SSC CGL 2025 (Held On: 17 Sept, 2025 Shift 3) (Previous Year Paper)

The logic followed here is:

Thus, the missing term in the series is ABC

Hence, the correct answer is " Option 3 "

The Master Address (MA) given in the problem is,

10, Rani Ghat Road,

Lucknow, Uttar Pradesh - 226003   

Compare each candidate address with the Master Address.

 

So, the candidate address that exactly matches the Master Address is option (3).

Hence, the correct answer is "Option (3)".

The given Address in the problem is,

Villa No. 204, Lake View Estate

Banjara Hills, Hyderabad, Telangana - 500034

Compare each Option address with the given Address.

 

So, the address that exactly matches the Given Address is option (1).

Hence, the correct answer is "Option (1)".

Problem: Frequent breakdown of ATM machines in remote areas.

Courses of action:

Action I: Banks should deploy mobile ATMs in these areas. → Follow (This action directly addresses the problem. If fixed ATMs frequently break down, deploying mobile ATMs would help ensure continuous banking services in remote areas. Therefore, this action is practical and helps solve the problem.)

Action II: Banks should shut down ATMs that face regular issues. → Does not Follow

(Shutting down ATMs would reduce banking access in remote areas and would not solve the core issue of breakdowns. Instead of improving the situation, it may worsen it).

So, only Action I follows.

Hence the correct answer is " Option 1"

The logic followed here is,

Logic: a @ b = (a × b) + (a − b)

For,

3 @ 2 ⇒ (3 × 2) + (3 − 2) = 6 + 1 = 7

6 @ 3 ⇒ (6 × 3) + (6 − 3) = 18 + 3 = 21

8 @ 2 ⇒ (8 × 2) + (8 − 2) = 16 + 6 = 22

Similarly,

5 @ 4 ⇒ (5 × 4) + (5 − 4) = 20 + 1 = 21

So, the value of 5 @ 4 is 21

Hence, the correct answer is "option 1 "

Given Equation:

(48 V 8 P 25 D 6 S 4 P 3) D (25 V 5 S 3 D 4 S 3)

BODMAS Rule:

Decoding the given information:

Now replacing the sign from left to right using BODMAS rule, we get

⇒ (48 ÷ 8 + 25 − 6 × 4 + 3) − (25 ÷ 5 × 3 − 4 × 3) = ?

⇒ (6 + 25 – 6 x 4 +3 ) – ( 5 x 3 – 4 x 3 ) = ?

⇒ ( 6 + 25 – 24 + 3 ) – ( 15 – 12 ) = ?

⇒ ( 31 – 21 ) – ( 3 ) = ?

⇒ 10 – 3 = 7

Hence the correct answer is " Option 4 "

Given Statements:

S > T = U, V ≥ W < T, O = S = P, W > Q > R

Now,

From S > T = U, it gives S > T and T = U.

From O = S = P, it gives O = S.

Since O = S and S > T, therefore O > T (which means T < O).

Conclusions:

(i) T = O → False (Because O > T)

(ii) T > O → False (Because O > T)

Here, neither conclusion I nor II is true.

Hence, the correct answer is "Option 3".

Preparing the family tree diagram using the following symbols

A possible tree diagram will be:

∴ From the above diagram P is the Grandson of S.

Hence, the correct answer is "Option 3".

The pattern followed here is:

∴ The correct answer is "Option 3".

The correct answer is 1 and 3 only.

Key Points

Directive Principles of State Policy (DPSPs):

They are contained in Articles 36–51 under Part IV of the Indian Constitution.

The concept of DPSPs was borrowed from the Irish Constitution.

Dr. B. R. Ambedkar described these principles as novel features of the Constitution.

They act as guidelines or instructions for the government while making policies and laws to promote welfare and social justice.

Hence, Assumption I is implicit.

The inclusion of DPSPs in the Constitution indicates the importance of social justice, welfare, and economic development in governance.

Hence, Assumption III is implicit.

Although DPSPs are non-justiciable, they still play an important role in governance and policy making.

Therefore, saying that they have limited significance is incorrect.

Hence, Assumption II is not implicit.

 

Therefore, only Assumptions I and III are implicit.

Given Statement:

The government has increased import duty on luxury cars.

Conclusion I :  Imported luxury cars will become more expensive.

✔ Follows

When import duty increases, the cost of importing goods rises. This additional cost is passed on to the buyer, making imported luxury cars more expensive.

Conclusion II: Local car manufacturers will stop making budget cars.

✘ Does not follow.

The statement only talks about import duty on luxury cars. There is no logical link between this and local manufacturers stopping budget car production.

Thus, Only Conclusion I follows.

Hence, the correct answer is "Option 1".

Given Statement:

Attendance in public libraries has increased in recent years.

Conclusions:

I. People are regaining interest in reading.

II. Digital platforms have become less popular.

Analysis:

I. People are regaining interest in reading – True (If attendance in libraries has increased, it indicates that more people are visiting libraries and showing interest in reading.)

II. Digital platforms have become less popular – False (The statement does not mention anything about digital platforms, so no definite conclusion can be drawn about their popularity.)

Hence, Only Conclusion I follows.

∴ The correct answer is "Option 1".

The pattern followed here is :

According to the alphabetical  positions of the letters, 

Similarly,

So, the missing term is " MN "

Thus, the correct answer is " Option 1 ".

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The logic followed here is : 

For, 'PATNA is written as ANTAP',

The word is reversed: PATNA → ANTAP

Similarly, for  'RAJASTHAN'

So, 'RAJASTHAN' will be written as 'NAHTSAJAR'.

Hence, the correct answer is "Option 2".

The Logic followed here is:

1. National Park → A protected area for conservation of wildlife and natural habitat.
2. Biosphere Reserve → A large protected area for conservation of biodiversity.
3. Sanctuary → A protected area for wildlife conservation.
4. Census → An official count or survey of population.

Options 1, 2, and 3 represent protected environmental conservation areas, whereas Option 4 is related to population data collection and not wildlife conservation.

Thus, Census is different from the others.

Hence, the correct answer is “Option 4”.

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The logic followed here is:

Each term consists of three consecutive letters of the English alphabet, and every next term shifts forward by one letter.

RST → STU → TUV → UVW → VWX → WXY → XYZ → YZA

Thus, the missing term in the series is ZAB.

Hence, the correct answer is "Option 1".

Given:

Length of train = 180 m

Time taken = 12 s

Formula used:

Speed = Distance ÷ Time

Calculations:

Distance covered = 180 m

⇒ Speed = 180 ÷ 12

⇒ Speed = 15 m/s

⇒ Speed in km/h = 15 × 18 ÷ 5 = 54 km/h

∴ The speed of the train is 54 km/h.

The logic followed here is,

Logic: A & A = 2(A)²

For,

4 & 4 ⇒ 2 (4)² = 32

5 & 5 ⇒ 2 (5)² =50

Similarly,

 6 & 6 ⇒ 2 (6)² = 72

So, the value of 6&6 is 72

Hence, the correct answer is "Option 1"

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The logic followed here is:

For, ‘TRUTH’ is written as ‘UQSVI’

Similarly, for ‘FALSE’

So, ‘FALSE’ will be written as ‘GZJUF’.

Hence, the correct answer is "Option 2".

Shortcut Trick

Use the direct inverse relationship formula for constant work:

M₁ × D₁ = M₂ × D₂

Substitute the given values into the formula:

⇒ 6 × 10 = 15 × D₂

⇒ D₂ = 60 ÷ 15 = 4 days

∴ The correct answer is 4 days.

Alternate Method

Given:

Initial number of machines (M₁) = 6

Initial number of days (D₁) = 10 days

New number of machines (M₂) = 15

Formula Used:

Total Work = Number of Machines × Days

Calculations:

⇒ Let the total work be the LCM of work components or the total machine-days required.

⇒ Total Work = 6 machines × 10 days = 60 units

⇒ Let the number of days required by 15 machines be D₂.

⇒ 15 × D₂ = 60

⇒ D₂ = 60 ÷ 15

⇒ D₂ = 4 days

∴ The correct answer is 4 days.

Additional Information

Inverse Variation Rule

When work remains constant, efficiency is inversely proportional to the time taken. If the number of machines increases, the days required to complete the same work will decrease proportionately.

General MDH Formula

For complex work structures: (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where M is resources, D is days, H is working hours, and W is work quantity.

Individual Machine Contribution

If machines operate at the same rate, each individual machine contributes exactly 1/N of the total combined output rate for N machines.

The logic followed here is,

Logic: A # B = A² + B² − 3

For,

8 # 2 ⇒ 8² + 2² − 3 = 64 + 4 − 3 = 65

7 # 3 ⇒ 7² + 3² − 3 = 49 + 9 − 3 = 55

Similarly,

6 # 5 ⇒ 6² + 5² − 3 = 36 + 25 − 3 = 58

So, the value of 6 # 5 is 58.

Hence, the correct answer is " Option 3 "

Family chart :

Given : Introducing a woman, Jay said, "She is the daughter of the only child of my grandfather."

     

So, the women is the 'sister' of jay.

Hence, the correct answer is " Option 2 ".

BODMAS Table:

Given equation : 10 – 5 + 3 × 2 = ?

Now, if  '+' means '×' and '×' means '-' and '-' means '÷', then:

⇒ 10 ÷ 5 × 3 - 2 = ?

⇒ 2 × 3 - 2 = ?

⇒ 6 - 2 = 4

Hence, the correct answer is " Option 4 "

The logic followed here is :

So, ' 127 ' is the missing number in given series

Thus, the correct answer is " Option 1 "

The logic followed here is:

So, 87 is the incorrect combination in given series, it will be 85.

Hence the correct answer is " Option 4 "

The correct answer is Only 1 and 3 are correct.

Key Points

• Victorian Gothic architecture in Mumbai: The Victorian Gothic buildings, constructed during the colonial era, exhibit Neo-Gothic elements such as pointed arches, ribbed vaults, and flying buttresses. These structures symbolize British colonial architecture in India.
• Art Deco architecture in Mumbai: Art Deco buildings in the city emerged in the 1930s and 1940s, featuring sleek, geometric designs and modern aesthetics. It was a departure from traditional colonial styles and reflected global architectural trends.
• The Oval Maidan as a divider: The Oval Maidan in South Mumbai distinctly separates the Victorian Gothic structures on one side and the Art Deco buildings on the other, showcasing two contrasting architectural styles within close proximity.
• UNESCO World Heritage Site: The Victorian Gothic and Art Deco Ensembles of Mumbai were recognized as a UNESCO World Heritage Site in 2018, signifying their historical and architectural significance.
• Art Deco architecture in Mumbai is globally significant, with the city having the second-largest collection of Art Deco buildings after Miami, USA.

Additional Information

• Option 2 (Incorrect): Art Deco buildings in Mumbai were not a part of the 19th-century colonial urban development. Instead, they emerged during the early 20th century, specifically in the 1930s and 1940s, influenced by modern architectural trends from Europe and America.
• Victorian Gothic architecture:
• It was introduced during British colonial rule in the mid-19th century.
• Famous examples include the Chhatrapati Shivaji Maharaj Terminus (formerly Victoria Terminus) and the Bombay High Court.
• The structures often incorporated Indian design elements, blending Gothic Revival with local influences.
• Art Deco architecture:
• Art Deco represented a shift towards modernism and simplicity in design.
• Key features include streamlined forms, bold geometric patterns, and the use of new materials like reinforced concrete.
• Notable examples in Mumbai include the Eros Cinema and Marine Drive buildings.
• Significance of the Oval Maidan:
• The Oval Maidan is a large recreational ground in South Mumbai.
• It serves as a physical and visual separator between the two architectural styles, enhancing the aesthetic and cultural value of the area.

The correct answer is grandeur.

Key Points

• The hornbill bird holds a significant place in Naga folklore and is revered for its boldness and grandeur, symbolizing strength and pride.
• The Hornbill Festival, celebrated in Nagaland, is named after this majestic bird to honor its symbolic representation of courage and magnificence.
• Grandeur, in this context, reflects the cultural richness and majestic traditions of Nagaland, which align with the bird's regal and striking appearance.
• The festival showcases the grandeur of Naga heritage through traditional music, dance, art, and craft, creating a vibrant and majestic cultural atmosphere.
• The hornbill bird's association with boldness and grandeur is a testament to its prominent role in inspiring the Naga tribes and their cultural practices.

Additional Information

• Wisdom:
• Wisdom typically refers to the quality of having experience, knowledge, and good judgment.
• While wisdom is a valued trait, it is not directly associated with the symbolism of the hornbill bird in Naga folklore.
• In some cultures, other animals like owls are often linked to wisdom rather than hornbills.
• Prosperity:
• Prosperity refers to a state of wealth, success, and abundance.
• Although prosperity is an important theme in cultural celebrations, it does not capture the essence of the hornbill bird's symbolism in Naga folklore.
• Festivals like Pongal or Onam are more closely linked to the theme of prosperity.
• Peace:
• Peace signifies harmony and the absence of conflict or disturbance.
• While peace is a universal value, the hornbill bird is not specifically associated with peace in Naga folklore.
• Other symbols like the olive branch are more commonly linked to the idea of peace.
• The Hornbill Festival:
• The Hornbill Festival, held annually in Nagaland, is a celebration of Naga culture, heritage, and traditions.
• It is named after the hornbill bird, which is admired for its boldness and grandeur.
• The festival features traditional music, dance, crafts, and cuisines, showcasing the cultural richness of Nagaland.
• It serves as a platform for inter-tribal interaction and cultural exchange, fostering unity and pride among the Naga people.

The correct answer is Talavataks - Village Accountant.

Key Points

• The Talavataks in Gupta administration were responsible for maintaining village-level financial records, making them essentially village accountants.
• Their primary role included recording agricultural yields, tax collections, and other economic data relevant to the village.
• This role was significant during the Gupta period, reflecting the sophisticated administrative setup of the empire.
• Their work ensured proper revenue collection and management, which was crucial for the Gupta Empire's economic stability.
• The title of Talavataks is often highlighted in historical texts as a vital administrative position in rural governance.

Additional Information

• Dhruvadhibaranika - Treasurer
• The title Dhruvadhibaranika is not associated with the role of a treasurer in Gupta administration.
• In the Gupta Empire, the treasurer was typically referred to as Bhandagarika, who managed the royal treasury and finances.
• Dhruvadhibaranika, as a title, remains ambiguous in historical texts and is not directly linked with any administrative role.
• Bhandagaradhikrita - Chief of Police
• Bhandagaradhikrita was not a police chief but rather referred to an official associated with the management of state treasuries or granaries.
• The chief of police or law enforcement roles in the Gupta period were often undertaken by officials referred to as Mahadandanayaka.
• They were responsible for maintaining law and order within the empire.
• Utkhetayita - Land-Survey Officer
• The term Utkhetayita does not correspond to a land-survey officer.
• In the Gupta Empire, land survey and revenue assessments were often carried out by officials known as Rajukas.
• The role of the Rajukas was crucial for tax collection and agricultural management, ensuring accurate revenue generation.
• Gupta Administration
• The Gupta Empire had a highly organized administrative structure with a well-defined hierarchy of officials.
• Key administrative divisions included provinces (Bhuktis), districts (Vishayas), and villages.
• Village-level administration played a crucial role in managing resources and collecting taxes.
• The central administration was headed by the king, supported by ministers and other high-ranking officials.

The correct answer is Sangeet Ratnakara.

Key Points

• Sangeet Ratnakara is a renowned treatise on Indian classical music, written by Sharangadeva in the 13th century CE in Maharashtra.
• It is considered one of the most comprehensive works on Indian musicology, covering both the ancient traditions (marga) and contemporary practices (desi) of its time.
• The text is divided into seven chapters, each detailing different aspects of music such as swaras (notes), ragas, talas (rhythmic cycles), and dance.
• Sangeet Ratnakara forms the foundation of both Hindustani and Carnatic music traditions, making it a pivotal text in the history of Indian classical music.
• The treatise also provides extensive information on musical instruments, vocal techniques, and the theoretical framework of music.

Additional Information

• Natya Shastra
• Natya Shastra, attributed to Bharata, is an ancient Indian treatise on performing arts, including drama, dance, and music, written around 200 BCE to 200 CE.
• It provides detailed guidelines on theatrical performances, stagecraft, and musical compositions.
• The text is a foundational work for Indian classical dance forms like Bharatanatyam, Kathakali, and Odissi.
• While it includes music, its primary focus is on dramaturgy and dance rather than a comprehensive study of musicology.
• Sangeet Sudha
• Sangeet Sudha is another important work in Indian music, authored by Govinda Dikshitar in the 17th century CE.
• It focuses on the Carnatic music tradition and provides insights into the theoretical aspects of ragas and musical compositions.
• The work is not as expansive or foundational as Sangeet Ratnakara in terms of covering both Hindustani and Carnatic traditions.
• Abhinaya Darpana
• Abhinaya Darpana, written by Nandikeshvara, is a treatise on the art of expression (abhinaya) in Indian classical dance.
• It outlines the principles of gestures, facial expressions, and body movements essential for Indian dance forms.
• The focus of this text is on dance and acting rather than music as a standalone art form.

The correct answer is 1946.

Key Points

• The Amateur Athletics Federation of India (AAFI) was established in the year 1946 as the apex body for athletics in India.
• The AAFI was founded with the goal of promoting and regulating athletics in the country and ensuring the participation of Indian athletes in international competitions.
• It is now known as the Athletics Federation of India (AFI) and serves as the governing body for athletics in India.
• AFI is affiliated with the World Athletics (formerly known as the International Association of Athletics Federations or IAAF), which governs athletics worldwide.
• The Athletics Federation of India organizes various national-level athletic events, trains athletes, and ensures their participation in global competitions, such as the Olympics, Asian Games, and Commonwealth Games.

Additional Information

• 1936
• The year 1936 is historically significant for Indian athletics as it marks the participation of Indian athletes in the Berlin Olympics. However, the AAFI had not been established at this time.
• During the 1936 Olympics, Indian hockey team won gold, and the event was notable for the legendary athlete Jesse Owens' remarkable performance.
• 1956
• The year 1956 is significant in Indian sports history as India participated in the Melbourne Olympics.
• Indian athletes competed in various events, but this year is not related to the establishment of the AAFI.
• 1966
• In 1966, the Asian Games were held in Bangkok, Thailand, where Indian athletes won several medals.
• This year also saw the progress of Indian sports on the global stage, but it is unrelated to the founding of the AAFI.
• Amateur Athletics Federation of India (AAFI)
• The AAFI was established to promote and develop athletics at grassroots, national, and international levels in India.
• It was renamed as the Athletics Federation of India (AFI) in later years to better reflect its evolving role and responsibilities.
• AFI works towards organizing championships, selecting and training athletes, and ensuring adherence to international standards in competitions.

The correct answer is Sher Shah Suri.

Key Points

• Sher Shah Suri defeated the Mughal emperor Humayun in the Battle of Chausa (1539) and the Battle of Kannauj (1540), forcing Humayun to flee to Persia.
• After his victory, Sher Shah Suri declared himself the ruler and established the Second Afghan Empire in India.
• He was a skilled administrator and introduced several reforms, including the standardization of currency and the development of an efficient revenue system.
• Sher Shah Suri is credited with constructing the Grand Trunk Road, which connected major regions of India and facilitated trade and communication.
• His reign (1540–1545) is remembered for its administrative efficiency, infrastructure development, and the promotion of trade and agriculture.

Additional Information

• Humayun
• Humayun was the second Mughal emperor and the son of Babur, the founder of the Mughal Empire.
• He faced a series of setbacks during his reign, including defeats at the hands of Sher Shah Suri, which led to his temporary exile.
• Humayun regained the throne in 1555 with the help of the Persian Empire but died shortly after in 1556.
• His son Akbar succeeded him and consolidated the Mughal Empire.
• Bahlul Lodi
• Bahlul Lodi was the founder of the Lodi dynasty, the last dynasty of the Delhi Sultanate.
• He ruled from 1451 to 1489 and was known for his efforts to consolidate his rule in northern India.
• Bahlul Lodi successfully established control over Delhi and its surrounding regions, laying the foundation for the Lodi dynasty.
• Sikandar Lodi
• Sikandar Lodi, the son of Bahlul Lodi, was the second ruler of the Lodi dynasty.
• He ruled from 1489 to 1517 and was known for his administrative reforms and efforts to expand his kingdom.
• Sikandar Lodi moved the capital from Delhi to Agra and promoted trade and cultural activities.
• Main Theme
• The Second Afghan Empire refers to the period of Sher Shah Suri's rule, which marked a brief interruption in the Mughal Empire.
• Sher Shah Suri's reign is widely regarded as a golden period in terms of administrative reforms and infrastructure development in medieval India.

The correct answer is To create buffer states to defend British territories.

Key Points

• The Ring-Fencing Policy was primarily aimed at creating buffer states to protect British territories in India, particularly from external threats like the Marathas and Afghan invasions.
• It was implemented during the late 18th century under Governor-General Warren Hastings' administration, as the British East India Company sought to secure its territorial acquisitions.
• States such as Awadh (Oudh) were turned into buffer zones through alliances or treaties, ensuring that these regions bore the brunt of invasions before they could threaten core British territories like Bengal.
• The policy involved maintaining a strong military presence and entering into subsidiary alliances to control the external policies of the Indian princely states while allowing them nominal sovereignty.
• This strategy laid the groundwork for the subsequent Subsidiary Alliance system introduced by Lord Wellesley, which further tightened British control over Indian states.

Additional Information

• Option 1: To expand British territory by annexing Indian states
• This was not the primary objective of the Ring-Fencing Policy. Territorial expansion became a more prominent strategy later under policies like the Doctrine of Lapse (introduced by Lord Dalhousie) and outright annexation through military conquest.
• The Ring-Fencing Policy was more about securing existing territories rather than expanding them aggressively.
• Option 2: To economically exploit coastal trading companies
• This option does not align with the core objective of the Ring-Fencing Policy, which was focused on military and territorial security.
• Economic exploitation of India by the British was carried out through trade monopolies, land revenue systems like the Permanent Settlement, and later, industrial policies. However, these were separate from the Ring-Fencing Policy.
• Option 4: To impose direct rule over all princely territories
• The Ring-Fencing Policy did not aim at imposing direct British rule over princely states. Instead, it sought to maintain the sovereignty of buffer states while controlling their external affairs.
• Direct rule over princely states was achieved later through policies like the Subsidiary Alliance and the Doctrine of Lapse.
• Main Theme: The Ring-Fencing Policy
• The Ring-Fencing Policy was one of the earliest strategies employed by the British East India Company to secure its territories in India.
• It was a defensive strategy focusing on the containment of threats from external powers like the Marathas, Afghans, and other regional rulers.
• It marked the beginning of British interference in the internal affairs of Indian princely states, paving the way for eventual domination over the Indian subcontinent.

The correct answer is India did not win any boxing medals at Sydney 2000.

Key Points

• India did not win any boxing medals at the 2000 Sydney Olympics.
• No Indian boxer progressed to a medal-winning position during the Sydney 2000 games.
• At the time, India’s boxing achievements on the Olympic stage were still developing.
• India's first Olympic boxing medal came much later, at the 2008 Beijing Olympics, when Vijender Singh won a bronze medal in the middleweight category.
• The 2000 Sydney Olympics highlighted the need for more structured training and support for Indian boxers.

Additional Information

• Option 2: India won multiple boxing medals at Sydney 2000.
• This statement is incorrect as India did not win any boxing medals at the 2000 Sydney Olympics.
• India’s boxing achievements began gaining momentum in later years, particularly after the 2008 Beijing Olympics.
• Option 3: Karnam Malleswari won a boxing bronze medal at Sydney 2000.
• Karnam Malleswari did not win a boxing medal; she won a bronze medal in weightlifting in the 69 kg category at the Sydney 2000 Olympics.
• She became the first Indian woman to win an Olympic medal, marking a historic achievement for India.
• Option 4: India won its first Olympic boxing medal at Sydney 2000.
• This statement is incorrect as India’s first Olympic boxing medal was won by Vijender Singh at the 2008 Beijing Olympics.
• His achievement placed Indian boxing on the global map and inspired many young boxers in the country.
• India’s Olympic Boxing History
• India’s boxing journey at the Olympics began in 1948, but the country struggled to make a mark for several decades.
• Notable progress in Indian boxing was observed in the 21st century, with Vijender Singh’s 2008 Olympic bronze as a turning point.
• Subsequently, Mary Kom also won a bronze medal in women’s boxing at the 2012 London Olympics.
• Indian boxers such as Lovlina Borgohain and others have continued to perform well in recent Olympic events.

The correct answer is Joint counter-insurgency in semi-urban zones under UN mandate.

Key Points

• The 10th India-Sri Lanka Mitra Shakti exercise was conducted in August 2024 to strengthen bilateral military cooperation and interoperability.
• The exercise focused on joint counter-insurgency operations in semi-urban zones, specifically under a United Nations (UN) mandate.
• The primary objective was to enhance the operational capabilities of both nations' armed forces in handling insurgency threats in urban and semi-urban areas.
• It highlighted the importance of coordination, intelligence sharing, and tactical execution in complex scenarios involving insurgents.
• The joint exercise aligns with UN peacekeeping protocols and international security standards, showcasing India and Sri Lanka's commitment to global peacekeeping efforts.

Additional Information

• Option 1: Maritime piracy response and naval drills
• Maritime piracy response refers to naval exercises aimed at combating piracy threats at sea.
• Such drills include search-and-rescue operations, anti-piracy maneuvers, and safeguarding maritime trade routes.
• While crucial for naval forces, this was not the focus of the Mitra Shakti exercise, which primarily involved land-based counter-insurgency operations.
• Option 2: NATO-style warfare in desert terrain
• NATO-style warfare emphasizes joint military operations following NATO protocols, often in diverse terrains, including deserts.
• Desert terrain operations involve strategies for managing extreme heat, limited visibility, and resource scarcity.
• Although valuable for military training, this was unrelated to the India-Sri Lanka Mitra Shakti exercise's counter-insurgency focus.
• Option 4: Cyber defence and digital warfare simulations
• Cyber defence involves protecting national and organizational digital assets from cyber threats, such as hacking and data breaches.
• Digital warfare simulations enable forces to practice scenarios for combating cyberattacks and securing critical infrastructure.
• While increasingly relevant in modern warfare, this was not the theme of the Mitra Shakti exercise in 2024.
• Main Theme: India-Sri Lanka Defence Cooperation
• The Mitra Shakti exercise is part of India and Sri Lanka's ongoing efforts to strengthen military ties and enhance regional security.
• These bilateral exercises focus on building mutual trust and operational synergy between the armed forces.
• Previous editions of Mitra Shakti have covered counter-terrorism, disaster management, and peacekeeping operations.

The correct answer is Aravind Adiga.

Key Points

• Aravind Adiga is the author of the novel The White Tiger, which won the prestigious Man Booker Prize in 2008.
• The book provides a satirical and gripping account of India's class struggle through the journey of its protagonist, Balram Halwai.
• It was Aravind Adiga's debut novel, and he became the fourth Indian-born author to win the Man Booker Prize after Salman Rushdie, Arundhati Roy, and Kiran Desai.
• The novel explores themes such as poverty, corruption, globalization, and the socio-economic divide in India.
• Adiga's work was praised for its unique narrative style and its unflinching portrayal of the dark realities of modern India.

Additional Information

• Rohinton Mistry:
• He is an Indian-born Canadian writer known for his novels that often explore the lives of Parsis in India.
• His notable works include Such a Long Journey, A Fine Balance, and Family Matters.
• A Fine Balance was shortlisted for the Booker Prize in 1996 and is considered one of his most acclaimed works.
• Arundhati Roy:
• She is an Indian author and activist, famous for her debut novel The God of Small Things, which won the Man Booker Prize in 1997.
• The novel is a semi-autobiographical tale set in Kerala, exploring themes of family, caste, and forbidden love.
• Roy is also known for her activism and non-fiction works, including Capitalism: A Ghost Story and Field Notes on Democracy.
• Vikram Seth:
• He is an Indian novelist and poet, best known for his monumental work A Suitable Boy, one of the longest novels ever published in a single volume.
• His other notable works include The Golden Gate and An Equal Music.
• Seth is celebrated for his diverse storytelling abilities and mastery of various literary forms.
• The Man Booker Prize:
• It is one of the most prestigious literary awards, established in 1969 to recognize outstanding works of fiction written in English.
• Eligible authors must be from the Commonwealth, Ireland, or Zimbabwe (until 2014, when it was expanded to any English-language work).
• The award aims to celebrate the finest in contemporary fiction and has brought global attention to many authors.

The correct answer is 1927.

Key Points

• The Indian Olympic Association (IOA) was officially formed in 1927 to promote and regulate sports in India.
• Sir Dorabji Tata served as the founding President of the IOA, playing a pivotal role in its establishment.
• Dr. A.G. Noehren was the first Secretary of the IOA, contributing to the organizational framework of Indian sports administration.
• The formation of the IOA marked India’s formal participation in international Olympic events, starting with the 1928 Amsterdam Olympics.
• The IOA is currently responsible for selecting athletes to represent India in the Olympics, Asian Games, Commonwealth Games, and other international events.

Additional Information

• 1920:
• In 1920, India sent its first official contingent to the Olympic Games held in Antwerp, Belgium.
• This marked the beginning of India’s journey in modern Olympic history, but the Indian Olympic Association had not been formed yet.
• 1922:
• By 1922, discussions around organizing sports at a national level were ongoing, but the Indian Olympic Association was not formally established until 1927.
• This period saw the groundwork for the eventual formation of the IOA.
• 1930:
• The IOA had already been established by 1930, and India participated in the 1930 Commonwealth Games (then called the British Empire Games) for the first time.
• This was a significant milestone for Indian sports on the global stage.

The correct answer is Both 1 and 2 are correct.

Key Points

• Maharashtra won both the men's and women's titles in the 56th National Kho Kho Championship 2023-24, becoming the overall champion of the tournament.
• The men's team from Maharashtra defeated Karnataka, while the women's team triumphed over Odisha in the finals.
• The championship matches were hosted at two venues: the Indira Gandhi Indoor Stadium and Karnail Singh Stadium in Delhi.
• This event was part of the National Kho Kho Federation's initiative to promote indigenous sports in India and witnessed participation from several states and union territories.
• The 56th National Kho Kho Championship 2023-24 showcased the increasing popularity of Kho Kho as a traditional Indian sport on a national level.

Additional Information

• About Kho Kho as a Sport:
• Kho Kho is a traditional Indian sport that is played by two teams, each consisting of 12 players, of which 9 enter the field.
• The game emphasizes speed, agility, teamwork, and strategy, making it one of India's most exciting indigenous sports.
• It is governed by the Kho Kho Federation of India (KKFI), which organizes various national and international tournaments to promote the game.
• Indira Gandhi Indoor Stadium:
• Located in Delhi, it is the largest indoor sports arena in India and one of the largest in Asia.
• The stadium is used for multiple sports and cultural events and has hosted prestigious events like the Asian Games and Commonwealth Games.
• Karnail Singh Stadium:
• This stadium, also located in Delhi, is primarily used for cricket but has been adapted to host various other sports events, including Kho Kho.
• It is named after Karnail Singh, who was a railway executive and known for his contributions to sports promotion in India.
• Significance of the National Kho Kho Championship:
• The championship serves as a platform for identifying and nurturing talent at the national level.
• It also helps in the promotion and preservation of India's traditional sports heritage.
• The event brings together players and enthusiasts from across the country, fostering a sense of unity and sportsmanship.

The correct answer is 42nd Constitutional Amendment.

Key Points

• The 42nd Constitutional Amendment Act, 1976, also known as the "Mini Constitution," brought significant changes to the Constitution of India.
• It transferred the subject of education from the State List to the Concurrent List, enabling both the Center and States to legislate on matters related to education.
• This amendment was enacted during the tenure of Prime Minister Indira Gandhi and reflected the growing importance of education in achieving national development goals.
• The 42nd Amendment introduced several other changes, including the incorporation of Fundamental Duties for citizens and provisions strengthening the central government.
• This shift to the Concurrent List was aimed at ensuring uniformity in educational policies across the country, promoting national integration, and addressing disparities in access to education.

Additional Information

• 24th Constitutional Amendment Act, 1971:
• It was enacted to affirm Parliament’s power to amend any part of the Constitution, including Fundamental Rights.
• This amendment was passed to counter the Supreme Court’s judgment in the Golaknath case (1967), which restricted Parliament’s power to amend Fundamental Rights.
• It also made it mandatory for the President to give assent to Constitutional Amendment Bills.
• 44th Constitutional Amendment Act, 1978:
• This amendment was enacted to reverse some provisions of the 42nd Amendment, particularly to restore the balance of powers between the central and state governments.
• It abolished the Right to Property as a Fundamental Right and made it a legal right under Article 300A.
• The amendment also strengthened the protection of Fundamental Rights during emergencies by limiting the scope of Article 352 (National Emergency).
• 61st Constitutional Amendment Act, 1988:
• This amendment reduced the voting age for Lok Sabha and State Assembly elections from 21 years to 18 years.
• It sought to enhance youth participation in the electoral process and strengthen democratic governance in India.
• Main Theme: Education in India
• Education plays a crucial role in national development, fostering human resource growth and innovation.
• By including education in the Concurrent List, the 42nd Amendment ensured a collaborative approach between the Center and States for policy formulation and implementation.
• This move was instrumental in addressing disparities and ensuring equitable access to education across all regions of the country.

The correct answer is Option 1: Only 1 and 2 are correct.

Key Points

• Statement 1: Transpiration is highest in dry and windy conditions because these conditions enhance the evaporation of water from the leaf surface, increasing the transpiration rate.
• Statement 2: Transpiration helps in the ascent of sap through the plant’s vascular system by creating a negative pressure in the xylem, which is supported by the cohesion-tension theory.
• The process of transpiration is essential for water movement in plants as it aids in nutrient uptake and maintains plant temperature.
• Both statements 1 and 2 are scientifically correct and aligned with modern botanical principles.
• Statement 3 is incorrect: Transpiration does not always result in wilting. Wilting occurs only when water loss due to transpiration exceeds the water absorption by roots, leading to a water deficit in plant cells.

Additional Information

• Transpiration:
• It is the process by which plants lose water vapor through stomata in their leaves.
• Transpiration plays a critical role in nutrient transport, temperature regulation, and maintaining water balance in plants.
• Factors like temperature, humidity, wind speed, and soil water availability influence the rate of transpiration.
• About Statement 3:
• Wilting occurs when transpiration exceeds water absorption, leading to a loss of turgor pressure in plant cells.
• However, in normal conditions, plants regulate transpiration effectively and do not wilt.
• Guard cells play a key role in controlling the opening and closing of stomata to balance water loss and gas exchange.
• Cohesion-Tension Theory:
• It explains the movement of water through the xylem of plants.
• Water molecules are cohesive (stick to each other) and adhesive (stick to xylem walls), enabling the ascent of sap.
• Transpiration creates a negative pressure in the leaves, pulling water upward from the roots.
• Dry and Windy Conditions:
• Low humidity and high wind speed increase the water vapor concentration gradient between the leaf and the surrounding air, enhancing transpiration.

The correct answer is Federal structure with Provincial Autonomy.

Key Points

• The Government of India Act, 1935, introduced the concept of a federal structure in India, dividing powers between the Centre and the Provinces.
• It provided for Provincial Autonomy, giving elected provincial legislatures and governments significant control over provincial subjects.
• Under this Act, the provinces were granted the right to legislate on subjects listed in the Provincial List without interference from the Centre.
• It marked the first time that Indian provinces were allowed to administer their own affairs independently, albeit under the overarching supervision of the British government.
• This federal principle, with a division of powers between the Centre and states, was later adopted and expanded in the Indian Constitution of 1950.

Additional Information

• Fundamental Duties
• Fundamental Duties were not part of the original Indian Constitution. They were added by the 42nd Amendment Act in 1976.
• They are enshrined in Part IVA (Article 51A) of the Constitution and outline the moral obligations of citizens to promote a spirit of patriotism and uphold the unity of India.
• Examples include respecting the Constitution, safeguarding public property, and protecting the natural environment.
• Parliamentary Sovereignty
• Parliamentary Sovereignty refers to the concept where the Parliament is the supreme legal authority, capable of creating or ending any law.
• This concept is a feature of the British Parliamentary system but is not fully applicable to India as the Indian Constitution is supreme and Parliament operates within its limits.
• In India, Parliament is not sovereign due to the system of judicial review and the federal structure of the Constitution.
• Universal Adult Franchise
• Universal Adult Franchise guarantees that every adult citizen, irrespective of caste, gender, religion, or economic status, has the right to vote in elections.
• This was adopted in India with the commencement of the Constitution on January 26, 1950.
• It was not introduced by the Government of India Act, 1935, but rather was a decision made during the drafting of the Indian Constitution.

The correct answer is Wooden sticks.

Key Points

• Tippani dance is a traditional folk dance form originating from the Saurashtra region of Gujarat, India.
• The dancers perform using wooden sticks as tools to rhythmically pound the floor, showcasing their strength and precision.
• This dance form was initially performed by women laborers while working on construction sites to alleviate fatigue and boredom.
• The wooden sticks used in Tippani are often decorated, adding to the vibrant visual appeal of the dance.
• The rhythm of the pounding is synchronized with the beats of folk songs, creating a unique and lively performance.

Additional Information

• Metal rods:
• Metal rods are not used in Tippani dance as they are heavy and unsuitable for rhythmic pounding.
• They are typically used in construction and engineering for structural support.
• In traditional Indian dances, metal rods do not have a significant role due to their weight and lack of flexibility.
• Bamboo poles:
• Bamboo poles are commonly associated with traditional dances like the Cheraw dance of Mizoram, also known as the bamboo dance.
• In Cheraw, dancers rhythmically move and manipulate bamboo poles, creating patterns for performers to step into.
• Bamboo poles are flexible and lightweight, making them an excellent choice for other dances, but they are not used in Tippani dance.
• Stones:
• Stones are not utilized in Tippani dance as they are not practical tools for a rhythmic performance.
• In some cultures, stones are used for percussion or as part of rituals, but they are not part of this specific dance form.
• About Tippani Dance:
• This dance form is performed during festive occasions, weddings, and celebrations in Gujarat.
• The traditional attire for Tippani dancers includes colorful sarees and jewelry, adding to the cultural essence of the performance.
• The dance reflects the hard-working spirit and unity of women in rural communities.

The correct answer is IMD Business School.

Key Points

• IMD Business School, located in Lausanne, Switzerland, is renowned for its focus on executive education and leadership development.
• The institute publishes the prestigious World Competitiveness Index annually, evaluating countries based on economic performance, government efficiency, business efficiency, and infrastructure.
• The World Competitiveness Center, an integral part of IMD, spearheads the research and development of the index to provide insights into global competitiveness.
• IMD's rankings and publications are widely respected and serve as a benchmark for policymakers, researchers, and business leaders worldwide.
• Established in 1990, the World Competitiveness Index by IMD has become an authoritative resource for analyzing the competitive landscape of nations.

Additional Information

• University of Geneva School
• The University of Geneva is a leading research institution in Switzerland, offering expertise in law, science, and humanities.
• It is not associated with the World Competitiveness Index but is known for its research contributions and high-quality education.
• ETH Zurich Institute
• ETH Zurich (Swiss Federal Institute of Technology) is one of the world's top science and technology universities.
• It is recognized for its groundbreaking research in engineering, natural sciences, and computer science but does not publish the World Competitiveness Index.
• University of St. Gallen
• The University of St. Gallen is a prominent Swiss university specializing in business administration, economics, and law.
• Although it is globally acclaimed for its MBA and executive education programs, it is not linked to the World Competitiveness Index.
• World Competitiveness Index
• The index assesses and ranks countries based on their ability to foster an environment that sustains business competitiveness.
• Key criteria include infrastructure, economic performance, government and business efficiency, and innovation.
• The index helps governments, organizations, and businesses identify areas for improvement and adopt strategies to enhance competitiveness.

The correct answer is Demand is elastic (elasticity greater than 1).

Key Points

• Price Elasticity of Demand (PED) measures the responsiveness of quantity demanded to a change in the price of a commodity.
• The formula for Price Elasticity of Demand is:
• PED = (% Change in Quantity Demanded) ÷ (% Change in Price)
• In the given question:
• Percentage increase in price = 10%
• Percentage decrease in quantity demanded = 20%
• PED = 20 ÷ 10 = 2
• Since the elasticity coefficient is 2, which is greater than 1, the demand is said to be elastic.
• Hence, demand is elastic (elasticity greater than 1).

Additional Information

• Elastic Demand (PED > 1):
• A small change in price causes a proportionately larger change in quantity demanded.
• Example: Luxury goods, branded products, and goods with close substitutes.
• Inelastic Demand (PED < 1):
• A change in price causes a proportionately smaller change in quantity demanded.
• Example: Salt, medicines, and essential commodities.
• Unitary Elastic Demand (PED = 1):
• The percentage change in quantity demanded equals the percentage change in price.
• Total expenditure remains unchanged.
• Perfectly Elastic Demand (PED = ∞):
• Consumers buy any quantity at a particular price but none at a higher price.
• The demand curve is perfectly horizontal.
• Perfectly Inelastic Demand (PED = 0):
• Quantity demanded remains unchanged regardless of price changes.
• The demand curve is perfectly vertical.

Important Points

• Elasticity = 2 implies that for every 1% increase in price, quantity demanded falls by approximately 2%.
• Goods with many substitutes generally have high price elasticity of demand.
• Price elasticity is an important concept used in pricing decisions, taxation policy, revenue forecasting, and market analysis.

The correct answer is Second.

Key Points

• The Mahalanobis Model, formulated by Indian statistician P.C. Mahalanobis, was introduced in the Second Five-Year Plan (1956-1961).
• This model emphasized the development of the heavy industries sector to accelerate economic growth.
• The Mahalanobis model aimed to achieve self-reliance and reduce dependency on foreign imports by focusing on industrialization.
• It was inspired by Soviet planning methods, emphasizing capital goods production over consumer goods.
• The model laid the foundation for long-term economic planning and played a pivotal role in shaping India's industrial policy during its early years of independence.

Additional Information

• First Five-Year Plan (1951-1956):
• The focus of this plan was on agriculture, irrigation, and energy to address food shortages and promote rural development.
• It followed the Harrod-Domar Model, emphasizing investment in agriculture and basic industries.
• Key achievements included the construction of major dams like Bhakra Nangal and Hirakud.
• Fourth Five-Year Plan (1969-1974):
• This plan aimed to achieve growth with stability and self-reliance in food production.
• It focused on reducing income inequality and poverty through direct anti-poverty programs.
• The Green Revolution was a major highlight during this period, significantly increasing agricultural productivity.
• Fifth Five-Year Plan (1974-1979):
• The emphasis was on poverty eradication and attaining self-reliance in essential commodities.
• The Garibi Hatao (Remove Poverty) slogan was introduced during this plan.
• This plan prioritized employment generation and focused on social justice.
• Mahalanobis Model:
• The model is named after Prasanta Chandra Mahalanobis, a renowned Indian statistician.
• It is based on the idea that a country should prioritize investment in capital goods industries to create a robust industrial base.
• This strategy aimed to increase the production of goods that would enable further industrialization.
• Critics argue that the model overlooked the importance of the agricultural sector and consumer goods, leading to imbalances in the economy.

The correct answer is Mission Mangrove Mitra.

Key Points

• Mission Mangrove Mitra is a sustainable development initiative launched in 2025 to regenerate coastal mangrove ecosystems while creating rural employment opportunities.
• The program integrates mangrove restoration efforts with the Mahatma Gandhi National Rural Employment Guarantee Scheme (MGNREGS) to ensure livelihood generation for rural communities.
• It aims to combat climate change by enhancing carbon sequestration through mangrove forests, which act as natural carbon sinks and provide coastal protection from erosion and storms.
• This initiative also enhances biodiversity as mangroves serve as breeding grounds for marine species, supporting coastal fisheries and local economies.
• By combining ecological restoration with rural job creation, the program aligns with India’s sustainable development goals and commitments under international agreements like the Paris Climate Accord.

Additional Information

• Sagar Suraksha Yojana
• This program is focused on coastal security and disaster preparedness to ensure the safety of coastal communities and resources.
• It involves deploying advanced technology and infrastructure to safeguard marine ecosystems and prevent illegal activities like poaching and smuggling in coastal areas.
• The scheme emphasizes collaboration with local governments and communities to protect coastal biodiversity and ensure maritime safety.
• EcoJobs for Coasts
• This conceptual framework aims at generating employment opportunities while focusing on the conservation of coastal and marine ecosystems.
• It promotes the creation of green jobs that align with the protection and sustainable utilization of coastal resources.
• While similar in intent, this initiative is not linked to MGNREGS or mangrove restoration efforts under Mission Mangrove Mitra.
• Blue Belt Programme
• The Blue Belt Programme is globally recognized for its focus on marine conservation and the sustainable management of marine resources.
• Primarily implemented in various countries, this program promotes marine protected areas and sustainable oceanic practices to combat overfishing and biodiversity loss.
• It is unrelated to mangrove restoration or rural employment generation under MGNREGS.

The correct answer is Foreign exchange.

Key Points

• The Balance of Payments (BOP) crisis of 1991 in India was primarily caused by a severe shortage of foreign exchange reserves. The reserves had dwindled to a point where India could barely finance three weeks' worth of imports.
• The crisis was triggered by a combination of factors, including a high fiscal deficit, an increasing current account deficit, and a surge in oil prices following the Gulf War.
• India's external debt had risen significantly, and the country faced challenges in repaying its borrowings and attracting foreign investments.
• To address the crisis, India had to pledge 67 tons of gold as collateral to the International Monetary Fund (IMF) to secure financial assistance.
• The crisis led to significant economic reforms in 1991, often referred to as the LPG (Liberalization, Privatization, and Globalization) reforms, which marked the beginning of India's shift towards a market-oriented economy.

Additional Information

• Water:
• Water scarcity is a global issue caused by overpopulation, climate change, and inefficient water management.
• While water crises can lead to economic and social challenges, they were not a factor in India's 1991 BOP crisis.
• Electricity:
• Electricity shortages can disrupt industrial production and economic growth but were not a contributing factor in the 1991 crisis.
• India's energy infrastructure in the 1990s was underdeveloped but unrelated to the balance of payments issue.
• Labour:
• Labour shortages can impact productivity and economic stability, but India has historically had a surplus of labour.
• The BOP crisis was not linked to labour shortages but to financial and economic mismanagement.
• Main Theme - Balance of Payments (BOP):
• The Balance of Payments is a comprehensive record of all economic transactions between residents of a country and the rest of the world over a specific period.
• A BOP crisis occurs when a country cannot meet its international financial obligations due to a shortage of foreign exchange reserves.
• Key components of the BOP include the current account (trade in goods and services), the capital account (investment flows), and the financial account (changes in foreign ownership of assets).

The correct answer is Both A and R are true and R is the correct explanation of A.

Key Points

• In 1991, India faced a severe balance of payments (BoP) crisis due to a sharp decline in foreign exchange reserves.
• The foreign exchange reserves had fallen to a level that could barely finance two weeks' worth of imports, creating an economic emergency.
• To stabilize the economy and overcome the crisis, the government approached the International Monetary Fund (IMF) and the World Bank for assistance.
• India received a bailout package of $2.2 billion from the IMF, conditional on implementing economic reforms and liberalization policies.
• This event marked the beginning of India's economic liberalization, which included measures like reducing import tariffs, deregulating markets, and opening the economy to foreign investments.

Additional Information

• Explanation of Option 2 (Both A and R are true, but R is not the correct explanation of A):
• While A and R are both true, R directly explains the reason for the economic crisis in 1991.
• The severe depletion of foreign exchange reserves was the immediate cause of India seeking assistance from IMF and the World Bank. Hence, this option is incorrect.
• Explanation of Option 3 (A is true but R is false):
• Assertion A is true as India did approach the IMF and World Bank in 1991 for a bailout loan.
• However, Reason R is also true because the main trigger for this action was the depletion of foreign exchange reserves. Thus, this option is incorrect.
• Explanation of Option 4 (A is false but R is true):
• Assertion A is not false as India did face an economic crisis in 1991 and sought help from international financial institutions.
• Reason R is also true, but this option does not apply to the given scenario.
• Context of the 1991 Economic Crisis:
• Key reasons for the crisis included high fiscal deficits, rising inflation, and a trade imbalance.
• The Gulf War exacerbated the situation by causing a spike in oil prices, further draining India's foreign exchange reserves.
• The economic reforms initiated in 1991 under the leadership of then Finance Minister Dr. Manmohan Singh and Prime Minister Narasimha Rao laid the foundation for liberalization, privatization, and globalization in India.

The correct answer is It merges tribal, folk, and classical Hindu elements.

Key Points

• Chhau is a unique Indian dance form that combines elements of tribal, folk, and classical traditions of Hindu culture, creating a syncretic art form.
• This dance form is predominantly practiced in the eastern regions of India, particularly in Odisha, Jharkhand, and West Bengal.
• Chhau incorporates vigorous martial movements, intricate footwork, and expressive facial gestures to narrate mythological and folk tales, often drawn from Hindu epics like the Ramayana and Mahabharata.
• It is recognized for its use of elaborate masks (especially in Purulia Chhau) and vibrant costumes, which are integral to the storytelling aspect of the performance.
• The dance form has been declared a part of the UNESCO Intangible Cultural Heritage of Humanity, underscoring its cultural significance and historical value.

Additional Information

• Option 1: It uses Sanskrit-only chants in temple rituals
• This is incorrect as Chhau is not associated with the exclusive use of Sanskrit chants or temple rituals. While it draws from Hindu mythology, it is a performance art that incorporates folk and tribal traditions rather than being limited to temple worship.
• Sanskrit chants are more closely linked with classical dance forms like Bharatanatyam or Odissi, which are temple-based traditions.
• Option 3: It evolved purely from Vaishnav temple dance
• This is incorrect as Chhau did not evolve solely from Vaishnav temple dances. While it draws from Hindu religious themes, its origins are rooted in tribal and martial traditions, making it a broader amalgamation of multiple influences.
• Vaishnav temple dances are more specifically associated with classical forms like Kathak and Manipuri.
• Option 4: It prohibits all forms of theatrical expression
• This is incorrect as Chhau is celebrated for its theatrical expressions, including elaborate facial movements, mask work, and dramatic gestures.
• Theatrical expression is a defining feature of Chhau, enabling performers to communicate stories effectively.
• Main Theme: Chhau Dance
• Chhau is a semi-classical Indian dance form that blends classical music with folk and tribal influences.
• There are three main styles of Chhau: Purulia Chhau (West Bengal), Mayurbhanj Chhau (Odisha), and Seraikella Chhau (Jharkhand), each with distinct characteristics.
• The dance is often performed during festivals, particularly in the spring season, and serves as a medium to preserve cultural heritage.

The correct answer is 1, 2, 3 (Berubari Union case, Kesavananda Bharati case, S.R. Bommai case).

Key Points

• Berubari Union Case (1960): This case addressed the interpretation of the Indian Constitution regarding the transfer of territory to another country. It clarified that a constitutional amendment under Article 368 is required for transferring any part of Indian territory.
• Kesavananda Bharati Case (1973): This landmark case established the doctrine of the Basic Structure of the Constitution, which restricts Parliament's power to amend the Constitution in a way that alters its fundamental framework.
• S.R. Bommai Case (1994): This case is a significant judgment regarding the scope and limitations of Article 356 (President's Rule). It emphasized the principle of federalism and judicial review of the imposition of President's Rule.
• The chronological order of these cases is essential in understanding the evolution of constitutional law in India.
• This question highlights milestones in India's judicial history that have shaped governance and federalism in the country.

Additional Information

• Berubari Union Case (1960):
• The issue arose following the Nehru-Noon Agreement (1958) between India and Pakistan to divide Berubari Union territory.
• The Supreme Court opined that the transfer of territory to Pakistan required a constitutional amendment, as it involved altering India's territorial integrity.
• This case clarified the interpretation of Article 3 and Article 368 regarding the alteration of India's boundaries.
• Kesavananda Bharati Case (1973):
• In this case, Swami Kesavananda Bharati challenged the Kerala government's land reform laws, questioning the extent of Parliament's power to amend the Constitution.
• The Supreme Court ruled that Parliament could amend the Constitution but could not alter its "Basic Structure," such as democracy, secularism, federalism, and judicial independence.
• This judgment is regarded as a cornerstone of constitutional law in India.
• S.R. Bommai Case (1994):
• This case arose when the Karnataka state government, led by S.R. Bommai, was dismissed by the central government under Article 356.
• The Supreme Court laid down guidelines for imposing President's Rule and emphasized that it cannot be used arbitrarily.
• It upheld the importance of federalism and judicial review in safeguarding democracy.

The correct answer is Alteration of ocean currents.

Key Points

• Space weather events such as solar flares and Coronal Mass Ejections (CMEs) primarily impact the Earth's magnetosphere and ionosphere, not oceanic systems.
• Ocean currents are driven by factors such as wind patterns, Earth's rotation (Coriolis effect), salinity, and temperature gradients, which are unaffected by solar activity.
• Space weather influences are limited to electromagnetic interference, high-energy particle radiation, and geomagnetic storms, none of which have direct impacts on ocean currents.
• Changes in ocean currents are more closely associated with climate phenomena, like El Niño and La Niña, and tectonic activities rather than external solar or space events.
• While space weather can affect technological systems on Earth, it does not have the capability to alter the physical processes governing ocean currents.

Additional Information

• Disruption of satellite communication
• Space weather events, such as solar flares and CMEs, release high-energy electromagnetic radiation and charged particles that can disrupt satellite communication systems.
• Solar flares can cause radio blackouts, especially in high-frequency (HF) communication systems used for aviation and maritime purposes.
• Geomagnetic storms can interfere with satellite positioning systems like GPS, causing errors in navigation and communication services.
• Blackouts in radio frequencies
• Solar flares can emit X-rays and ultraviolet radiation that ionize the Earth's upper atmosphere, disrupting radio wave propagation.
• This ionization can lead to signal degradation or complete loss of radio communication over certain frequencies, particularly in the HF band.
• Such radio blackouts are often temporary but can have significant impacts on communication and navigation systems.
• Damage to power grids
• Geomagnetic storms caused by CMEs can induce electric currents in power transmission lines, potentially overloading and damaging transformers and other electrical infrastructure.
• Major geomagnetic storms in the past, such as the 1989 Quebec blackout, have caused widespread power outages due to geomagnetically induced currents (GICs).
• Power grid operators monitor space weather to prepare for potential disruptions and minimize risks.

Shortcut Trick

Plants arranged in the square formation = Total plants − Left out plants.

⇒ Plants in square = 3984 − 15 = 3969

For a perfect square formation, rows = columns, so the number of plants per row is √3969.

Since 60² = 3600 and 70² = 4900, and 3969 ends in 9, the root must end in 3.

⇒ Number of plants per row = 63

∴ The correct answer is 63 plants.

Alternate Method

Given:

Total number of plants = 3984

Number of plants left out = 15

n × n = n2 plants Area = 3969

n plants

n rows

• 15 plants left out

Total = n2 + 15 = 3984

Formula Used:

Total plants = (Number of rows × Number of plants per row) + Plants left out

Calculations:

Let the number of rows be n. Since it is a square formation, the number of plants per row is also n.

⇒ Total plants used in the square formation = n × n = n²

⇒ n² + 15 = 3984

⇒ n² = 3984 − 15

⇒ n² = 3969

⇒ n = √3969

⇒ n = 63

∴ The correct answer is 63 plants.

Additional Information

Square Formation Principle

When objects are organized in a solid square arrangement, the number of columns is equal to the number of rows. Therefore, the total number of objects making up the square will always be a perfect square number (n²).

Unit Digits of Perfect Squares

Perfect squares can only end in the digits 0, 1, 4, 5, 6, or 9. If a perfect square ends in 9, its square root must end in either 3 or 7 (since 3 × 3 = 9 and 7 × 7 = 49). Numbers ending in 2, 3, 7, or 8 are never perfect squares.

Shortcut Trick

Convert the given percentage increases into multiplying fractions:

25% more means 125% = 5/4

20% more means 120% = 6/5

A : C = (A/B) × (B/C) = (5/4) × (6/5) = 30/20 = 3/2

∴ The correct answer is 3 : 2.

Alternate Method

Given:

A is 25% more than B.

B is 20% more than C.

C = 100

+20%

B = 120

+25%

A = 150

Ratio A : C = 150 : 100

Calculations:

⇒ Let the value of C be 100.

⇒ Value of B = 100 + 20% of 100 = 100 + 20 = 120

⇒ Value of A = 120 + 25% of 120

⇒ Value of A = 120 + (25/100) × 120 = 120 + 30 = 150

⇒ Ratio of A to C = 150 : 100

⇒ A : C = 3 : 2

∴ The correct answer is 3 : 2.

Additional Information

Compound Ratio

The compound ratio of two individual ratios a:b and c:d is obtained by multiplying their respective terms: (a/b) × (c/d) = (a × c) : (b × d).

Identifying the Base Value

In percentage comparison statements like "A is x% more than B", the quantity appearing immediately after the word "than" (which is B in this case) is taken as the original base (100%).

Successive Percentage Change

When a value undergoes multiple successive changes of a% and b%, the net percentage change can be calculated using the formula: a + b + (a × b)/100.

Shortcut Trick

For an infinite series of the form √(n + √(n + √(n + ...))), check if n is a product of two consecutive integers.

If n = a × (a + 1), then the answer is the larger integer (a + 1).

Here, the given number is 12.

12 can be factored into consecutive integers as 3 × 4.

Since the series has a positive (+) sign, the answer is the larger factor, which is 4.

∴ The correct answer is 4.

Alternate Method

Given:

The expression is √(12 + √(12 + √(12 + ...∞)))

Method Used:

Assume the given infinite series is equal to x, then substitute x back into the expression to form a quadratic equation.

Calculations:

⇒ Let x = √(12 + √(12 + √(12 + ...∞)))

Since the series continues infinitely, the term inside the first square root is also equal to x:

⇒ x = √(12 + x)

Squaring both sides of the equation:

⇒ x² = 12 + x

⇒ x² − x − 12 = 0

Factorising the quadratic equation:

⇒ x² − 4x + 3x − 12 = 0

⇒ x(x − 4) + 3(x − 4) = 0

⇒ (x − 4)(x + 3) = 0

⇒ x = 4 or x = −3

Since the principal square root is always non-negative, x cannot be −3.

⇒ x = 4

∴ The correct answer is 4.

Additional Information

Infinite Series with Subtraction

For √(n − √(n − √(n ...∞))), if n = a × (a+1), the answer is the smaller integer, a.

Infinite Series with Multiplication

For √(n × √(n × √(n ...∞))), the answer is always n.

Finite Series with Multiplication

For √(n × √(n × ... k times)), the exact formula used is n^{(2k − 1) ÷ 2k}.

When Factors are not Consecutive Integers

For √(n + √(n + ...∞)), use the direct root formula: x = (√(4n+1) + 1) ÷ 2.

Shortcut Trick

Selling Price (SP) = 80% of Marked Price (MP) = 0.8 × 600 = ₹480.

Loss = Cost Price (CP) − SP = 500 − 480 = ₹20.

Loss % = (20 ÷ 500) × 100 = 4%.

∴ The correct answer is 4% Loss.

Alternate Method

Given:

Cost Price (CP) = ₹500

Marked Price (MP) = ₹600

Discount = 20%

Formula Used:

Selling Price (SP) = MP × [(100 − Discount %) ÷ 100]

Loss % = (Loss ÷ CP) × 100

CP = ₹500

SP = ₹480

MP = ₹600

Discount = 20%

Loss = ₹20

Calculations:

⇒ SP = 600 × [(100 − 20) ÷ 100]

⇒ SP = 600 × (80 ÷ 100) = ₹480

⇒ Here, Cost Price is greater than Selling Price, so there is a loss.

⇒ Loss = CP − SP = 500 − 480 = ₹20

⇒ Loss % = (20 ÷ 500) × 100

⇒ Loss % = 4%

∴ The correct answer is 4% Loss.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). So, Selling Price = MP − Discount.

Profit/Loss Percentage

Profit or loss is always calculated on the Cost Price (CP) unless specifically stated otherwise. Loss % = (Loss ÷ CP) × 100.

Successive Discounts

If two successive discounts of x% and y% are given on an article, the equivalent single discount percentage is (x + y − xy ÷ 100)%.

Shortcut Trick

Total capacity of the tank = LCM of 20, 30 and 60 = 60 units.

Efficiency of A = +3, B = +2 and C (drainpipe) = −1 unit/min.

Combined efficiency of all pipes = 3 + 2 − 1 = 4 units/min.

Time taken to fill = 60 ÷ 4 = 15 minutes.

∴ The correct answer is 15 min.

Alternate Method

Given:

Time taken by Pipe A to fill the tank = 20 minutes

Time taken by Pipe B to fill the tank = 30 minutes

Time taken by drainpipe C to empty the tank = 60 minutes

Formula Used:

Efficiency = Total Work ÷ Time Taken

Time = Total Work ÷ Combined Efficiency

Calculations:

⇒ Total efficiency when all pipes are open = Efficiency of A + Efficiency of B + Efficiency of C

⇒ Combined Efficiency = 3 + 2 + (−1)

⇒ Combined Efficiency = 4 units/min

⇒ Time taken to fill the tank = 60 ÷ 4

⇒ Time taken = 15 minutes

∴ The correct answer is 15 min.

Additional Information

Inlet vs Outlet Pipes

An inlet pipe fills the tank, hence its efficiency (work per unit time) is considered positive. An outlet or drainpipe empties the tank, so its efficiency is considered negative.

Combined Work Formula

If pipe A fills a tank in x units of time, pipe B fills it in y units, and pipe C empties it in z units, then the net part filled in 1 unit of time is (1/x + 1/y − 1/z).

Total Time to Fill or Empty

If the net efficiency is positive, the tank gets filled over time. If the net efficiency is negative, a partially or completely full tank will eventually get emptied.

Shortcut Trick

Let A = x − y, B = y − z, and C = z − x.

Sum = A + B + C = (x − y) + (y − z) + (z − x) = 0.

If A + B + C = 0, then directly A³ + B³ + C³ = 3ABC.

Substituting A, B, and C back directly yields 3(x − y)(y − z)(z − x).

∴ The correct answer is 3(x − y)(y − z)(z − x).

Alternate Method

Given:

⇒ x + y + z = 0

⇒ x³ + y³ + z³ = 3xyz

Formula Used:

⇒ If a + b + c = 0, then a³ + b³ + c³ = 3abc

Calculations:

⇒ We need to evaluate (x − y)³ + (y − z)³ + (z − x)³

⇒ Let a = x − y, b = y − z, and c = z − x

⇒ Checking the sum of these variables:

⇒ a + b + c = (x − y) + (y − z) + (z − x)

⇒ a + b + c = x − y + y − z + z − x = 0

⇒ Since the sum of a, b, and c is 0, the special algebraic identity applies directly:

⇒ a³ + b³ + c³ = 3abc

⇒ Substitute the values of a, b, and c back into the equation:

⇒ (x − y)³ + (y − z)³ + (z − x)³ = 3 × (x − y) × (y − z) × (z − x)

⇒ (x − y)³ + (y − z)³ + (z − x)³ = 3(x − y)(y − z)(z − x)

∴ The correct answer is 3(x − y)(y − z)(z − x).

Additional Information

Standard Cubic Identity

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Modified Cubic Identity

a³ + b³ + c³ − 3abc = (1 ÷ 2) × (a + b + c) × [(a − b)² + (b − c)² + (c − a)²]

Condition for 3abc

If a + b + c = 0 OR if a = b = c, then a³ + b³ + c³ perfectly evaluates to 3abc.

Shortcut Trick

Overall percentage of interest = (390 ÷ 5000) × 100 = 7.8%

By alligation method for 6% and 9% interest rates:

Ratio of parts = (9 − 7.8) : (7.8 − 6) = 1.2 : 1.8 = 2 : 3

Sum lent at 6% = 5000 × [2 ÷ (2 + 3)] = 5000 × (2 ÷ 5) = ₹2000

∴ The correct answer is ₹2000.

Alternate Method

Given:

Total Sum (P) = ₹5000

Total simple interest (I) = ₹390

Rates of interest = 6% and 9%

Time (T) = 1 year

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

₹ x at 6% ₹ (5000 − x) at 9%

Total Principal = ₹5000 Total Interest = ₹390

Calculations:

⇒ Let the sum lent at 6% be ₹x.

⇒ Then, the sum lent at 9% will be ₹(5000 − x).

⇒ Total Interest = Interest on first part + Interest on second part

⇒ [(x × 6 × 1) ÷ 100] + [((5000 − x) × 9 × 1) ÷ 100] = 390

⇒ 6x + 45000 − 9x = 39000

⇒ 3x = 45000 − 39000

⇒ 3x = 6000

⇒ x = 2000

∴ The correct answer is ₹2000.

Additional Information

Simple Interest (SI)

It is calculated only on the principal amount for the entire tenure. Formula: SI = (P × R × T) ÷ 100.

Compound Interest (CI)

Interest is calculated on the principal and also on the accumulated interest of previous periods. Formula: Amount = P × (1 + R ÷ 100)^T.

Difference between CI and SI

For a period of 2 years, the difference between Compound Interest and Simple Interest on a given principal is calculated as: D = P × (R ÷ 100)².

Alligation Method

A technique used to find the ratio in which two quantities at different rates or percentages are mixed to yield a mixture of a known average rate.

Shortcut Trick

Total interest for 1 year = 4950 ÷ 3 = ₹1650.

Assume the entire ₹15,000 is lent at X's rate of 10%. Expected interest = 10% of 15000 = ₹1500.

Extra interest generated = 1650 − 1500 = ₹150.

This ₹150 extra is due to the additional 2% rate (12% − 10%) on Y's share.

2% of Y = 150 ⇒ Y = 7500. Therefore, X's share = 15000 − 7500 = ₹7500.

∴ The correct answer is ₹7,500.

Alternate Method

Given:

Total principal = ₹15,000

Total Simple Interest (SI) for 3 years = ₹4,950

Rate for X = 10%, Rate for Y = 12%

Formula Used:

SI = (P × R × T) ÷ 100

Total = ₹15,000

Lent to X Rate = 10% p.a. Time = 3 years

Lent to Y Rate = 12% p.a. Time = 3 years

Total SI = ₹4,950

Calculation:

⇒ Let the amount lent to X be P.

⇒ Then, the amount lent to Y = 15000 − P.

⇒ Interest from X = (P × 10 × 3) ÷ 100 = 0.3P

⇒ Interest from Y = ((15000 − P) × 12 × 3) ÷ 100 = (15000 − P) × 0.36

⇒ Total Interest = 0.3P + 5400 − 0.36P = 4950

⇒ 5400 − 0.06P = 4950

⇒ 0.06P = 5400 − 4950

⇒ 0.06P = 450

⇒ P = 450 ÷ 0.06 = 7500

∴ The correct answer is ₹7,500.

Additional Information

Alligation Method for SI

Calculate the overall average rate of interest using the formula: Average Rate = (Total SI × 100) ÷ (Total Principal × Time). Use the alligation cross method to quickly find the ratio in which the total sum is divided.

Shift / Assume Method

Whenever a total amount is split into two parts at two different rates, assuming the entire amount is invested at the lower rate calculates the minimum expected interest. The excess interest is solely due to the higher rate part, directly revealing its value.

Simple Interest Key Fact

Unlike Compound Interest, Simple Interest remains constant every year if the principal, rate, and time do not change.

Shortcut Trick

In a 30°-60°-90° right-angled triangle, the ratio of sides opposite to the angles is 1 : √3 : 2.

The base adjacent to the 60° angle (which is opposite to 30°) corresponds to 1 part.

The length of the wire forms the hypotenuse, corresponding to 2 parts.

Given the base length is 10 m, we can multiply by 2 to get the hypotenuse directly.

Length of the wire = 10 × 2 = 20 m.

∴ The correct answer is 20 m.

Alternate Method

A B C 10 m 60° L = ?

Given:

Distance of the wire fixed on the ground from the base of the pole = 10 m

Angle of elevation of the wire from the ground = 60°

Formula Used:

cos(θ) = Base ÷ Hypotenuse

Calculation:

⇒ Let the length of the taut wire be L.

⇒ From the right-angled triangle formed, cos(60°) = 10 ÷ L

⇒ 1/2 = 10 ÷ L

⇒ L = 10 × 2

⇒ L = 20 m

∴ The correct answer is 20 m.

Additional Information

Trigonometric Ratios

For any right-angled triangle, sine = Perpendicular ÷ Hypotenuse, cosine = Base ÷ Hypotenuse, and tangent = Perpendicular ÷ Base.

Angle of Elevation

The angle formed by the line of sight with the horizontal plane when viewing an object located above the observer's eye level.

Standard 30°-60°-90° Triangle

The sides opposite to the angles 30°, 60°, and 90° respectively are always strictly in the ratio of 1 : √3 : 2.

Shortcut Trick

Volume of Cone = Volume of Sphere ⇒ (1/3)πr_c²h = (4/3)πr_s³

Substitute cone height h = 2r_c directly into the equation:

⇒ r_c² × 2r_c = 4r_s³

⇒ 2r_c³ = 4r_s³ ⇒ r_c³/r_s³ = 2/1

Taking cube roots on both sides gives the direct ratio of their radii.

∴ The correct answer is ∛2 : 1.

Alternate Method

Given:

Volume of the cone = Volume of the sphere

Height of the cone (h) = 2 × Radius of the cone (r_c)

Formula Used:

Volume of a Cone = (1/3)πr²h

Volume of a Sphere = (4/3)πr³

h = 2rc rc Cone

rs Sphere

Volume of Cone = Volume of Sphere

Calculations:

Let the radius of the cone be r_c and the radius of the sphere be r_s.

⇒ (1/3) × π × r_c² × h = (4/3) × π × r_s³

Substitute h = 2r_c in the above equation:

⇒ (1/3) × π × r_c² × (2r_c) = (4/3) × π × r_s³

Cancel out (π/3) from both sides of the equation:

⇒ 2r_c³ = 4r_s³

⇒ r_c³ / r_s³ = 4 / 2

⇒ (r_c / r_s)³ = 2 / 1

Taking the cube root on both sides:

⇒ r_c / r_s = ∛2 / 1

∴ The correct answer is ∛2 : 1.

Additional Information

Volume of a Hemisphere

A hemisphere is exactly half of a sphere. Its volume is calculated using the formula V = (2/3)πr³.

Surface Area of a Sphere

The total surface area of a sphere is equivalent to 4 times the area of its great circle: TSA = 4πr².

Curved Surface Area of a Cone

The lateral or curved surface area is CSA = πrl, where l = √(r² + h²) is the slant height.

Shortcut Trick

Total Surface Area (TSA) of Hemisphere = 3πr²

Total Surface Area (TSA) of Cylinder = 2πr(h + r)

Equating both: 3πr² = 2πr(h + r)

⇒ 3r = 2h + 2r ⇒ r = 2h

⇒ h/r = 1/2

∴ The correct answer is 1:2.

Alternate Method

Given:

Radius of hemisphere = Radius of cylinder = r

Total Surface Area (TSA) of hemisphere = TSA of cylinder

Formula Used:

TSA of a solid hemisphere = 3πr²

TSA of a solid cylinder = 2πrh + 2πr²

r Hemisphere

r

h

Cylinder

Calculation:

⇒ 3πr² = 2πr(r + h)

⇒ 3r = 2(r + h)

⇒ 3r = 2r + 2h

⇒ 3r − 2r = 2h

⇒ r = 2h

⇒ h/r = 1/2

⇒ Ratio of height to radius (h : r) = 1 : 2

∴ The correct answer is 1:2.

Additional Information

Cylinder Formulas

Curved Surface Area (CSA) = 2πrh | Total Surface Area (TSA) = 2πr(h + r) | Volume = πr²h

Hemisphere Formulas

Curved Surface Area (CSA) = 2πr² | Total Surface Area (TSA) = 3πr² | Volume = (2/3)πr³

Sphere Formulas

Total Surface Area (TSA) = 4πr² | Volume = (4/3)πr³

Cone Formulas

Curved Surface Area (CSA) = πrl | Total Surface Area (TSA) = πr(l + r) | Volume = (1/3)πr²h

Shortcut Trick

For a cube to be divided into n³ identical pieces, it must be cut into 'n' equal parts along all 3 dimensions.

Total identical pieces = 64 = 4³

⇒ Number of parts along each dimension (n) = 4

Number of cuts required for 'n' parts = n − 1 cuts per dimension.

⇒ Minimum total cuts = 3 × (4 − 1) = 3 × 3 = 9

∴ The correct answer is 9 cuts.

Alternate Method

Given:

Total number of identical smaller cubical pieces = 64

Formula Used:

Total number of pieces = (x + 1) × (y + 1) × (z + 1)

Where x, y, and z are the number of parallel straight cuts along the length, breadth, and height of the cube respectively.

To strictly minimize the total number of cuts (x + y + z), the individual factors must be as close to each other as possible.

Large Cube cut into 64 pieces (4 × 4 × 4) 3 cuts along Height 3 cuts along Breadth 3 cuts along Length

Calculations:

⇒ 64 = 4 × 4 × 4

⇒ (x + 1) = 4 ⇒ x = 3

⇒ (y + 1) = 4 ⇒ y = 3

⇒ (z + 1) = 4 ⇒ z = 3

⇒ Minimum number of total cuts = x + y + z

⇒ Minimum cuts = 3 + 3 + 3 = 9

∴ The correct answer is 9 cuts.

Additional Information

Maximum Pieces from N Cuts

To get the maximum number of pieces from a given number of cuts (N), distribute the cuts equally among all three axes. Maximum pieces = (N/3 + 1)³.

Cubes with 3 Faces Painted

When a fully painted large cube is cut into n × n × n smaller identical pieces, the number of cubes with exactly 3 faces painted is always 8 (these are situated at the corners).

Cubes with 2 Faces Painted

The number of smaller cubes with exactly 2 faces painted lie precisely along the middle of the edges and is given by the formula 12 × (n − 2).

Cubes with 1 Face Painted

The number of smaller cubes with exactly 1 face painted lie in the center of the outer faces and is given by the formula 6 × (n − 2)².

Shortcut Trick

The volume of a cone is proportional to r² × h, so the percentage change depends on three successive changes: +20%, +20%, and −10%.

First, apply the successive percentage formula (x + y + xy/100) on the radius (+20% and +20%):

⇒ 20 + 20 + (20 × 20) ÷ 100 = 40 + 4 = +44%

Next, apply the formula on the combined radius change (+44%) and height change (−10%):

⇒ 44 − 10 + (44 × −10) ÷ 100 = 34 − 4.4 = +29.6%

Since the result is positive, the overall change is a 29.6% increase.

∴ The correct answer is 29.6% increase.

Alternate Method

Given:

Percentage increase in radius = 20%

Percentage decrease in height = 10%

Formula Used:

Volume of a cone = 1/3 × π × r² × h

r h

Original Cone Volume = 100%

+29.6%

1.2r 0.9h

New Cone Volume = 129.6%

Calculations:

⇒ Let the original radius (r) be 10 units and original height (h) be 10 units.

⇒ Original Volume (V₁) = 1/3 × π × (10)² × 10 = 1000π / 3 cubic units.

⇒ New radius = 10 + (20% of 10) = 10 + 2 = 12 units.

⇒ New height = 10 − (10% of 10) = 10 − 1 = 9 units.

⇒ New Volume (V₂) = 1/3 × π × (12)² × 9 = 1/3 × π × 144 × 9 = 1296π / 3 cubic units.

⇒ Change in volume = V₂ − V₁ = (1296π / 3) − (1000π / 3) = 296π / 3 cubic units.

⇒ Percentage change = (Change in volume ÷ Original Volume) × 100

⇒ Percentage change = [(296π / 3) ÷ (1000π / 3)] × 100

⇒ Percentage change = (296 ÷ 1000) × 100 = 29.6%

∴ The correct answer is 29.6% increase.

Additional Information

Volume of Cone vs Cylinder

The volume of a cone is exactly one-third the volume of a cylinder that shares the same base radius and height (V = 1/3 × πr²h).

Successive Percentage Change

When a value undergoes multiple percentage changes sequentially, the net percentage change for two variables is found using (a + b + ab/100)%. For formulas depending on three variables like r × r × h, apply this successive change formula twice.

Surface Area of a Cone

The curved surface area is given by πrl and the total surface area is πr(r + l), where l = √(r² + h²) is the slant height of the cone.

Shortcut Trick

Since A lies in the 2nd quadrant, sine is positive and cosine is negative.

Using the 3-4-5 right angle triplet, if sinA = 3/5, then cosA = −4/5.

Expression: (sinA + cosA)²

⇒ (3/5 − 4/5)²

⇒ (−1/5)² = 1/25

∴ The correct answer is 1/25.

Alternate Method

Given:

sinA = 3/5

A lies in the second quadrant.

Formula Used:

Algebraic Identity: (a + b)² = a² + b² + 2ab

Trigonometric Identity: sin²A + cos²A = 1

A Base = −4 Perp = 3 Hyp = 5 y-axis x-axis 2nd Quadrant

Calculation:

⇒ In the 2nd quadrant, cosine values are negative.

⇒ cosA = −√(1 − sin²A)

⇒ cosA = −√(1 − 9/25) = −√(16/25) = −4/5

Now, expanding the given expression to solve it directly:

⇒ (sinA + cosA)² = sin²A + cos²A + 2 × sinA × cosA

⇒ (sinA + cosA)² = 1 + 2 × sinA × cosA

⇒ (sinA + cosA)² = 1 + 2 × (3/5) × (−4/5)

⇒ (sinA + cosA)² = 1 − 24/25

⇒ (sinA + cosA)² = (25 − 24) / 25 = 1/25

∴ The correct answer is 1/25.

Additional Information

ASTC Rule (Signs in Quadrants)

1st Quadrant: All positive. 2nd Quadrant: sin & csc positive. 3rd Quadrant: tan & cot positive. 4th Quadrant: cos & sec positive.

Pythagorean Identity

The foundational identity is sin²θ + cos²θ = 1 for any generic angle θ.

Common Pythagorean Triplets

Sets of integers that perfectly satisfy a² + b² = c². The most frequent sets in exams include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Shortcut Trick

According to the basic trigonometric identity, 1 + tan² A = sec² A.

We know that sec² A = 1 / cos² A = 1 / (1 − sin² A).

Substitute sin A = m / n into the equation:

⇒ sec² A = 1 / [1 − (m / n)²] = 1 / [(n² − m²) / n²]

⇒ sec² A = n² / (n² − m²)

∴ The correct answer is n² / (n² − m²).

Alternate Method

Given:

sin A = m / n = Perpendicular / Hypotenuse

A m (Perpendicular) n (Hypotenuse) Base = √(n² - m²)

Calculations:

⇒ Perpendicular (P) = m

⇒ Hypotenuse (H) = n

Using Pythagoras theorem:

⇒ Base (B) = √(H² − P²) = √(n² − m²)

⇒ tan A = P / B = m / √(n² − m²)

Now, we need to find the value of (1 + tan² A):

⇒ 1 + [m / √(n² − m²)]²

⇒ 1 + m² / (n² − m²)

⇒ (n² − m² + m²) / (n² − m²)

⇒ n² / (n² − m²)

∴ The correct answer is n² / (n² − m²).

Additional Information

Pythagorean Identities

Fundamental relations between trigonometric functions: sin² θ + cos² θ = 1, sec² θ − tan² θ = 1, and cosec² θ − cot² θ = 1.

Reciprocal Identities

Functions that are inverses of each other: sin θ = 1 / cosec θ, cos θ = 1 / sec θ, and tan θ = 1 / cot θ.

Quotient Identities

Relation of tangent and cotangent with sine and cosine: tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.

Shortcut Trick

Slope (m) is the ratio of the vertical change to the horizontal change between two points.

m = (Change in y) ÷ (Change in x)

m = (7 − 3) ÷ (4 − 2)

m = 4 ÷ 2 = 2

∴ The correct answer is 2.

Alternate Method

Given:

Points on the line: (x₁, y₁) = (2, 3) and (x₂, y₂) = (4, 7)

Formula Used:

Slope of a line, m = (y₂ − y₁) / (x₂ − x₁)

X Y 0

(2, 3) (4, 7) Run = 2 Rise = 4 Slope (m) = Rise ÷ Run = 4 ÷ 2 = 2

Calculations:

⇒ Substitute the given coordinates into the slope formula.

⇒ m = (7 − 3) / (4 − 2)

⇒ m = 4 / 2

⇒ m = 2

∴ The correct answer is 2.

Additional Information

Equation of a Straight Line

The point-slope form of the line equation is given by (y − y₁) = m(x − x₁), where m is the slope.

Parallel and Perpendicular Lines

Parallel lines always have equal slopes (m₁ = m₂). Perpendicular lines have negative reciprocal slopes (m₁ × m₂ = −1).

Distance Between Two Points

The straight-line distance d between (x₁, y₁) and (x₂, y₂) is calculated using d = √((x₂ − x₁)² + (y₂ − y₁)²).

Shortcut Trick

For sectors with the same radius, their areas are directly proportional to their central angles.

Angle of the first sector = 180° = π radians.

Angle of the second sector = π/2 radians.

Ratio of areas = π ÷ (π/2) = 2 : 1.

∴ The correct answer is 2:1.

Alternate Method

Given:

Radius of both sectors (r) = 12 cm

Central angle of first sector (θ₁) = 180°

Central angle of second sector (θ₂) = π/2 radians

180° r = 12 cm Sector 1

:

π/2 rad r = 12 cm Sector 2

Formula Used:

Area of a sector (in degrees) = (θ ÷ 360°) × π × r²

Area of a sector (in radians) = (1/2) × r² × θ

Calculations:

⇒ Area of first sector = (180° ÷ 360°) × π × (12)²

⇒ Area of first sector = (1/2) × π × 144 = 72π cm²

⇒ Area of second sector = (1/2) × (12)² × (π/2)

⇒ Area of second sector = (1/2) × 144 × (π/2) = 36π cm²

⇒ Ratio = Area of first sector : Area of second sector

⇒ Ratio = 72π : 36π = 2 : 1

∴ The correct answer is 2:1.

Additional Information

Area of a Sector

When the angle θ is in degrees, Area = (θ ÷ 360°) × π × r². When θ is in radians, Area = (1/2) × r² × θ.

Arc Length

The length of an arc is given by l = (θ ÷ 360°) × 2πr in degrees, and l = r × θ in radians.

Radians to Degrees Conversion

To convert an angle from radians to degrees, multiply it by (180° ÷ π). Therefore, π radians = 180°.

Shortcut Trick

The sum of all interior angles of any polygon depends directly on its number of sides (n).

Sum = (n − 2) × 180°

For a 10-sided polygon, substitute n = 10.

Sum = (10 − 2) × 180° = 8 × 180° = 1440°

∴ The correct answer is 1440°.

Alternate Method

Decagon (10 Sides) Number of triangles = n − 2 Triangles = 10 − 2 = 8 Each triangle sums to 180° Total = 8 × 180° = 1440°

Given:

The polygon is a decagon, which has 10 sides.

Formula Used:

Sum of interior angles of an n-sided polygon = (n − 2) × 180°

Calculations:

⇒ Number of sides (n) = 10

⇒ Sum of interior angles = (10 − 2) × 180°

⇒ Sum = 8 × 180°

⇒ Sum = 1440°

∴ The correct answer is 1440°.

Additional Information

Sum of Exterior Angles

The sum of all exterior angles for any convex polygon is always 360°, regardless of the number of sides.

Interior Angle of a Regular Polygon

Each interior angle of a regular n-sided polygon can be found using the formula: [(n − 2) × 180°] ÷ n.

Number of Diagonals

The total number of diagonals that can be drawn in an n-sided polygon is given by the formula: n(n − 3) ÷ 2.

Shortcut Trick

Midpoint of the line connecting (2, 8) and (6, 4) is ((2 + 6) ÷ 2, (8 + 4) ÷ 2) = (4, 6).

Slope of the given line segment = (4 − 8) ÷ (6 − 2) = −4 ÷ 4 = −1.

Slope of its perpendicular bisector = −1 ÷ (−1) = 1.

Equation of the bisector passing through (4, 6) with slope 1: y − 6 = 1 × (x − 4).

Simplifying the equation gives: y = x + 2.

∴ The correct answer is y = x + 2.

Alternate Method

Given:

Two points: A(2, 8) and B(6, 4)

Formula Used:

Midpoint formula: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)

Slope formula: m = (y₂ − y₁) ÷ (x₂ − x₁)

Perpendicular slope condition: m₁ × m₂ = −1

Equation of a straight line: y − y₁ = m × (x − x₁)

A (2, 8) B (6, 4) M (4, 6)

y = x + 2

Calculation:

⇒ Let the line segment be AB. The perpendicular bisector passes exactly through the midpoint M of AB.

⇒ Midpoint M = ((2 + 6) ÷ 2, (8 + 4) ÷ 2)

⇒ M = (8 ÷ 2, 12 ÷ 2) = (4, 6)

⇒ Slope of line AB (m₁) = (4 − 8) ÷ (6 − 2)

⇒ m₁ = −4 ÷ 4 = −1

⇒ Let the slope of the perpendicular bisector be m₂.

⇒ m₁ × m₂ = −1

⇒ −1 × m₂ = −1 ⇒ m₂ = 1

⇒ Now, substitute the point M(4, 6) and slope m₂ = 1 into the straight line equation.

⇒ y − 6 = 1 × (x − 4)

⇒ y − 6 = x − 4

⇒ y = x − 4 + 6

⇒ y = x + 2

∴ The correct answer is y = x + 2.

Additional Information

Distance Formula

The linear distance between two points (x₁, y₁) and (x₂, y₂) on a Cartesian plane is given by D = √((x₂ − x₁)² + (y₂ − y₁)²).

Section Formula

The coordinates of a point dividing a line segment internally in the ratio m:n are calculated as ((m×x₂ + n×x₁) ÷ (m+n), (m×y₂ + n×y₁) ÷ (m+n)).

Parallel and Perpendicular Lines

Two lines are parallel if their slopes are strictly equal (m₁ = m₂). Two lines are exactly perpendicular if the product of their respective slopes is negative one (m₁ × m₂ = −1).

Shortcut Trick

The ratio of the areas of similar triangles is the square of the ratio of their perimeters.

Ratio of areas = 3² : 5² = 9 : 25.

Total area in ratio units = 9 + 25 = 34 units.

Given total area = 34 cm², which means 34 units = 34 cm² ⇒ 1 unit = 1 cm².

Area of the larger triangle = 25 units × 1 = 25 cm².

∴ The correct answer is 25 cm².

Alternate Method

Given:

Ratio of perimeters of two similar triangles = 3 : 5

Sum of their areas = 34 cm²

Formula Used:

For two similar triangles, Ratio of Areas = (Ratio of Perimeters)²

Perimeter = 3x Area = 9a

Perimeter = 5x Area = 25a

Similar Triangles Area Relationship Total Area = 9a + 25a = 34 cm²

Calculations:

⇒ Let the areas of the smaller and larger triangles be A₁ and A₂ respectively.

⇒ A₁ : A₂ = 3² : 5²

⇒ A₁ : A₂ = 9 : 25

⇒ Let A₁ = 9a and A₂ = 25a

⇒ Total Area = 9a + 25a = 34a

⇒ 34a = 34

⇒ a = 1 cm²

⇒ Area of the larger triangle = 25a = 25 × 1 = 25 cm²

∴ The correct answer is 25 cm².

Additional Information

Areas of Similar Triangles Theorem

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides, altitudes, or perimeters.

Perimeters of Similar Triangles Theorem

The ratio of the perimeters of two similar triangles is exactly equal to the ratio of their corresponding sides or corresponding medians.

Volumes of Similar Figures

If two 3D geometrical figures are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions (sides or radii).

Shortcut Trick

If a + b + c = 0, then a³ + b³ + c³ = 3abc.

Here, a = 19, b = 20, and c = −39. Since 19 + 20 − 39 = 0, we can apply the trick.

19³ + 20³ − 39³ = 3 × 19 × 20 × (−39) = −44460.

Now, add 118 to this result: −44460 + 118 = −44342.

∴ The correct answer is −44342.

Alternate Method

Given:

19³ + 20³ − 39³ + 118

Formula Used:

If a + b + c = 0, then a³ + b³ + c³ = 3abc

Calculations:

⇒ Let a = 19, b = 20, and c = −39

⇒ Sum of terms: a + b + c = 19 + 20 − 39 = 0

⇒ Therefore, 19³ + 20³ + (−39)³ = 3 × 19 × 20 × (−39)

⇒ 3 × 19 = 57

⇒ 57 × 20 = 1140

⇒ 1140 × (−39) = −44460

⇒ Substituting this value back into the original expression:

⇒ −44460 + 118 = −44342

∴ The correct answer is −44342.

Additional Information

Algebraic Identity for Cubes

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca). If a + b + c = 0, the right-hand side becomes 0, leading to the direct shortcut: a³ + b³ + c³ = 3abc.

Sum of Cubes Formula

a³ + b³ = (a + b)(a² − ab + b²)

Difference of Cubes Formula

a³ − b³ = (a − b)(a² + ab + b²)

BODMAS Rule

Always follow the correct order of operations in algebraic expressions: Brackets, Orders (powers/roots), Division × Multiplication, Addition − Subtraction.

Shortcut Trick

Using the trigonometric identity: cosec²A = 1 + cot²A

Substitute cot A = x + 1/x directly into the identity.

cosec²A = 1 + (x + 1/x)²

cosec²A = 1 + x² + 1/x² + 2 = x² + 1/x² + 3

∴ The correct answer is x² + 1/x² + 3.

Alternate Method

Given:

cot A = x + 1/x

Formula Used:

cosec²θ − cot²θ = 1

(a + b)² = a² + b² + 2ab

Calculations:

⇒ cosec²A = 1 + cot²A

⇒ Substitute the given value of cot A:

⇒ cosec²A = 1 + (x + 1/x)²

⇒ Expanding the term using the algebraic identity:

⇒ (x + 1/x)² = x² + (1/x)² + 2 × x × (1/x)

⇒ (x + 1/x)² = x² + 1/x² + 2

⇒ Now substitute this back into the expression for cosec²A:

⇒ cosec²A = 1 + x² + 1/x² + 2

⇒ cosec²A = x² + 1/x² + 3

∴ The correct answer is x² + 1/x² + 3.

Additional Information

Fundamental Trigonometric Identities

1. sin²θ + cos²θ = 1
   
2. sec²θ − tan²θ = 1
   
3. cosec²θ − cot²θ = 1

Important Algebraic Identities

1. (a + b)² = a² + b² + 2ab
   
2. (a − b)² = a² + b² − 2ab

Reciprocal Trigonometric Relations

sin θ = 1 / cosec θ | cos θ = 1 / sec θ | tan θ = 1 / cot θ

Shortcut Trick

A tangent line forms a 90° angle with the radius at the point of contact, creating a right-angled triangle.

The sides of this triangle are the radius (8 cm), the tangent length, and the distance to the center (17 cm).

These values form a standard Pythagorean triplet: (8, 15, 17).

Since the radius is 8 cm and the hypotenuse is 17 cm, the tangent must be the remaining leg, which is 15 cm.

∴ The correct answer is 15 cm.

Alternate Method

O P A

8 cm 17 cm PA = ?

ΔOAP forms a right-angled triangle

Given:

Radius of the circle, OA = 8 cm

Distance from the external point P to the center O, OP = 17 cm

Formula Used:

By Pythagoras Theorem: Hypotenuse² = Base² + Perpendicular²

Calculations:

⇒ In right-angled ΔOAP, OP is the hypotenuse because the angle at the point of tangency (angle OAP) is 90°.

⇒ OP² = OA² + PA²

⇒ 17² = 8² + PA²

⇒ 289 = 64 + PA²

⇒ PA² = 289 − 64

⇒ PA² = 225

⇒ PA = √225 = 15 cm

∴ The correct answer is 15 cm.

Additional Information

Tangent-Radius Theorem

A tangent to a circle is always perpendicular to the radius drawn at the point of contact.

Tangents from an External Point

The lengths of the two distinct tangents drawn from an external point to a circle are always equal.

Secant-Tangent Theorem

If a tangent segment PA and a secant segment PBC are drawn to a circle from an exterior point P, then PA² = PB × PC.

Shortcut Trick

When the angle between two tangents from an external point is 90°, the tangents and the radii to the points of contact form a square.

The side of this square is exactly equal to the radius of the circle (r = 5 cm).

The distance from the external point to the center is simply the diagonal of this square.

Distance OP = r × √2 = 5 × √2 = 5√2 cm.

∴ The correct answer is 5√2 cm.

Alternate Method

P O A B

5 cm 5 cm 90°

PO = 5√2 cm

Given:

⇒ Radius of the circle (OA = OB) = 5 cm.

⇒ Angle between tangents PA and PB = ∠APB = 90°.

Formula Used:

⇒ Diagonal of a square = Side × √2

Calculations:

⇒ A tangent to a circle is always perpendicular to the radius drawn through the point of contact.

⇒ ∴ ∠OAP = 90° and ∠OBP = 90°.

⇒ In quadrilateral OAPB, the sum of all interior angles is 360°.

⇒ ∠AOB = 360° − (90° + 90° + 90°) = 90°.

⇒ Since all four angles of the quadrilateral are 90° and the adjacent sides are equal (OA = OB = 5 cm), OAPB is a square.

⇒ The distance from point P to the center O is represented by the diagonal OP of the square OAPB.

⇒ Length of diagonal OP = Side × √2 = 5 × √2 = 5√2 cm.

∴ The correct answer is 5√2 cm.

Additional Information

Tangents from an External Point

When two tangents are drawn to a circle from a single external point, their lengths are always strictly equal (PA = PB).

Tangent-Radius Theorem

The tangent line is always perpendicular to the radius of the circle drawn to the exact point of tangency.

Properties of a Square

A quadrilateral where all four angles are 90° and at least two adjacent sides are equal is a square. The diagonal bisects the internal angles and has a length of Side × √2.

Shortcut Trick

Step 1: Ignore the decimals and multiply the integers directly: 45 × 6 = 270.

Step 2: Count the total number of decimal places in the given numbers: 2 (in 0.45) + 1 (in 0.6) = 3 decimal places.

Step 3: Place the decimal point 3 positions from the right in the product: 0.270 = 0.27.

∴ The correct answer is 0.27.

Alternate Method

Given:

The expression to simplify is 0.45 × 0.6

Method Used:

Convert the decimal numbers into fractions, multiply the numerators and denominators, and then convert the result back to a decimal.

Calculations:

⇒ 0.45 = 45 / 100

⇒ 0.6 = 6 / 10

⇒ 0.45 × 0.6 = (45 / 100) × (6 / 10)

⇒ 0.45 × 0.6 = (45 × 6) / (100 × 10)

⇒ 0.45 × 0.6 = 270 / 1000

⇒ 0.45 × 0.6 = 27 / 100

⇒ 0.45 × 0.6 = 0.27

∴ The correct answer is 0.27.

Additional Information

Multiplication of Decimals

When multiplying decimal numbers, multiply them exactly as if they are whole numbers. The number of decimal places in the final product will always be equal to the total sum of the decimal places present in the original factors.

Converting Decimals to Fractions

To convert a decimal to a fraction, write the decimal number without the point as the numerator. For the denominator, write 1 followed by as many zeros as there are decimal places in the original number (e.g., 0.85 = 85/100).

BODMAS Rule

When simplifying mathematical expressions containing multiple operations, always follow the BODMAS sequence: Bracket, Order (Powers/Roots), Division, Multiplication, Addition, and Subtraction.

The correct answer is: Disobedient.

Key Points

• The word "Rebellious" refers to a person or behavior that resists authority, control, or convention. It signifies defiance and a refusal to conform. (विद्रोही)
• Example: The rebellious teenager refused to follow the school rules and often challenged the teachers.
• "Disobedient" means refusing to obey rules or someone in authority, which aligns closely with the meaning of "rebellious." (आज्ञा न मानने वाला)
• Example: The disobedient child ignored his parents' instructions and continued playing outside.
• Hence, we can infer that the synonym of "rebellious" is "disobedient".

Therefore, the correct answer is: Disobedient.

Additional Information

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

• Submissive (आज्ञाकारी): Ready to conform to the authority or will of others; meekly obedient or passive.
• Example: The submissive employee always followed instructions without questioning.
• Obedient (आज्ञाकारी): Willing to comply with orders or requests; dutiful.
• Example: The obedient dog followed every command its owner gave.
• Agreeable (सहमत): Willing to agree or consent; pleasant and easy to get along with.
• Example: She is an agreeable person who enjoys making others feel comfortable.

The correct answer is: Tribute.

Key Points

• The word "Eulogy" means a speech or piece of writing that praises someone or something highly, especially someone who has just died. (प्रशंसा / स्तुति)
• Example: The priest delivered a heartfelt eulogy at the funeral, remembering the deceased's kindness and contributions.
• "Tribute" refers to an act, statement, or gift that is intended to show gratitude, respect, or admiration. (श्रद्धांजलि / सम्मान)
• Example: The statue was built as a tribute to the soldiers who sacrificed their lives for the country.
• Hence, the word "Tribute" is a synonym of "Eulogy", as they both convey admiration and respect for someone or something.

Therefore, the correct answer is: Tribute.

Additional Information

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

• Criticism (आलोचना): The expression of disapproval of someone or something based on perceived faults or mistakes.
• Example: The movie received harsh criticism from the audience for its weak storyline.
• Insult (अपमान): A disrespectful or scornful remark or action.
• Example: His rude comment was taken as an insult by the audience.
• Condemnation (निंदा): The expression of very strong disapproval or censure.
• Example: The government faced widespread condemnation for its handling of the crisis.

The correct answer is: Morality.

Key Points

• The word "Turpitude" refers to wickedness, depravity, or immoral behavior. (दुष्टता, नीचता)
• Example: The court condemned the turpitude displayed by the corrupt officials.
• "Morality" denotes principles concerning the distinction between right and wrong or good and bad behavior. It reflects virtuous conduct and ethics. (नैतिकता)
• Example: He is known for his strong morality and ethical decision-making in business.
• Hence, we can infer that the opposite of 'turpitude' is 'morality'.

Therefore, the correct answer is: Morality.

Additional Information

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

• Depravity (दुष्टता): Moral corruption or wickedness.
• Example: The novel describes the depravity of the aristocratic society during that era.
• Vice (दोष): Immoral or wicked behavior; a bad habit.
• Example: Gambling is often considered a vice that can lead to financial ruin.
• Sin (पाप): An act considered morally wrong or a transgression against divine law.
• Example: According to religious teachings, stealing is a sin.