by the President during the appointment of High Court judges as per Article 217.
• The Governor plays no role in determining the total number of judges required for the High Court.
• Article 214:
• This article mandates that there shall be a High Court for each State.

The correct answer is Fazl Ali Commission.

Key Points

• The Fazl Ali Commission, formally known as the States Reorganisation Commission (SRC), was established by the Government of India in December 1953 to address demands for reorganizing states.
• The commission was headed by Justice Fazl Ali and included two other members, H.N. Kunzru and K.M. Panikkar, who examined the linguistic, cultural, and administrative aspects of state boundaries.
• In its report submitted in September 1955, the commission broadly accepted language as the basis of state reorganization, moving away from the stances of the Dhar Commission and JVP Committee.
• However, it rejected the rigid theory of one language-one state, emphasizing that the unity of India, administrative efficiency, and national security must remain primary considerations.
• The recommendations led to the States Reorganisation Act, 1956, which abolished the classification of states into Part A, B, C, and D and reorganized the country into 14 states and 6 union territories on November 1, 1956.

 Additional Information

• Sarkaria Commission:
• Set up in 1983 under the chairmanship of Justice R.S. Sarkaria to review the working of Centre-State relations and suggest constitutional reforms.
• Punchhi Commission:
• Formed in 2007 under Justice Madan Mohan Punchhi to examine new issues in federal relations, including the role of the Governor and inter-state cooperation.
• Rajamannar Commission:
• Appointed by the Tamil Nadu Government in 1969 to study Centre-State relations and suggest ways to increase state autonomy.

The correct answer is Punjab.

Key Points

• Bhangra is a traditional folk dance that originated in the Majha region of the Punjab province, specifically in districts like Sialkot and Gujranwala (in modern-day Pakistan) and across the Indian Punjab border.
• The dance was historically performed by Punjabi farmers during the festival of Vaisakhi, which marks the arrival of the spring harvest and the successful reaping of the Rabi crops such as wheat.
• It is characterized by high-energy physical movements, including jumps, kicks, and wide arm gestures, designed to mimic agricultural activities like sowing seeds, tilling soil, and harvesting.
• The rhythmic foundation of Bhangra is provided by the Dhol, a large, double-headed barrel drum that dictates the pace and intensity of the performance through traditional Bolis (couplets).
• Over the 20th century, Bhangra evolved from a localized rural celebration into a globally recognized performance art, heavily influencing the music industry and diasporic culture in the United Kingdom and North America.

 Additional Information

• Rajasthan:
• Home to the famous Ghoomar dance, originally performed by the Bhil tribe, and Kalbelia, which is inscribed on the UNESCO Intangible Cultural Heritage list.
• Gujarat:
• Renowned for Garba and Dandiya Raas, which are circular dances traditionally performed during the nine-night Navratri festival in honor of the Goddess Amba.
• Maharashtra:
• The most prominent folk form is Lavani, performed to the beats of the Dholki, often featuring women in traditional nine-yard (Nauvari) sarees.
• Musical Accompaniments:
• Besides the Dhol, Bhangra utilizes instruments like the Chimta (metal tongs with bells), Tumbi (single-stringed instrument), and Algoza (double flute) to create its unique polyphonic sound.

The correct answer is The objects have different masses.

Key Points

• According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This law dictates that the forces between two interacting objects are always equal in magnitude.
• The relationship between the force applied and the resulting motion is governed by Newton's Second Law of Motion, which states that acceleration (a) is directly proportional to the net force (F) and inversely proportional to the mass (m), expressed as a = F / m.
• Even though the action-reaction force pair is identical in strength, the forces act on two different objects. If these objects possess different masses, their inertial resistance to the force will differ.
• Consequently, for a constant force F, an object with a smaller mass will experience a significantly greater acceleration, while an object with a larger mass will experience a much smaller acceleration.

 Additional Information

• Interacting Pairs:
• Action and reaction forces never act on the same object; they always act on different bodies. If they were to act on the same body, they would cancel each other out, resulting in a net force of zero and no acceleration.
• Inertia and Mass:
• Mass is a fundamental property that determines an object's inertia, or its resistance to changes in its state of motion.
• A more massive object requires a much larger force to achieve the same acceleration as a less massive object, which is why reaction forces often seem invisible (such as the Earth's reaction when a person jumps).
• Practical Application:
• Consider a rifle firing a bullet: the force exerted on the bullet is equal to the recoil force on the rifle. However, because the bullet's mass is tiny compared to the rifle's, the bullet accelerates to high speeds while the rifle only jolts back slightly.
• Similarly, when a person walks, they push the Earth backward with the same force the Earth pushes them forward. The Earth's massive size results in an acceleration so negligible it cannot be measured.

The correct answer is Phanishwar Nath Renu.

Key Points

• Maila Aanchal, first published in 1954, is the most celebrated work of Phanishwar Nath Renu and is considered a masterpiece of modern Hindi literature.
• It is widely recognized as the first Anchalik Upanyas (regional novel) in Hindi, a genre that emphasizes the unique culture, local dialects, and socio-economic conditions of a specific geographical region.
• The novel is set in the village of Maryganj, located in the Purnia district of Bihar, and captures the complex social tapestry of rural India during the transition to Independence.
• The plot revolves around Dr. Prashant, a young physician who arrives in the village to research malaria and kala-azar, only to be drawn into the web of local caste politics and corruption.
• Phanishwar Nath Renu was honored with the Padma Shri in 1970 for his significant literary contributions, particularly for bringing regional realism to the forefront of Hindi fiction.

 Additional Information

• Munshi Premchand:
• Known as the Upanyas Samrat (Emperor of Novels), he pioneered the transition of Hindi literature into social realism with legendary works like Godan, Gaban, and Nirmala.
• Yashpal:
• A prominent Hindi writer and political revolutionary whose epic novel Jhootha Sach provides one of the most detailed accounts of the Partition of India.
• Bhisham Sahni:
• An acclaimed author and playwright best known for his novel Tamas, which earned him the Sahitya Akademi Award for its powerful depiction of the 1947 riots.

The correct answer is 2001.

Key Points

• Pullela Gopichand etched his name in sports history by winning the prestigious All England Open Badminton Championships in the year 2001.
• In the final match held in Birmingham, he defeated the Chinese shuttler Chen Hong in straight sets with a score of 15-12, 15-6.
• With this monumental victory, he became only the second Indian to claim the title, following Prakash Padukone, who won it in 1980.
• His path to the championship was notable for a stunning victory over the then world number one, Peter Gade of Denmark, in the semi-finals.
• This win remains a significant milestone in Indian badminton, ending a 21-year drought for the nation at the world's oldest badminton tournament.

 Additional Information

• Prakash Padukone:
• He was the pioneer of Indian badminton, winning the All England title in 1980 by defeating Liem Swie King.
• Awards and Recognition:
• Pullela Gopichand has been honored with India's highest sporting honor, the Major Dhyan Chand Khel Ratna, in 2001.
• He received the Arjuna Award in 1999 and the Dronacharya Award in 2009 for his exceptional coaching contributions.
• He was also conferred with the Padma Bhushan, India's third-highest civilian award, in 2014.
• Legacy in Coaching:
• Post-retirement, he established the Pullela Gopichand Badminton Academy in Hyderabad.
• He has mentored elite athletes including Saina Nehwal, P.V. Sindhu, and Srikanth Kidambi, leading them to Olympic and World Championship successes.

The correct answer is The plan failed due to wars and droughts, leading to import dependence.

Key Points

• The Third Five-Year Plan (1961-1966), also known as the Gadgil Yojana, aimed at making the Indian economy self-reliant and self-generating, but it is considered the most unsuccessful plan due to its failure to meet a target growth rate of 5.6%, achieving only 2.84%. Hence, statement 1 is correct.
• Resources intended for industrial and economic infrastructure were diverted to national defense following the Sino-Indian War of 1962 and the Indo-Pakistani War of 1965, which severely hindered industrial performance. Hence, statement 1 is correct.
• The plan period witnessed a catastrophic drought in 1965-1966, which led to a sharp decline in agricultural output and forced India to become dependent on food grain imports, specifically under the PL-480 program from the United States. Hence, statement 1 is correct.
• Industrial growth failed to meet expectations as the lack of raw materials from the agricultural sector and a severe foreign exchange crisis limited the capacity of heavy industries. Hence, statement 2 and statement 3 are incorrect.

 Additional Information

• Plan Holiday (1966-1969):
• Due to the miserable failure of the Third Plan, the government was unable to draft a Fourth Plan immediately and instead implemented three Annual Plans.
• This period focused on stabilizing the economy and increasing agricultural productivity through the Green Revolution.
• Privatization and Liberalization:
• These concepts refer to the reduction of state control and the opening of the economy to private investment.
• They were formally introduced as part of the LPG (Liberalization, Privatization, and Globalization) reforms in 1991, not during the 1960s. Hence, statement 4 is incorrect.
• Rupee Devaluation:
• In June 1966, the Indian government devalued the Indian Rupee by approximately 36.5% to boost exports and address the Balance of Payments (BoP) crisis resulting from the 1965 war.

The correct answer is Vertebral column.

Key Points

• The spinal cord is a vital part of the Central Nervous System (CNS), acting as the primary highway for nerve impulses traveling between the brain and the rest of the body.
• Due to its soft and delicate nervous tissue composition, the spinal cord requires heavy protection, which is provided by the vertebral column (also known as the spine or backbone).
• The vertebral column is composed of a series of bones called vertebrae; there are typically 33 vertebrae in humans (some of which fuse to form the sacrum and coccyx).
• Each vertebra has a central opening called the vertebral foramen, and when stacked together, these openings form the vertebral canal (or spinal canal), which safely houses the spinal cord.
• This bony structure provides rigid protection against mechanical trauma and impact, while also supporting the weight of the body and allowing for flexibility and movement.

 Additional Information

• Ribs:
• These consist of 12 pairs of curved bones that form the thoracic cage, primarily protecting the heart and lungs rather than the spinal cord.
• Cerebellum:
• This is a major part of the hindbrain located at the back of the skull, responsible for coordinating voluntary movements, balance, and posture.
• Pons:
• A component of the brainstem located above the medulla oblongata, it serves as a communication bridge between different parts of the brain and regulates functions like sleep and respiration.
• Meninges and CSF:
• The spinal cord is further shielded by three layers of membranes called meninges (dura mater, arachnoid mater, and pia mater) and is cushioned by cerebrospinal fluid (CSF).

The correct answer is Poverty alleviation and employment generation.

Key Points

• The Fifth Five-Year Plan was designed for the period 1974 to 1979, with the primary objective of Garibi Hatao (Removal of Poverty) and the attainment of self-reliance.
• The plan placed significant emphasis on employment generation and social justice to reduce the gap between different economic strata of the population.
• The Minimum Needs Programme (MNP) was launched in the first year of the plan (1974) to provide essential services such as rural health, drinking water, primary education, and nutrition to the underprivileged.
• In 1975, the Indira Gandhi government introduced the Twenty Point Programme, which focused on improving the quality of life in rural areas through land reforms and liquidation of rural indebtedness.
• From a statistical perspective, the plan set a targeted growth rate of 4.4% per annum, and it successfully exceeded this by achieving an actual growth rate of 4.8%.
• This plan was unique as it was terminated one year ahead of its schedule in March 1978 by the newly elected Janata Party government.

 Additional Information

• Trade liberalization and Export-oriented growth:
• These concepts became the cornerstone of Indian economic policy much later, specifically during the 1991 LPG (Liberalization, Privatization, and Globalization) reforms.
• The Eighth Five-Year Plan (1992–1997) was the first to fully integrate these principles to stabilize the Balance of Payments.
• Industrialization:
• While industry is part of every plan, rapid industrialization with a focus on heavy and basic industries was the specific hallmark of the Second Five-Year Plan (1956–1961), based on the Mahalanobis Model.
• Rolling Plan (1978–1980):
• Following the termination of the Fifth Plan, the Janata Party introduced the Rolling Plan, which involved annual assessments of economic performance rather than a fixed five-year target.

The correct answer is 5.

Key Points

• In Olympic-style boxing, also known as amateur boxing, a panel consisting of five judges is responsible for scoring the bout to ensure a fair and transparent result.
• These five judges are positioned on all four sides of the boxing ring, which provides them with different vantage points to observe the technical execution and scoring blows of the athletes.
• The scoring is based on the 10-Point Must System, which was officially adopted for Olympic competition starting from the 2016 Rio de Janeiro Games, replacing the previous electronic punch-counting method.
• Under this system, the winner of each round is awarded 10 points, while the loser receives anywhere from 7 to 9 points based on their performance level as perceived by the panel.
• The use of five judges minimizes the risk of a single biased or incorrect scorecard determining the outcome, as the final winner is decided by the majority consensus of the panel.

 Additional Information

• Scoring Criteria:
• Judges evaluate boxers based on the number of quality blows landed on the target area, tactical superiority, and competitiveness shown throughout the rounds.
• A quality blow is defined as a punch that lands with the knuckle part of the glove on the front or sides of the head or body above the belt.
• Decision Types:
• A Unanimous Decision is declared when all five judges nominate the same boxer as the winner.
• A Split Decision occurs when three judges favor one boxer while the remaining two judges favor the opponent.
• Role of the Referee:
• While the five judges handle the scoring, the referee inside the ring focuses on enforcing rules, preventing fouls, and ensuring the safety of the boxers, but does not score the fight.

The correct answer is Atal Bhujal Yojana.

Key Points

• Atal Bhujal Yojana (ATAL JAL) is a Central Sector Scheme implemented by the Ministry of Jal Shakti to address the critical issue of groundwater depletion in India.
• The scheme was launched on December 25, 2019, to commemorate the 95th birth anniversary of former Prime Minister Atal Bihari Vajpayee.
• Its primary objective is to improve groundwater management through community participation, behavioral change, and demand-side interventions such as micro-irrigation and crop diversification.
• The project is implemented in identified water-stressed areas across seven states: Gujarat, Haryana, Karnataka, Madhya Pradesh, Maharashtra, Rajasthan, and Uttar Pradesh.
• It has a total outlay of Rs. 6,000 crore, which is shared in a 50:50 ratio between the Government of India and the World Bank.
• The initiative focuses on Gram Panchayat led groundwater management plans and capacity building to ensure sustainable water usage for agriculture and domestic needs.

 Additional Information

• Pradhan Mantri Kisan Samman Nidhi (PM-KISAN):
• A Central Sector Scheme launched in 2019 to provide income support of Rs. 6,000 per year to all landholding farmer families.
• The amount is transferred directly into the bank accounts of beneficiaries in three equal installments.
• Jal Jeevan Mission (JJM):
• Announced in August 2019 with the vision to provide Functional Household Tap Connections (FHTC) to every rural household by 2024.
• It follows a bottom-up approach where the community plays a key role in planning and implementing Har Ghar Jal.
• Atal Pension Yojana (APY):
• Launched in May 2015, this social security scheme targets workers in the unorganized sector.
• It provides a guaranteed minimum pension of Rs. 1,000 to Rs. 5,000 per month based on the contribution and age of joining.

The correct answer is Iron.

Key Points

• Iron is widely recognized as the backbone of modern civilization and the primary key metal of industrial development because it serves as the foundational material for almost all other industries.
• It is the essential raw material for manufacturing industrial machinery, construction equipment, and transportation systems like railways, bridges, and ships, which are vital for economic growth.
• The Industrial Revolution was fundamentally powered by the mass production of iron and its alloy, steel, enabling the transition from manual labor to mechanized manufacturing.
• The per capita consumption of steel (derived from iron) is a critical economic indicator used globally to measure a country's level of industrialization and infrastructure maturity.
• Iron ore is processed in blast furnaces to produce pig iron, which is then refined into various grades of steel suited for everything from surgical instruments to heavy defense tanks.

 Additional Information

• Copper
• Characterized by high electrical conductivity and malleability, it is primarily used in electronics, telecommunications, and power distribution.
• Aluminum
• Gained importance due to its low density and resistance to corrosion; it is indispensable in the aerospace industry and automobile manufacturing for reducing vehicle weight.
• Manganese
• Acts as a vital deoxidizing agent and alloying element; approximately 10 kg of manganese is required to manufacture one tonne of steel to increase its tensile strength and hardness.

The correct answer is National Action for Mechanized Sanitation Ecosystem.

Key Points

• The NAMASTE scheme is a central sector initiative designed to ensure the safety, dignity, and empowerment of sanitation workers by eliminating hazardous manual cleaning practices.
• It is a joint venture between the Ministry of Social Justice and Empowerment (MoSJE) and the Ministry of Housing and Urban Affairs (MoHUA), aiming for zero fatalities in sanitation work.
• The scheme focuses on the identification of Sewage and Septic Tank Workers (SSWs) across all Urban Local Bodies (ULBs) in India and provides them with specialized training and Personal Protective Equipment (PPE) kits.
• A core component of the project is the mechanization of sanitation operations, where workers are encouraged to become sanipreneurs by owning and operating mechanized cleaning vehicles through capital subsidies and interest subvention.
• It replaces the earlier Self-Employment Scheme for Rehabilitation of Manual Scavengers (SRMS) to better address the modern challenges of urban sanitation infrastructure.

 Additional Information

• Social Security and Health Benefits:
• Enrolled sanitation workers and their families are provided with health insurance coverage under the Ayushman Bharat-Pradhan Mantri Jan Arogya Yojana (AB-PMJAY).
• The scheme facilitates access to livelihood assistance, allowing workers to diversify their income sources and transition away from hazardous manual labor.
• Institutional Framework:
• Implementation is supported by the National Safai Karamcharis Finance and Development Corporation (NSKFDC).
• Cities are mandated to set up Sanitation Response Units (SRU) to manage emergency cleaning requests and ensure that only trained professionals with mechanized equipment handle septic management.
• The scheme aligns with the broader goals of Swachh Bharat Mission 2.0 to create garbage-free and water-secure cities.

The correct answer is 5.

Key Points

• The Union Cabinet, chaired by Prime Minister Narendra Modi, approved the expansion of the Ayushman Bharat Pradhan Mantri Jan Arogya Yojana (AB PM-JAY) to provide health coverage to all senior citizens aged 70 years and above.
• Senior citizens belonging to families already covered under AB PM-JAY will receive an additional top-up cover of up to Rs 5 lakh per year.
• This specific top-up cover is meant exclusively for the senior citizen and does not have to be shared with other family members who are below the age of 70.
• For senior citizens aged 70 and above who are part of families not currently covered by the scheme, a cover of Rs 5 lakh per year will be provided on a family basis.
• Eligible senior citizens will be issued a new, distinct card under the AB PM-JAY framework to access these benefits.

 Additional Information

• Ayushman Bharat PM-JAY:
• Launched in September 2018, it is recognized as the world’s largest publicly funded health assurance scheme.
• The scheme provides a health cover of Rs 5 lakh per family per year for secondary and tertiary care hospitalization.
• It originally aimed to cover approximately 12 crore poor and vulnerable families, representing the bottom 40% of the Indian population.
• Senior citizens already enrolled in other public health schemes like CGHS, ECHS, or Ayushman CAPF are given the choice to either continue their current scheme or migrate to AB PM-JAY.
• The expansion aims to benefit approximately 6 crore senior citizens across 4.5 crore households in India.

The correct answer is Vakataka dynasty.

Key Points

• Rudrasena II was a prominent ruler of the Vakataka dynasty, specifically belonging to the Nandivardhana-Pravarapura branch that controlled parts of the Deccan and Central India.
• He was the son of Prithvisena I and is primarily remembered for his significant matrimonial alliance with the Gupta Empire.
• He married Prabhavatigupta, the daughter of the powerful Gupta Emperor Chandragupta II (Vikramaditya). This alliance was a strategic move by the Guptas to secure their southern borders while campaigning against the Sakas (Western Kshatrapas).
• Rudrasena II reigned for a short period, approximately from 385 CE to 390 CE. After his premature death, his queen Prabhavatigupta acted as a regent for their minor sons, Divakarasena and Damodarasena, effectively bringing the Vakataka administration under Gupta influence for nearly two decades.
• The Vakatakas were known as Brahmins and were great patrons of Sanskrit literature and Brahmanical rituals, though they also supported the development of the Ajanta Caves.

 Additional Information

• Nanda dynasty
• Founded by Mahapadma Nanda in the 4th century BCE, this dynasty ruled the Magadha region.
• They were known for possessing a massive army and vast wealth, which deterred Alexander the Great from advancing further into India.
• Maurya dynasty
• Established by Chandragupta Maurya in 322 BCE after overthrowing the Nandas with the assistance of Chanakya.
• It was the first empire to unify most of the Indian subcontinent, reaching its zenith under Ashoka the Great.
• Gurjar-Pratihar dynasty
• An imperial power that ruled much of Northern India from the 8th to the 11th century CE.
• They are celebrated for their resistance against Arab invasions and their involvement in the Tripartite Struggle for the control of Kannauj.

The correct answer is 5.

Key Points

• The Augmented Satellite Launch Vehicle (ASLV) was a specialized project by the Indian Space Research Organisation (ISRO) designed to enhance payload capabilities to 150 kg for Low Earth Orbits (LEO).
• It was configured as a five-stage launch vehicle, utilizing solid propellant for all its stages to simplify the transition between experimental and operational phases.
• The configuration included two identical strap-on boosters acting as the first stage, which provided the necessary thrust to lift the 40-tonne vehicle off the launch pad.
• The core of the vehicle consisted of four successive stages, which were largely evolved from the technologies established during the SLV-3 program.
• ASLV acted as a critical technology demonstrator for closed-loop guidance, bulbous heat shields, and vertical integration techniques necessary for future heavy-lift vehicles.
• The first successful mission of the ASLV program was the ASLV-D3, launched on May 20, 1992, which successfully deployed the SROSS-C satellite into orbit.

 Additional Information

• SLV-3 (Satellite Launch Vehicle-3):
• India's first experimental launch vehicle, which was a four-stage all-solid propellant rocket.
• It successfully launched the Rohini satellite in 1980, making India the sixth nation to possess satellite launch capability.
• PSLV (Polar Satellite Launch Vehicle):
• A highly reliable four-stage vehicle that alternates between solid and liquid propulsion systems.
• It famously utilized the Vikas engine for its second stage and has been the mainstay for Sun-Synchronous Polar Orbit missions.
• GSLV (Geosynchronous Satellite Launch Vehicle):
• A three-stage heavy-lift vehicle that includes a Cryogenic Upper Stage (CUS) powered by liquid oxygen and liquid hydrogen.

The correct answer is C. Rajagopalachari.

Key Points

• Chakravarti Rajagopalachari, popularly known as Rajaji or CR, was a prominent Indian statesman, writer, and independence activist who became the first and only Indian Governor-General of independent India.
• He assumed the office of Governor-General on June 21, 1948, succeeding Lord Mountbatten, and served until January 26, 1950, when the office was abolished upon India becoming a Republic.
• During his tenure, he played a crucial role in the constitutional transition of India from a British Dominion to a Sovereign Democratic Republic.
• He was a leading figure in the Indian National Congress and was one of the first recipients of India's highest civilian award, the Bharat Ratna, in 1954.
• Before his appointment as Governor-General, he served as the Governor of West Bengal and later held positions as the Union Minister for Home Affairs and the Chief Minister of Madras State.

 Additional Information

• Vallabh Bhai Patel:
• Known as the Iron Man of India, he served as the first Deputy Prime Minister and Home Minister of independent India.
• He is credited with the political integration of over 560 princely states into the Indian Union.
• Rajendra Prasad:
• He was the first President of India, serving the longest term from 1950 to 1962.
• He was the President of the Constituent Assembly that drafted the Constitution of India.
• Jawaharlal Nehru:
• He was the first Prime Minister of independent India, holding the office from August 15, 1947, until his death in 1964.
• He is considered the architect of modern India and was a central figure in international politics through the Non-Aligned Movement.

The correct answer is 23.

Key Points

• The National Commission on Population (NCP), operating under the Ministry of Health and Family Welfare (MoHFW), constituted a Technical Group on Population Projections to estimate India’s demographic shifts for the period 2011–2036.
• According to the report, India is witnessing a significant demographic transition where the population of senior citizens (those aged 60 years and above) is expected to grow rapidly from 10.4 crores in 2011 to 22.7 crores by the year 2036.
• The projected figure of 22.7 crores, rounded to 23 crores, reflects the increasing life expectancy and the gradual aging of the Indian population as health services improve and fertility rates decline.
• The report highlights that the share of the elderly population in the total demographic is expected to rise from 8.6 percent in 2011 to approximately 14.9 percent by 2036.
• This demographic shift is more pronounced in southern states like Kerala and Tamil Nadu, where the aging process is faster compared to northern states, necessitating robust geriatric healthcare and social security frameworks.

 Additional Information

• Demographic Trends (2011–2036):
• Total Population: India’s total population is projected to increase from 121.1 crores in 2011 to 152.2 crores in 2036, a growth of 25.7 percent over twenty-five years.
• Median Age: The median age of the Indian population is expected to rise from 24.9 years in 2011 to 34.5 years by 2036, indicating that the nation is transitioning from a 'youthful' to a 'mature' demographic.
• Total Fertility Rate (TFR): The TFR is expected to decline from 2.34 during 2011–2015 to 1.73 during 2031–2035, which is below the replacement level of 2.1.
• Sex Ratio: The overall Sex Ratio of the population is projected to improve from 943 in 2011 to 952 by 2036, showing a positive trend in gender distribution.
• Youth Proportion: The proportion of the population in the age group 0–14 years is expected to decline sharply from 30.9 percent in 2011 to 20.1 percent by 2036 due to falling birth rates.

The correct answer is 7.

Key Points

• The 3000 metres steeplechase is a standard track and field event that requires athletes to clear a total of 35 obstacles throughout the race.
• The race typically consists of an initial distance of approximately 270 metres without any obstacles, followed by seven complete laps of the track.
• Each of these seven full laps contains five jumps, which are strategically placed around the 400-metre circuit.
• The total obstacle count is divided into 28 hurdle jumps (dry hurdles) and 7 water jumps, as each lap features exactly one water jump.
• The distribution of jumps per lap includes four standard hurdles and one water jump, usually located on the second curve of the track.

 Additional Information

• Obstacle Specifications:
• The hurdles for the men's event are set at a height of 0.914 metres (36 inches), while for the women's event, they are 0.762 metres (30 inches).
• Unlike standard hurdles, steeplechase barriers are solid and stationary, designed to be stepped upon by the athletes if necessary.
• Each barrier must be at least 3.94 metres wide to allow multiple runners to clear the obstacle at the same time.
• Water Jump Details:
• The water pit is 3.66 metres long and 3.66 metres wide, starting immediately after the barrier.
• The water depth is approximately 70 centimetres at the barrier end and slopes upward to match the track surface level at the other end.
• Athletes usually step on the water jump barrier to gain leverage and leap further into the shallower part of the pit to maintain momentum.
• Race Structure:
• The order of obstacles is generally: hurdle 1, hurdle 2, hurdle 3, water jump, and hurdle 4 before crossing the finish line for the next lap.

The correct answer is Japan.

Key Points

• The Global Firepower Index 2025 ranks the military strength of nations based on over 60 individual factors, including manpower, equipment, logistics, and geography.
• The United States retains its position at the top of the index with the most powerful military, followed closely by Russia in second place.
• China holds the 3rd position globally, maintaining its status in the top 5 due to its massive naval fleet and technological advancements.
• India is ranked 4th in the world, staying within the top 5 due to its significant active personnel and vast land power.
• South Korea has successfully secured the 5th rank, largely driven by its advanced defense industry and high state of military readiness.
• Japan is currently ranked 7th in the 2025 index, falling behind the top 5 nations despite having a highly sophisticated Maritime Self-Defense Force.

 Additional Information

• Global Firepower Index:
• A perfect PowerIndex score is 0.0000, which is realistically unattainable; the closer a country is to this score, the more powerful its military.
• The index does not account for nuclear capabilities, focusing solely on conventional warfare potential.
• It considers financial factors like defense budget and purchasing power parity (PPP) to assess sustainment capabilities.
• Japan's Military Profile:
• Japan operates under the Article 9 of its Constitution, which limits its forces to Self-Defense purposes (JSDF).
• Despite being 7th, Japan possesses one of the most advanced Anti-Submarine Warfare (ASW) and Air Defense systems in the Indo-Pacific region.

Shortcut Trick

Solve Brackets first: 78 + 45 = 123.

Then perform Multiplication: 64 × 2 = 128.

Combine results: 123 − 128 + 93.

Calculate difference and add: −5 + 93 = 88.

∴ The correct answer is 88.

Alternate Method

Given: (78 + 45) − 64 × 2 + 93

Rule Used: Apply the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rule.

⇒ 123 − 64 × 2 + 93 (Solving Bracket)

⇒ 123 − 128 + 93 (Solving Multiplication)

⇒ 123 + 93 − 128 (Rearranging for Addition)

⇒ 216 − 128 (Solving Addition)

⇒ 88 (Solving Subtraction)

∴ The correct answer is 88.

Additional Information

BODMAS Rule

It defines the precedence of operations where Brackets are solved first, followed by Orders (powers/roots), Division and Multiplication (same priority), and finally Addition and Subtraction (same priority).

Left-to-Right Rule

When operations like Addition and Subtraction appear together, they should be solved from left to right to maintain mathematical accuracy.

Negative Result Handling

If a larger number is subtracted from a smaller number, the result carries a negative sign (e.g., 123 − 128 = −5).

Shortcut Trick

Solve using the BODMAS rule priority order.

First, solve the bracket: 61 + 18 = 79.

Next, perform multiplication: 79 × 2 = 158.

Then, simplify the remaining terms: 87 − 45 + 158 − 49 = 151.

∴ The correct answer is 151.

Alternate Method

Given:

87 − 45 + (61 + 18) × 2 − 49

Method:

Follow the BODMAS rule (Bracket, Orders, Division, Multiplication, Addition, Subtraction).

⇒ 87 − 45 + (79) × 2 − 49

⇒ 87 − 45 + 158 − 49

⇒ (87 + 158) − (45 + 49)

⇒ 245 − 94

⇒ 151

∴ The correct answer is 151.

Additional Information

BODMAS Rule

The rule defines the order of operations as Brackets, Orders (roots/powers), Division, Multiplication, Addition, and finally Subtraction.

Grouping Positive and Negative Terms

For faster calculation after multiplication and division, group all positive integers and all negative integers separately before doing the final subtraction.

Shortcut Trick

Total number of terms in the series = 6 (as denominators are 1×3, 3×5, ..., 11×13).

Sum of integer parts = 666 × 6 = 3996.

Sum of fractional parts = Number of terms ÷ (First factor × Last factor) = 6 ÷ (1 × 13) = 6/13.

Total sum = 3996 + 6/13 = 3996 6/13.

∴ The correct answer is 3996 6/13.

Alternate Method

Given: 666(1/3) + 666(1/15) + 666(1/35) + 666(1/63) + 666(1/99) + 666(1/143)

Formula: A^b/_c = A + b/c and 1/(n × (n+d)) = (1/d) × [1/n − 1/(n+d)]

⇒ Separate the integer and fractional parts:

⇒ (666 + 666 + 666 + 666 + 666 + 666) + (1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 1/143)

⇒ Sum of integers = 666 × 6 = 3996

⇒ Fractional part = 1/(1×3) + 1/(3×5) + 1/(5×7) + 1/(7×9) + 1/(9×11) + 1/(11×13)

⇒ Using telescoping series: 1/2 × [(1 − 1/3) + (1/3 − 1/5) + ... + (1/11 − 1/13)]

⇒ Fraction sum = 1/2 × [1 − 1/13] = 1/2 × [12/13] = 6/13

⇒ Total = 3996 + 6/13 = 3996 6/13

∴ The correct answer is 3996 6/13.

Additional Information

Mixed Fraction Property

A mixed fraction A^b/_c can always be written as the sum of an integer and a proper fraction: A + b/c.

Telescoping Series Formula

For a series of type 1/[a×(a+d)], the sum is given by (1/d) × [1/First Factor − 1/Last Factor].

Shortcut for Unit Numerator Series

If the difference between factors in the denominator is constant (d) and the numerator is 1, the sum is also equal to (Number of terms) ÷ (First factor × Last factor).

Shortcut Trick

Identify a perfect square (x) less than 56 such that the sum of the number and its square root equals 56.

Testing 49: √49 = 7.

Sum check: 49 + 7 = 56 (Condition satisfied).

Square of the number = 49² = 2401.

∴ The correct answer is 2401.

Alternate Method

Given: Sum of a number and its positive square root is 56.

Formula Used: x + √x = 56

Let the number be x. According to the problem:

⇒ x + √x = 56

Let √x = y (where y > 0)

⇒ y² + y = 56

⇒ y² + y − 56 = 0

⇒ y² + 8y − 7y − 56 = 0

⇒ y(y + 8) − 7(y + 8) = 0

⇒ (y + 8)(y − 7) = 0

⇒ y = 7 or y = −8

Since the square root is positive, y = 7.

⇒ x = y² = 7² = 49

⇒ Square of the number = x² = 49²

⇒ 49² = 2401

∴ The correct answer is 2401.

Additional Information

Quadratic Equations

A quadratic equation in the form ay² + by + c = 0 can be solved using the factorisation method or the formula y = (−b ± √(b² − 4ac)) ÷ 2a.

Squares ending in 9

The square of any number ending in 9 will always end in 1 (since 9 × 9 = 81). For example, 9² = 81, 19² = 361, 49² = 2401.

Calculation Shortcut for 49²

Using (a − b)² = a² − 2ab + b²: 49² = (50 − 1)² = 2500 − 100 + 1 = 2401.

Shortcut Trick

Check Divisibility by 3 (sum of digits) and Divisibility by 11 (alternate digit difference).

For 10131: Sum = 1 + 0 + 1 + 3 + 1 = 6 (Divisible by 3).

Difference of alternate digits = (1 + 1 + 1) − (0 + 3) = 3 − 3 = 0 (Divisible by 11).

Since it satisfies both rules, the number is divisible by 33.

∴ The correct answer is 10131.

Alternate Method

Given: A number must be divisible by both 3 and 11.

Check each option systematically:

Option 1: 10010

⇒ Sum of digits = 1 + 0 + 0 + 1 + 0 = 2 (Not divisible by 3).

Option 2: 10131

⇒ Sum of digits = 1 + 0 + 1 + 3 + 1 = 6 (Divisible by 3 because 6 ÷ 3 = 2).

⇒ Sum of odd-position digits (1, 3, 5) = 1 + 1 + 1 = 3.

⇒ Sum of even-position digits (2, 4) = 0 + 3 = 3.

⇒ Difference = 3 − 3 = 0 (Divisible by 11).

⇒ 10131 is divisible by both 3 and 11.

Option 3: 10340

⇒ Sum of digits = 1 + 0 + 3 + 4 + 0 = 8 (Not divisible by 3).

Option 4: 10233

⇒ Sum of digits = 1 + 0 + 2 + 3 + 3 = 9 (Divisible by 3).

⇒ Sum of odd-position digits = 1 + 2 + 3 = 6.

⇒ Sum of even-position digits = 0 + 3 = 3.

⇒ Difference = 6 − 3 = 3 (Not divisible by 11).

∴ The correct answer is 10131.

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 its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.

Divisibility Rule of 33

Since 3 and 11 are co-prime, any number divisible by both 3 and 11 is also divisible by their product (3 × 11 = 33).

Shortcut Trick

Break the expression into individual square roots: √1024, √0.49, and √0.0049.

Solve √1024 directly: 32² = 1024, so √1024 = 32.

For decimals, √0.49 = 0.7 and √0.0049 = 0.07 (decimal places are halved).

Sum = 32 + 0.7 + 0.07 = 32.77.

∴ The correct answer is 32.77.

Alternate Method

Given: √1024 + √0.49 + √0.0049

Step-by-step Calculation:

⇒ √1024 = 32 (since 30² = 900 and 40² = 1600, 32² = 1024)

⇒ √0.49 = √(49 ÷ 100) = 7 ÷ 10 = 0.7

⇒ √0.0049 = √(49 ÷ 10000) = 7 ÷ 100 = 0.07

⇒ Required Value = 32 + 0.7 + 0.07

⇒ Required Value = 32.77

∴ The correct answer is 32.77.

Additional Information

Square Root of Decimal Fractions

If a perfect square has 2n decimal places, its square root will have exactly n decimal places. For example, √0.0001 = 0.01.

BODMAS Rule

Always evaluate terms within brackets, orders (powers/roots), then division, multiplication, addition, and subtraction in sequence.

Estimation for Squares

To find √x, identify the nearest base squares (like 10², 20², 30²) to narrow down the range before checking the unit digit.

Shortcut Trick

Side (a) of rhombus = Perimeter ÷ 4 = 116 ÷ 4 = 29 cm.

Half of the given diagonal (d₁/2) = 40 ÷ 2 = 20 cm.

Using Pythagorean triplet (20, 21, 29): the other half-diagonal (d₂/2) = 21 cm.

Full length of second diagonal (d₂) = 21 × 2 = 42 cm.

Area = (1/2) × d₁ × d₂ = (1/2) × 40 × 42 = 840 cm².

∴ The correct answer is 840 cm².

Alternate Method

Given: Perimeter = 116 cm, Diagonal 1 (d₁) = 40 cm.

Formula Used:

1. Side (a) = Perimeter ÷ 4
2. Area = (1/2) × d₁ × d₂
3. Relation: a² = (d₁/2)² + (d₂/2)²

Calculations:

⇒ Side (a) = 116 ÷ 4 = 29 cm

⇒ Let d₂ be the second diagonal.

⇒ a² = (d₁/2)² + (d₂/2)²

⇒ 29² = (40/2)² + (d₂/2)²

⇒ 841 = 20² + (d₂/2)²

⇒ 841 = 400 + (d₂/2)²

⇒ (d₂/2)² = 841 − 400 = 441

⇒ d₂/2 = √441 = 21 cm

⇒ Diagonal 2 (d₂) = 21 × 2 = 42 cm

⇒ Area = (1/2) × 40 × 42

⇒ Area = 20 × 42 = 840 cm²

∴ The correct answer is 840 cm².

Additional Information

Properties of a Rhombus

All four sides are equal, and diagonals bisect each other at 90 degrees.

Area via Trigonometry

Area = a² × sin(θ), where a is the side and θ is any internal angle.

Diagonal and Side Relation

4a² = d₁² + d₂². This formula is derived directly from the Pythagorean theorem applied to the four right-angled triangles formed by diagonals.

Shortcut Trick

The given expression is the sum of first n consecutive odd numbers starting from 1.

Number of terms (n) = (Last term + 1) ÷ 2 = (355 + 1) ÷ 2 = 178.

Shortcut formula: Sum of first n odd numbers = n².

Total Sum = 178² = 31684.

∴ The correct answer is 31684.

Alternate Method

Given: An Arithmetic Progression (AP) series: 1, 3, 5, ..., 355.

First term (a) = 1, Common difference (d) = 2, Last term (l) = 355.

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

⇒ 355 = 1 + (n − 1) × 2

⇒ 354 = (n − 1) × 2

⇒ n − 1 = 177 → n = 178

⇒ S = (178 ÷ 2) × (1 + 355)

⇒ S = 89 × 356

⇒ S = 31684

∴ The correct answer is 31684.

Additional Information

Sum of first n natural numbers

The sum of the first n natural numbers is calculated as S_n = n(n + 1) ÷ 2.

Sum of first n even numbers

The sum of the first n even numbers (2, 4, 6, ...) is given by the formula S_n = n(n + 1).

Sum of squares and cubes

Sum of squares = n(n + 1)(2n + 1) ÷ 6 | Sum of cubes = [n(n + 1) ÷ 2]².

Shortcut Trick

If every observation in a series is divided by a constant k, the average of the series is also divided by the same constant k.

Here, the original average is N and each number is divided by 9.

New Average = Original Average ÷ 9

New Average = N/9

∴ The correct answer is N/9.

Alternate Method

Given:

Total numbers (n) = 25

Average of 25 numbers = N

Operation: Each number is divided by 9.

Formula Used:

Average = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ Sum of 25 numbers = Average × Total numbers = N × 25 = 25N

⇒ Let the numbers be x₁, x₂, ..., x₂₅. Then x₁ + x₂ + ... + x₂₅ = 25N

⇒ New numbers are x₁/9, x₂/9, ..., x₂₅/9

⇒ New Sum = (x₁/9) + (x₂/9) + ... + (x₂₅/9) = (x₁ + x₂ + ... + x₂₅) ÷ 9

⇒ New Sum = 25N ÷ 9

⇒ New Average = New Sum ÷ 25 = (25N/9) ÷ 25

⇒ New Average = N/9

∴ The correct answer is N/9.

Additional Information

Addition and Subtraction Rule

If a constant k is added to or subtracted from every term, the new average becomes (Old Average + k) or (Old Average − k) respectively.

Multiplication Rule

If every term is multiplied by a constant k, the new average becomes (Old Average × k).

Weighted Average

When combining two groups with different counts (n₁, n₂) and averages (A₁, A₂), Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

If the Average of a group remains unchanged after adding a new member, then the value of that new member must be exactly equal to the initial average.

Given initial average of 9 persons = 12 years.

Since the average remains same after adding the 10th person, the age of the 10th person = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given:

Initial count of persons = 9

Initial average age = 12 years

New count of persons (after adding 10th person) = 10

New average age = 12 years

Formula Used:

Sum of observations = Average × Number of observations

Age of new person = (New Sum) − (Initial Sum)

Calculations:

⇒ Total age of 9 persons = 9 × 12 = 108 years

⇒ Total age of 10 persons = 10 × 12 = 120 years

⇒ Age of 10th person = Total age of 10 persons − Total age of 9 persons

⇒ Age of 10th person = 120 − 108 = 12 years

∴ The correct answer is 12 years.

Additional Information

Effect of Adding/Removing on Average

If a value higher than the current average is added, the average increases. If a value lower than the average is added, the average decreases.

Deviation Method

The sum of deviations of all observations from their average is always zero. New Value = Old Average + (Increase in Average × New Total Count).

Combined Average Formula

Average_combined = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂), where n is the count and A is the average of respective groups.

Shortcut Trick

The smallest number that is a multiple of several numbers is their Least Common Multiple (LCM).

LCM(6, 8, 15, 9): Identify the prime factors and select the highest power of each.

Factors: 2³ (from 8), 3² (from 9), and 5¹ (from 15).

Calculation: 8 × 9 × 5 = 360.

∴ The correct answer is 360.

Alternate Method

Given: The numbers are 6, 8, 15, and 9.

Method: Prime Factorization Method to find LCM.

⇒ Factorizing 6: 2¹ × 3¹ ⇒ Factorizing 8: 2³ ⇒ Factorizing 9: 3² ⇒ Factorizing 15: 3¹ × 5¹ ⇒ LCM = Product of the highest powers of all prime factors involved. ⇒ LCM = 2³ × 3² × 5¹ ⇒ LCM = 8 × 9 × 5 ⇒ LCM = 360

∴ The correct answer is 360.

Additional Information

Relation between HCF and LCM

For any two positive integers 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).

LCM of Fractions

The LCM of a set of fractions is calculated as: LCM of Numerators ÷ HCF of Denominators.

Division Method for LCM

In this method, divide the numbers by common prime factors until the remaining numbers are co-prime, then multiply all divisors and remaining numbers.

Shortcut Trick

Convert all units to centimetres: 500 cm, 320 cm, and 940 cm.

Required length = HCF (Highest Common Factor) of (500, 320, 940).

HCF(500, 320, 940) = 20.

∴ The correct answer is 20 cm.

Alternate Method

Given:

Length 1 = 5 metres

Length 2 = 3 metres 20 cm

Length 3 = 9 metres 40 cm

Formula Used:

To find the greatest possible length that can measure exactly multiple lengths, we calculate the HCF of those values in the same unit.

1 metre = 100 cm

Calculations:

⇒ Length 1 = 5 × 100 = 500 cm

⇒ Length 2 = (3 × 100) + 20 = 320 cm

⇒ Length 3 = (9 × 100) + 40 = 940 cm

⇒ Finding HCF of (500, 320, 940):

⇒ Factors of 500 = 2² × 5³

⇒ Factors of 320 = 2⁶ × 5¹

⇒ Factors of 940 = 2² × 5¹ × 47

⇒ Common factors = 2² × 5¹ = 4 × 5 = 20

⇒ HCF = 20 cm

∴ The correct answer is 20 cm.

Additional Information

HCF (Highest Common Factor)

It is the greatest number which divides each of the two or more numbers exactly. It is also known as G.C.D (Greatest Common Divisor).

LCM (Least Common Multiple)

It is the smallest number which is exactly divisible by each of the given numbers. Relationship: Product of two numbers = HCF × LCM.

Unit Standardization

Always ensure all measurements are in the same unit (either all in m or all in cm) before calculating HCF or LCM.

Shortcut Trick

Total units in the Mixture = 8 (Water) + 17 (Milk) = 25 units.

To find the Percentage, divide the water part by the total parts: 8 ÷ 25.

Since 1 ÷ 25 = 4%, then 8 ÷ 25 = 8 × 4% = 32%.

∴ The correct answer is 32%.

Alternate Method

Given:

Weight of Water = 8 kg

Weight of Milk = 17 kg

Formula Used:

Percentage of a component = (Component Weight ÷ Total Weight) × 100

Calculations:

⇒ Total Weight of the Mixture = 8 kg + 17 kg = 25 kg

⇒ Water Percentage = (8 ÷ 25) × 100

⇒ Water Percentage = 8 × (100 ÷ 25)

⇒ Water Percentage = 8 × 4

⇒ Water Percentage = 32%

∴ The correct answer is 32%.

Additional Information

Percentage Concentration

The concentration of a substance in a Mixture is defined as the weight of that substance divided by the total weight of the solution, expressed as a Percentage.

Ratio to Percentage Conversion

If a Mixture has two components in ratio a:b, the Percentage of component 'a' is [a ÷ (a + b)] × 100.

Fractional Values

Common conversions: 1/4 = 25%, 1/5 = 20%, 1/20 = 5%, and 1/25 = 4%. These help in fast mental calculations.

Shortcut Trick

In profit and loss, the difference between CP and SP is the absolute Loss or Profit.

Here, Loss percentage 18% → Rs. 504.

Dividing by 18, 1% of CP → 504 ÷ 18 = Rs. 28.

Since there is a loss, Selling Price (SP) = 100% − 18% = 82%.

SP = 82 × 28 = Rs. 2296.

∴ The correct answer is Rs. 2296.

Alternate Method

Given:

Difference (Loss) = Rs. 504

Loss Percentage = 18%

Formula Used:

Loss = (Loss% ÷ 100) × Cost Price (CP)

Selling Price (SP) = CP − Loss

Calculations:

⇒ 18% of CP = 504

⇒ (18 ÷ 100) × CP = 504

⇒ CP = (504 × 100) ÷ 18

⇒ CP = 28 × 100 = 2800

⇒ SP = CP − Loss

⇒ SP = 2800 − 504

⇒ SP = 2296

∴ The correct answer is Rs. 2296.

Additional Information

Loss and CP Relationship

When an article is sold at a loss, the Cost Price is always greater than the Selling Price. CP = SP + Loss.

Selling Price Formula

SP = CP × (100 − Loss%) ÷ 100. This directly relates SP to the percentage of CP remaining after the loss.

Percentage Change

Loss% = (Loss ÷ CP) × 100. Always remember that Profit and Loss percentages are calculated on the Cost Price unless specified otherwise.

Shortcut Trick

Total units = 80 (LCM of 40 and 80); Efficiencies: M = 2, N = 1.

Combined efficiency = 2 + 1 = 3 units/day.

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

Work left = 80 − 24 = 56 units.

Percentage of total work left = (56 ÷ 80) × 100 = 70%.

∴ The correct answer is 70%.

Alternate Method

Given:

Time taken by M = 40 days

Time taken by N = 80 days

Working duration = 8 days

Formula Used:

Total Work = LCM of individual days

Efficiency = Total Work ÷ Time

⇒ Combined efficiency of M and N = 2 + 1 = 3 units/day

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

⇒ Remaining work = Total Work − Work Done = 80 − 24 = 56 units

⇒ Percentage of work left = (Remaining Work ÷ Total Work) × 100

⇒ Percentage = (56 ÷ 80) × 100 = 70%

∴ The correct answer is 70%.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken. If the ratio of time is x:y, the ratio of efficiency is y:x.

Combined Work Rate

When multiple people work together, their daily efficiencies are added to find the total work done per day.

Work Done Fraction

Work done in n days = n × (1/A + 1/B), where A and B are the total days required by each person individually.

Shortcut Trick

Efficiency ratio (Q+R) : P = 5 : 1 (Sum = 6) and (P+R) : Q = 3 : 1 (Sum = 4).

Equate total efficiency (LCM of 6 and 4 = 12): P = 2, Q = 3, and (P+Q+R) = 12.

Total Work = 12 × 6 = 72 units.

Time for Q alone = 72 ÷ 3 = 24 days.

∴ The correct answer is 24 days.

Alternate Method

Given:

Efficiency of (Q + R) = 5 × (Efficiency of P)

Efficiency of (P + R) = 3 × (Efficiency of Q)

Time taken by (P + Q + R) = 6 days

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Total Efficiency = P + (Q + R) = P + 5P = 6P

⇒ Total Efficiency = Q + (P + R) = Q + 3Q = 4Q

⇒ Since Total Efficiency is constant, 6P = 4Q

⇒ P : Q = 4 : 6 = 2 : 3

⇒ Let Efficiency of P = 2 and Q = 3, then Total Efficiency = 6 × 2 = 12 units/day

⇒ Total Work = 12 units/day × 6 days = 72 units

⇒ Time for Q alone = 72 units ÷ 3 units/day = 24 days

∴ The correct answer is 24 days.

Additional Information

Work and Efficiency Relation

Time is inversely proportional to Efficiency (Time = Work ÷ Efficiency). Higher efficiency results in less time taken.

Combined Efficiency

When multiple people work together, their total efficiency is the sum of their individual efficiencies (E_total = E₁ + E₂ + ... + E_n).

Wages and Efficiency

Wages are generally distributed in the ratio of work done, which is equivalent to the ratio of efficiencies when everyone works for the same duration.

Shortcut Trick

Since the distance is constant, speed is inversely proportional to time.

Ratio of Time = 6.5 hr : 5 hr = 13 : 10

Ratio of Speed = 10 : 13

Given walking speed (10 units) = 10 km/hr, then cycle speed (13 units) = 13 km/hr.

∴ The correct answer is 13 km/hr.

Alternate Method

Given:

Walking Speed (S₁) = 10 km/hr

Walking Time (T₁) = 6 hr 30 min = 6.5 hr

Cycling Time (T₂) = 5 hr

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Total Distance = S₁ × T₁

⇒ Total Distance = 10 × 6.5 = 65 km

⇒ Speed of cycle (S₂) = Total Distance ÷ T₂

⇒ S₂ = 65 ÷ 5

⇒ S₂ = 13 km/hr

∴ The correct answer is 13 km/hr.

Additional Information

Relation between Speed, Time and Distance

Speed is defined as the rate at which an object covers distance. Formula: Speed = Distance ÷ Time.

Inverse Proportion in Speed

If the distance remains constant, Speed₁ × Time₁ = Speed₂ × Time₂.

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal halves of a journey at speeds x and y, Average Speed = 2xy ÷ (x + y).

Shortcut Trick

Downstream speed = 28 km/hr.

Upstream speed = Downstream speed − (2 × Stream speed) = 28 − (2 × 6) = 16 km/hr.

Total Time = (Downstream Distance ÷ Downstream Speed) + (Upstream Distance ÷ Upstream Speed).

Total Time = (280 ÷ 28) + (80 ÷ 16) = 10 + 5 = 15 hr.

∴ The correct answer is 15 hr.

Alternate Method

Given:

Downstream speed (D) = 28 km/hr

Speed of stream (S) = 6 km/hr

Formula Used:

Speed of boat in still water (B) = D − S

Upstream speed (U) = B − S

Time = Distance ÷ Speed

Calculations:

⇒ Speed of boat in still water (B) = 28 − 6 = 22 km/hr

⇒ Upstream speed (U) = 22 − 6 = 16 km/hr

⇒ Time taken for downstream = 280 ÷ 28 = 10 hr

⇒ Time taken for upstream = 80 ÷ 16 = 5 hr

⇒ Total time = 10 + 5 = 15 hr

∴ The correct answer is 15 hr.

Additional Information

Speed of Boat and Stream

Speed of boat in still water (B) = (Downstream Speed + Upstream Speed) ÷ 2.

Speed of Current

Speed of current or stream (S) = (Downstream Speed − Upstream Speed) ÷ 2.

Relative Speed in Boats

In downstream, the stream helps the boat (B + S), while in upstream, it opposes the boat (B − S).

Shortcut Trick

Selling Price (SP) = 130% of Cost Price = 1.3 × 2000 = ₹2600.

Discount = Marked Price − Selling Price = 3000 − 2600 = ₹400.

Discount % = (Discount ÷ Marked Price) × 100 = (400 ÷ 3000) × 100 = 13.33%.

∴ The correct answer is 13.33%.

Alternate Method

Given:

Marked Price (MP) = ₹3000

Cost Price (CP) = ₹2000

Profit Percentage = 30%

Formula Used:

1. Selling Price (SP) = CP × (1 + Profit%/100)
2. Discount % = [(MP − SP) ÷ MP] × 100

Calculations:

⇒ Profit Amount = 30% of ₹2000

⇒ Profit Amount = (30 ÷ 100) × 2000 = ₹600

⇒ Selling Price (SP) = CP + Profit = 2000 + 600 = ₹2600

⇒ Discount Amount = MP − SP = 3000 − 2600 = ₹400

⇒ Discount % = (400 ÷ 3000) × 100

⇒ Discount % = (4 ÷ 30) × 100 = 40 ÷ 3 = 13.33%

∴ The correct answer is 13.33%.

Additional Information

Relationship between CP and MP

The ratio of Marked Price to Cost Price is given by MP/CP = (100 + Profit%) ÷ (100 − Discount%).

Mark-up Percentage

Mark-up % = [(MP − CP) ÷ CP] × 100. It is the percentage by which the cost price is increased to set the marked price.

Effective Discount for Successive Discounts

For two successive discounts of a% and b%, the single equivalent discount is (a + b − ab/100)%.

Shortcut Trick

To ensure no loss, the Selling Price (SP) must be equal to the Cost Price (CP).

Maximum Discount % = [Markup % ÷ (100 + Markup %)] × 100

Maximum Discount % = [45 ÷ (100 + 45)] × 100 = (45 ÷ 145) × 100

Maximum Discount % = (9 ÷ 29) × 100 ≈ 31.03%

∴ The correct answer is 31.03 percent.

Alternate Method

Given:

Marked Price (MP) is 45% more than Cost Price (CP).

Condition for no loss: SP ≥ CP.

Formula Used:

1. MP = CP × (1 + Markup%/100)
2. Discount % = [(MP − SP) ÷ MP] × 100

Calculations:

Let the Cost Price (CP) of the article be 100.

⇒ Marked Price (MP) = 100 + 45% of 100 = 145.

⇒ For no loss, the minimum Selling Price (SP) allowed is equal to CP.

⇒ SP = 100.

⇒ Maximum Discount = MP − SP = 145 − 100 = 45.

⇒ Maximum Discount % = (Discount ÷ MP) × 100

⇒ Maximum Discount % = (45 ÷ 145) × 100

⇒ Maximum Discount % = (9 ÷ 29) × 100 ≈ 31.034%

∴ The correct answer is 31.03 percent.

Additional Information

Relationship between CP, MP, and Discount

The formula relating CP and MP with Profit and Discount is: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

Markup Percentage

Markup % is always calculated on the Cost Price: Markup % = [(MP − CP) ÷ CP] × 100.

No Profit No Loss Condition

This state occurs when Selling Price equals Cost Price, meaning Profit = 0 and Loss = 0.

The correct answer is 'information'.

Key Points

• The passage explores the importance of libraries and the various services they provide to the community.
• The context of the sentence refers to the types of resources and services that libraries offer for free to the public.
• 'Information' is a fundamental concept associated with libraries, as they serve as repositories of knowledge, data, and learning materials.
• When listed alongside 'books' and 'resources', 'information' completes the group logically, as books and resources are primary sources of information.
• Other options like 'food', 'games', or 'money' do not represent the core, essential service that defines a library in a general educational context.

Therefore, the correct answer is 'Option 3'.

Complete Passage: Libraries have always been an important part of society. They offer free access to books, resources, and 1. information for people of all ages. Libraries are also places where people can read, learn, and 2. study quietly. Many now provide computers and internet access, helping users with research and job 3. applications. Librarians help visitors find what they need and often 4. run workshops or reading programs. Despite the rise of digital media, libraries still play a vital 5. role in learning and community development.

Additional Information

• Food: While some libraries have cafes, it is not a primary resource they are known for providing 'free access' to as a core mission.
• Games: Some modern libraries include games in their collections, but it is less universal and less central than the provision of information.
• Money: Libraries are publicly funded or charitable entities that provide services to the public, rather than places that distribute money.

The correct answer is 'study'.

Key Points

• The sentence describes common activities that take place within a library environment.
• The passage mentions that libraries are places where people can read and learn.
• The word 'study' fits perfectly in this context, as it refers to the act of acquiring knowledge or investigating a subject, which is a primary purpose of visiting a library.
• The adverb 'quietly' further supports the choice of 'study', as libraries are traditionally known for maintaining a silent atmosphere conducive to concentration and academic work.
• Other options like 'sleep', 'shop', or 'meet' do not align with the educational theme established by the verbs 'read' and 'learn'.

Therefore, the correct answer is 'Option 2'.

Complete Passage: Libraries have always been an important part of society. They offer free access to books, resources, and 1. information for people of all ages. Libraries are also places where people can read, learn, and 2. study quietly. Many now provide computers and internet access, helping users with research and job 3. applications. Librarians help visitors find what they need and often 4. run workshops or reading programs. Despite the rise of digital media, libraries still play a vital 5. role in learning and community development.

Additional Information

• Sleep (सोना): To rest in a state of sleep; not the primary intended use of a public library.
• Shop (खरीददारी): To visit a store to buy goods; libraries offer free borrowing services rather than retail.
• Meet (मिलना): To come together; while people do meet in libraries, the context of 'reading' and 'learning quietly' specifically highlights 'study'.

The correct answer is 'applications'.

Key Points

• The sentence describes how modern libraries provide computers and internet access to assist users with specific tasks.
• The phrase 'job applications' is a standard collocation referring to the formal process or forms submitted to apply for employment.
• In the context of the passage, libraries support community development and employment by helping users complete their applications online.
• Therefore, 'applications' is the most appropriate noun to follow 'job' in this specific context of using library resources for career-related tasks.

Therefore, the correct answer is 'Option 4'.

Complete Passage: Libraries have always been an important part of society. They offer free access to books, resources, and 1. information for people of all ages. Libraries are also places where people can read, learn, and 2. study quietly. Many now provide computers and internet access, helping users with research and job 3. applications. Librarians help visitors find what they need and often 4. run workshops or reading programs. Despite the rise of digital media, libraries still play a vital 5. role in learning and community development.

Additional Information

• Hunting: Often used in the phrase 'job hunting', but 'job applications' more specifically describes the task performed using a computer.
• Search: While 'job search' is a common term, it usually refers to the act of looking for a job rather than the specific process of applying.
• Looking: This word is grammatically incorrect when placed directly after 'job' without a preposition like 'for'.

The correct answer is 'run'.

Key Points

• The sentence describes the various tasks and responsibilities performed by librarians within a community setting.
• The verb in the blank needs to describe the action of managing, organizing, or conducting activities like workshops or reading programs.
• "Run" is commonly used in English to mean to be in charge of or to organize/manage a program, business, or activity.
• Therefore, "run" fits perfectly as it indicates that librarians organize and lead these workshops.

Therefore, the correct answer is 'Option 1'.

Complete Passage: Libraries have always been an important part of society. They offer free access to books, resources, and 1. information for people of all ages. Libraries are also places where people can read, learn, and 2. study quietly. Many now provide computers and internet access, helping users with research and job 3. applications. Librarians help visitors find what they need and often 4. run workshops or reading programs. Despite the rise of digital media, libraries still play a vital 5. role in learning and community development.

Additional Information

• Hide: To put something in a place where it cannot be seen or found. This does not fit the context of organizing public programs.
• Open: While a workshop can be opened, "run" is the more appropriate and idiomatic term for the ongoing management and execution of such programs.
• Fix: To repair or mend something. This is not related to the management of educational programs or workshops.

The correct answer is 'role'.

Key Points

• The passage discusses the enduring importance of libraries as essential hubs for learning and community development.
• The sentence requires a noun that fits the idiomatic expression 'play a vital role', which means to be an important part of a process or situation.
• 'Role' refers to the function or part played by something in a particular context, which aligns with how libraries contribute to society.
• Other options like 'building', 'house', or 'rule' do not logically fit the context of describing a function or contribution within the given phrase.

Therefore, the correct answer is 'Option 3'.

Complete Passage: Libraries have always been an important part of society. They offer free access to books, resources, and 1. information for people of all ages. Libraries are also places where people can read, learn, and 2. study quietly. Many now provide computers and internet access, helping users with research and job 3. applications. Librarians help visitors find what they need and often 4. run workshops or reading programs. Despite the rise of digital media, libraries still play a vital 5. role in learning and community development.

Additional Information

• Building: Refers to a physical structure, which does not fit the abstract concept of having an impact or function.
• House: Refers to a home or a specific type of building; it is contextually incorrect here.
• Rule: Refers to a regulation or a law, which does not describe the contribution of libraries to development.

The correct answer is: Vitiate.

Key Points

• The word 'Vitiate' means to spoil or impair the quality, value, or efficiency of something; it can also mean to make something legally invalid or ineffective. (बिगाड़ना)
• Example: Strategic mistakes can vitiate the entire plan and lead to failure.
• 'Vitiate' is correctly spelt and refers to the act of corrupting or making something faulty or defective. (दूषित करना)
• Example: A technical error in the filing process might vitiate the legal contract.
• Hence, we can infer that the word 'Vitiate' is the correctly spelt option among the given choices.

Therefore, the correct answer is: Vitiate.

Additional Information

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

• Veracity (सत्यता): The quality of being true, accurate, or the habit of telling the truth.
• Example: The jury had serious doubts about the veracity of the witness's testimony.
• Vermilion (सिंदूरी रंग): A brilliant red color or a pigment made from mercury sulfide.
• Example: The traditional bride wore a mark of vermilion on her forehead.
• Varmine (अशुद्ध वर्तनी): This is an incorrect spelling. The correct word is 'Vermin', which refers to small animals or insects that are harmful to crops or carry disease. (नुकसानदेह कीड़े-मकोड़े)
• Example: The old warehouse was infested with vermin and had to be professionally cleaned.

The correct answer is sacrifice.

Key Points

• The word sacrifise as written in the provided sentence is orthographically incorrect. The correct English spelling is sacrifice, which uses the letter c instead of s in the third syllable.
• The term is defined as the act of giving up something highly valued for the sake of something else considered more important or worthy. In the context of the sentence, it refers to the selfless acts of healthcare workers.
• Etymologically, the word is derived from the Old French sacrifise (though modern French uses sacrifice) and the Latin sacrificium. The Latin root consists of sacer (holy) and facere (to make).
• The spelling error occurs due to phonetic confusion, as the letter c followed by i or e produces a soft /s/ sound, leading writers to mistakenly substitute it with the letter s.

 Additional Information

• Review of other terms in the sentence:
• Dedication: This is a correctly spelled noun referring to the quality of being committed to a task or purpose. It originates from the Latin dedicare, meaning to proclaim or devote.
• Relentless: This adjective is spelled correctly and signifies something that is harsh, inflexible, or unceasing. It is a combination of the word relent and the suffix -less.
• Pandemic: A correctly spelled noun/adjective describing an outbreak of a disease that occurs over a wide geographic area. It stems from the Greek pan (all) and demos (people), relating to its global scale impact.

The correct answer is: simple.

Key Points

• The word 'challenging' refers to something that is difficult in a way that tests a person's ability, determination, or skill. (चुनौतीपूर्ण)
• Example: Learning a new language can be a very challenging but rewarding process.
• 'Simple' refers to something that is easy to understand or do, and does not require much effort or complexity. (सरल)
• Example: The solution to the problem was quite simple once we understood the basic rules.
• Hence, we can infer that the most appropriate opposite of 'challenging' is 'simple'.

Therefore, the correct answer is- simple.

Additional Information

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

• Onerous (कष्टदायक/भारी): A task or responsibility that involves a great deal of effort, trouble, or difficulty.
• Example: He found the onerous duties of his new job quite overwhelming.
• Taxing (थकाऊ): Something that is physically or mentally demanding and makes you feel tired.
• Example: It was a taxing journey that left everyone exhausted by the end of the day.
• Formidable (भयानक/दुर्जेय): Inspiring fear or respect through being impressively large, powerful, or capable.
• Example: The champion was a formidable opponent who had never lost a single match.

The correct answer is Has the vaccine been administered to all patients by the doctors?.

Key Points

• The original sentence is in the Present Perfect Tense and follows the Interrogative structure: Have/Has + Subject + V3 + Object?
• In the conversion to Passive Voice, the Object of the active sentence (the vaccine) becomes the Subject of the passive sentence.
• Because the vaccine is a Singular Noun, the auxiliary verb must change from 'Have' to Has to ensure proper Subject-Verb Agreement.
• The passive form of the Present Perfect requires the inclusion of the auxiliary verb been placed between the new subject and the Past Participle (V3) form of the verb (administered).
• The agent or original subject (the doctors) is introduced at the end of the sentence using the preposition by.
• The final structure for the Passive Interrogative becomes: Has + New Subject (the vaccine) + been + V3 (administered) + by + Agent?

 Additional Information

• Subject-Verb Agreement:
• The word Have is used with plural subjects or the pronouns I, you, we, and they.
• The word Has is strictly used with third-person singular subjects like 'the vaccine'.
• Tense Preservation:
• Using Were would incorrectly change the tense to Simple Past.
• The construction must remain in the Present Perfect to maintain the original meaning.
• Sentence Type:
• An interrogative sentence must retain its Question format by placing the auxiliary verb before the subject.
• Changing the order to 'The vaccine has been...' transforms it into an Assertive sentence, which is grammatically incorrect for this conversion.

The correct answer is Were prayers being chanted by the monks in the monastery?.

Key Points

• The given sentence is an Interrogative Sentence in the Past Continuous Tense. The active voice structure for this tense is: Was/Were + Subject + Verb (ing form) + Object?
• To convert a Past Continuous interrogative sentence into Passive Voice, the structure used is: Was/Were + Object (New Subject) + being + Past Participle (V3) + by + Subject (New Object)?
• In the active sentence, the monks is the Subject, chanting is the Verb, and prayers is the Object.
• When converting to passive, the plural object prayers becomes the new subject. Since it is plural, the auxiliary verb Were is retained at the beginning of the sentence.
• The verb chanting is transformed into being chanted to maintain the continuous aspect in the passive form.
• The original subject the monks is placed after the preposition by. The prepositional phrase in the monastery remains at the end to provide context.

 Additional Information

• Understanding the construction of other tenses helps in identifying the incorrect options:
• Simple Past Passive: Uses the structure Was/Were + V3. This is why 'Were prayers chanted...' is incorrect as it lacks the continuous marker being.
• Past Perfect Passive: Uses the structure Had + been + V3. This changes the timeline of the action from 'ongoing in the past' to 'completed before another past action'.
• Present Continuous Passive: Uses Is/Am/Are + being + V3. This is incorrect because the original sentence is set in the Past Tense, and the tense must remain consistent during voice conversion.
• Voice Change Principle: In English grammar, while the Voice (Active to Passive) changes, the Tense of the sentence must remain the same. The focus simply shifts from the doer of the action to the receiver of the action.

The correct answer is 'at'.

 

Key Points

• In English grammar, the noun 'attempt' is commonly followed by the preposition 'at' when referring to an effort made to achieve a specific target, goal, or record.
• The phrase 'attempt at something' or 'attempt at doing something' is a standard idiomatic collocation used to describe trying to accomplish a feat.
• In this context, Deepak is trying to break or reach the world record, so 'at' is the most appropriate preposition to link the attempt to the objective.

Therefore, the correct answer is Option 2.

 

Complete Sentence: 'Deepak made several attempts at the world record in the long jump, but in vain.'

 

Additional Information

• Option 1: 'for' is often used with the verb 'strive' or 'aim', but for the noun 'attempt' in the context of a record, 'at' is preferred.
• Option 3: 'in' is typically used for locations or time periods and does not fit the target-oriented nature of the sentence.
• Option 4: 'about' is used to indicate a subject or theme, which is incorrect in this grammatical structure.

The correct answer is drag their feet.

Key Points

• The underlined phrase drag their foot is an incorrect variation of the established English idiom drag one's feet.
• The idiom drag one's feet (or drag their feet) means to act with reluctance or to deliberately delay a process because one does not want to do it.
• In the context of the sentence, the authorities are stalling the implementation of a court order, which fits the figurative meaning of avoiding or postponing action.
• Linguistically, idioms are fixed expressions; the plural noun feet is a mandatory component of this specific phrase, making the singular foot grammatically unacceptable in this context.
• Options such as drag in their foot or drag with their feet are incorrect because they introduce superfluous prepositions that are not part of the standard idiomatic structure.

 Additional Information

• Idiomatic Consistency:
• Fixed expressions like drag one's feet do not follow standard compositional rules, meaning their parts cannot be substituted for synonyms or different grammatical numbers without losing the intended meaning.
• The term foot-dragging is a derived noun used in political and legal discourse to describe prevarication or intentional obstruction.
• Synonymous Expressions:
• Stonewall: To refuse to provide information or help, especially to delay progress.
• Procrastinate: To keep delaying something that must be done, often out of laziness or reluctance.
• Dilly-dally: To waste time through indecision or aimless action.

The correct answer is 'in accord'.

 

Key Points

• The prepositional phrase 'in accord' means to be in agreement, harmony, or unison with someone or something.
• In the given sentence, the clause 'they make a very good team' indicates a positive relationship and effective cooperation between the chairman and the officers.
• The phrase 'in accord with' is commonly used to show that different parties are working together harmoniously toward a common goal.

Therefore, the correct answer is Option 4.

 

Complete Sentence:'The chairman is in accord with the officers and they make a very good team.'

 

Additional Information

• Option 1: 'in conflict' means to be in disagreement or at odds, which contradicts the idea of being a 'very good team'.
• Option 2: 'in doubt' refers to a state of uncertainty or skepticism, which does not fit the context of professional teamwork here.
• Option 3: 'away' means to be absent or at a distance; while grammatically possible, it does not explain why they form a 'very good team'.

The correct answer is Three-fourths of the cake has been eaten.

Key Points

• Pluralization of Fractions: In English grammar, when a fraction has a numerator greater than 1 (such as 2, 3, or 5), the denominator must be in its plural form. Therefore, while we say one-fourth, we must say three-fourths.
• Subject-Verb Agreement with Fractions: When a fraction is followed by the preposition of, the verb agrees with the noun that follows the preposition. If the noun is singular or uncountable, a singular verb is used. If the noun is plural, a plural verb is used.
• Analysis of the Noun: In this sentence, the noun following the fraction is cake, which is singular. Therefore, the auxiliary verb must also be singular. The singular auxiliary verb has is the correct choice to accompany cake.
• Grammatical Consolidation: The original sentence used Three-fourth, which lacks the necessary plural suffix -s for the denominator. The correct improvement must include both the pluralized denominator and the singular verb has.
• Therefore, the option Three-fourths of the cake has been eaten is the correct one.

 Additional Information

• Countable vs. Uncountable Contexts:
• If the sentence referred to multiple separate cakes, such as three-fourths of the cakes, the verb would change to have to maintain agreement with the plural noun.
• The word cake in this context refers to a single whole item being partitioned, thus necessitating has.
• Hyphenation Rules:
• While the provided answer does not use a hyphen, it is common in formal writing to hyphenate fractions when they function as adjectives (e.g., a three-fourths share). When acting as a noun, the hyphen is often omitted, though usage varies between style guides.
• Fractional Proportions:
• This rule applies to all proportions, including percentages. For example, fifty percent of the cake has been eaten, but fifty percent of the guests have arrived.

The correct answer is Option 2.

 

Key Points

• The primary grammatical error in the sentence is the use of the verb form comes after the modal verb will.
• In English grammar, modal auxiliary verbs (such as will, shall, can, could, must, may, and might) are always followed by the base form (infinitive without 'to') of the main verb.
• The word comes is the third-person singular present form. To correct the sentence, it must be replaced with the base form come.
• Thus, the error lies in the word comes.

Therefore, the correct answer is comes.

 

Correct Sentence: 'He will come to the office next week.'

 

Additional Information

• Will: This is a modal verb used to indicate the future tense. It does not change its form regardless of the subject (I, you, he, she, they).
• To the office: This is a prepositional phrase acting as an adverb of place, indicating the destination. It is grammatically correct.
• Next week: This is a time expression used to denote a point in the future, which is consistent with the use of the future tense helper will.