SSC GD Constable 2026 Official Paper (Held On 20 May, 2026 Shift 3) (Previous Year Paper)

Logic followed here is:

Logic: The series is formed by applying a constant numerical increment to the positional value of the first letter and a constant decrement to the positional value of the second letter in each term.

Hence, the correct answer is "Option 4".

Logic followed here is.

Logic: The series consists of two letters in each term where the first letters follow an increment of 5 and the second letters follow a decrement of 5 in their positional values.

The missing term in the series is ZM.

Hence, the correct answer is "Option 2".

The logic followed here is that the series consists of two patterns, one for the first letter and another for the second letter of each term, based on their positional values in the English alphabet.

The missing term is LC.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: In each set, the second letter cluster is formed by adding 2 to the positional values of the letters of the first cluster. The third letter cluster is formed by adding 3 to the positional values of the letters of the second cluster.

For the given sets:

(1) (QX, SZ, VC)

(2) (SZ, UB, XE)

Similarly, for the alternatives:

Option 2) (KH, MJ, PM)

As we can see, (KH, MJ, PM) follows the same logic as the given sets.

Hence, the correct answer is "Option 2".

Concept:

A month has 5 of a specific weekday if that weekday falls within the first few days of the month, depending on the total number of days:

• In a month with 31 days, any weekday that falls on the 1^st, 2^nd, or 3^rd of the month occurs 5 times.
• In a month with 30 days, any weekday that falls on the 1^st or 2^nd of the month occurs 5 times.
• In a month with 28 days, every weekday occurs exactly 4 times.

Calculation:

First, we determine the day of the week for January 1, 1915. Using the reference that January 1, 1900 was a Monday:

Number of years from 1900 to 1914 = 15 years.

Number of leap years in this period (1904, 1908, 1912) = 3.

Total odd days = 15 + 3 = 18 days.

18 ÷ 7 = 2 weeks and 4 odd days.

Day on January 1, 1915 = Monday + 4 days = Friday.

I. August 1915:

August has 31 days.

Odd days from January 1 to August 1, 1915 = Jan(3) + Feb(0) + Mar(3) + Apr(2) + May(3) + Jun(2) + Jul(3) = 16 days.

16 ÷ 7 = 2 weeks and 2 odd days.

Day on August 1, 1915 = Friday + 2 days = Sunday.

If August 1 is Sunday, then August 2 is Monday and August 3 is Tuesday.

Since the 3^rd of August is a Tuesday and the month has 31 days, Tuesday occurs 5 times (on the 3^rd, 10^th, 17^th, 24^th, and 31^st).

II. December 1915:

December has 31 days.

Odd days from August 1 to December 1, 1915 = Aug(3) + Sep(2) + Oct(3) + Nov(2) = 10 days.

10 ÷ 7 = 1 week and 3 odd days.

Day on December 1, 1915 = Sunday + 3 days = Wednesday.

The first three days of December are Wednesday (1^st), Thursday (2^nd), and Friday (3^rd).

As Tuesday does not fall on the 1^st, 2^nd, or 3^rd, there are only 4 Tuesdays in December 1915 (on the 7^th, 14^th, 21^st, and 28^th).

Therefore, only August 1915 had 5 Tuesdays.

Hence, the correct answer is Only I.

Logic followed here is.

Logic: The figure in the box on the right side has one line less than the figure in the box on the left side.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: All the letters and shapes are shiifted 2 places in clockwise direction

Hence, the correct answer is "Option 2".

Given:

QF100 : RH220

MK270 : NM390

Similarly, LX150 : ?

Hence, the related letter-number cluster is MZ270.

Hence, the correct answer is 'Option 1'.

Given:

DKM140 : HNE240 :: TPF160 : ? :: LTJ320 : EWM420

DKM140 : HNE240

LTJ320 : EWM420

TPF160 : ?

Hence, the correct answer is 'Option 2'.

The logic followed here is:

Logic: Second Number = First Number + 40

For the pair 8345 : 8385

⇒ 8345 + 40 = 8385.

For the pair 9297 : 9337

⇒ 9297 + 40 = 9337.

Applying the same logic to the first pair

2349 : ?

⇒ 2349 + 40 = 2389.

Hence, the correct answer is 'Option 2'.

The logic followed here is:

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

For the first pair 159 : 483

⇒ (159 × 3) + 6

⇒ 477 + 6 = 483.

Applying the same logic to the third pair

914 : 2748

⇒ (914 × 3) + 6

⇒ 2742 + 6 = 2748.

Applying the same logic to the second pair

726 : ?

⇒ (726 × 3) + 6

⇒ 2178 + 6 = 2184.

Hence, the correct answer is 'Option 3'.

Logic followed here is.

Logic: The code for each word is determined by comparing the given sentences to find common words and their corresponding codes across different sentences.

Hence, the correct answer is "Option 4".

Logic followed here is.

Logic: Each term in the series consists of two letters and a number, where each component follows a specific incremental pattern.

Hence, the correct answer is "Option 4".

The logic followed for the series involves analyzing the patterns of the letters and the numbers independently.

As per the established logic, the second term should have been QJX400. Because the letters K and Y do not follow the −3 and +4 positional shifts respectively, QKY400 is the wrong term.

Hence, the correct answer is "Option 4".

Concept:

Hour hand covers 360° in 12 hours.

Angular distance covered by the hour hand in 1 hour = 360/12 = 30°

Angular distance covered by the hour hand in 60 minutes = 30°

Angular distance covered by the hour hand in 1 minute = 30/60 = ½°

Minute hand covers 360° in 60 minutes.

Angular distance covered by the minute hand in 1 minute = 360/60 = 6°

Calculation:

Given time is 4:50 AM.

Value of minute = 50

Angle covered by the minute hand from the 12 o clock position = 50 × 6 = 300°

Angle covered by the hour hand from the 12 o clock position = (4 × 30) + (50 × ½) = 120 + 25 = 145°

Angle between hour and minute hands = 300° − 145° = 155°

Hence, the angle between the hour hand and minute hand at 4:50 AM is 155°.

Alternate Method

The angle between the hour hand and minute hand can be calculated using the formula:

Angle = $|60H - 11M|\over 2$

Here, H = 4 and M = 50.

So, Angle = $|(60 \times 4 - 11 \times 50)|\over 2$

Angle = $|240 - 550|\over 2$

Angle = $310 \over 2$ = 155°

Therefore, the correct option is 1.

Concept:

Hour hand covers 360° in 12 hours

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

Angular distance covered in 60 minutes = 30°

Angular distance covered in 1 minute = 1/2°

Minute hand covers 360° in 60 minutes

1 minute = 360/60 ⇒ 1 minute = 6°

Calculation:

Given time is 9:10 PM

Minute = 10

Angle covered by the minute hand = 10 × 6 = 60°

Angle covered by the hour hand = 9 × 30 + 10 × 1/2 = 270 + 5 = 275°

Angle between the hour and minute hands = 275 − 60 = 215°

Since the question asks for the angle between the hands and typically refers to the interior angle (less than 180°):

Angle = 360 − 215 = 145°

Hence, the angle between the hour hand and minute hand is 1450

Alternate Method

The angle between the hour hand and minute hand = $|60H - 11M| \over 2$

Here, H = 9 and M = 10.

So, Angle = $(60 \times 9 - 11 \times 10) \over 2$

Angle = $(540 - 110) \over 2$ = 430 / 2 = 215°

The interior angle = 360° − 215° = 145°

Hence, the correct answer is 145°

The logic followed in this series: Rotation of box in clockwise direction and incresing the line half by half.

Hence, the correct figure is "Option 2".

The logic followed here is:

Hence, the correct answer is "Option 1".

The logic followed here is: Decreasing number of arrows by 1 and shifting the triangle left and right to the corner also changing dark and light shade alternatively.

Hence, the correct figure is "Option 3".

Given:

Present age ratio = 9 : 10

Sum of present ages = 95 years

Calculation:

Total ratio = 9 + 10 = 19 parts

19 parts = 95 years

1 part = 95 ÷ 19 = 5 years

Present ages:

First person = 9 × 5 = 45 years

Second person = 10 × 5 = 50 years

After 8 years:

First person = 45 + 8 = 53 years

Second person = 50 + 8 = 58 years

Required ratio = 53 : 58

Hence, the correct answer is "Option 4".

The correct answer is Ganga and Narmada.

Key Points

• The Vindhya Range is a vast, discontinuous chain of mountain ridges, highlands, and plateau escarpments in Central India, traditionally forming the boundary between North India and South India.
• It acts as a primary geographical watershed, a natural divide that separates the drainage basins of the Ganga River system in the north from the Narmada River system in the south.
• The northern slopes of the Vindhyas drain into the Ganga basin through tributaries such as the Chambal, Betwa, Ken, and Son rivers, which eventually join the Yamuna or the Ganga.
• The Narmada River flows through a narrow rift valley located immediately south of the Vindhya Range, separating it from the parallel Satpura Range.
• Historically and geologically, the range has prevented the mixing of the perennial Himalayan-fed systems of the north with the rain-fed peninsular rivers flowing through the central rift.

 Additional Information

• Narmada and Tapi:
• These are the two major west-flowing rivers of India.
• They are separated by the Satpura Range, which lies between the two river valleys.
• Satpura Range:
• Located south of the Vindhyas, it originates in eastern Gujarat and runs through Maharashtra and Madhya Pradesh to Chhattisgarh.
• It separates the Narmada basin from the Tapi basin to its south.
• Godavari and Krishna:
• These are the largest east-flowing rivers in the Peninsular Plateau.
• Their basins are separated by the Balaghat Range and the Ajanta Hills in the Deccan Plateau region.
• Amarkantak Plateau:
• This is a significant geological region where the Vindhya and Satpura ranges meet, serving as the source for the Narmada, Son, and Johila rivers.

The correct answer is Gujarat.

Key Points

• The Vallabhi kingdom was the seat of power for the Maitraka dynasty, which ruled the Saurashtra region of western India from approximately 475 CE to 775 CE.
• The city of Vallabhi, the capital of this kingdom, is situated in the present-day Bhavnagar district of Gujarat.
• The dynasty was founded by Senapati Bhatarka, who was a military governor under the Gupta Empire; as the central authority of the Guptas collapsed, the Maitrakas established an independent and powerful state.
• Vallabhi emerged as a premier center of learning in ancient India, often ranked alongside Nalanda for its academic rigor and intellectual environment, attracting students from across the subcontinent.
• The kingdom is historically significant for hosting the Second Jain Council in the 5^th or 6^th century CE, which played a pivotal role in the formal codification of the Svetambara Jain Agamas.
• The region benefited from its coastal location in Gujarat, fostering extensive maritime trade and economic prosperity during the early medieval period.

 Additional Information

• Maitraka Dynasty and Culture:
• The rulers of Vallabhi were largely followers of Shaivism, yet they demonstrated religious pluralism by providing significant grants to Buddhist monasteries and Jain temples.
• Famous Chinese traveler Xuanzang (Hsuan-tsang), who visited in the 7^th century, recorded that the city had over 100 Buddhist monasteries and was a thriving commercial port.
• The kingdom reached its zenith under rulers like Dhruvasena II, who was a contemporary and son-in-law of the North Indian emperor Harshavardhana.
• Other Regional Dynasties:
• Rajasthan: This state was the primary domain of the Gurjara-Pratiharas and the Chauhan dynasties during the post-Gupta and early medieval eras.
• Maharashtra: In the same period, this region was dominated by the Vakatakas, followed by the Early Chalukyas of Badami and the Rashtrakutas.
• Madhya Pradesh: The Malwa region within this state was ruled by the Aulikaras and later became the center for the Paramara dynasty.

The correct answer is Late expanding.

Key Points

• The Demographic Transition Model (DTM) is a framework that describes the historical shift of birth and death rates in societies as they develop economically.
• India is currently categorized in Stage 3, known as the Late expanding stage, characterized by a declining birth rate and a low death rate.
• Statistical data from the National Family Health Survey (NFHS-5) confirms that India’s Total Fertility Rate (TFR) has fallen to 2.0, which is below the replacement level fertility of 2.1.
• While the mortality rate has stabilized at a low level due to advancements in healthcare, sanitation, and immunization, the population continues to grow because of population momentum.
• The decline in birth rates is attributed to factors such as increasing female literacy, higher levels of urbanization, and widespread awareness of family planning methods.

 Additional Information

• Stage 1: High stationary
• Characterized by high birth and high death rates, resulting in minimal population growth.
• In India, this phase ended around 1921, which is historically recognized as the Year of the Great Divide due to the onset of a consistent decline in mortality.
• Stage 2: Early expanding
• Marked by a high birth rate and a rapidly falling death rate, leading to a population explosion.
• India navigated this stage between 1921 and 1981, during which massive improvements in food security and medicine drastically reduced the death rate.
• Stage 4: Low stationary
• Defined by low birth and low death rates, leading to a stable or slowly growing population.
• This stage is typically observed in highly developed countries with advanced industrial economies.

The correct answer is Government of India Act, 1935.

Key Points

• The Government of India Act, 1935 is considered the blueprint of the Indian Constitution because nearly 60 to 70 percent of the current Constitution’s provisions are derived from it.
• It was the longest and most detailed act passed by the British Parliament, featuring 321 sections and 10 schedules, providing a comprehensive administrative framework for the country.
• The Act proposed the establishment of an All-India Federation comprising British Indian provinces and Princely States as voluntary units.
• It introduced Provincial Autonomy by abolishing Diarchy in the provinces and allowing them to function as autonomous administrative units.
• Key structural elements such as the Federal Scheme, the Office of Governor, Public Service Commissions, Judiciary, and Emergency Provisions were adopted from this Act into the Indian Constitution.
• It also established the Reserve Bank of India (1935) and a Federal Court (1937) to further institutionalize the governance of British India.

 Additional Information

• Morley-Minto Reforms (1909):
• Formally known as the Indian Councils Act 1909, it introduced separate electorates for Muslims.
• It is often criticized for sowing the seeds of communalism in Indian politics.
• Montagu-Chelmsford Reforms (1919):
• Enacted as the Government of India Act 1919, it introduced the system of Diarchy (rule of two) in the provinces.
• It established a bicameral legislature at the central level for the first time.
• Indian Independence Act, 1947:
• This act ended British sovereignty over India and provided for the creation of two independent dominions: India and Pakistan.
• It abolished the office of the Secretary of State for India and the title of Emperor of India.

The correct answer is 78^th Independence Day.

Key Points

• During his address from the ramparts of the Red Fort on India's 78^th Independence Day on August 15, 2024, Prime Minister Narendra Modi highlighted pivotal initiatives for youth empowerment and national progress.
• The Pradhan Mantri Viksit Bharat Rozgaar Yojana stands as a key welfare scheme designed to facilitate sustainable employment and skill enhancement among Indian youth.
• This initiative aligns with the vision of Viksit Bharat @ 2047, focusing on expanding job opportunities, encouraging first-time employees through financial incentives, and boosting industrial training.
• The scheme forms a core part of the central government's comprehensive package aimed at supporting over 4.1 crore youth over a five-year period.

 Additional Information

• Viksit Bharat Vision:
• It is the national roadmap to transition India into a fully developed nation by the centenary year of its independence in 2047.
• Key sectors of focus include technological innovation, modern infrastructure, sustainable agriculture, and quality education.
• Other Key Occasions:
• 76^th Republic Day: Celebrated on January 26, 2025, marking the anniversary of the implementation of the Constitution of India in 1950.
• 155^th Gandhi Jayanti: Observed on October 2, 2024, honoring the birth anniversary of Mahatma Gandhi, celebrated globally as the International Day of Non-Violence.

The correct answer is 500.

Key Points

• The demonetization of 1978 was officially carried out under the High Denomination Bank Notes (Demonetisation) Act, 1978, which came into effect on January 16, 1978.
• The Janata Party coalition government, led by Prime Minister Morarji Desai, initiated this move with the primary goal of curbing black money, tax evasion, and the shadow economy.
• The specific high-value currency notes that were declared no longer legal tender were the 1,000, 5,000, and 10,000 rupee denominations.
• The 500 rupee note was not demonetized in 1978 because it was not in active circulation at that time. It was reintroduced by the Reserve Bank of India (RBI) much later, in October 1987, to manage the growing volume of cash transactions and inflation.
• At the time of the 1978 exercise, I. G. Patel served as the Governor of the Reserve Bank of India, and the ordinance was issued by the then President Neelam Sanjiva Reddy.

 Additional Information

• History of High-Denomination Notes:
• 10,000 Rupee Note: This was the highest denomination ever printed. It was first introduced in 1938, demonetized in 1946, reintroduced in 1954, and finally demonetized again in 1978.
• 5,000 Rupee Note: Introduced in 1954 along with the 1,000 and 10,000 notes, it remained in circulation until the 1978 demonetization.
• 1,000 Rupee Note: This denomination has been demonetized three times in Indian history (1946, 1978, and 2016).
• Other Demonetization Events:
• 1946 Demonetization: The first instance in India, where 500, 1,000, and 10,000 rupee notes were withdrawn by the British administration.
• 2016 Demonetization: Occurred on November 8, 2016, where the 500 and 1,000 rupee notes were scrapped, representing nearly 86 percent of the cash in circulation.

The correct answer is 2023.

Key Points

• The Digital Personal Data Protection (DPDP) Act was officially enacted in 2023 after receiving the Presidential assent on August 11, 2023.
• On January 3, 2025, the Ministry of Electronics and Information Technology (MeitY) unveiled the much-anticipated draft rules to operationalize the provisions of this landmark legislation.
• The Act represents India's first dedicated comprehensive data protection law, designed to regulate how Data Fiduciaries (entities that process data) handle the personal information of Data Principals (individuals).
• The 2023 framework focuses on the principles of consent-based processing, purpose limitation, and data minimization to ensure digital privacy in an increasingly connected economy.
• The draft rules released in January 2025 provide specific procedures for grievance redressal, the functioning of the Data Protection Board of India, and the requirements for obtaining verifiable parental consent for children's data.

 Additional Information

• Core Components of the DPDP Act 2023:
• Data Protection Board of India: An independent regulatory body established to monitor compliance, conduct inquiries, and impose financial penalties.
• Financial Penalties: The Act prescribes significant penalties for data breaches or non-compliance, reaching up to Rs 250 crore for specific violations.
• Rights of Data Principals: Individuals hold the right to access information, the right to correction and erasure, and the right to nominate a person to exercise their rights in case of death or incapacity.
• Duties of Data Fiduciaries: Organizations must implement security safeguards, notify the Board and affected individuals in case of a breach, and appoint a Data Protection Officer (DPO) if they are categorized as Significant Data Fiduciaries.
• Evolution from Previous Frameworks:
• Before the 2023 Act, data privacy was primarily governed by the Information Technology (Reasonable Security Practices and Procedures and Sensitive Personal Data or Information) Rules, 2011, which were limited in scope.
• The IT Act, 2000 provided the initial legal foundation for electronic governance but lacked the robust protections required for modern digital personal data.

The correct answer is Kutiyattam.

Key Points

• Kutiyattam, a Sanskrit theatrical tradition from Kerala, is one of India's oldest living art forms, dating back over 2,000 years.
• It was the first Indian art form to be recognized by UNESCO as a Masterpiece of the Oral and Intangible Heritage of Humanity in 2001, and was later included in the Representative List in 2008.
• The performance is traditionally held in Koothambalams, which are specialized theaters located within Hindu temple complexes in Kerala.
• It is characterized by a unique combination of Sanskrit drama and local Malayalam stylistic elements, involving highly stylized Abhinaya (acting) and complex hand gestures.
• The lead male actors belong to the Chakyar community, while female roles are performed by the Nangyiar community; the Nambiars play the Mizhavu, a sacred copper percussion instrument.
• The repertoire includes plays by celebrated Sanskrit dramatists like Bhasa, Harsha, and Mahendra Pallava, focusing on elaborate character development that can span several nights.

 Additional Information

• Kummi:
• A popular folk dance in Tamil Nadu and Kerala, typically performed by women in a circle.
• It relies on hand-clapping to maintain rhythm rather than musical instruments, often performed during festivals like Pongal.
• Bagurumba:
• A traditional folk dance of the Bodo tribe in Assam, often called the Butterfly Dance due to the dancers mimicking the movement of butterflies.
• It is performed during the Bwisagu festival in mid-April.
• Perini Shivatandavam:
• A vigorous ancient dance form from Telangana, also known as the Dance of Warriors.
• Originating during the Kakatiya dynasty, it was performed by soldiers in front of Lord Shiva's idol before heading to war.

The correct answer is Uttar Pradesh.

Key Points

• The state of Uttar Pradesh has been selected to host India’s first industrial-scale Biopolymer manufacturing plant, a major milestone in the country’s shift toward sustainable materials.
• The project is a venture by Balrampur Chini Mills Limited (BCML), which is transitioning from a traditional sugar-producing entity into a biorefinery model.
• The facility is being set up in Lakhimpur Kheri, a region strategically chosen due to its high volume of sugarcane production, which serves as the essential raw material for the plant.
• This manufacturing unit will focus on producing Polylactic Acid (PLA), a biodegradable material that offers a renewable alternative to petroleum-based single-use plastics.
• The total investment for this pioneering facility is estimated at approximately Rs 2,000 crore, to be implemented in a phased manner over 30 months.
• The plant is designed to support the Make in India initiative and align with the national objective of achieving Net Zero emissions by the year 2070.

 Additional Information

• Biopolymers and PLA Technology:
• Polylactic Acid (PLA) is 100% bio-based and compostable, commonly used in food packaging, 3D printing, and medical implants.
• The production process involves the fermentation of sugarcane-derived sugars into lactic acid, followed by polymerization to create the bioplastic.
• To ensure global quality standards, BCML is collaborating with international technology providers like Sulzer and Thyssenkrupp Uhde.
• Impact on Uttar Pradesh:
• As the largest sugarcane producer in India, Uttar Pradesh provides an abundant supply of bagasse and sugar, facilitating a circular economy for farmers.
• The plant will help diversify the state’s industrial base and create significant skilled employment in the biotechnology and chemical engineering sectors.
• By reducing the dependency on fossil fuels, the state contributes to lowering the environmental hazards associated with microplastics and non-degradable waste.

The correct answer is Lakshadweep.

Key Points

• Attolu Eidu is a significant cultural festival celebrated in the Union Territory of Lakshadweep, primarily on the island of Minicoy (locally known as Maliku).
• The term Attolu refers to an Atoll (a ring-shaped coral reef), and the festival is a localized version of Eid-ul-Adha, reflecting the deep-rooted Islamic traditions of the archipelago.
• The celebration is distinguished by its unique Mahl cultural influences, which are closely related to the culture and language of the Maldives, setting it apart from the Malayalam-influenced culture of the northern islands.
• A major highlight of the festival is the performance of the Lava Dance, a traditional folk dance performed by men in vibrant costumes to the rhythmic beat of drums and traditional songs.
• Community activities such as Jahadhoni (traditional boat) races and communal feasting represent the social cohesion and maritime heritage of the people living in these Arabian Sea islands.

 Additional Information

• Meghalaya:
• Famous for the Wangala Festival, also known as the 100 Drums Festival, celebrated by the Garo tribe to honor Saljong, the Sun God.
• Other major festivals include Behdienkhlam (Jaintia tribe) and Nongkrem Dance (Khasi tribe).
• Telangana:
• Known for Bathukamma, a beautiful floral festival celebrated by women during Navratri to worship Goddess Gauri.
• Bonalu is another key festival dedicated to Goddess Mahakali, involving the offering of rice cooked in milk and jaggery in brass pots.
• Goa:
• Celebrates Shigmo, a spring festival featuring traditional folk dances like Ghode Modni and Fugdi.
• The Goa Carnival is a world-famous event introduced by the Portuguese, characterized by parades, masks, and music under the theme of Viva Carnival.

The correct answer is G.

Key Points

• The Universal Law of Gravitation, formulated by Sir Isaac Newton in 1687, describes the gravitational attraction between two objects possessing mass.
• This law states that the force of attraction is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers.
• To represent this relationship as an equation, the constant of proportionality known as G is used.
• The mathematical formula is written as F = G × (m1 × m2) / r², where F is the gravitational force, m1 and m2 are the masses, and r is the separation distance.
• The symbol G is specifically designated as the Universal Gravitational Constant because its value is assumed to be the same everywhere in the universe.

 Additional Information

• Universal Gravitational Constant (G):
• The precise value of G is approximately 6.674 × 10⁻¹¹ N m²/kg².
• It was first measured accurately by Henry Cavendish in 1798 using a sophisticated torsion balance.
• Unlike g (acceleration due to gravity), G is a scalar quantity and does not change with location.
• Other Symbols in Physics:
• mu (μ): Commonly denotes the coefficient of friction between surfaces or magnetic permeability in electromagnetism.
• k: Often represents the Boltzmann constant in thermodynamics or the Coulomb constant in electrostatics.
• phi (φ): Typically signifies magnetic flux, the work function in quantum mechanics, or a phase angle in wave optics.

The correct answer is Coins.

Key Points

• Legal tender is defined as any form of payment that is recognized by the legal system of a country as valid for the settlement of public or private debts and financial obligations.
• In India, coins are issued by the Government of India under the provisions of the Coinage Act, 2011. They are considered a form of Limited Legal Tender.
• Unlike banknotes, which are liabilities of the Reserve Bank of India (RBI), coins are assets issued directly by the central government. The government determines the denominations, designs, and quantities of coins to be minted at the four India Government Mints located in Mumbai, Kolkata, Hyderabad, and Noida.
• According to Section 13 of the Coinage Act, 2011, coins of any denomination not lower than one rupee are legal tender for any sum not exceeding 1,000 rupees. Coins of 50 paise are legal tender for any sum up to 10 rupees.
• While the public can use coins for transactions, they are Limited Legal Tender because a person cannot be legally forced to accept them beyond the specified statutory limits mentioned in the act.

 Additional Information

• Debit and Credit Cards:
• These are categorized as Plastic Money. They facilitate electronic fund transfers but are not legal tender.
• No individual or merchant is legally bound to accept a Debit card or Credit card for payment; their use is based on contractual agreements between the merchant, the customer, and the bank.
• Cheque:
• A cheque is a type of Fiduciary Money, which is money that is accepted as a medium of exchange because of the trust (fides) between the payer and the payee.
• It is an order to a bank to pay a specific amount from a person's account. Since it is not legal tender, a creditor can legally refuse to accept a cheque and insist on payment in currency notes or coins.

The correct answer is Diamond.

Key Points

• Conflict diamonds, popularly known as blood diamonds, refer to rough diamonds used by rebel movements or their allies to finance armed conflict aimed at undermining legitimate governments.
• The term gained global prominence during the late 1990s due to brutal civil wars in African nations such as Sierra Leone, Angola, Liberia, and the Democratic Republic of Congo (DRC).
• To address this crisis, the United Nations and various stakeholders established the Kimberley Process Certification Scheme (KPCS) in 2003, which requires member nations to certify that shipments of rough diamonds are conflict-free.
• Statistical data from the early 2000s estimated that conflict diamonds accounted for approximately 4 percent to 15 percent of the global diamond trade, leading to millions of deaths and displacements.
• The Clean Diamond Trade Act, passed by the United States Congress in 2003, further strengthened international efforts by prohibiting the import of diamonds from countries not participating in the Kimberley Process.

 Additional Information

• Cobalt:
• Primarily mined in the Copperbelt region of the Democratic Republic of Congo, which holds over 70 percent of the world's reserves.
• Essential for the production of lithium-ion batteries used in electric vehicles and smartphones.
• While not traditionally called a blood mineral in the same historical context as diamonds, its extraction is heavily scrutinized for human rights abuses and child labor.
• Gypsum:
• A common evaporite mineral chemically known as calcium sulfate dihydrate.
• Mainly utilized in the manufacture of wallboard (drywall), cement, and fertilizers.
• Nickel:
• A transition metal primarily found in laterite and magmatic sulfide deposits.
• Key industrial applications include stainless steel production and the manufacturing of rechargeable batteries.

The correct answer is Mumbai.

Key Points

• The grand finale of the Rugby Premier League (RPL) 2025 was successfully hosted in the city of Mumbai, which served as the neutral venue for the championship match.
• Mumbai was chosen due to its superior sporting infrastructure and long-standing association with rugby, dating back to the establishment of the Bombay Gymkhana in 1875.
• The event was organized under the supervision of the Indian Rugby Football Union (IRFU), aiming to boost the commercial viability of the sport through a high-profile metropolitan final.
• The 2025 final saw a record attendance for a non-cricket event in the city, highlighting the successful expansion of Rugby Union and Rugby Sevens across urban centers in India.
• Selection of this venue align with the Maharashtra Government policy of promoting diverse sports to establish the state as a premier global sporting hub.

 Additional Information

• Indian Rugby Football Union (IRFU):
• Commonly known as Rugby India, it is the sole governing body for the sport in the country and is a full member of World Rugby and Asia Rugby.
• The union has been instrumental in the inclusion of rugby in the National Games and the Khelo India University Games.
• Growth of Rugby in India:
• India has seen a surge in participation, particularly in the Rugby Sevens format, which is an Olympic sport.
• The Rugby Premier League follows a franchise-based model designed to provide a professional platform for domestic athletes and attract international talent.
• Significance of Venue Cities:
• While cities like Chennai and Jaipur have hosted national tournaments, Mumbai remains the primary hub for the All India & South Asia Rugby Championship, the oldest rugby tournament in the region.

The correct answer is 2019.

Key Points

• The 13^th South Asian Games were officially held from December 1 to December 10, 2019, in Nepal. This was the third time the country hosted the event, previously doing so in 1984 and 1999.
• The games were hosted across three major cities: Kathmandu, Pokhara, and Janakpur, involving various venues such as the Dasharath Rangasala Stadium for the opening and closing ceremonies.
• A total of seven nations participated in the competition: India, Nepal, Bangladesh, Bhutan, Maldives, Pakistan, and Sri Lanka.
• India finished at the top of the medal table for the 13^th consecutive time, securing a record 312 medals, which included 174 gold, 93 silver, and 45 bronze medals.
• The official mascot of the tournament was the Blackbuck (Krishnashar), which is an endangered antelope species found in the southern plains of Nepal.
• The 2019 games featured 26 sports, with Cricket returning to the event after an eight-year gap since the 2010 edition.

 Additional Information

• South Asian Olympic Council (SAOC):
• The SAOC is the governing body for the South Asian Games and was established in 1983 to promote sportsmanship and regional cooperation.
• The games were originally known as the South Asian Federation Games before being renamed in 2004.
• Historical Context and Future Editions:
• The first edition of the South Asian Games took place in Kathmandu in 1984, featuring only five sports: Athletics, Boxing, Football, Swimming, and Weightlifting.
• The 12^th South Asian Games were held in India in 2016, specifically in the cities of Guwahati and Shillong.
• The 14^th edition of the South Asian Games is scheduled to be hosted by Pakistan.

The correct answer is Allahabad Bank.

Key Points

• On August 30, 2019, the Government of India announced a massive structural reform involving the consolidation of ten Public Sector Banks (PSBs) into four large entities, which officially came into force on April 1, 2020.
• As a result of this mega consolidation, Allahabad Bank was merged with Indian Bank, with Indian Bank acting as the anchor bank.
• The merger transformed Indian Bank into the seventh-largest public sector bank in India, significantly increasing its nationwide footprint and operational scale.
• The combined entity achieved a total business volume of approximately Rs 8.07 lakh crore at the time of the merger, benefiting from Allahabad Bank’s strong presence in Northern and Eastern India.
• The primary objective behind this consolidation was to create globally competitive banks with larger balance sheets, improved capital adequacy, and enhanced lending capacity to support the 5 trillion dollar economy goal.

 Additional Information

• Oriental Bank of Commerce and United Bank of India:
• These two banks were amalgamated into Punjab National Bank (PNB), making PNB the second-largest state-owned bank in India after SBI.
• Syndicate Bank:
• This bank was merged into Canara Bank, which resulted in the creation of the fourth-largest Public Sector Bank in the country.
• Andhra Bank and Corporation Bank:
• These entities were merged into Union Bank of India, elevating its position to the fifth-largest PSB by total business.
• Evolution of PSBs:
• The merger process reduced the total number of Public Sector Banks from 27 in 2017 to just 12 by 2020.
• Earlier consolidations included the State Bank of India merger with its associates in 2017 and the Bank of Baroda merger with Vijaya Bank and Dena Bank in 2019.

The correct answer is 14.

Key Points

• According to the regulations set by the International Table Tennis Federation (ITTF), the playing space for international competitions must be rectangular.
• The official rules specify that for World Title events and Olympic Games, the length of the playing space must not be less than 14 metres.
• The minimum width of this rectangular playing space is required to be 7 metres to allow for adequate side-to-side movement during play.
• The minimum height from the floor to any overhead obstruction must be at least 5 metres.
• These dimensions ensure that high-level athletes have sufficient room to execute advanced maneuvers, such as lopping or defensive play far from the table, without being restricted by physical barriers.
• For other International Competitions, the space may be reduced slightly to 12 metres long and 6 metres wide, but the standard for top-tier tournaments remains 14 metres.

 Additional Information

• Table Dimensions:
• The standard table is 2.74 metres long and 1.525 metres wide.
• The playing surface must be 76 centimetres above the floor and lie in a horizontal plane.
• Net Assembly:
• The net is 15.25 centimetres high, and its ends must extend 15.25 centimetres beyond the side lines of the table.
• Playing Environment:
• The lighting intensity for elite competitions must be at least 1000 lux uniformly over the whole playing surface.
• The floor should not be light-coloured, brightly reflective, or slippery; it is typically made of wood or a specialized synthetic material.
• The surrounds (barriers) separating the playing areas must be approximately 75 centimetres high.

The correct answer is Nicaragua.

Key Points

• Nicaragua officially deposited its instrument of acceptance for the Agreement on Fisheries Subsidies on July 19, 2024.
• By submitting its instrument, Nicaragua became the 101^st World Trade Organisation (WTO) member to formally accept this landmark global agreement.
• The Agreement on Fisheries Subsidies was adopted by consensus during the 12^th Ministerial Conference (MC12) held in Geneva in June 2022.
• For the agreement to enter into force, two-thirds of the total 164 WTO members, which equals 110 countries, must deposit their instruments of acceptance.
• This treaty is the first multilateral trade agreement that places environmental sustainability at its core by targeting harmful subsidies.

 Additional Information

• Agreement Objectives:
• The accord strictly prohibits subsidies for Illegal, Unreported, and Unregulated (IUU) fishing.
• It bans subsidies for fishing overfished stocks and fishing activities in unregulated high seas.
• It provides Special and Differential Treatment (S&DT) for developing and least-developed countries (LDCs) to help them transition to sustainable practices.
• Nicaragua Context:
• Located in Central America, Nicaragua has significant marine interests in both the Pacific Ocean and the Caribbean Sea.
• Its formal acceptance signals a commitment from developing nations to safeguard marine biodiversity and ensure the long-term viability of the blue economy.
• WTO Ministerial Conferences:
• The 13^th Ministerial Conference (MC13) took place in Abu Dhabi in early 2024, where members continued negotiations on Phase 2 of the fisheries agreement to address overcapacity.

The correct answer is 2.

Key Points

• In the Global Terrorism Index (GTI) 2025, Pakistan is ranked as the second most impacted country by terrorism globally.
• This ranking signifies a deterioration in the security landscape of Pakistan, which saw a substantial rise in both the frequency of attacks and the number of fatalities compared to previous years.
• The surge in violence is primarily attributed to heightened activity by militant organizations, most notably the Tehreek-e-Taliban Pakistan (TTP) and the Balochistan Liberation Army (BLA).
• The report highlights that the provinces of Khyber Pakhtunkhwa and Balochistan remain the epicenters of conflict, accounting for the vast majority of terrorist incidents and deaths in the country.
• The 2025 GTI report reflects data collected and analyzed throughout the preceding year, 2024, showcasing the evolving threats in the South Asian region.

 Additional Information

• Global Terrorism Index (GTI):
• The index is an annual report published by the Institute for Economics and Peace (IEP), a global think tank headquartered in Sydney, Australia.
• It utilizes data from the Dragonfly Terrorism Tracker to rank 163 countries based on the multi-dimensional impact of terrorism.
• The score is calculated using four indicators: total incidents, fatalities, injuries, and hostage-taking, weighted over a five-year period.
• Other Global Rankings:
• Burkina Faso retained the 1^st rank in the GTI 2025, remaining the country most affected by terrorism in the world for the second year in a row.
• The Sahel region in Sub-Saharan Africa continues to be the global epicenter of terrorism, accounting for a large percentage of total global terrorist deaths.

The correct answer is 3.

Key Points

• The World Air Quality Report is an annual analysis provided by IQAir, a Swiss air quality technology company that monitors PM2.5 air pollution levels across the globe.
• In the 2022 World Air Quality Report (data often utilized in competitive exams throughout 2023 and early 2024), Pakistan was officially ranked as the 3^rd most polluted country in the world.
• During this period, the top two positions were held by Chad (1^st) and Iraq (2^nd), making Pakistan the most polluted country in the South Asian region at that time.
• The ranking is determined by the average annual concentration of PM2.5, which for Pakistan was recorded at approximately 70.9 µg/m³, nearly 14 times the WHO annual air quality guideline value.
• The report aggregates data from over 30,000 air quality monitoring stations across 131 countries and territories to provide a comprehensive view of global atmospheric health.

 Additional Information

• In the most recent 2023 World Air Quality Report, which was released in March 2024, the rankings underwent significant shifts:
• Bangladesh emerged as the most polluted country globally with an average PM2.5 of 79.9 µg/m³.
• Pakistan moved up to the 2^nd position with a concentration of 73.7 µg/m³.
• India was ranked as the 3^rd most polluted country, recording an average concentration of 54.4 µg/m³.
• Lahore, a major city in Pakistan, has frequently been cited as the individual city with the worst air quality index (AQI) during peak pollution months.
• PM2.5 particles are considered particularly dangerous because they are small enough to enter the bloodstream and cause respiratory and cardiovascular diseases.

Shortcut Trick

Solve using the BODMAS sequence: Bracket → Multiplication → Addition/Subtraction.

96 − 58 + 81 − (36 + 21) + 48 × 2

96 − 58 + 81 − 57 + 96

Combine positive terms: 96 + 81 + 96 = 273

Combine negative terms: 58 + 57 = 115

Net result: 273 − 115 = 158

∴ The correct answer is 158.

Alternate Method

Given Expression: 96 − 58 + 81 − (36 + 21) + 48 × 2

According to the BODMAS rule, we must solve the operations in a specific priority order.

Step 1: Solve the Bracket (B)

⇒ 36 + 21 = 57

The expression becomes: 96 − 58 + 81 − 57 + 48 × 2

Step 2: Solve the Multiplication (M)

⇒ 48 × 2 = 96

The expression becomes: 96 − 58 + 81 − 57 + 96

Step 3: Solve the Addition (A)

⇒ 96 + 81 + 96 = 273

Step 4: Solve the Subtraction (S)

⇒ 273 − 58 − 57

⇒ 215 − 57

⇒ 158

∴ The correct answer is 158.

Additional Information

BODMAS / VBODMAS Rule

It defines the order of operations: Vincular (bar), Brackets, Of (multiplication/orders), Division, Multiplication, Addition, and Subtraction.

Grouping Property

In expressions involving only addition and subtraction, grouping all positive terms and all negative terms separately can reduce calculation errors.

Bracket Precedence

Always solve inner brackets first: () parenthetical → {} curly → [] square brackets.

Shortcut Trick

Identify the operations using VBODMAS: Bracket → Division → Multiplication → Addition → Subtraction.

Expression: 86 + 55 − 39 + 28 − 28 + 4

Quickly cancel the opposite terms (+28 and −28).

Solve remaining: 86 + 55 − 39 + 4 = 141 − 35 = 106.

∴ The correct answer is 106.

Alternate Method

Given: 86 + 55 − 39 + (14 × 2) − 28 + 16 ÷ 4

Solve the Bracket and Division first:

⇒ 86 + 55 − 39 + 28 − 28 + 4

Perform Addition:

⇒ (86 + 55 + 28 + 4) − 39 − 28

⇒ 173 − 39 − 28

Perform Subtraction:

⇒ 134 − 28

⇒ 106

∴ The correct answer is 106.

Additional Information

BODMAS Rule

It stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It determines the correct hierarchy of operations in any mathematical expression.

Vinculum (Bar Bracket)

In VBODMAS, the 'V' stands for Vinculum, which is a horizontal line over numbers indicating they must be simplified before any other operation.

Subtraction Property

Adding and then subtracting the same value results in zero change (x + a − a = x), which is a useful shortcut for fast calculation.

Shortcut Trick

Convert the given mixed fractions to decimals for quick comparison.

Lower Bound: 2(3/10) = 2.3

Upper Bound: 2(4/5) = 2.8

Approximate Option (3): 47 ÷ 18 ≈ 2.61

Since 2.3 < 2.61 < 2.8, the fraction lies within the range.

∴ The correct answer is 47/18.

Alternate Method

Given:

First number = 2(3/10) = 23/10

Second number = 2(4/5) = 14/5

Calculations:

⇒ 23/10 = 2.30

⇒ 14/5 = 2.80

⇒ We need a value x such that 2.30 < x < 2.80.

⇒ Option (1): 41 ÷ 18 ≈ 2.27 (Less than 2.30)

⇒ Option (2): 59 ÷ 20 = 2.95 (Greater than 2.80)

⇒ Option (3): 47 ÷ 18 ≈ 2.61 (Between 2.30 and 2.80)

⇒ Option (4): 62 ÷ 21 ≈ 2.95 (Greater than 2.80)

∴ The correct answer is 47/18.

Additional Information

Mixed Fraction Conversion

To convert a mixed fraction a(b/c) to an improper fraction, use the formula: (a × c + b) ÷ c.

Comparing Fractions

Fractions can be compared by converting them to decimals or by finding a common denominator.

Cross-Multiplication Method

To check if a/b < c/d, verify if (a × d) < (b × c).

Shortcut Trick

Apply the algebraic identity: (a + b)² − (a − b)² = 4ab.

In this expression, let a = √5 and b = √2.

Substituting the values: 4 × √5 × √2 = 4√(5 × 2).

Result = 4√10.

∴ The correct answer is 4√10.

Alternate Method

Given Expression: (√5 + √2)² − (√5 − √2)²

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

⇒ Step 1: Expand (√5 + √2)² = (√5)² + (√2)² + 2(√5)(√2)

⇒ (√5 + √2)² = 5 + 2 + 2√10 = 7 + 2√10

⇒ Step 2: Expand (√5 − √2)² = (√5)² + (√2)² − 2(√5)(√2)

⇒ (√5 − √2)² = 5 + 2 − 2√10 = 7 − 2√10

⇒ Step 3: Subtract the two expansions: (7 + 2√10) − (7 − 2√10)

⇒ 7 + 2√10 − 7 + 2√10

⇒ (7 − 7) + (2√10 + 2√10) = 4√10

∴ The correct answer is 4√10.

Additional Information

Sum of Squares Identity

The sum of squared terms can be simplified as (a + b)² + (a − b)² = 2(a² + b²).

Difference of Squares

The identity a² − b² = (a + b)(a − b) is frequently used for the rationalization of denominators involving surds.

Multiplication Rule for Surds

For any non-negative numbers x and y, the product of their square roots is √x × √y = √(xy).

Shortcut Trick

To find the square root of a surd in the form √(a + 2√b), find two numbers whose sum is 'a' and product is 'b'.

In √(5 + 2√6): Sum = 5, Product = 6.

The factors of 6 whose sum is 5 are 3 and 2.

The simplified value is √3 + √2.

∴ The correct answer is √3 + √2.

Alternate Method

Given: √(5 + 2√6)

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

⇒ Let the expression be √(a + 2√b).

⇒ We can write 5 as (3 + 2) and √6 as √(3 × 2).

⇒ 5 + 2√6 = 3 + 2 + 2 × √3 × √2

⇒ 5 + 2√6 = (√3)² + (√2)² + 2 × (√3) × (√2)

⇒ This is in the form of a² + b² + 2ab where a = √3 and b = √2.

⇒ 5 + 2√6 = (√3 + √2)²

⇒ Square root = √[(√3 + √2)²]

⇒ √3 + √2

∴ The correct answer is √3 + √2.

Additional Information

Square Root of a Mixed Surd

For an expression √(a ± 2√b), if x + y = a and xy = b, the square root is √x ± √y (where x > y).

Normalization of the Inner Root

If the coefficient of the inner root is not 2, you must multiply and divide by 2 or move factors inside the root to get it into the 2√b format.

Conjugate Surds

The conjugate of (√x + √y) is (√x − √y). Their product is always a rational number (x − y).

Shortcut Trick

The Area of a Square is calculated by squaring its side length.

Area = (Side)²

Area = 8 × 8 = 64 cm²

∴ The correct answer is 64 cm².

Alternate Method

Given:

Side of the Square (a) = 8 cm

Formula Used:

Area of a square = Side × Side

⇒ Area = Side²

⇒ Area = 8 cm × 8 cm

⇒ Area = 64 cm²

∴ The correct answer is 64 cm².

Additional Information

Perimeter of a Square

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

Diagonal of a Square

The diagonal of a square is calculated as side × √2 (a√2).

Area using Diagonal

If the diagonal (d) is known, the area can also be found using Area = d² ÷ 2.

Shortcut Trick

Given Perimeter of square = 36 cm

Side (a) = Perimeter ÷ 4 = 36 ÷ 4 = 9 cm

Area = a² = 9 × 9 = 81 cm²

∴ The correct answer is 81 cm².

Alternate Method

Given:

Perimeter (P) of the square = 36 cm

Formula Used:

1. Perimeter of a square = 4 × Side
2. Area of a square = (Side)²

Calculations:

⇒ 4 × Side = 36 cm

⇒ Side = 36 ÷ 4

⇒ Side = 9 cm

⇒ Area = 9 × 9

⇒ Area = 81 cm²

∴ The correct answer is 81 cm².

Additional Information

Diagonal of a Square

The length of the diagonal (d) of a square is given by d = side × √2.

Area in terms of Diagonal

If the diagonal is known, Area = d² ÷ 2.

Inradius and Circumradius

The radius of the inscribed circle is a/2 and the radius of the circumscribed circle is a/√2.

Shortcut Trick

The given expression follows the algebraic identity: a² + b² + c² + 2(ab + bc + ca) = (a + b + c)².

Here, a = 15, b = 10, and c = 25.

Sum of terms = (15 + 10 + 25) = 50.

Final Value = (50)² = 2500.

∴ The correct answer is 2500.

Alternate Method

Given: 15² + 10² + 25² + 2(15 × 10 + 10 × 25 + 25 × 15)

Formula Used: The expansion of the square of a trinomial is (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

⇒ Let a = 15, b = 10, and c = 25.

⇒ The expression matches the RHS of the identity: a² + b² + c² + 2(ab + bc + ca).

⇒ Therefore, Expression = (a + b + c)²

⇒ Expression = (15 + 10 + 25)²

⇒ Expression = (50)²

⇒ Expression = 2500

∴ The correct answer is 2500.

Additional Information

Trinomial Square Identity

The formula (a + b + c)² = a² + b² + c² + 2(ab + bc + ca) is used to simplify polynomial expressions efficiently without manual squaring of each term.

Standard Algebraic Identities

1. (a + b)² = a² + 2ab + b²

2. (a − b)² = a² − 2ab + b²

3. (a + b + c)³ involves much more complex terms and is distinct from the square identity.

Calculation Tip

When you see a pattern of three squares followed by their doubled cyclic products, always look to group the base values first.

Shortcut Trick

The expression follows the Algebraic Identity: a² + b² + c² + 2(ab + bc + ca) = (a + b + c)².

Let a = 22, b = 18, and c = 30.

Sum (a + b + c) = 22 + 18 + 30 = 70.

Result = 70² = 4900.

∴ The correct answer is 4900.

Alternate Method

Given:

Expression: 22² + 18² + 30² + 2(22 × 18 + 18 × 30 + 30 × 22)

Formula Used:

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Calculations:

⇒ a = 22, b = 18, c = 30

⇒ 22² + 18² + 30² + 2(22 × 18 + 18 × 30 + 30 × 22) = (22 + 18 + 30)²

⇒ (22 + 18 + 30)² = (40 + 30)²

⇒ 70² = 70 × 70

⇒ 4900

∴ The correct answer is 4900.

Additional Information

Basic Algebraic Square Identities

(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b² are the fundamental expansions for two variables.

Difference of Squares

a² − b² = (a + b)(a − b), which is useful for simplifying products of sums and differences.

Diagonal of a Cuboid

The identity a² + b² + c² is related to the square of the diagonal of a cuboid with sides a, b, and c.

Shortcut Trick

Total items after addition = 80 + 20 = 100

Total sum of 100 numbers = 100 × 32.1 = 3210

Total sum of initial 80 numbers = 80 × 23.5 = 1880

Sum of new 20 numbers = 3210 − 1880 = 1330

∴ The correct answer is 1330.

Alternate Method

Given:

Initial number of observations = 80

Initial average = 23.5

New observations added = 20

Final average after addition = 32.1

Formula Used:

Sum = Average × Number of observations

Calculations:

⇒ Total sum of 100 numbers = 100 × 32.1 = 3210

⇒ Sum of the first 80 numbers = 80 × 23.5 = 1880

⇒ Sum of the newly added 20 numbers = Total Sum − Initial Sum

⇒ Sum = 3210 − 1880

⇒ Sum = 1330

∴ The correct answer is 1330.

Additional Information

Basic Average Formula

The average of a set of values is the sum of the values divided by the number of values: Average = Σx ÷ n.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Sum Calculation

To find the total sum when the average is known, multiply the average by the total number of entries: Sum = Average × Count.

Shortcut Trick

The number must be divisible by the LCM of 5, 7, and 11.

Since 5, 7, and 11 are prime numbers, their LCM = 5 × 7 × 11 = 385.

Check the options to see which is a multiple of 385: 385 × 5 = 1925.

Alternatively, 1925 is the only option satisfying all divisibility rules (ends in 5, sum diff for 11 is 11).

∴ The correct answer is 1925.

Alternate Method

Given: Divisors are 5, 7, and 11.

To find the number divisible by all three, we check individual divisibility rules for the given options:

Step 1: Divisibility by 5

⇒ Unit digit must be 0 or 5. Options (1) 1935 and (2) 1925 are eligible.

Step 2: Divisibility by 11

⇒ Difference of sums of digits at odd and even places must be 0 or a multiple of 11.

⇒ For 1925: (1 + 2) − (9 + 5) = 3 − 14 = −11 (Divisible by 11).

⇒ For 1935: (1 + 3) − (9 + 5) = 4 − 14 = −10 (Not divisible by 11).

Step 3: Divisibility by 7

⇒ 1925 ÷ 7 = 275 (Remainder is 0).

∴ The correct answer is 1925.

Additional Information

Divisibility by 7

Double the last digit and subtract it from the remaining number. If the result is divisible by 7, the original number is too.

LCM of Prime Numbers

For any set of coprime or prime numbers, their LCM is always equal to their product.

Divisibility by 11 Rule

Sum of digits at odd positions − Sum of digits at even positions = 0, 11, 22, ... or any multiple of 11.

Shortcut Trick

To find the maximum number of students, calculate the HCF (Highest Common Factor) of 198 and 330.

Difference method: 330 − 198 = 132.

The HCF must be a factor of 132. Factors of 132 are 132, 66, 44, 33, 22...

Checking 66: 198 ÷ 66 = 3 and 330 ÷ 66 = 5. Both are divisible.

∴ The correct answer is 66.

Alternate Method

Given:

Number of chips = 198

Number of toffees = 330

Calculations:

Prime factorization of 198:

⇒ 198 = 2 × 3 × 3 × 11 = 2¹ × 3² × 11¹

Prime factorization of 330:

⇒ 330 = 2 × 3 × 5 × 11 = 2¹ × 3¹ × 5¹ × 11¹

The HCF is the product of the lowest powers of common prime factors:

⇒ HCF = 2¹ × 3¹ × 11¹

⇒ HCF = 66

∴ The correct answer is 66.

Additional Information

Highest Common Factor (HCF)

The HCF of two or more numbers is the greatest number that divides each of them exactly. It is also known as the Greatest Common Divisor (GCD).

HCF and Difference Rule

The HCF of two numbers is always a factor of their difference. This property is very useful for quickly finding the HCF of large numbers.

Relationship 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).

Shortcut Trick

Combine the percentages: 8% + 10% = 18%.

According to the question, 18% of the number = 2664.

Value of 1% = 2664 ÷ 18 = 148.

Value of 100% (the number) = 148 × 100 = 14800.

∴ The correct answer is 14800.

Alternate Method

Given:

Sum of 8% and 10% of a number = 2664.

Calculations:

Let the number be x.

⇒ (8% of x) + (10% of x) = 2664

⇒ (8/100) × x + (10/100) × x = 2664

⇒ (8x + 10x) / 100 = 2664

⇒ 18x / 100 = 2664

⇒ 18x = 2664 × 100

⇒ x = 266400 ÷ 18

⇒ x = 14800

∴ The correct answer is 14800.

Additional Information

Percentage Addition

When percentages of the same base are added or subtracted, they can be treated as like terms: a% of x + b% of x = (a + b)% of x.

Fraction to Percentage

To convert a fraction to a percentage, multiply by 100. For example, 1/5 × 100 = 20%.

Percentage Change Formula

Percentage Change = [(New Value − Old Value) / Old Value] × 100.

Shortcut Trick

Ratio of CP : SP = 3 : 5

Profit = 5 − 3 = 2 units

Given, 2 units = ₹720

⇒ 1 unit = ₹360

⇒ Cost Price (CP) = 3 units = 3 × 360 = ₹1080

∴ The correct answer is ₹1080.

Alternate Method

Given:

Ratio of Cost Price (CP) to Selling Price (SP) = 3 : 5

Actual Profit = ₹720

Formula Used:

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

Calculations:

Let the Cost Price be 3x and the Selling Price be 5x.

⇒ Profit = 5x − 3x

⇒ 2x = 720

⇒ x = 720 ÷ 2

⇒ x = 360

⇒ Cost Price (CP) = 3x = 3 × 360

⇒ CP = ₹1080

∴ The correct answer is ₹1080.

Additional Information

Profit Percentage

It is the profit earned per ₹100 of the Cost Price. Formula: Profit% = (Profit ÷ CP) × 100.

Loss Condition

A loss occurs when the Cost Price is greater than the Selling Price. Formula: Loss = CP − SP.

Relation between SP and CP

SP = CP × (100 + Profit%) ÷ 100 or SP = CP × (100 − Loss%) ÷ 100.

Shortcut Trick

Direct difference of Q percentages: 50% − 30% = 20%

Equating with P: 40% of P = 20% of Q

Ratio P : Q = 20 : 40 = 1 : 2

P as percentage of Q = (1 ÷ 2) × 100 = 50%

∴ The correct answer is 50%.

Alternate Method

Given:

40% of P + 30% of Q = 50% of Q

Calculations:

⇒ (40 ÷ 100) × P + (30 ÷ 100) × Q = (50 ÷ 100) × Q

⇒ 0.4P + 0.3Q = 0.5Q

⇒ 0.4P = 0.5Q − 0.3Q

⇒ 0.4P = 0.2Q

⇒ P ÷ Q = 0.2 ÷ 0.4

⇒ P ÷ Q = 1 ÷ 2

⇒ Required Percentage = (P ÷ Q) × 100

⇒ Required Percentage = (1 ÷ 2) × 100 = 50%

∴ The correct answer is 50%.

Additional Information

Percentage Comparison

To find what percent X is of Y, use the formula: (X ÷ Y) × 100.

Basic Fraction to Percent

Standard conversions: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 3/4 = 75%.

Percentage Change

Percentage change = (New Value − Original Value) ÷ Original Value × 100.

Shortcut Trick

Multiply the quantity and price using the cross-method for 1 unit comparison.

CP of 1 article = 400 / 880 = ₹5 / 11

SP of 1 article = ₹7 / 11

Ratio of CP : SP = 5/11 : 7/11 = 5 : 7

Profit % = (Difference / CP) × 100 = (2 / 5) × 100 = 40%.

∴ The correct answer is 40%.

Alternate Method

Given:

Total cost price (CP) of 880 articles = ₹400

Total selling price (SP) of 11 articles = ₹7

Formula Used:

Profit % = [(Total SP − Total CP) / Total CP] × 100

Calculations:

⇒ Number of groups of 11 articles in 880 = 880 ÷ 11 = 80 groups

⇒ Selling Price of 880 articles = 80 × SP of 11 articles

⇒ Total SP = 80 × 7 = ₹560

⇒ Total Profit = Total SP − Total CP = 560 − 400 = ₹160

⇒ Profit Percentage = (160 / 400) × 100

⇒ Profit % = 40%

∴ The correct answer is 40%.

Additional Information

Profit and Loss Percentage

Profit % = (Profit / CP) × 100 and Loss % = (Loss / CP) × 100. Both are always calculated on the Cost Price (CP) unless stated otherwise.

Selling Price Calculation

SP = CP × (100 + Profit%)/100 for profit, and SP = CP × (100 − Loss%)/100 for loss.

Equal Quantity Rule

To compare CP and SP directly, always ensure the number of articles (quantity) bought and sold is the same.

Shortcut Trick

Let Total Work be LCM(14, 21, 42) = 42 units.

Combined Efficiency of A, B, and C = 3 + 2 + 1 = 6 units/day.

Target work to complete = 1/7 × 42 = 6 units.

Time taken = 6 ÷ 6 = 1 day.

∴ The correct answer is 1 day.

Alternate Method

Given: Time taken by A = 14 days, B = 21 days, C = 42 days.

Formula Used: Efficiency = Total Work ÷ Time; Time = Work ÷ Efficiency.

⇒ Total Efficiency of (A + B + C) = 3 + 2 + 1 = 6 units/day.

⇒ Portion of work to be completed = (100/7)% = (100/7) ÷ 100 = 1/7.

⇒ Work to be done = 1/7 × 42 = 6 units.

⇒ Time taken = Work ÷ Combined Efficiency = 6 ÷ 6 = 1 day.

∴ The correct answer is 1 day.

Additional Information

Efficiency-Time Relationship

Efficiency is inversely proportional to the Time taken to complete the work (Efficiency ∝ 1/Time).

Work and Wages

Wages are generally distributed in the ratio of efficiency or the ratio of work done by each individual.

Pipes and Cisterns

This concept is identical to Time and Work, where an inlet pipe has positive efficiency and an outlet pipe has negative efficiency.

Shortcut Trick

Apply the Chain Rule formula: M₁ × D₁ × W₂ = M₂ × D₂ × W₁

Substitute values: 40 × 84 × 25% = 56 × D₂ × 100%

40 × 84 × 25 = 56 × D₂ × 100

84000 = 5600 × D₂

D₂ = 84000 ÷ 5600 = 15 days

∴ The correct answer is 15 days.

Alternate Method

Given: Initial men (M₁) = 40, Days (D₁) = 84, Final men (M₂) = 56, Target work (W₂) = 25% of total work.

Formula Used: Total Work = Men × Days; Days = Work ÷ Men

⇒ Total Work = 40 × 84 = 3360 units.

⇒ Efficiency of 56 men = 56 units/day.

⇒ Work to be completed = 25% of 3360 = 3360 ÷ 4 = 840 units.

⇒ Required Days = 840 ÷ 56

⇒ Required Days = 15 days.

∴ The correct answer is 15 days.

Additional Information

The Chain Rule

The general formula for work is (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where M is men, D is days, H is hours, and W is work.

Inverse Proportion in Time & Work

For a constant amount of work, the number of men is inversely proportional to the time taken (M ∝ 1/D).

Work & Wages

Wages are always distributed in the ratio of work done by the individuals, not just based on their efficiency or time alone.

Shortcut Trick

Speed (km/hr) = (Length of Train ÷ Time) × (18 ÷ 5)

Speed = (200 ÷ 12) × (18 ÷ 5)

Speed = (50 ÷ 3) × (18 ÷ 5) = 10 × 6 = 60 km/hr.

∴ The correct answer is 60 km/hr.

Alternate Method

Given:

Length of the Train (Distance) = 200 metres

Time taken = 12 seconds

Formula Used:

Speed = Distance ÷ Time

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

Calculations:

⇒ Speed of the train = 200 ÷ 12 m/s

⇒ Speed = 50 ÷ 3 m/s

⇒ Speed in km/hr = (50 ÷ 3) × (18 ÷ 5)

⇒ Speed = (50 ÷ 5) × (18 ÷ 3)

⇒ Speed = 10 × 6 = 60 km/hr

∴ The correct answer is 60 km/hr.

Additional Information

Unit Conversion Factor

1 m/s = 18/5 km/hr and 1 km/hr = 5/18 m/s. This is derived from 3600 seconds in an hour and 1000 metres in a kilometre.

Relative Speed Concept

If two objects move in the opposite direction, relative speed = S₁ + S₂. If they move in the same direction, relative speed = |S₁ − S₂|.

Train passing an object with length

When a train of length L passes a platform, bridge, or tunnel of length P, the total distance covered is L + P.

Shortcut Trick

Relative Speed = Distance ÷ Time = 420 ÷ 42 = 10 m/s.

Ratio of Speed of Train to Man = 2 : 1.

In the same direction, Relative Speed ratio = 2 − 1 = 1 unit.

1 unit = 10 m/s ∴ Speed of Train (2 units) = 2 × 10 = 20 m/s.

∴ The correct answer is 20 m/s.

Alternate Method

Given:

Length of train (L) = 420 m

Time taken (t) = 42 sec

Formula Used:

Relative Speed (V_rel) = Total Distance ÷ Total Time

When moving in the same direction: V_rel = V₁ − V₂

Calculations:

⇒ Let the Speed of Train be V m/s.

⇒ Speed of Man = 0.5V m/s.

⇒ Relative Speed = V − 0.5V = 0.5V m/s.

⇒ 0.5V = 420 ÷ 42

⇒ 0.5V = 10

⇒ V = 10 ÷ 0.5

⇒ V = 20 m/s.

∴ The correct answer is 20 m/s.

Additional Information

Relative Speed in Opposite Direction

When two objects move toward each other, the Relative Speed is the sum of their individual speeds (V₁ + V₂).

Unit Conversion

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

Crossing a Stationary Object

When a train crosses a pole or a stationary man, the distance covered is exactly equal to the length of the train.

The correct answer is Option (3) i.e. To change one's behaviour, usually in a positive way.

Key Points

• The idiom 'Turn over a new leaf' means to start behaving in a better way, to make a fresh start, or to improve one's conduct. (एक नई शुरुआत करना या व्यवहार में सुधार लाना)
• Example: After the accident, he decided to turn over a new leaf and take his health seriously.
• 'To change one's behaviour, usually in a positive way' refers to a person making a significant transformation to become more responsible or ethical. (अपने व्यवहार में सुधार करना, आमतौर पर सकारात्मक तरीके से)
• Example: The principal encouraged the students to turn over a new leaf and be more diligent with their assignments.
• Hence, we can infer that the correct meaning of 'Turn over a new leaf' is to change for the better.

Therefore, the correct answer is: To change one's behaviour, usually in a positive way.

Additional Information

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

• To change one's behaviour, usually in a negative way (नकारात्मक तरीके से व्यवहार बदलना): This implies a decline in character or habits, which is the opposite of the idiom's meaning.
• Example: It was sad to see him change his behaviour in a negative way after he lost his job.
• Not to change one's behaviour (व्यवहार न बदलना): This suggests stagnation or refusal to improve despite the circumstances.
• Example: Despite multiple warnings, she chose not to change her behaviour and continued to be late.
• Search something in a heap of leaves (पत्तियों के ढेर में कुछ खोजना): This is a literal interpretation of the words and does not represent the idiomatic expression.
• Example: The gardener had to search for his keys in a huge heap of leaves after cleaning the lawn.

The correct answer is: Characterized by ruthless behaviour and competition, as of a society, situation, industry, etc..

Key Points

• The idiom 'dog eat dog' is used to describe a situation in which people or organizations are willing to harm each other or act unethically in order to succeed. (निर्दयी और गलाकाट प्रतिस्पर्धा)
• Example: It is a dog eat dog world in the advertising business, where everyone is trying to steal each other's clients.
• The phrase 'Characterized by ruthless behaviour and competition' refers to an environment, such as a workplace or society, where individuals act without compassion or fairness to get ahead of others. (क्रूर व्यवहार और गलाकाट प्रतिस्पर्धा की विशेषता)
• Example: The stock market is often seen as a place characterized by ruthless behaviour and intense competition among traders.
• Hence, the idiom 'dog eat dog' directly corresponds to a situation of extreme and merciless competition.

Therefore, the correct answer is- Characterized by ruthless behaviour and competition, as of a society, situation, industry, etc.

Additional Information

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

• To fail to put forth the effort (प्रयास करने में विफल होना): This means not working hard enough or lacking the necessary drive to complete a task.
• Example: If you fail to put forth the effort in your studies, you cannot expect to get top grades.
• To stay with one and haunt one (पीछा करना या डराना): This refers to a persistent memory, guilt, or fear that continues to trouble a person over time.
• Example: The mistakes of his past continued to stay with him and haunt him throughout his career.
• Make something totally without light or colour naturally (किसी चीज़ को प्रकाशहीन या बेरंग कर देना): This refers to the absence of brightness or vibrant hues in an object or environment.
• Example: The artist decided to make the background totally without colour to emphasize the subject of the painting.

The correct answer is: Labyrinth.

Key Points

• The word 'Labyrinth' refers to a complicated irregular network of passages or paths in which it is difficult to find one's way; it is synonymous with a maze. (भूलभुलैया)
• Example: We spent hours wandering through the labyrinth of narrow streets in the old city.
• Among the given options, 'Labyrinth' is the word that is correctly spelled. It describes something highly intricate or convoluted. (सही वर्तनी)
• Example: The tax laws in this country are a labyrinth of complexity that few people understand.
• Hence, we can infer that the correctly spelled word is 'Labyrinth'.

Therefore, the correct answer is: Labyrinth.

Additional Information

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

• Laconic (मितभाषी): The option 'Lacconic' is misspelled. The correct spelling is 'Laconic', which means using very few words.
• Example: His laconic reply made it clear that he did not want to continue the conversation.
• Languish (दुर्बल होना): The option 'Lenguish' is misspelled. The correct spelling is 'Languish', which means to grow weak or feeble.
• Example: Many political prisoners languish in cells for years without a trial.
• Lassitude (थकान): The option 'Lasitude' is misspelled. The correct spelling is 'Lassitude', referring to a state of physical or mental weariness.
• Example: After the long hike in the sun, she was overcome by a sense of lassitude.

The correct answer is: strong.

Key Points

• The word 'sturdy' refers to something that is physically strong and solid; it often describes objects or people that are built to last or endure pressure without breaking. (मजबूत)
• Example: The house was built with sturdy foundations to withstand the heavy storms.
• 'strong' means having great physical power or being able to resist force or pressure; it is the most appropriate synonym for sturdy. (मजबूत / बलवान)
• Example: He used a strong rope to pull the car out of the ditch.
• Hence, we can infer that the word that is most similar in meaning to 'sturdy' is 'strong'.

Therefore, the correct answer is: strong.

Additional Information

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

• Fragile (नाजुक / भंगुर): Something that is easily broken or damaged.
• Example: The fragile glass vase shattered into tiny pieces when it fell.
• Weak (कमजोर): Lacking physical strength, energy, or power.
• Example: The patient felt too weak to walk without assistance after the surgery.
• Brittle (भंगुर / कुरकुरा): Hard but liable to break or shatter easily when under stress.
• Example: Cold temperatures can make certain types of plastic very brittle.

The correct answer is: Pronunciation.

Key Points

• The word 'Pronounciation' is a common misspelling of the word 'pronunciation' because people associate it with the verb 'pronounce'. (अशुद्ध वर्तनी)
• Example: Many students make a spelling mistake by writing 'pronounciation' in their essays.
• 'Pronunciation' refers to the way in which a language or a particular word or sound is spoken. (उच्चारण)
• Example: Regular practice with native speakers can help improve your pronunciation.
• Hence, we can infer that the misspelt word in the options is 'Pronounciation', and the correct spelling is 'Pronunciation'.

Therefore, the correct answer is: Pronunciation.

Additional Information

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

• Occasionally (कभी-कभी): At infrequent or irregular intervals; now and then.
• Example: They occasionally go for long walks in the evening.
• Embarrassment (शर्मिंदगी): A feeling of self-consciousness, shame, or awkwardness.
• Example: She couldn't hide her embarrassment when she forgot her lines on stage.
• Exaggeration (अतिशयोक्ति): A statement that represents something as better or worse than it really is.
• Example: It is an exaggeration to say that the entire city was destroyed by the rain.

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

Key Points

• The word 'Existence' refers to the state or fact of living or having objective reality; the way in which a person or thing exists. (अस्तित्व)
• Example: Scientists are continuously looking for signs of the existence of water on other planets.
• 'Nonexistence' refers to the state or fact of not existing; the absence of existence or reality. (अस्तित्वहीनता)
• Example: The case was eventually closed due to the nonexistence of any credible witnesses.
• Hence, we can infer that the opposite of 'Existence' is 'Nonexistence'.

Therefore, the correct answer is: Nonexistence.

Additional Information

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

• Reality (वास्तविकता): The state of things as they actually exist, as opposed to an idealistic or notional idea of them.
• Example: He finally had to face the reality that his business was failing.
• Being (होना / जीव): The nature or essence of a person; the state of existing.
• Example: Every human being has the right to live with dignity.
• Presence (उपस्थिति): The state or fact of existing, occurring, or being present in a place or thing.
• Example: Her presence at the party made him feel much more comfortable.

The correct answer is: Fallacy.

Key Points

• The phrase 'A mistaken belief based on an unsound argument' refers to an idea or opinion that is incorrect because it is based on flawed logic or poor reasoning. (तर्कदोष)
• Example: Believing that wearing a specific shirt will guarantee a sports victory is based on an unsound argument.
• 'Fallacy' refers to a failure in reasoning which renders an argument invalid; it is a deceptive or false notion often used in rhetoric. (भ्रांति)
• Example: It is a common fallacy to believe that expensive products are always of better quality.
• Hence, we can infer that the one-word substitution for the given phrase is 'fallacy'.

Therefore, the correct answer is: Fallacy.

Additional Information

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

• Largesse (उदारता): Generosity in bestowing money or gifts upon others.
• Example: The university library was built through the largesse of a wealthy alumnus.
• Malaise (अस्वस्थता): A general feeling of discomfort, illness, or unease whose exact cause is difficult to identify.
• Example: After the scandal, a general malaise settled over the entire company.
• Equanimity (धैर्य): Mental calmness, composure, and evenness of temper, especially in a difficult situation.
• Example: She accepted both victory and defeat with equal equanimity.

The correct answer is: Nonagenarian.

Key Points

• The phrase 'one who is between ninety and one hundred years of age' refers to a person whose age falls within the range of 90 to 99 years. (नब्बे और सौ साल के बीच की आयु का व्यक्ति)
• Example: The local newspaper interviewed a man who is between ninety and one hundred years of age to learn about his life experiences.
• 'Nonagenarian' is the specific one-word substitution for a person who is in their nineties (90-99 years old). (नब्बे साल का)
• Example: The nonagenarian grandmother was celebrated by her entire family on her 95^th birthday.
• Hence, we can conclude that the term for someone in that age bracket is 'nonagenarian'.

Therefore, the correct answer is- Nonagenarian.

Additional Information

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

• Octogenarian (अस्सी साल का): A person who is between 80 and 89 years old.
• Example: My grandfather is an octogenarian who still goes for a jog every morning.
• Centenarian (सौ साल का व्यक्ति): A person who is 100 years old or older.
• Example: The town council sent a special plaque to the centenarian on her 100^th birthday.
• Septuagenarian (सत्तर साल का): A person who is between 70 and 79 years old.
• Example: Many septuagenarian citizens remain very active in community service.

The correct answer is 'by'.

Key Points

• The preposition 'by' is used to express a unit of measurement or a rate when buying, selling, or calculating something.
• In English grammar, the standard construction to indicate the unit of sale is 'by + the + unit' (e.g., by the metre, by the dozen, by the kilo, by the litre).
• The sentence implies that the metre is the standard measure used for selling cloth everywhere.
• Options 1, 2, and 4 do not fit the grammatical context of measurement and sale.

Therefore, the correct answer is Option 3.

Complete Sentence: "Cloth is sold by the metre everywhere."

Additional Information

• Option 1: 'in' is generally used for location, time, or contained spaces, but not for the unit of measure in this specific idiomatic sense.
• Option 2: 'of' typically indicates belonging, origin, or composition.
• Option 4: 'out' is a preposition or adverb indicating movement or position away from a center or interior.

The correct answer is Uncharted territories were being mapped by the explorers when they went missing..

Key Points

• The given sentence is in the Past Continuous Tense, which is used to describe an action that was ongoing at a specific point in the past.
• The grammatical structure of the active voice in this tense is: Subject (The explorers) + was/were + V1+ing (mapping) + Object (uncharted territories).
• When converting a Past Continuous sentence into the Passive Voice, the object of the active sentence becomes the subject of the passive sentence.
• The formula for the passive voice in this context is: New Subject + was/were + being + V3 (Past Participle) + by + Agent.
• Since the new subject uncharted territories is plural, the auxiliary verb were is used, followed by the continuous marker being and the past participle form mapped.
• The secondary clause when they went missing remains unchanged as it functions as an adverbial clause of time.

 Additional Information

• Analysis of incorrect options:
• Simple Past Passive: Option 2 uses were mapped. This represents the passive form of the Simple Past Tense, which fails to capture the continuous nature of the original action.
• Past Perfect Passive: Option 3 uses had been mapped. This corresponds to the Past Perfect Tense, which indicates an action completed before another past action, thus changing the intended meaning.
• Present Continuous Passive: Option 4 uses are being mapped. This is the Present Continuous form, which is chronologically inconsistent with the past context established by went missing.

The correct answer is Had the committee reviewed the financial proposal before it was forwarded to the higher authorities?.

Key Points

• The original sentence is in the Interrogative form of the Past Perfect Tense in the Passive Voice. The structure used is Had + Object + been + V3 + by + Subject.
• To convert a sentence from Passive to Active Voice, the logical agent or doer of the action, which is the committee, must be moved to the subject position.
• The Active Voice structure for the Past Perfect Tense in an interrogative sentence is Had + Subject + Past Participle (V3) + Object.
• In this transformation, the auxiliary verb Had remains at the beginning to maintain the question format, followed by the subject the committee and the main verb reviewed.
• The recipient of the action, the financial proposal, is placed as the direct object following the verb.
• The subordinate clause starting with before remains unchanged as it provides the temporal context for the main action and is already in the passive voice referring to the same object.

 Additional Information

• Voice and Tense Consistency:
• Past Perfect Active: Utilizes had + past participle. It is used to show that one action happened before another action in the past.
• Voice Change Rule: While changing voice, the tense of the sentence must never change. Options using Did (Simple Past), Was reviewing (Past Continuous), or Does (Simple Present) are grammatically incorrect for this specific transformation.
• Interrogative Syntax: When a sentence starts with an auxiliary verb in the passive voice, the active counterpart must also start with the corresponding auxiliary verb to preserve the sentence type.

The correct answer is No one has ever defeated her in any debate..

Key Points

• The given sentence is in the Passive Voice and follows the Present Perfect Tense structure: Subject + has/have + been + V3 (Past Participle) + Complement.
• To convert this into Active Voice, the object of the passive sentence (which is implied here as anyone or no one because the agent is missing) must become the subject. Hence, No one is used as the active subject to maintain the negative sense of never.
• The verb phrase has never been defeated (Passive) transforms into has ever defeated when used with the negative subject No one to maintain the original meaning.
• The original subject She becomes the object her in the active voice construction.
• The sentence No one has ever defeated her in any debate correctly maintains the Present Perfect Tense and the universal negative meaning of the original statement. Hence, this option is the correct conversion.

 Additional Information

• Active Voice vs. Passive Voice:
• In Active Voice, the subject performs the action (e.g., No one has defeated).
• In Passive Voice, the subject receives the action (e.g., She has been defeated).
• When the agent (doer) is not mentioned in a passive sentence using never, it is standard practice to introduce No one or Nobody as the subject in the active voice.
• Common Conversion Errors:
• Tense Shift: A common mistake is changing the tense (e.g., moving from Present Perfect to Simple Past), which is grammatically incorrect for voice conversion.
• Subject-Object Reversal: Option 3 (She never defeated anyone) is incorrect because it changes the meaning entirely, making her the person who fails to win rather than the person who is undefeated.
• Quantifier Modification: Changing any debate to every debate (as seen in Option 2) alters the logical scope of the sentence.

The correct answer is Option 4.

Key Points

• The error lies in part (D) of the sentence: protected by the chilling weather.
• The verb protected is typically followed by the preposition from or against when referring to a threat, danger, or unpleasant condition.
• In this context, the mother is keeping the child safe from the cold, not being protected by the cold itself.
• Using by would imply that the chilling weather is the agent providing the protection, which is logically incorrect.

Therefore, the correct answer is protected by the chilling weather.

Correct Sentence: 'Before going to bed, the mother ensured that the child was protected from the chilling weather.'