SSC GD Constable 2026 Official Paper (Held On 18 May, 2026 Shift 1) (Previous Year Paper)

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Pattern followed here is,

Hence, the correct answer is “Option 1”.

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Pattern followed here is,

Hence, the correct answer is “Option 4”.

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Pattern followed here is,

Hence, the correct answer is “Option 1”.

The logic followed in this pattern is a series of alphabetical shifts applied to the first and second letters of each cluster within the set.

For the set '(AT, CV, GA)':

For the set '(BZ, DB, HG)':

Applying the same logic to the option clusters:

Thus, the set (YO, AQ, EV) follows the same logic.

Hence, the correct answer is 'Option 1'.

First, we find the day of the week on January 1, 1919.

We use January 1, 1900 (Monday) as a reference point.

Number of years from 1900 to 1918 = 19 years.

Number of leap years in this period = 4 (1904, 1908, 1912, 1916).

Total odd days = (Number of years + Number of leap years) = 19 + 4 = 23 odd days.

23 ÷ 7 = 3 weeks and 2 odd days.

Since January 1, 1900 was a Monday, January 1, 1919 was Monday + 2 = Wednesday.

I. For August 1919:

We calculate the odd days from January to July:

Jan (31 days) = 3 odd days

Feb (28 days, 1919 is a non-leap year) = 0 odd days

Mar (31) = 3

Apr (30) = 2

May (31) = 3

Jun (30) = 2

Jul (31) = 3

Total odd days until July 31 = 3 + 0 + 3 + 2 + 3 + 2 + 3 = 16.

16 ÷ 7 = 2 weeks and 2 odd days.

Day on August 1, 1919 = Wednesday + 2 = Friday.

If August 1 is Friday, then August 2 is Saturday.

Saturdays in August 1919: 2, 9, 16, 23, 30. (Total = 5 Saturdays).

II. For December 1919:

We calculate odd days from August to November:

Aug (31) = 3

Sep (30) = 2

Oct (31) = 3

Nov (30) = 2

Total odd days from August to November = 3 + 2 + 3 + 2 = 10.

Total odd days from January to November = 16 (from earlier) + 10 = 26.

26 ÷ 7 = 3 weeks and 5 odd days.

Day on December 1, 1919 = Wednesday + 5 = Monday.

If December 1 is Monday, the first Saturday falls on December 6.

Saturdays in December 1919: 6, 13, 20, 27. (Total = 4 Saturdays).

Therefore, only August had 5 Saturdays in the year 1919.

Hence, the correct answer is Only I.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Similarly,

Hence, the correct answer is “Option 2”.

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TK460  : SN360 → 

 

JQ210 : IT110 → 

Similarly,

For , PR320 : ? 

 

Hence, the correct answer is 'Option 3'.

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LPR110 : KOQ210

 

ZKW90 : YJV190

Similarly,

For, PRT40 : ?

 

Hence, the correct answer is 'Option 2'.

The logic followed here is:

Logic: Second Number = First Number + 40

For the first pair 3249 : 3289

⇒ 3249 + 40 = 3289

Applying the same logic to the second pair

3658 : 3698

⇒ 3658 + 40 = 3698

Applying the same logic to the third pair

? : 8635

⇒ 8635 − 40 = 8595

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Logic: Second Number = (First Number × 2) + 4

For the pair 523 : 1050

⇒ (523 × 2) + 4

⇒ 1046 + 4 = 1050.

For the pair 513 : 1030

⇒ (513 × 2) + 4

⇒ 1026 + 4 = 1030.

Applying the same logic to find the missing number in the first pair

? : 1836

⇒ (First Number × 2) + 4 = 1836

⇒ First Number × 2 = 1836 − 4

⇒ First Number × 2 = 1832

⇒ First Number = 1832 ÷ 2 = 916.

Hence, the correct answer is 'Option 4'.

For**,** BLUSH is coded as FQTPC

For, GOATS is coded as KTZQN:

Similarly,

'WOODS' be coded in the same code language as,

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 1”.

Given time is 5:05 AM

For the hour hand, the time is 5 hours and 5 minutes.

Angle covered by the hour hand = (5 × 30) + (5 × 1/2) = 150 + 2.5 = 152.5^o

Angle covered by the minute hand = 5 × 6 = 30^o

Angle between the hour and minute hands = |152.5^o − 30^o| = 122.5^o

Hence, the angle between the hands is 122.5^o

Alternate Method

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

Here, H = 5 and M = 5.

So, Angle = $|60 \times 5 - 11 \times 5|\over 2$

Angle = $|300 - 55|\over 2$

Angle = 245/2 = 122.5^o

Hence, the correct answer is 122.5^o

<sup>

 Important Points</sup>

​Hour hand covers 360o in 12 hours

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

Angular distance covered in 60 minutes = 30o

Angular distance covered in 1 minute = 1/2o

Minute hand covers 360o in 60 minutes

1 minute = 360/60 ⇒ 1 minute = 6o

Minute hand covers 360° in 60 minutes

60 minutes = 360°

1 minute = 360/60 ⇒ 1 minute = 6°

Here the given time is 7:45 AM

Minute = 45

Angle covered by the minute hand = 45 × 6 = 270°

Angle covered by the hour hand = 7 × 30 + 45 × 1/2 = 210 + 22.5 = 232.5°

Angle between the hour hand and minute hand = 270 − 232.5 = 37.5°

Hence, the angle between the hour hand and minute hand is 37.5°.

Alternate Method

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

Here, H = hours and M = minutes.

Given H = 7 and M = 45.

So, Angle = $|60 \times 7 - 11 \times 45|\over 2$

Angle = $|420 - 495|\over 2$

Angle = $|-75|\over 2$ = 37.5°

Hence, the correct answer is 37.5°.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

The ratio of present ages of M and S = 1 : 5

Difference between their ages = 8 years (Since M is 8 years younger than S)

Let the present age of M be 1x and the present age of S be 5x.

According to the problem:

5x − 1x = 8

4x = 8

x = 8 ÷ 4

x = 2

So, the present ages are:

Present age of M = 1 × 2 = 2 years

Present age of S = 5 × 2 = 10 years

Age of M after 7 years = 2 + 7 = 9 years

Age of S after 7 years = 10 + 7 = 17 years

Ratio of M's age to S's age after 7 years = 9 : 17

Hence, the correct answer is “Option 4”.

The correct answer is Guru Gobind Singh Ji initiated the Khalsa.

Key Points

• On the day of Vaisakhi in 1699, the tenth Sikh Guru, Guru Gobind Singh Ji, convened a massive assembly at Anandpur Sahib in Punjab to strengthen the Sikh faith against oppression.
• The Guru called for volunteers to sacrifice their lives, resulting in the selection of the Panj Pyare (the Five Beloved Ones), who were the first to be initiated into the Khalsa Panth.
• The initiation involved the Amrit Sanchar ceremony, where Amrit (holy nectar) was prepared in a steel bowl using a Khanda (double-edged sword) and administered to the devotees.
• This event formalised the Sikh identity by introducing the Five Ks, which every initiated Sikh must wear as symbols of their commitment and faith.
• The creation of the Khalsa aimed to establish a community of Saint-Soldiers who would uphold Dharma, promote social equality, and fight against the tyranny of the Mughal Empire.

 Additional Information

• Historical Context of Other Options:
• Guru Nanak Dev Ji: The founder of Sikhism was born in 1469 in Nankana Sahib, which occurred over 200 years prior to the 1699 Vaisakhi event.
• The First Sikh Temple: Historically, the first Gurdwara was established by Guru Nanak Dev Ji in Kartarpur around 1521.
• The Quran: The central scripture of Islam was revealed to Prophet Muhammad starting in 610 AD in the cave of Hira.
• Significance of the Titles:
• Following the initiation, the Guru gave the name Singh (Lion) to men and Kaur (Princess) to women to eliminate caste hierarchies and foster universal brotherhood.
• The Guru himself received initiation from the Panj Pyare, reinforcing that the Guru and the Khalsa are one entity.

The correct answer is Lesser.

Key Points

• Pressure is defined as the physical force exerted on an object per unit Area. It is mathematically represented as Pressure = Force / Area.
• When a person is on sand, the Force acting downwards is the Weight of the person, which is calculated as the product of Mass and Acceleration due to gravity (g). This force remains constant whether the person is standing or lying down.
• While Standing, the contact area between the body and the sand is limited to the soles of the Feet. This Small Area results in a high concentration of force, leading to Higher Pressure.
• While Lying Down, the body weight is distributed over a significantly Larger Area (the entire back or front of the body).
• According to the principle of Inverse Proportion, for a constant force, as the area of contact increases, the pressure exerted Decreases.
• Therefore, because the area of contact is much larger when lying down compared to standing, the pressure exerted on the sand is Lesser.

 Additional Information

• The standard SI Unit of pressure is the Pascal (Pa), where 1 Pa = 1 Newton per square meter (N/m²).
• Understanding the relationship between area and pressure is vital in various engineering and biological contexts:
• Foundation of Buildings: Wide bases are used for pillars and walls to reduce the pressure on the ground, ensuring the structure does not sink.
• Camel's Feet: Camels have broad, padded feet that increase the Surface Area in contact with the desert sand, allowing them to exert Lesser Pressure and walk easily without sinking.
• Tools: Cutting tools like Knives and Needles have extremely small contact areas (sharp edges) to exert High Pressure with minimal force.

The correct answer is Peninsular Plateau.

Key Points

• The Meghalaya Plateau, also known as the Shillong Plateau, is geologically an extension of the Indian Peninsular Plateau, which is one of the oldest and most stable landmasses on Earth.
• It is separated from the main Peninsular block (specifically the Chotanagpur Plateau) by a massive tectonic depression known as the Malda Fault or the Garo-Rajmahal Gap.
• This gap was created due to the intense down-faulting caused by the northeastward movement of the Indian Plate during the Himalayan orogeny, which was later filled by the sediments of the Ganga and Brahmaputra rivers.
• The plateau comprises three distinct hill ranges named after the indigenous tribes: the Garo Hills in the west, the Khasi Hills in the center, and the Jaintia Hills in the east.
• The region is composed of Archean and Pre-Cambrian rocks, including gneisses, granites, and schists, which are identical to the rock structures found in the Peninsular shield.

 Additional Information

• Deccan Plateau:
• A large triangular plateau located south of the Narmada River.
• It is primarily composed of basaltic rocks of volcanic origin, known as the Deccan Traps.
• Western Ghats:
• A continuous mountain range running parallel to the western coast of India.
• It serves as the western boundary of the Deccan Plateau and is a global biodiversity hotspot.
• Chotanagpur Plateau:
• Located in eastern India, covering most of Jharkhand and parts of West Bengal, Odisha, and Chhattisgarh.
• Known as the mineral heartland of India, it is famous for its Pat lands and rich deposits of coal and iron ore.

The correct answer is High GDP growth without proportionate employment expansion.

Key Points

• The term jobless growth refers to an economic phenomenon where a country experiences a significant increase in its Gross Domestic Product (GDP) without a corresponding increase in employment opportunities.
• Following the 1991 Economic Reforms (Liberalization, Privatization, and Globalization), India witnessed a shift from a state-led to a market-led economy, resulting in rapid growth in high-value sectors.
• The growth was predominantly driven by capital-intensive industries and the Service Sector (such as IT and Finance), which utilize advanced technology to increase productivity rather than relying on a large manual workforce.
• While the aggregate output of the economy expanded significantly, the employment elasticity—which measures how employment responds to GDP growth—declined, leading to a situation where wealth increased but the unemployment rate did not decrease proportionately.

 Additional Information

• Employment Elasticity:
• This economic indicator reflects the ability of an economy to generate jobs for every unit of GDP growth. Post-1991, this ratio fell sharply in India, particularly in the secondary and tertiary sectors.
• Sectoral Mismatch:
• The Agriculture sector continues to employ nearly half of the Indian workforce despite its shrinking contribution to the total GDP, leading to high levels of disguised unemployment.
• The Manufacturing sector, which traditionally absorbs low-skilled labor in developing economies, did not grow fast enough to accommodate the labor force exiting agriculture.
• Skill Gap:
• The post-reform growth favored highly skilled professionals, creating a skill-biased technological change that left many semi-skilled and unskilled workers in the informal sector with low wages and no job security.

The correct answer is South Asia, Central Asia, and the Middle East.

Key Points

• Chabahar Port is located on the Makran Coast of the Sistan and Baluchestan Province in southeastern Iran, situated along the Gulf of Oman.
• The port acts as a primary maritime gateway for South Asia, specifically providing India with a strategic trade route that bypasses land boundaries to access Afghanistan and beyond.
• It serves as a critical transit hub for Central Asia, offering landlocked nations such as Uzbekistan, Turkmenistan, and Kazakhstan essential access to the Indian Ocean and global shipping lanes.
• As a major infrastructure project within Iran, it facilitates economic integration across the Middle East (West Asia) by connecting the Arabian Sea with the Caspian Sea region through internal rail and road networks.
• The strategic positioning of the port at these crossroads makes it a cornerstone of the International North-South Transport Corridor (INSTC), aimed at reducing transit time and freight costs between India, Russia, and Europe.

 Additional Information

• Terminal Infrastructure:
• The port consists of two main terminals: Shahid Beheshti and Shahid Kalantari. India has been actively involved in developing the Shahid Beheshti terminal to enhance regional connectivity.
• It is the only Iranian port with direct access to the ocean, allowing it to handle large cargo vessels that cannot enter the shallower Persian Gulf.
• Economic Agreements:
• The Trilateral Transit Agreement signed between India, Iran, and Afghanistan in 2016 established a dedicated corridor for the movement of goods and passengers.
• It supports the Ashgabat Agreement, which is an international transport and transit corridor facilitating trade between Central Asia and the Persian Gulf.
• The development of the Chabahar-Zahedan railway is intended to further link the port to the Zaranj-Delaram road in Afghanistan, boosting regional stability and commerce.

The correct answer is Encourage small-scale modernization and technology absorption..

Key Points

• The Industrial Policy Statement of 1980 was announced on July 23, 1980, with the primary objective of reviving the industrial sector by promoting economic federalism and increasing productivity through technological upgradation. Hence, statement 1 is correct.
• The policy aimed to promote the small-scale sector by introducing the concept of nucleus plants, which were intended to generate a network of ancillary industries and ensure a spread of modernization and technology absorption at the grassroots level. Hence, statement 1 is correct.
• Unlike the previous 1977 policy, the 1980 policy focused on correcting industrial stagnation by removing regional imbalances and allowing for automatic expansion of production capacities in core industries. Hence, statement 3 is incorrect.
• The policy sought to integrate the private sector more effectively into the national development plan by streamlining licensing procedures and encouraging investment, rather than seeking to close private enterprises. Hence, statement 2 is incorrect.
• The focus shifted from simple nationalization to improving the efficiency and management of existing Public Sector Undertakings (PSUs), ensuring they generated adequate surpluses for reinvestment. Hence, statement 4 is incorrect.

 Additional Information

• Industrial Policy Resolution, 1956:
• Often termed the Economic Constitution of India, it classified industries into Schedule A (state monopoly), Schedule B (mixed), and Schedule C (private).
• It placed heavy emphasis on the public sector and nationalization of key strategic sectors to achieve a socialistic pattern of society.
• Industrial Policy Statement, 1977:
• Introduced by the Janata Government, it prioritized cottage and tiny industries over large-scale development.
• Established District Industries Centers (DICs) to provide all support services to small entrepreneurs under one roof.
• New Industrial Policy, 1991:
• Marked a paradigm shift towards Liberalization, Privatization, and Globalization (LPG).
• Abolished industrial licensing for most sectors and reduced the role of the public sector to just a few strategic areas.

The correct answer is Setting prices of all goods.

Key Points

• A mixed economy is an economic system that combines the price mechanism of a market economy with government intervention to ensure social welfare and economic stability.
• Regulation of markets is a core function where the government implements anti-trust laws and competition policies to prevent monopolistic practices and protect consumer interests. Hence, statement 2 is correct.
• Provision of public goods involves the state supplying services that are non-excludable and non-rivalrous, such as national defense, street lighting, and public parks, which the private sector usually fails to provide. Hence, statement 3 is correct.
• Redistribution of income is managed through fiscal measures like progressive taxation and social security benefits to reduce wealth inequality and support the economically weaker sections. Hence, statement 4 is correct.
• Setting prices of all goods is a characteristic of a centrally planned or command economy. In a mixed economy, prices are determined by market forces (demand and supply), and the government only intervenes in essential commodities (like electricity or basic food grains) rather than all products. Hence, statement 1 is incorrect.

 Additional Information

• Economic Frameworks:
• Command Economy: The state has total control over the allocation of resources and production targets.
• Market Economy: Driven by the Invisible Hand where laissez-faire principles minimize state interference.
• Price Intervention in Mixed Economies:
• Price Ceilings: Maximum legal price set for essential goods to keep them affordable.
• Price Floors: Minimum legal price, such as the Minimum Support Price (MSP) for agricultural produce, to protect producers.

The correct answer is Cotton cultivation in regur basins.

Key Points

• Regur soil, popularly known as Black Cotton Soil, is predominantly found in the Deccan Trap region of India, covering approximately 5.46 lakh sq km.
• This soil is formed by the weathering of basaltic lava rocks from the Cretaceous period, making it rich in minerals like iron, magnesium, and aluminum.
• It possesses a very high clay content (often 60% or more), which gives it a superior moisture-retention capacity, a critical factor for the Cotton crop that requires consistent hydration during its growth cycle.
• Geographical concentration is highest in states like Maharashtra, Gujarat, Madhya Pradesh, and parts of Karnataka and Telangana.
• The soil exhibits a unique swell-shrink property due to the presence of Montmorillonite clay; it swells when wet and develops deep cracks when dry, facilitating self-aeration or self-ploughing.
• The agro-ecological association is so strong that the presence of regur soil is the primary determinant for the location of textile industries in western India.

 Additional Information

• Jute cultivation in alluvial floodplains
• Jute (the Golden Fibre) requires the fertile, renewable silt provided by alluvial floodplains, mainly in the Ganges-Brahmaputra delta (West Bengal and Bihar).
• Tea cultivation in acidic hill soils
• Tea thrives in deep, fertile, and well-drained acidic soils (pH 4.5 to 5.5) rich in organic matter, typically found in Assam, Darjeeling, and the Nilgiri Hills.
• Rice cultivation in deltaic alluvium
• Rice (Paddy) necessitates heavy clayey alluvium found in coastal deltas (like those of the Godavari and Mahanadi) because it requires soil that can hold standing water for long periods.

Therefore, the correct answer is Cotton cultivation in regur basins.

The correct answer is Ministry of Home Affairs.

Key Points

• The Nyaya Shruti App was officially launched in August 2024 by the Union Minister of Home Affairs and Cooperation, Amit Shah, during a high-level review meeting in Chandigarh.
• The application is designed to facilitate the seamless implementation of the three new criminal laws: Bharatiya Nyaya Sanhita (BNS), Bharatiya Nagarik Suraksha Sanhita (BNSS), and Bharatiya Sakshya Adhiniyam (BSA).
• The primary objective of the Nyaya Shruti system is to enable video conferencing for judicial proceedings, allowing witnesses, medical experts, and police officials to provide testimony remotely from a secure environment.
• By integrating with the Inter-operable Criminal Justice System (ICJS), the app ensures that digital evidence and statements are recorded efficiently, reducing the physical burden on the judiciary and law enforcement agencies.
• The launch marks a critical step towards e-Forensics and e-Courts, aiming to expedite the delivery of justice and minimize the backlog of cases in the Indian legal system.

 Additional Information

• Bharatiya Nagarik Suraksha Sanhita (BNSS):
• Replaces the colonial-era Code of Criminal Procedure (CrPC).
• Mandates the use of technology for various stages of investigation, including the recording of search and seizure operations via mobile phones or electronic devices.
• Ministry of Law and Justice:
• While this ministry oversees the drafting of legislation and legal affairs, the operational rollout of technology for the new criminal laws and internal security is managed by the Ministry of Home Affairs.
• Digital Transformation:
• The Nyaya Shruti app is a component of the broader Digital India mission, specifically targeting the Criminal Justice System to ensure transparency and accountability.

The correct answer is Supreme Court of India.

Key Points

• In November 2024, the Supreme Court of India ruled that a sexual harassment case cannot be quashed merely because the accused and the complainant have reached a compromise.
• The Court observed that offences involving sexual harassment, sexual assault, and crimes against children are not purely private disputes and have a serious impact on society.
• The judgment was delivered by a bench comprising Justice C. T. Ravikumar and Justice P. V. Sanjay Kumar.
• The Court set aside an order of the Rajasthan High Court, which had earlier quashed an FIR against a school teacher accused of sexually harassing a minor girl after a compromise was reached with the victim's family.
• The case involved provisions of the Protection of Children from Sexual Offences (POCSO) Act, highlighting the judiciary's commitment to protecting children from sexual crimes.
• The Supreme Court emphasized that heinous offences affecting public interest cannot ordinarily be terminated through private settlements because such crimes are considered offences against society as a whole.

 Additional Information

• Supreme Court of India
• Established on 26 January 1950 under Part V, Chapter IV of the Constitution of India.
• It is the highest judicial authority in the country.
• The Court has the power of judicial review and acts as the final interpreter of the Constitution.
• Its decisions are binding on all courts within India under Article 141 of the Constitution.
• Patna High Court
• Established in 1916.
• It is the highest judicial body for the state of Bihar.
• Its principal seat is located in Patna.
• Madras High Court
• One of India's oldest High Courts, established in 1862.
• Exercises jurisdiction over the state of Tamil Nadu and the Union Territory of Puducherry.
• Its principal seat is located in Chennai.
• POCSO Act, 2012
• Enacted to protect children below 18 years of age from sexual offences.
• Provides for child-friendly procedures during investigation and trial.
• Recognizes offences such as sexual assault, aggravated sexual assault, sexual harassment, and use of children for pornography.

The correct answer is Pulakesin II.

Key Points

• The battle between Harshavardhana and Pulakesin II occurred on the banks of the Narmada River around 618-619 CE.
• Pulakesin II belonged to the Chalukyas of Vatapi (Badami) and was one of the most powerful rulers of the Deccan.
• Harshavardhana, the ruler of Kannauj, attempted to expand his empire into southern India but was decisively checked by the Chalukyan forces.
• The Aihole Inscription, authored by the court poet Ravikirti, provides a detailed account of this victory and the valor of Pulakesin II.
• Following this victory, Pulakesin II assumed the title of Paramesvara and established the Narmada River as the permanent boundary between the two empires.
• The Chinese traveler Xuanzang (Hiuen Tsang), who visited the courts of both kings, also recorded the military strength of Pulakesin II and his success in resisting Harsha.

 Additional Information

• Rajendra I:
• He was a preeminent ruler of the Chola Dynasty (1014−1044 CE).
• He is famous for his naval expeditions to Southeast Asia and his campaign to the Ganga River, after which he took the title Gangaikonda.
• Krishna III:
• He was the last great emperor of the Rashtrakuta Dynasty of Manyakheta.
• He defeated the Cholas at the Battle of Takkolam in 949 CE and extended his influence as far as Rameswaram.
• Rajasimha:
• Also known as Narasimhavarman II, he was a notable ruler of the Pallava Dynasty.
• He is renowned for his patronage of Dravidian architecture, specifically the construction of the Shore Temple at Mahabalipuram and the Kailasanathar Temple at Kanchipuram.

The correct answer is choliya.

Key Points

• Choliya, also known as Chholiya, is one of the oldest and most famous folk dances of the Kumaon region in Uttarakhand.
• It is traditionally a sword dance that dates back over a thousand years, reflecting the martial traditions of the Khasa and Rajput communities of the Himalayan belt.
• Originally performed at wedding processions to ward off evil spirits, the dance involves a mock combat sequence where dancers wield swords (talwar) and shields (dhala) with rhythmic precision.
• The performance is characterized by high-energy movements, acrobatic stunts, and synchronized formations that showcase the bravery and agility of the warriors.
• It is accompanied by traditional musical instruments of Uttarakhand, specifically the Dhol, Damau, Turi, Ransingha, and Masakbeen (bagpipes).
• Dancers typically wear traditional Kumaoni attire, consisting of white chudidar pajamas, a long chola (tunic), and a turban, often decorated with colorful embroidery.

 Additional Information

• Kolkali:
• A rhythmic folk dance performed in the state of Kerala and the Union Territory of Lakshadweep.
• Dancers move in a circle, striking wooden sticks in unison to create a unique percussive sound.
• Sambalpuri:
• Originates from the western region of Odisha.
• It is often associated with the Dalkhai dance and is performed during festivals like Nuakhai and Bhai Jiuntia.
• Sawlakin (Sarlamkai):
• This is a prominent folk dance from the state of Mizoram.
• Historically, it was a war dance performed to celebrate a victory in battle and is also known as Solakia in some tribal dialects.
• Other Folk Dances of Uttarakhand:
• Jhora: A community dance performed during Vasant Panchami.
• Chhapeli: A romantic dance style representing the courtship between lovers.
• Langvir Nritya: An acrobatic dance performed by men involving climbing a pole.

The correct answer is Chennai.

Key Points

• In early 2025, Indian Railways reached a major milestone in green transportation by successfully testing its first hydrogen-powered coach at the Integral Coach Factory (ICF) in Chennai.
• The coach is a part of the ambitious Hydrogen for Heritage initiative, which aims to replace carbon-heavy diesel engines with environment-friendly hydrogen fuel cell technology on historical and sensitive rail routes.
• Technologically, these coaches utilize fuel cells to combine hydrogen and oxygen to generate electricity, with the only emissions being water vapor and heat, making them a zero-emission alternative to traditional rolling stock.
• The successful prototype testing at Chennai facilitates the deployment of these trains on various narrow-gauge sections, such as the Kalka-Shimla and Darjeeling Himalayan Railway.
• This development aligns with India's national commitment to achieve Net Zero Carbon Emission by 2030 and reduces the dependence on imported fossil fuels.

 Additional Information

• Integral Coach Factory (ICF), Chennai:
• Established in 1955, it is the world's largest rail coach manufacturer and is renowned for designing the Vande Bharat Express (Train 18).
• Rail Coach Factory (RCF), Kapurthala:
• Located in Punjab, this unit was established in 1986 and is a primary manufacturer of LHB (Linke Hofmann Busch) coaches used in high-speed trains.
• Modern Coach Factory (MCF), Rae Bareilly:
• Commissioned in 2012 in Uttar Pradesh, it is a state-of-the-art facility focused on automated manufacturing of specialized railway coaches.
• Kolkata:
• It is the headquarters of the Eastern Railway and South Eastern Railway, and was the first city in India to launch a Metro Railway system in 1984.

The correct answer is Uttar Pradesh.

Key Points

• According to the Census 2011, Uttar Pradesh recorded the highest rural population in India, with a total of 155,110,594 individuals living in rural areas.
• The state accounts for nearly 18.62% of the total rural population of the country, which stood at approximately 833.7 million during the 2011 survey.
• Approximately 77.73% of the total population of Uttar Pradesh resides in rural regions, emphasizing its role as a primarily agrarian and rural-based economy.
• The 15th National Census of India, conducted in two phases (House Listing and Population Enumeration), serves as the primary source for these demographic statistics.

 Additional Information

• Comparison with other states:
• Bihar: It holds the second-highest rural population in India, with approximately 92.3 million people living in villages.
• West Bengal: This state ranks among the top contributors with a rural population of about 62.1 million.
• Maharashtra: While it has the highest urban population in India (50.8 million), its rural population is approximately 61.5 million.
• Key Census Facts:
• Sikkim: Recorded as the state with the lowest total population in India.
• Himachal Pradesh: Holds the highest percentage of rural population, where nearly 90% of the people live in rural areas.
• Goa: Known for having the highest percentage of urban population among Indian states at 62.2%.
• The Registrar General and Census Commissioner of India is responsible for conducting the decennial census under the Ministry of Home Affairs.

The correct answer is 1848.

Key Points

• The Doctrine of Lapse was an annexation policy implemented by Lord Dalhousie, who served as the Governor-General of India from 1848 to 1856.
• According to this policy, if a ruler of a princely state under British protection died without a natural male heir, the state would 'lapse' and be annexed to the British East India Company’s territories.
• Satara, a state in present-day Maharashtra, became the first princely state to be annexed under this doctrine in 1848.
• The annexation occurred following the death of the ruler Appa Sahib. Although he had adopted a son before his passing, the British authorities refused to recognize the adopted son as the legal successor to the throne.
• The policy disregarded the long-standing Indian tradition where an adopted son possessed the same legal and religious rights as a biological son, leading to significant political unrest.

 Additional Information

• Successive Annexations: After Satara, several other states were annexed under the same policy:
• Sambalpur and Jaitpur were annexed in 1849.
• Baghat was annexed in 1850.
• Udaipur was annexed in 1852.
• Jhansi was annexed in 1853 after the death of Raja Gangadhar Rao.
• Nagpur was annexed in 1854.
• Annexation of Awadh: While most states were annexed due to lack of heirs, Awadh was annexed in 1856 by Lord Dalhousie on the grounds of maladministration and misgovernance.
• Historical Impact: The aggressive expansionist policies under the Doctrine of Lapse created a sense of insecurity and resentment among Indian rulers, becoming one of the primary political causes of the Revolt of 1857.
• Administrative Reforms: Despite his controversial policies, Dalhousie is also known for introducing the first railway line (Bombay to Thane in 1853) and the telegraph system in India.

The correct answer is 2024.

Key Points

• The Royal Challengers Bengaluru (RCB) secured their first-ever Women's Premier League (WPL) title in the year 2024.
• The final match of the 2024 season was played on March 17, 2024, at the Arun Jaitley Stadium in New Delhi.
• RCB defeated Delhi Capitals by 8 wickets in a low-scoring final, successfully chasing down a target of 114 runs with three balls remaining.
• The team was captained by the Indian opening batter Smriti Mandhana, who led the franchise to its first trophy across both the men's and women's leagues.
• Australian all-rounder Ellyse Perry was a standout performer for RCB, winning the Orange Cap for scoring the most runs (347 runs) in the tournament.
• Shreyanka Patil, an emerging Indian off-spinner for RCB, won the Purple Cap for being the highest wicket-taker of the season with 13 wickets.

 Additional Information

• Women's Premier League (WPL) Overview:
• The WPL is a premier women's Twenty20 cricket league established by the Board of Control for Cricket in India (BCCI).
• The inaugural season was held in 2023, which was won by Mumbai Indians under the captaincy of Harmanpreet Kaur.
• The league currently features five franchises: Mumbai Indians, Delhi Capitals, Royal Challengers Bengaluru, UP Warriorz, and Gujarat Giants.
• The 2024 edition was the second season of the tournament, featuring a format where the top team in the points table qualified directly for the final.
• Deepti Sharma from UP Warriorz was named the Most Valuable Player (MVP) of the 2024 season for her all-round performance.

The correct answer is Doha.

Key Points

• The 21st Asian Games are scheduled to be hosted in Doha, Qatar, in the year 2030.
• The decision was finalized during the 39th General Assembly of the Olympic Council of Asia (OCA), which took place in Muscat, Oman, on 16 December 2020.
• Doha was awarded the 2030 edition after winning the majority of votes in a contest against Riyadh, Saudi Arabia. As part of a consensus, the OCA subsequently awarded the 22nd Asian Games to Riyadh for the year 2034.
• This event marks the second time Qatar will host the continental multi-sport competition, having previously organized the 15th Asian Games in 2006.
• The 2030 Games are expected to utilize many of the state-of-the-art venues developed for the 2022 FIFA World Cup, demonstrating Qatar's established sports infrastructure.

 Additional Information

• Host City Timeline:
• 19th Asian Games (2022): Held in Hangzhou, China, in 2023 due to pandemic-related delays.
• 20th Asian Games (2026): Set to be co-hosted by Aichi Prefecture and Nagoya, Japan.
• 22nd Asian Games (2034): Scheduled for Riyadh, Saudi Arabia.
• Olympic Council of Asia (OCA):
• The OCA is the governing body for all sports in Asia, recognized by the International Olympic Committee (IOC). It is headquartered in Kuwait City.
• Beijing, China:
• Beijing hosted the 11th Asian Games in 1990 and has a long history of hosting global events, including the 2008 and 2022 Olympic Games.
• Tokyo, Japan:
• Tokyo served as the host for the 3rd Asian Games in 1958 and the inaugural games were held in New Delhi in 1951.

The correct answer is Gymnastics.

Key Points

• Gymnastics is a sport that involves the performance of systematic exercises requiring physical strength, flexibility, power, agility, coordination, and balance. It has been a part of the Summer Olympic Games since the first modern edition in 1896.
• The Pommel Horse is an artistic gymnastics apparatus used exclusively by male gymnasts. It originated as a tool to train soldiers to mount and dismount horses quickly. The apparatus is approximately 115 cm in height and features two circular handles called pommels on top of a leather-covered frame.
• The Parallel Bars consist of two wooden rails placed parallel to each other and supported by a metal upright structure. This event is also primarily for men and focuses on swinging, balancing, and flight elements, testing a gymnast's upper body strength and core control.
• The International Gymnastics Federation (FIG) is the governing body that regulates technical standards for these apparatuses and oversees international competitions like the World Gymnastics Championships.

 Additional Information

• Cricket:
• A sport played between two teams of eleven players. Common terminologies include Googly, Leg Before Wicket (LBW), Yorker, Duck, and Silly Point.
• Badminton:
• A racquet sport played using a shuttlecock. Specific terms include Smash, Drop Shot, Deuce, Let, and Service Court.
• Kho-Kho:
• A traditional Indian tag sport. Key terms include Chaser, Active Runner, Lobby, Pole Dive, and Central Lane.
• Other Gymnastics Apparatus:
• Men's events also include the Still Rings, Horizontal Bar, and Floor Exercise. Women's artistic gymnastics includes the Uneven Bars, Balance Beam, Vault, and Floor Exercise.

The correct answer is UNESCO.

Key Points

• The Global Education Monitoring (GEM) Report is an editorially independent, authoritative, and evidence-based annual report published by UNESCO.
• The report is mandated to monitor progress towards the education targets in the Sustainable Development Goals (SDGs) framework, with a specific focus on SDG 4, which aims to ensure inclusive and equitable quality education.
• Originally established in 2002, it was formerly known as the Education for All (EFA) Global Monitoring Report before being rebranded in 2016 following the adoption of the 2030 Agenda for Sustainable Development.
• Each edition of the report focuses on a specific theme, such as inclusion and education, non-state actors, or technology in education, providing a comprehensive assessment of global education trends and policy recommendations.
• It serves as a vital tool for advocacy and accountability, using the latest available data to hold governments and international organizations responsible for their educational commitments.

 Additional Information

• UNESCO (United Nations Educational, Scientific and Cultural Organization):
• Founded in 1945 and headquartered in Paris, France, its mission is to build peace through international cooperation in Education, the Sciences, and Culture.
• UNDP (United Nations Development Programme):
• Headquartered in New York, it is primarily known for publishing the Human Development Report (HDR) and the Human Development Index (HDI).
• World Bank:
• An international financial institution that provides loans and grants; it publishes the World Development Report (WDR) and the Global Economic Prospects.
• WIPO (World Intellectual Property Organization):
• A specialized agency of the UN that promotes the protection of intellectual property and publishes the Global Innovation Index (GII).

The correct answer is 4.

Key Points

• The Urban Governance Index (UGI) is a comprehensive research study conducted by the Praja Foundation to map and evaluate the level of democratic empowerment in Urban Local Bodies (ULBs) across Indian states.
• The 2024 index evaluates the states based on 4 primary themes or categories that collectively measure the implementation of the 74th Constitutional Amendment Act in letter and spirit.
• The first category, Empowered City Elected Representatives and Legislative Structure, assesses the authority and tenure of the Mayor and the decision-making powers of the City Council.
• The second category, Empowered City Administration, focuses on the autonomy of the municipal administration regarding its personnel and its ability to manage city-wide functions without external state agency interference.
• The third category, Empowered Citizens, evaluates the institutionalization of community participation through the formation and functionality of Ward Committees and Area Sabhas.
• The fourth category, Fiscal Empowerment, examines the financial independence of cities, specifically their power to levy taxes, independent budgetary control, and the stability of inter-governmental fiscal transfers.

 Additional Information

• Praja Foundation:
• Founded in 1997 in Mumbai, it is a non-partisan organization dedicated to improving the quality of life and governance in Indian cities.
• The foundation’s Urban Governance Index serves as a vital tool for policymakers to identify gaps in urban decentralization and local self-government.
• 74th Constitutional Amendment Act (1992):
• This landmark legislation granted constitutional status to Municipalities and mandated the creation of three types of urban bodies.
• It introduced the Twelfth Schedule to the Constitution of India, which lists 18 specific functions that should ideally be transferred to Urban Local Bodies to ensure self-governance.

Shortcut Trick

Solve brackets and multiplication first: (29 + 15) × 2 = 44 × 2 = 88.

Simplify the rest by grouping positive and negative terms.

Calculation: (66 + 48 + 84) − (88 + 33) = 198 − 121 = 77.

∴ The correct answer is 77.

Alternate Method

Given: 66 + 48 − (29 + 15) × 2 + 84 − 33

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

⇒ 66 + 48 − (44) × 2 + 84 − 33

⇒ 66 + 48 − 88 + 84 − 33

⇒ 114 − 88 + 84 − 33

⇒ 26 + 84 − 33

⇒ 110 − 33

⇒ 77

∴ The correct answer is 77.

Additional Information

BODMAS Rule

It is the standard order of operations: Brackets first, then Orders (exponents), followed by Division and Multiplication (left to right), and finally Addition and Subtraction (left to right).

Addition and Subtraction Priority

According to the BODMAS rule, addition and subtraction have the same priority level and are generally performed from left to right as they appear in the expression.

Shortcut Trick

Evaluate the Of and Multiplication first: 18 of 2 = 36 and 31 × 1 = 31.

Sum positive terms: 89 + 31 + 36 + 27 = 183.

Sum negative terms: 42 + 19 = 61.

Subtract negative sum from positive sum: 183 − 61 = 122.

∴ The correct answer is 122.

Alternate Method

Given Expression: 89 − 42 + 31 × 1 + (18 of 2) + 27 − 19

Applying the BODMAS rule (Bracket, Of, Division, Multiplication, Addition, Subtraction):

⇒ 89 − 42 + 31 × 1 + 36 + 27 − 19 (Evaluating Of: 18 × 2 = 36)

⇒ 89 − 42 + 31 + 36 + 27 − 19 (Evaluating Multiplication: 31 × 1 = 31)

⇒ (89 + 31 + 36 + 27) − 42 − 19 (Grouping Addition terms)

⇒ 183 − 42 − 19

⇒ 183 − 61 (Performing Subtraction)

⇒ 122

∴ The correct answer is 122.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets, Of (Orders), Division, Multiplication, Addition, and Subtraction.

The 'Of' Operator

In mathematical expressions, 'Of' signifies multiplication and is prioritized higher than standard division and multiplication operations.

Sign Convention

When adding or subtracting multiple numbers, it is often easier to group all positive terms together and all negative terms together before finding the final result.

Shortcut Trick

Rewrite 8 × (4.5)³ as 2³ × (4.5)³ = (2 × 4.5)³ = 9³.

Numerator: 9³ − 1 = 729 − 1 = 728.

Denominator: 10² − 9 = 100 − 9 = 91.

Final result = 728 ÷ 91 = 8.

∴ The correct answer is 8.

Alternate Method

Given: Expression = (8 × (4.5)³ − 1) ÷ (10² − 9)

Method: Step-by-step simplification following BODMAS rules and Power Properties.

⇒ Numerator = 8 × (4.5)³ − 1

⇒ 8 × 91.125 − 1

⇒ 729 − 1 = 728

⇒ Denominator = 10² − 9

⇒ 100 − 9 = 91

⇒ Final Expression = 728 ÷ 91

⇒ 8

∴ The correct answer is 8.

Additional Information

BODMAS Rule

It stands for Brackets, Orders (Powers/Roots), Division, Multiplication, Addition, and Subtraction, defining the correct sequence for mathematical operations.

Power Property

The rule aⁿ × bⁿ = (a × b)ⁿ allows multiplying bases when the exponents are identical, simplifying complex terms like 2³ × 4.5³.

Algebraic Identity (a³ − b³)

The difference of cubes is given by (a − b)(a² + ab + b²), which can be useful for simplifying expressions involving cubic terms.

Shortcut Trick

Find the square root of 2025, which is 45.

Simplify the ratio: √x = 100 ÷ 45 = 20 ÷ 9.

Squaring both sides to find x: (20 ÷ 9)² = 400 ÷ 81.

∴ The correct answer is 400/81.

Alternate Method

Given:

√x = 100 ÷ √2025

Calculation:

⇒ √x = 100 ÷ 45

⇒ √x = (20 × 5) ÷ (9 × 5)

⇒ √x = 20 ÷ 9

Squaring both sides of the equation:

⇒ (√x)² = (20 ÷ 9)²

⇒ x = 20² ÷ 9²

⇒ x = 400 ÷ 81

∴ The correct answer is 400/81.

Additional Information

Square Root of Numbers Ending in 25

For a number ending in 25, the square root ends in 5. The remaining digits are the product of two consecutive integers (e.g., 20 = 4 × 5, so √2025 = 45).

Power of a Quotient

According to laws of indices, (a ÷ b)ⁿ = aⁿ ÷ bⁿ. This is used when squaring fractions to find the value of x.

Isolating the Variable

To solve for a variable inside a radical, apply the inverse operation (squaring for square roots) to both sides of the equation.

Shortcut Trick

Use the property: 1/(√a − √b) = (√a + √b) / (a − b).

Here, a = 6 and b = 2, so 1/(√6 − √2) = (√6 + √2) / 4.

Total = (√6 + √2) + (√6 + √2) / 4 = (1 + 1/4) × (√6 + √2) = 5/4 (√6 + √2).

∴ The correct answer is 5/4 (√6 + √2).

Alternate Method

Given expression: (√6 + √2) + 1/(√6 − √2)

To solve this, we will perform Rationalization of the Denominator for the second term.

⇒ 1/(√6 − √2) = [1 × (√6 + √2)] / [(√6 − √2) × (√6 + √2)]

⇒ Using Identity (a − b)(a + b) = a² − b² in the denominator:

⇒ 1/(√6 − √2) = (√6 + √2) / [(√6)² − (√2)²]

⇒ 1/(√6 − √2) = (√6 + √2) / (6 − 2) = (√6 + √2) / 4

⇒ Now, substitute this back into the original expression:

⇒ Result = (√6 + √2) + (√6 + √2) / 4

⇒ Result = [4 × (√6 + √2) + 1 × (√6 + √2)] / 4

⇒ Result = 5(√6 + √2) / 4 = 5/4 (√6 + √2)

∴ The correct answer is 5/4 (√6 + √2).

Additional Information

Rationalizing Factor

The Conjugate of a binomial surd like (√x − √y) is (√x + √y). Multiplying them removes the square root from the denominator.

Algebraic Identity for Surds

The formula (a − b)(a + b) = a² − b² is essential for simplifying fractions involving Square Roots.

Simplified Form

Always check if terms can be combined by taking a common factor after rationalization to reach the final Simplified Value.

Shortcut Trick

The diagonal of a square is directly proportional to its side.

Diagonal = Side × √2

Given Side = 10 cm.

Diagonal = 10 × √2 = 10√2 cm.

∴ The correct answer is 10√2 cm.

Alternate Method

Given:

Side of the square (a) = 10 cm

Formula Used:

According to Pythagoras Theorem in a square, the diagonal (d) forms the hypotenuse of a right-angled triangle with two sides (a).

d² = a² + a² ⇒ d = √(2a²) = a√2

Calculations:

⇒ Side (a) = 10 cm

⇒ Diagonal (d) = √(10² + 10²)

⇒ d = √(100 + 100)

⇒ d = √200

⇒ d = √(100 × 2)

⇒ d = 10√2 cm

∴ The correct answer is 10√2 cm.

Additional Information

Area of a Square

The area can be calculated using the side as Area = a² or using the diagonal as Area = d² ÷ 2.

Perimeter of a Square

The total boundary length is given by Perimeter = 4 × side.

Relation with Circle

For a square inscribed in a circle, the diagonal of the square is equal to the diameter of the circle.

Shortcut Trick

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

Sum of digits of 95P9 = 9 + 5 + P + 9 = 23 + P.

Testing the options for P, we find that 23 + 7 = 30, which is divisible by 3.

∴ The correct answer is 7.

Alternate Method

Given: The four-digit number 95P9 is exactly divisible by 3.

Divisibility Rule of 3: The sum of all the individual digits of the number must be divisible by 3.

⇒ Sum = 9 + 5 + P + 9

⇒ Sum = 23 + P

⇒ For the number to be divisible by 3, (23 + P) must be 24, 27, 30, 33, etc.

⇒ If 23 + P = 24, then P = 1 (Not in options)

⇒ If 23 + P = 27, then P = 4 (Not in options)

⇒ If 23 + P = 30, then P = 7 (Present in options)

⇒ If 23 + P = 33, then P = 10 (Not a single digit)

∴ The correct answer is 7.

Additional Information

Divisibility Rule of 9

A number is divisible by 9 if the sum of its digits is divisible by 9. Every number divisible by 9 is also divisible by 3.

Divisibility Rule of 6

A number is divisible by 6 if it is even (ends in 0, 2, 4, 6, or 8) and is also divisible by 3.

Divisibility Rule of 4

A number is divisible by 4 if the last two digits of the number are divisible by 4 or if the last two digits are 00.

Shortcut Trick

Apply Pythagorean Triplets logic: (3, 4, 5) scaled by factor 3.

Given Length = 9 cm (3 × 3) and Diagonal = 15 cm (5 × 3).

The missing side Breadth must be (4 × 3) = 12 cm.

Required Ratio = Length : Breadth = 9 : 12 = 3 : 4.

∴ The correct answer is 3 : 4.

Alternate Method

Given:

Length (l) of the rectangle = 9 cm

Diagonal (d) of the rectangle = 15 cm

Formula Used:

In a rectangle, d² = l² + b² (where b is the breadth).

Calculations:

⇒ (15)² = (9)² + b²

⇒ 225 = 81 + b²

⇒ b² = 225 − 81

⇒ b² = 144

⇒ b = √144 = 12 cm

⇒ Ratio of Length to Breadth = l : b

⇒ Ratio = 9 : 12

⇒ Ratio = 3 : 4

∴ The correct answer is 3 : 4.

Additional Information

Properties of a Rectangle

Opposite sides are equal and parallel, and each internal angle is 90°.

Area and Perimeter

Area = Length × Breadth | Perimeter = 2 × (Length + Breadth).

Pythagorean Theorem

For a right-angled triangle, a² + b² = c², where c is the hypotenuse (diagonal in a rectangle).

Shortcut Trick

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

Identify a = 460 and b = 240.

Substituting the values: (460 − 240)² = 220².

Calculating the square: 220 × 220 = 48400.

∴ The correct answer is 48400.

Alternate Method

Given: (460 + 240)² − 4 × 460 × 240

Method: Step-by-step simplification using BODMAS rules.

⇒ (700)² − 4 × 460 × 240

⇒ 490000 − 4 × 110400

⇒ 490000 − 441600

⇒ 48400

∴ The correct answer is 48400.

Additional Information

Square of the Sum Identity

The algebraic expansion is (a + b)² = a² + 2ab + b².

Square of the Difference Identity

The algebraic expansion is (a − b)² = a² − 2ab + b².

Relationship between Identities

The difference between the two squares is given by (a + b)² − (a − b)² = 4ab.

Shortcut Trick

If the Average age remains unchanged after some members leave, the Average age of those leaving members must be equal to the Original Average.

Average age of 2 leaving boys = 19 years

Sum of ages of 2 leaving boys = 2 × 19 = 38 years

Value of x = 38 − 21 = 17

∴ The correct answer is 17.

Alternate Method

Given: Initial Average = 19, Number of boys = 28, Boys leaving = 2, Final Average = 19.

Formula Used: Total Age = Average × Number of persons

⇒ Total Age of 28 boys = 28 × 19 = 532 years

⇒ Remaining boys in the class = 28 − 2 = 26 boys

⇒ Total Age of 26 boys = 26 × 19 = 494 years

⇒ Sum of ages of 2 boys who left = (Total age of 28) − (Total age of 26)

⇒ x + 21 = 532 − 494

⇒ x + 21 = 38

⇒ x = 38 − 21 = 17

∴ The correct answer is 17.

Additional Information

Average Formula

The Average of a set of observations is the sum of the observations divided by the total number of observations. Average = Sum ÷ Count.

Replacement Rule

If a person leaves and is replaced by another, New Average = Old Average + (Age Gain/Loss ÷ Total Count).

Weighted Average

When two groups with different averages are combined, Combined Average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Shortcut Trick

To find the least number exactly divisible by 5, 7, 9, and 21, we calculate their LCM.

Since 7 is a factor of 21, the LCM of (5, 7, 9, 21) is equivalent to the LCM of (5, 9, 21).

Multiply the largest number 21 by the prime factors of other numbers not already present in it.

LCM = 21 × 3 (remaining factor of 9) × 5 (factor of 5) = 63 × 5 = 315.

∴ The correct answer is 315.

Alternate Method

Given: The set of numbers is 5, 7, 9, and 21.

Formula Used: The Least Common Multiple (LCM) is the product of the highest powers of all prime factors involved in the numbers.

⇒ Prime factors of 5 = 5¹

⇒ Prime factors of 7 = 7¹

⇒ Prime factors of 9 = 3 × 3 = 3²

⇒ Prime factors of 21 = 3 × 7 = 3¹ × 7¹

⇒ LCM = 3² × 5¹ × 7¹

⇒ LCM = 9 × 5 × 7

⇒ LCM = 315

∴ The correct answer is 315.

Additional Information

LCM and HCF Relation

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

LCM of Prime Numbers

The Least Common Multiple of a set of prime numbers is simply the product of those numbers.

Divisibility Rule of 9

A number is divisible by 9 if the sum of its individual digits is a multiple of 9. For 315: 3 + 1 + 5 = 9, which is divisible by 9.

Shortcut Trick

Find the differences between the given numbers: (50 − 38), (74 − 50), and (98 − 74).

Differences are 12, 24, and 24.

The HCF (Highest Common Factor) of 12, 24, and 24 is 12.

Thus, 12 is the largest number that leaves the same remainder (2) in each case.

∴ The correct answer is 12.

Alternate Method

Given: The numbers are 38, 50, 74, and 98.

Formula: To find the largest number that divides several numbers leaving the same remainder, find the HCF of the absolute differences between the numbers.

⇒ First difference = |50 − 38| = 12

⇒ Second difference = |74 − 50| = 24

⇒ Third difference = |98 − 74| = 24

⇒ Required Number = HCF of (12, 24, 24)

⇒ Factors of 12 = 1, 2, 3, 4, 6, 12

⇒ Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

⇒ Common Factors = 1, 2, 3, 4, 6, 12

⇒ Highest Common Factor (HCF) = 12

∴ The correct answer is 12.

Additional Information

HCF with Specific Remainders

To find the largest number that divides A, B, and C leaving remainders x, y, and z respectively, find the HCF of (A − x), (B − y), and (C − z).

LCM with Same Remainder

The smallest number which when divided by x, y, and z leaves the same remainder 'r' in each case is [LCM(x, y, z) + r].

HCF Property

The HCF of a set of numbers always divides the difference between any two numbers in that set.

Shortcut Trick

The difference between Selling Price (SP) and Cost Price (CP) is the Profit.

Given Profit percentage = 7%, which corresponds to the difference of ₹385.

⇒ 7% of CP = ₹385

⇒ 1% of CP = 385 ÷ 7 = ₹55

⇒ 100% of CP = 55 × 100 = ₹5500

∴ The correct answer is ₹5500.

Alternate Method

Given:

Difference (SP − CP) = ₹385

Profit percentage = 7%

Formula Used:

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

Calculations:

⇒ Profit = Selling Price − Cost Price = ₹385

⇒ Profit % = (Profit ÷ CP) × 100

⇒ 7 = (385 ÷ CP) × 100

⇒ CP = (385 × 100) ÷ 7

⇒ CP = 55 × 100

⇒ CP = ₹5500

∴ The correct answer is ₹5500.

Additional Information

Relationship between SP and CP

Selling Price (SP) = CP × (100 + Profit%) ÷ 100. If there is a loss, SP = CP × (100 − Loss%) ÷ 100.

Cost Price Calculation

When the difference between SP and CP is known (Profit or Loss), CP = (Difference ÷ Profit/Loss %) × 100.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Shortcut Trick

Effective percentage = 70% × 60% = 42%

According to the question, 42% of the number = 420

Dividing both sides by 4.2 gives 10% of the number = 100

∴ The correct answer is 100.

Alternate Method

Given: 70 percent of 60 percent of a number is 420.

Formula Used: Value = (P₁ ÷ 100) × (P₂ ÷ 100) × Total Number

⇒ Let the number be x.

⇒ (70 ÷ 100) × (60 ÷ 100) × x = 420

⇒ 0.42 × x = 420

⇒ x = 420 ÷ 0.42

⇒ x = 1000

⇒ 10 percent of x = (10 ÷ 100) × 1000

⇒ 10 percent of 1000 = 100

∴ The correct answer is 100.

Additional Information

Product of Percentages

When multiple percentages are applied to a single number, they can be multiplied together to find the effective percentage: a% of b% = (a × b) ÷ 100%.

Fractional Equivalents

Using fractions like 7/10 for 70% and 3/5 for 60% often simplifies complex multiplication and division in competitive exams.

Base Value Conversion

To find the original 100% value from a known percentage P, use the formula: Total = (Given Value × 100) ÷ P.

Shortcut Trick

Calculate Cost Price (CP) = Selling Price (SP) + Loss

CP = 2300 + 200 = 2500

Loss Percentage = (Loss ÷ CP) × 100

Loss % = (200 ÷ 2500) × 100 = 8%

∴ The correct answer is 8%.

Alternate Method

Given:

Selling Price (SP) = ₹2300

Value of Loss = ₹200

Formula Used:

1. Cost Price (CP) = Selling Price (SP) + Loss
2. Loss Percentage = (Loss ÷ Cost Price) × 100

Calculations:

⇒ CP = 2300 + 200

⇒ CP = ₹2500

⇒ Loss % = (200 ÷ 2500) × 100

⇒ Loss % = 200 ÷ 25

⇒ Loss % = 8%

∴ The correct answer is 8%.

Additional Information

Profit and Loss Percentage

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

Relation between CP and SP

When there is a loss, Selling Price (SP) = CP × (100 − Loss%) ÷ 100. When there is a profit, SP = CP × (100 + Profit%) ÷ 100.

Marked Price and Discount

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

Shortcut Trick

Assume Total Income = 100 parts, then Expenditure = 70 and Savings = 30.

Apply the weighted average concept: Total Change = (Change in Exp × Exp parts) + (Change in Sav × Sav parts).

30% × 100 = (x% × 70) + (40% × 30)

3000 = 70x + 1200 ⇒ 70x = 1800 ⇒ x = 180 ÷ 7 = 25.71%.

∴ The correct answer is 25.71 percent.

Alternate Method

Given: Initial spending = 70%, Income increase = 30%, Savings increase = 40%.

Formula Used: Income = Expenditure + Savings; % Change = ((New − Old) ÷ Old) × 100.

Let the initial Income be 100.

⇒ Initial Expenditure = 70% of 100 = 70

⇒ Initial Savings = 100 − 70 = 30

⇒ New Income = 100 + (30% of 100) = 130

⇒ New Savings = 30 + (40% of 30) = 30 + 12 = 42

⇒ New Expenditure = New Income − New Savings = 130 − 42 = 88

⇒ Increase in Expenditure = 88 − 70 = 18

⇒ Percentage Increase in Expenditure = (18 ÷ 70) × 100

⇒ % Increase = 180 ÷ 7 ≈ 25.71%

∴ The correct answer is 25.71 percent.

Additional Information

Income, Expenditure, and Savings Relationship

The fundamental relation is Income = Expenditure + Savings. Any change in one or more components must balance this equation.

Alligation Method for Income Problems

Percentage changes in Expenditure and Savings can be alligated to find the percentage change in Income, where the ratio of parts is Expenditure : Savings.

Percentage Change Formula

Percentage change is calculated as ((Final Value − Initial Value) ÷ Initial Value) × 100. Always ensure the base value used is the original (initial) value.

Shortcut Trick

Ratio of efficiency of A and B = 6 : 1

Combined efficiency of A and B = 6 + 1 = 7 units/day

Total work = Combined efficiency × Time = 7 × 18 = 126 units

Time taken by B alone = Total work ÷ Efficiency of B = 126 ÷ 1 = 126 days

∴ The correct answer is 126 days.

Alternate Method

Given that A is 6 times as efficient as B.

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

⇒ Efficiency of A = 6 × 1 = 6 units/day.

⇒ Total efficiency of (A + B) = 6 + 1 = 7 units/day.

⇒ Total work = Combined efficiency × Time taken together

⇒ Total work = 7 × 18 = 126 units.

⇒ Time taken by B alone = Total work ÷ Efficiency of B

⇒ Time = 126 ÷ 1 = 126 days.

∴ The correct answer is 126 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to time taken. If the efficiency ratio of two workers is x : y, the ratio of time taken to complete the same work is y : x.

Work and Wages

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

Combined Work Formula

If A can do work in x days and B in y days, they together finish the work in (x × y) ÷ (x + y) days.

Shortcut Trick

Use the Chain Rule formula: M₁ × D₁ × H₁ = M₂ × D₂ × H₂

Substitute the values: 50 × 30 × 6 = M₂ × 45 × 4

⇒ 9000 = M₂ × 180

⇒ M₂ = 9000 ÷ 180 = 50

∴ The correct answer is 50 men.

Alternate Method

Given:

Initial men (M₁) = 50

Initial days (D₁) = 30

Initial hours per day (H₁) = 6

Final days (D₂) = 45

Final hours per day (H₂) = 4

Formula Used:

For the same work (wall): M₁D₁H₁ = M₂D₂H₂

⇒ Total work in man-hours = M₁ × D₁ × H₁

⇒ Total work = 50 × 30 × 6 = 9000 man-hours

⇒ Required men × 45 × 4 = 9000

⇒ M₂ × 180 = 9000

⇒ M₂ = 9000 ÷ 180

⇒ M₂ = 50 men

∴ The correct answer is 50 men.

Additional Information

The General Chain Rule

When work (W) and efficiency (E) are different, use the complete formula: (M₁ × D₁ × H₁ × E₁) ÷ W₁ = (M₂ × D₂ × H₂ × E₂) ÷ W₂.

Inverse Proportion in Work

The number of men is inversely proportional to the days and hours taken to complete a constant amount of work.

Man-Days Concept

Total work is often measured in Man-Days or Man-Hours, representing the effort of one person working for one day or one hour respectively.

Shortcut Trick

Relative Speed = Total distance ÷ Time taken

Total distance = 300 + 500 = 800 m

Relative Speed = 800 ÷ 10 = 80 m/s

Speed of Train B = Relative Speed − Speed of Train A = 80 − 20 = 60 m/s

∴ The correct answer is 60 m/s.

Alternate Method

Given:

Length of Train A (L_A) = 300 m

Length of Train B (L_B) = 500 m

Speed of Train A (S_A) = 20 m/s

Time taken (T) = 10 s

Formula Used:

When two trains cross each other in opposite directions:

Relative Speed = S_A + S_B = (L_A + L_B) ÷ T

Calculations:

⇒ Total distance = 300 + 500 = 800 m

⇒ S_A + S_B = 800 ÷ 10

⇒ 20 + S_B = 80

⇒ S_B = 80 − 20

⇒ S_B = 60 m/s

∴ The correct answer is 60 m/s.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction at speeds u and v ( v), the relative speed is (u − v).

Speed Conversion

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

Crossing a Point Object

When a train crosses a pole or a standing person, the distance covered is equal to the length of the train.

Shortcut Trick

Initial Speed = (48 ÷ 72) × 60 = 40 km/hr.

New Speed = 40 − 10 = 30 km/hr.

Ratio of Speed = 40 : 30 = 4 : 3.

For constant Distance, Time is inversely proportional to Speed ⇒ Time Ratio = 3 : 4.

3 units = 72 min ⇒ 1 unit = 24 min ⇒ 4 units = 4 × 24 = 96 min.

∴ The correct answer is 96 min.

Alternate Method

Given:

Distance = 48 km

Initial Time (T₁) = 72 min = 72/60 hr = 1.2 hr

Speed reduction = 10 km/hr

Formula Used:

Speed = Distance ÷ Time

Time = Distance ÷ Speed

Calculations:

⇒ Initial Speed (S₁) = 48 ÷ 1.2 = 40 km/hr

⇒ New Speed (S₂) = 40 − 10 = 30 km/hr

⇒ New Time (T₂) = Distance ÷ S₂

⇒ T₂ = 48 ÷ 30 hr

⇒ T₂ (in min) = (48 ÷ 30) × 60

⇒ T₂ = 48 × 2 = 96 min

∴ The correct answer is 96 min.

Additional Information

Unit Conversion

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

Inversely Proportional Logic

If Distance is constant, Speed₁ × Time₁ = Speed₂ × Time₂. This allows solving for any variable without finding actual distance.

Average Speed

If a car covers two equal distances at speeds x and y, the Average Speed = 2xy ÷ (x + y).

The correct answer is: An event that happens despite the absence of a key player.

Key Points

• The idiom 'Hamlet without the prince' refers to an event, performance, or situation where the most crucial or vital element or person is missing. (मुख्य पात्र के बिना कोई आयोजन)
• Example: Attending the film festival without its star director was like watching Hamlet without the prince.
• 'An event that happens despite the absence of a key player' describes a scenario that proceeds even though the individual who is central to the activity is not present. (एक घटना जो मुख्य व्यक्ति की अनुपस्थिति के बावजूद होती है)
• Example: The political rally went on, but without the Prime Minister, it felt like Hamlet without the prince.
• Hence, the idiom signifies that while the event takes place, it lacks its essence or core because of the absence of a key figure.

Therefore, the correct answer is: An event that happens despite the absence of a key player.

Additional Information

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

• An actor with a small or insignificant part in a performance (एक छोटी या महत्वहीन भूमिका वाला अभिनेता): Refers to a minor role or a character that does not influence the main plot significantly.
• Example: He was disappointed to be cast as a background extra with a very small part in the play.
• A tragedy where the prince dies (एक त्रासदी जहां राजकुमार की मृत्यु हो जाती है): This is a literal interpretation of Shakespearean plays like Hamlet, but it does not represent the idiomatic meaning.
• Example: The audience was moved to tears by the tragic ending where the young prince dies.
• The dilemma of choosing between two important persons (दो महत्वपूर्ण व्यक्तियों के बीच चयन करने की दुविधा): Refers to a state of uncertainty or a difficult choice between two equally significant options or people.
• Example: The manager faced a tough dilemma when he had to choose between his two best employees for the promotion.

The correct answer is 'A film that is entertaining to watch but is generally not of a very high quality or rich in emotional or intellectual depth'.

Key Points

• The idiom 'Popcorn film' refers to a movie that is watched primarily for entertainment and enjoyment rather than for its artistic value, deep message, or intellectual complexity. (एक ऐसी फिल्म जो केवल मनोरंजन के लिए देखी जाती है और जिसमें अधिक बौद्धिक गहराई नहीं होती)
• Example: After a stressful week at work, I just wanted to watch a simple popcorn film and relax.
• The meaning 'A film that is entertaining to watch but is generally not of a very high quality or rich in emotional or intellectual depth' perfectly matches the definition of a popcorn film as it highlights the focus on light-hearted entertainment over substance. (एक ऐसी फिल्म जो देखने में मनोरंजक हो लेकिन सामान्यतः उच्च गुणवत्ता या भावनात्मक गहराई वाली न हो)
• Example: Most big-budget superhero movies are considered popcorn films because they are fun but often follow a predictable formula.
• Therefore, the correct answer is- A film that is entertaining to watch but is generally not of a very high quality or rich in emotional or intellectual depth.

Additional Information

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

• A film that shows the actual murder or death of a person (वास्तविक हत्या या मृत्यु दिखाने वाली फिल्म): This describes a 'snuff film', which is illegal and contains actual footage of death.
• Example: The urban legend about the existence of snuff films has circulated for decades.
• A film with a very large budget and production value that is meant to provide substantial revenue to the production company (भारी बजट और बड़े स्तर पर निर्मित फिल्म): This refers to a 'blockbuster' or a 'tentpole film'.
• Example: The studio is counting on its summer blockbuster to recover from its earlier financial losses.
• A film that has a passionate fan base despite lacking critical acclaim, box office success, or mainstream interest (कल्ट फिल्म): This is known as a 'cult film' or a 'cult classic'.
• Example: Although it failed at the box office, the quirky comedy became a cult film with thousands of dedicated fans.

The correct answer is: Deference.

Key Points

• The term 'Spelling' refers to the correct arrangement of letters that form a word. Identifying the correctly spelt word requires knowledge of English vocabulary and phonetics. (वर्तनी)
• Example: The teacher asked the students to check the spelling of every difficult word in the paragraph.
• 'Deference' is a noun that means humble submission and respect for someone or something, often shown by following their wishes or opinions. (सम्मान)
• Example: He bowed his head in deference as the king entered the grand hall.
• Among the given options, only 'Deference' is spelled correctly, following the standard rules of English orthography.

Therefore, the correct answer is- Deference.

Additional Information

Here are the remaining options with their correct spellings and meanings:

• Daliance (क्रीड़ा): The correct spelling is 'Dalliance'. It refers to a brief or casual involvement in something or a romantic relationship.
• Example: Their brief dalliance ended as soon as the summer vacation was over.
• Dubeous (संदिग्ध): The correct spelling is 'Dubious'. It describes something that is hesitating, doubting, or not to be relied upon.
• Example: I was dubious about the safety of the old bridge, so I decided not to cross it.
• Dipravity (नैतिक भ्रष्टाचार): The correct spelling is 'Depravity'. It refers to moral corruption or a wicked act.
• Example: The movie depicts the depravity of war and its effect on human life.

The correct answer is: Incredible.

Key Points

• The word amazing means causing great surprise or wonder; it refers to something astonishing or very impressive. (आश्चर्यजनक)
• Example: The sunset over the Himalayas was truly amazing.
• Incredible refers to something that is extraordinary, impossible to believe, or extremely good, making it the closest synonym to amazing. (अविश्वसनीय)
• Example: The magician performed an incredible act that left the audience in awe.
• Therefore, the correct answer is- Incredible.

Additional Information

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

• ordinary (साधारण): Something that is common, normal, or lacks any special features.
• Example: It was just an ordinary day at work with nothing exciting happening.
• Boring (उबाऊ): Something that is not interesting or tedious.
• Example: The documentary was so boring that I fell asleep halfway through.
• Ugly (कुरुप): Something that is unpleasant or repulsive in appearance.
• Example: The abandoned building was covered in ugly graffiti.

The correct answer is: Miscellaneous.

Key Points

• The word 'Miscellanous' is misspelt in the given options. The correct spelling is 'Miscellaneous', which means consisting of a mixture of various things that are not usually connected with each other. (मिश्रित)
• Example: The drawer was filled with a miscellaneous collection of old keys, stamps, and letters.
• 'Miscellaneous' is the correct spelling of the word, which refers to diverse or varied elements. (विविध)
• Example: His library has a miscellaneous collection of books on different subjects.
• Hence, we can infer that the misspelt word is 'Miscellaneous'.

Therefore, the correct answer is: Miscellaneous.

Additional Information

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

• Vociferous (मुखर): Expressing or characterized by vehement, loud, and forceful opinions or feelings.
• Example: The protesters were vociferous in their demands for immediate reform.
• Amalgamation (समामेलन): The action, process, or result of combining or uniting multiple things into one single body.
• Example: The amalgamation of the two smaller schools into one large academy took place last year.
• Innocuous (हानिरहित): Not harmful, offensive, or likely to cause any injury.
• Example: It was an innocuous question, but she still managed to take offense at it.

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

Key Points

• The word Entire means with no part left out; whole or complete. (संपूर्ण / पूरा)
• Example: She spent the entire day cleaning the house.
• Partia (often a variant or misspelling of partial) refers to something that is existing only in part; incomplete or not whole. It is used as the opposite of something that is total or entire. (आंशिक / अधूरा)
• Example: The jury reached a partia agreement on the charges but could not decide on the final verdict.
• Hence, we can infer that the antonym of Entire is Partia.

Therefore, the correct answer is- Partia.

Additional Information

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

• Whole (पूरा): All of something; entire.
• Example: He ate the whole apple in just two bites.
• Complete (पूर्ण): Having all the necessary or appropriate parts.
• Example: My collection of vintage stamps is finally complete.
• Total (कुल): Comprising the whole number or amount.
• Example: The total cost of the repairs was much higher than expected.

The correct answer is: Bohemian.

Key Points

• The phrase 'An unconventional lifestyle' refers to a way of living that deviates from established social norms, traditional expectations, or standard cultural practices. (अपरंपरागत जीवनशैली)
• Example: She lived 'an unconventional lifestyle', spending half the year in a remote cabin and the other half traveling.
• 'Bohemian' refers to a person, often an artist, writer, or musician, who lives and acts free of regard for conventional rules and practices. (रूढ़िमुक्त / बोहेमियन)
• Example: The artist's 'bohemian' existence was characterized by late-night gatherings and a complete lack of a regular schedule.
• Hence, we can infer that 'Bohemian' is the most suitable one-word substitution for 'an unconventional lifestyle'.

Therefore, the correct answer is: Bohemian.

Additional Information

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

• Chauvinism (अंध-देशभक्ति / कट्टरता): Aggressive patriotism or blind enthusiasm for military glory; it can also refer to biased belief in the superiority of one's own group.
• Example: His extreme chauvinism made it difficult for him to appreciate the achievements of other nations.
• Hedonism (सुखवाद): The ethical theory that pleasure is the highest good and proper aim of human life.
• Example: The ancient city was often criticized for its culture of hedonism and excessive luxury.
• Dogmatism (हठधर्मिता / सिद्धांतवाद): The tendency to lay down principles as undeniably true, without consideration of evidence or the opinions of others.
• Example: The scientist warned against dogmatism, urging his students to always remain open to new evidence.

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

Key Points

• The phrase 'the killing of one's son or daughter' refers to the act where a parent causes the death of their own offspring. (अपनी संतान की हत्या)
• Example: The tragic play centers around a character driven to the killing of one's son or daughter due to extreme circumstances.
• 'Filicide' is the specific one-word substitution for the act of a parent murdering their son or daughter. (संतान-हत्या)
• Example: The defendant was charged with filicide after the investigation concluded that the child's death was intentional.
• Hence, we can infer that the most suitable term for the given phrase is filicide.

Therefore, the correct answer is- Filicide.

Additional Information

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

• Fratricide (भाई की हत्या): The act of killing one's own brother.
• Example: In many ancient myths, the struggle for the throne often ended in fratricide.
• Matricide (माता की हत्या): The act of killing one's own mother.
• Example: The character in the tragedy was haunted by the guilt of committing matricide.
• Parricide (माता-पिता या किसी नजदीकी रिश्तेदार की हत्या): The killing of a parent or other near relative.
• Example: The law provides for severe penalties in cases of parricide to protect the sanctity of family relations.

The correct answer is 'in'.

 

Key Points

• The preposition 'in' is used here to indicate the state or condition of someone's appearance.
• The phrase 'in disguise' is a standard idiomatic expression meaning wearing clothes or a mask to hide one's true identity.
• In the given sentence, the kings used a disguise to blend in with the common people without being recognized.

Therefore, the correct answer is Option 2.

 

Complete Sentence: 'Famous kings often went out in disguise among the common people in order to know about them.'

 

Additional Information

• Option 1: 'on' is generally used to denote a position on a surface or specific dates/days.
• Option 3: 'by' is used to indicate the means of doing something or proximity.
• Option 4: 'for' is used to indicate a purpose, reason, or a period of time.

The correct answer is He was looked after by his grandmother all these years..

Key Points

• The original sentence 'His grandmother looked after him all these years' is in the Active Voice and follows the Simple Past Tense structure.
• In the Simple Past Tense, the active voice structure is Subject + V2 (Past Tense Verb) + Object.
• To convert this into Passive Voice, the structure must be: New Subject (Object of active) + was/were + V3 (Past Participle) + by + New Object (Subject of active).
• The pronoun him (objective case) changes to He (nominative case) when it moves to the subject position.
• The verb looked after is a phrasal verb. When converting phrasal verbs to passive voice, the preposition (after) must remain immediately after the verb; it cannot be omitted or moved elsewhere in the sentence.
• Since the subject He is singular, the auxiliary verb was is used followed by the third form of the verb, which remains looked.
• The phrase all these years is an adverbial adjunct of time and typically remains at the end of the clause.

 Additional Information

• Phrasal Verbs in Passive Construction:
• A phrasal verb consists of a standard verb and a particle (preposition or adverb).
• In Passive Voice, the particle stays attached to the verb. For instance, 'laugh at' becomes 'be laughed at', and 'break into' becomes 'be broken into'.
• Incorrect variations often try to move the particle (e.g., 'after looked' or 'looked... after'), which violates English syntax rules.
• Pronoun Case Changes:
• Active Object: Me, Us, You, Him, Her, Them.
• Passive Subject: I, We, You, He, She, They.

The correct answer is The board will conduct the final round of interviews next Monday in the main auditorium..

Key Points

• The original sentence is in the Passive Voice of the Simple Future Tense, identified by the verb structure will be conducted.
• In English grammar, when converting a sentence from Passive Voice to Active Voice, the object of the passive sentence (the agent identified by 'by') becomes the subject of the active sentence.
• The Simple Future Tense in active voice follows the structural formula: Subject + will + V1 (base form of the verb) + Object.
• In this context, the agent the board moves to the subject position, and the auxiliary be is removed, changing will be conducted to will conduct.
• The recipient of the action, the final round of interviews, shifts from the subject position to the direct object position.
• The adverbial phrases next Monday and in the main auditorium remain at the end to provide temporal and locational context.
• Therefore, the sentence The board will conduct the final round of interviews next Monday in the main auditorium is the grammatically correct active transformation.

 Additional Information

• Understanding Verb Tense Variations in Voice Conversion:
• Simple Present Tense: Uses the verb conducts. It is generally used for habitual actions or general truths, which does not match the future intention of the original statement.
• Simple Past Tense: Uses the verb conducted. This form refers to an action that has already happened, contradicting the time marker next Monday.
• Present Perfect Tense: Uses the auxiliary has conducted. This tense describes an action completed at an unspecified time in the past or one that has a connection to the present.
• Future Indefinite (Active): Uses will + V1. This is the standard form for expressing future intentions, predictions, or scheduled events.

The correct answer is Let the students arrange the concert..

Key Points

• The original sentence 'Let the concert be arranged by the students' is in the Passive Voice. It follows the structure for Imperative sentences starting with 'Let'.
• In the Passive Voice, the construction is: Let + Object (the concert) + be + Past Participle (arranged) + by + Agent (the students).
• To convert an imperative 'Let' sentence into the Active Voice, the standard grammatical formula used is: Let + Agent/Noun/Pronoun + Base Form of Verb (V1) + Object.
• Identifying the components: The Agent (the doer) is 'the students', the Action (verb) is 'arrange', and the Object (receiver of action) is 'the concert'.
• Following the transformation rule, the Agent 'the students' is placed immediately after 'Let', the verb 'be arranged' is changed to its Bare Infinitive form 'arrange', and the Object 'the concert' is placed at the end.
• This result produces the grammatically correct active sentence: 'Let the students arrange the concert.'

 Additional Information

• Active Voice:
• In the active voice, the Subject performs the action denoted by the Verb.
• It is generally more direct and concise than the passive voice.
• For imperative suggestions, 'Let' serves to initiate the proposal or command followed by the Subject.
• Analysis of Incorrect Options:
• The students let the concert arrange: This incorrectly suggests that the students gave permission to the concert to perform an action.
• The concert lets the students arrange it: This changes the Subject of the sentence to 'the concert', which is logically incorrect as an inanimate object cannot perform the act of letting.
• Arrange the students to let the concert: This sentence is syntactically incorrect and completely changes the intended meaning of the original statement.

The correct answer is Option 1.

 

Key Points

• The error lies in the use of the preposition over after the verb longed in part A.
• The verb long, when meaning to have a strong desire for something or to miss something from the past, is always followed by the preposition for.
• The phrase longed for is a standard phrasal verb used to express a yearning or a strong wish for something that is no longer present.
• The correct expression should be The poet longed for the instead of The poet longed over the.

Therefore, the correct answer is Option 1.

 

Correct Sentence: 'The poet longed for the bygone days and mused over the time spent with friends and relatives.'

 

Additional Information

• Mused over: This part in Option 2 is correct. To muse over means to think about something carefully and thoroughly or to meditate on a subject.
• Bygone days: This refers to days that are past or gone by, which is a common and correct idiomatic expression.
• Time spent with friends and relatives: These segments (Options 3 and 4) are grammatically sound and follow standard English syntax.