SSC CGL 2025 (Held On: 26 Sept, 2025 Shift 2) (Previous Year Paper)

Given Address:

Flat No. 6A, Pearl View, Salt Lake, Kolkata, West Bengal - 700091

Option 1

Flat No. 6A, Pearl View, Salt Lake, Kolkata, West Bengal - 700091

Flat Number — Same

Building Name — Same

Area — Same

City — Same

State — Same

PIN Code — Same

Option 2

Flat No. 6A, Pearl View, Salt Lake, Kolkata, Assam - 700091

 State is different

Option 3

Flat No. 6A, Pearl View, Salt Lake, Kolkata, Odisha - 700091

State is different

Option 4

Flat No. 6A, Pearl View, Salt Lake, Kolkata, Bihar - 700091

State is different

Hence, the correct answer is Option 1.

Logical arrangement using elimination

⇒ Raipur ≠ 11th ⇒ Raipur is either 7th or 9th

⇒ If Raipur = 9th ⇒ Bhopal must be 7th (since Indore after Bhopal)

⇒ Then Indore = 11th (valid)

⇒ Check all conditions satisfied

⇒ If Raipur = 7th ⇒ Bhopal must be before Indore

⇒ Possible: Bhopal = 9th, Indore = 11th

⇒ But Raipur already 7th, still valid

⇒ Both cases give Indore = 11th

∴ Indore seminar was held on 11th August

The logic is followed here

76 → 80 (+4)

80 → 71 (−9)

71 → 87 (+16)

87 → 62 (−25)

The pattern is

+2², −3², +4², −5²

Next should be:

+6² = +36

62 + 36 = 98

Hence, the correct answer is Option 2.

The logic is followed here

Checking the pattern

9 × 2 + 1 = 19 

19 × 2 + 1 = 39 

39 × 2 + 1 = 79  (But given 78)

79 × 2 + 1 = 159 

159 × 2 + 1 = 319 

Multiply by 2 and add 1.

Hence, the WRONG number is Option 3.

Given:

Find the remainder when 987654321 is divided by 9.

Rule:

A number is divisible by 9 if the sum of its digits is divisible by 9. The remainder when dividing by 9 is the same as the remainder of the sum of its digits divided by 9.

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45

Divide 45 by 9

45 ÷ 9 = 5 (remainder 0)

Hence, the remainder is Option 3.

Given

11 → 1331

12 → 1728

Finding the pattern:

11³ = 11 × 11 × 11 = 1331 

12³ = 12 × 12 × 12 = 1728 

Pattern: Number → Cube of the number (n³)

Now,

13³ = 13 × 13 × 13 = 2197

Hence, the correct answer is Option 3.

Given

P + Q = 2R …… (1)

R + S = 2P …… (2)

From equation (1)

Q = 2R − P

From equation (2)

S = 2P − R

Q + S

Q + S = (2R − P) + (2P − R)

= 2R − P + 2P − R

= R + P

So,  P + R=Q + S

Hence, the correct answer is Option 1.

Given Options:

Lucknow, Kanpur, Varanasi, Jaipur, Agra

Observation:

Lucknow, Kanpur, Varanasi and Agra are cities in Uttar Pradesh.

Jaipur is in Rajasthan.

Hence, the correct answer is Option 3.

Given:

Codes: 5 4 3 2 1

Letters: R O I C D

Formula used:

Match numbers with corresponding letters and form meaningful word

Calculation:

⇒ 5 → R

⇒ 4 → O

⇒ 3 → I

⇒ 2 → C

⇒ 1 → D

⇒ Check option 1: 2, 4, 5, 3, 3, 1, 4, 5

⇒ C, O, R, I, I, D, O, R

⇒ CORIIDOR (not meaningful)

⇒ Check option 2: 2, 4, 5, 5, 3, 1, 4, 5

⇒ C, O, R, R, I, D, O, R

⇒ CORRIDOR (meaningful word)

∴ Correct answer is option (2)

Given Number:

8372625374895

Arrange digits in descending order

Digits: 8, 3, 7, 2, 6, 2, 5, 3, 7, 4, 8, 9, 5

Descending order: 9, 8, 8, 7, 7, 6, 5, 5, 4, 3, 3, 2, 2

New number: 9887765543322

Identify required digits

4th digit from the left = 7

3rd digit from the right = 3

Subtract

7 − 3 = 4

Hence, the correct answer is Option 3.

Given:

Distance downstream = 12 km in 3 hours

Distance upstream = 6 km in 2 hours

Find speeds

Downstream speed = 12 ÷ 3 = 4 km/h

Upstream speed = 6 ÷ 2 = 3 km/h

Use formula

Speed of stream = (Downstream speed − Upstream speed) ÷ 2

= (4 − 3) ÷ 2

= 1 ÷ 2

= 0.5 km/h

Hence, the correct answer is "Option 2".

Given

12 : 441

Find the pattern

12² = 144

Reverse of 144 = 441

13² = 169

Reverse of 169 = 961

Hence, the correct answer is Option 1.

Given Statements:

1. Some trees are tall.
2. All tall things are visible.

Conclusions:

I. Some trees are visible → True (Since some trees are tall and all tall things are visible, it follows that the trees which are tall are also visible.)

II. All trees are visible → False (The statements only establish that trees which are tall are visible; there is no information to confirm that every tree is visible.)

Thus, Only conclusion I follows.

Hence, the correct answer is "Option 1".

Statement:

Assumption I: If phones are banned inside classrooms, it is reasonable to assume that they may distract students. Otherwise, there would be no need to prohibit them. So, this assumption is implicit.

Assumption II: The circular implies that students bring phones to class; otherwise, there would be no need to issue such a rule. Hence, this assumption is also implicit.

Hence, the correct answer is Option 3.

The logic is followed here:

625 ÷ 5 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

Each number is divided by 5.

Hence, the correct answer is Option 2.

Given Series:

AZ, BY, CX, DW, ?

Observe the pattern

A ↔ Z

B ↔ Y

C ↔ X

D ↔ W

Each pair consists of opposite letters in the English alphabet.

(A is opposite of Z, B is opposite of Y, C is opposite of X, D is opposite of W)

E is opposite of V.

Hence, the correct answer is Option 1.

The logic is followed here

DELHI → CDKGH

Each letter is shifted one step backward in the alphabet.

MUMBAI → LTLAZH

Hence, the correct answer is Option 2.

The logic is followed here

AG, BH, CI, ?

Observe the pattern

First letters: A, B, C → increasing by 1 → Next = D

Second letters: G, H, I → increasing by 1 → Next = J

Form the next pair

D + J = DJ

Hence, the correct answer is Option 1.

The logic is followed here

2, 3, 5, 7 are prime numbers.

The next prime number after 7 is 11.

Hence, the correct answer is "Option 2".

Given:

Length = 50 m

Width = 30 m

Use Pythagoras Theorem

Diagonal² = Length² + Width²

= 50² + 30²

= 2500 + 900

= 3400

Diagonal = √3400 ≈ 58.3 m

Closest option = 58 m

Hence, the correct answer is Option 1.

The logic is followed here

S → U (+2)

M → N (+1)

A → C (+2)

R → T (+2)

T → U (+1)

Pattern: +2, +1, +2, +2, +1

Applying the same pattern to TRICK

T → V (+2)

R → S (+1)

I → K (+2)

C → E (+2)

K → L (+1)

TRICK → VSKEL

Hence, the correct answer is "Option 2".

Since the product includes 0, and any number multiplied by 0 becomes 0, the final product is 0.

Correct answer: Option 1.

Given:

BRIDGE → CSJEHF

Finding the pattern:

B → C (+1)

R → S (+1)

I → J (+1)

D → E (+1)

G → H (+1)

E → F (+1)

Each letter is shifted one step forward in the alphabet.

C → D (+1)

S → T (+1)

J → K (+1)

E → F (+1)

H → I (+1)

F → G (+1)

CSJEHF → DTKFIG

Hence, the correct answer is Option 1.

The logic is followed here

M → N (+1)

O → P (+1)

B → C (+1)

I → J (+1)

L → M (+1)

I → J (+1)

T → U (+1)

Y → Z (+1)

Each letter is shifted one step forward in the alphabet.

E → F (+1)

X → Y (+1)

A → B (+1)

M → N (+1)

P → Q (+1)

L → M (+1)

E → F (+1)

Hence, the correct answer is Option 1.

The logic is followed here

Check letters of INTEGRAL

Letters: I, N, T, E, G, R, A, L

Compare options

1. ALERTING → A, L, E, R, T, I, N, G  (Same letters)
   

2. RELATING → R, E, L, A, T, I, N, G  (Same letters)
   

3. TRIANGLE → T, R, I, A, N, G, L, E  (Same letters)
   

4. LITERAL → L, I, T, E, R, A, L (Missing N and G; extra L)

LITERAL is not an anagram of INTEGRAL.

**Hence, the correct answer is **Option 4.

The correct answer is Lander Hazard Detection and Avoidance Camera and Processing Algorithm.

Key Points

• The Chandrayaan-3 lander, Vikram, utilized advanced technology known as the Lander Hazard Detection and Avoidance Camera and Processing Algorithm for identifying and avoiding potential hazards during its landing process.
• This technology is crucial for ensuring a safe and precise landing on the uneven lunar surface, which is scattered with craters, rocks, and slopes.
• The hazard detection system works by employing high-resolution cameras and computational algorithms to scan the landing site in real-time, identifying safe zones and avoiding risky areas.
• It plays a pivotal role in the autonomous decision-making of the lander, enabling it to adjust its trajectory and orientation without human intervention.
• Such technology significantly enhances the mission’s success rate, as it ensures the lander avoids areas that could potentially damage the spacecraft or jeopardize the mission.

Additional Information

• Chandrayaan-3 Mission:
• Chandrayaan-3 is India's third lunar exploration mission, launched by the Indian Space Research Organisation (ISRO).
• The mission's primary objective is to demonstrate safe landing and rover operations on the lunar surface.
• It builds upon the learnings from Chandrayaan-2, which faced landing challenges in 2019.
• The spacecraft comprises a lander (Vikram) and a rover (Pragyan) with advanced scientific instruments for studying the lunar surface.
• Key Features of Lander Hazard Detection Technology:
• The system uses optical cameras and sensor arrays to analyze the terrain during descent.
• It integrates with navigation systems to provide real-time data for trajectory correction.
• The onboard algorithms are capable of recognizing features like craters, slopes, and boulders and selecting a safe landing spot.
• Other Technologies Used in Chandrayaan-3:
• Laser Doppler Velocimeter: Measures the speed of the lander relative to the lunar surface during descent.
• Al-assisted navigation systems: Enhance the precision of landing and rover mobility.
• Synthetic Aperture Radar (SAR): Used for detailed mapping of the lunar surface prior to landing.
• Global Context:
• India joins the elite group of countries with advanced lunar landing capabilities, including the USA, Russia, and China.
• Such missions contribute to the global understanding of lunar geology and open avenues for future human exploration.

Important Points

• ISRO’s Achievements:
• India's space agency, ISRO, has successfully launched over 100 spacecraft missions.
• Its lunar exploration missions, including Chandrayaan-1, Chandrayaan-2, and Chandrayaan-3, demonstrate India's growing expertise in space technology.
• Scientific Goals of Chandrayaan Missions:
• To study the lunar surface composition, mineralogy, and elemental distribution.
• To explore potential sites for future lunar bases and resource utilization.
• To enhance understanding of the Moon's geological history and evolution.

The correct answer is Anthropogenically induced sea surface temperature increases.

Key Points

• Coral bleaching occurs when corals lose their symbiotic algae (zooxanthellae), which provide them with energy through photosynthesis. This phenomenon is primarily triggered by stress due to elevated sea surface temperatures.
• The primary cause of increased sea surface temperatures is anthropogenic climate change, driven by greenhouse gas emissions from human activities like burning fossil fuels, deforestation, and industrial processes.
• When sea temperatures rise beyond the tolerance level of corals (typically 1-2°C above the seasonal maximum), the corals expel their zooxanthellae, leading to a loss of color and energy sources, which can result in mass mortality.
• Studies in the Indian Ocean have shown widespread coral bleaching events linked to El Niño events and long-term warming trends, both of which are exacerbated by anthropogenic influences.
• This phenomenon poses a significant threat to the health of coral reefs, which are biodiversity hotspots and provide critical ecosystem services like coastal protection and fisheries support.

Additional Information

• Ocean Acidification:
• Ocean acidification refers to the decrease in pH levels of seawater due to the absorption of excess atmospheric carbon dioxide (CO2).
• While it negatively impacts coral growth by reducing the availability of calcium carbonate needed for reef-building, it is not the direct cause of coral bleaching.
• Deep-Sea Mining:
• Deep-sea mining involves extracting minerals from the ocean floor. While it poses threats to deep-sea ecosystems, it has no direct link to coral bleaching in shallow reefs.
• Arctic Ice Melt:
• Melting Arctic ice contributes to global sea level rise and ocean circulation changes but is indirectly linked to coral bleaching as a consequence of global warming.
• Significance of Coral Reefs:
• Coral reefs support around 25% of all marine life, making them critical for biodiversity.
• They provide services such as coastal protection, food security, and tourism, contributing billions of dollars to global economies annually.
• Global Efforts to Mitigate Coral Bleaching:
• International initiatives like the Paris Agreement aim to limit global warming to below 2°C, reducing the risk of widespread coral bleaching.
• Programs like the Coral Triangle Initiative focus on sustainable management and conservation of coral reefs in the Indian and Pacific Oceans.

Important Points

• Coral Bleaching Events:
• The 2016 global bleaching event was one of the most severe, with extensive damage reported in the Great Barrier Reef and the Indian Ocean.
• Bleaching events are becoming more frequent and severe due to persistent global warming trends.
• Adaptation Strategies:
• Restoration efforts include coral farming and the development of heat-tolerant coral species.
• Marine protected areas (MPAs) are being established to safeguard coral reef ecosystems from human-induced pressures.

The correct answer is Ensuring the long-term sustainability of water sources and the quality of water supplied..

Key Points

• Ensuring the long-term sustainability of water sources: The success of the Jal Jeevan Mission depends on the availability of sustainable water sources. Over-extraction of groundwater, pollution, and irregular rainfall patterns have posed significant challenges in maintaining the availability of water resources.
• Water quality issues: Delivering safe drinking water is critical. Contaminants like arsenic, fluoride, and nitrates in groundwater, as well as bacterial contamination, make it difficult to ensure the supply of potable water to rural households.
• Climate change impact: Erratic rainfall patterns, frequent droughts, and depletion of water tables due to climate change exacerbate the problem of water source sustainability, directly impacting the mission's goals.
• Community participation and awareness: While the mission emphasizes local-level involvement, many communities lack the technical knowledge or resources to ensure the long-term sustainability of water sources and to monitor the quality of water supplied.
• Infrastructure maintenance: Even when functional household tap connections are provided, the infrastructure for water treatment, storage, and distribution must be regularly maintained to ensure sustainability and quality over time.

Additional Information

• Jal Jeevan Mission Overview:
• Launched by the Government of India in 2019, the mission aims to provide Functional Household Tap Connections (FHTCs) to every rural household by 2024.
• The mission promotes ‘Har Ghar Jal’ to ensure equitable water distribution.
• It focuses on community-led water management and emphasizes local governance through Gram Panchayats and Village Water & Sanitation Committees (VWSCs).
• Challenges Related to Other Options:
• Lack of sufficient funding: While funding is a challenge, the government has allocated substantial resources for the Jal Jeevan Mission. However, the issue of fund utilization and accountability is more critical than the lack of funding.
• Limited participation of local communities: Though local involvement is encouraged, it is secondary to the primary challenge of resource sustainability and water quality.
• Absence of a robust monitoring mechanism: Jal Jeevan Mission has implemented a digital dashboard to monitor progress, making this less critical compared to sustainability and quality issues.
• Key Data and Reports:
• As of 2023, 60% of rural households have been provided with tap water connections under the mission.
• WHO and UNICEF reports highlight that poor water quality is a major cause of waterborne diseases in rural areas, emphasizing the need for quality assurance.
• States like Rajasthan and Maharashtra face acute water scarcity, increasing the importance of sustainable water resource management.
• Solutions to Sustainability and Quality Challenges:
• Promoting rainwater harvesting and groundwater recharge.
• Conducting regular water quality testing to ensure safety standards.
• Building awareness campaigns for community participation in water resource management.
• Incorporating climate-resilient technologies for water conservation and distribution.

Important Points

• Budget Allocation: The Union Budget 2023-24 allocated ₹70,000 crore to the Jal Jeevan Mission, reflecting the government’s commitment to achieving its targets.
• Water Quality Monitoring: The mission mandates water quality testing through ISO-certified laboratories and field testing kits.
• Global Comparisons: Similar initiatives like China’s South-to-North Water Diversion Project highlight the importance of resource sustainability in water management projects.
• Digital Monitoring: The Jal Jeevan Mission dashboard provides real-time data on coverage, ensuring transparency and accountability.
• Significant Achievement: Villages declared ‘Har Ghar Jal’ are recognized for achieving 100% household tap water connection.

The correct answer is Pillared hall for worshippers.

Key Points

• The term mandapa refers to a pillared hall or pavilion that is an integral part of traditional Indian temple architecture. It is typically placed in front of the main sanctum (garbhagriha) of the temple.
• Mandapas serve as spaces where worshippers gather for prayers, rituals, and other religious activities. They act as transitional spaces leading to the sanctum.
• In most temples, the mandapa is intricately carved and decorated with sculptures, motifs, and symbols depicting mythological and religious themes.
• Depending on the scale of the temple, there may be multiple mandapas, such as the ardha-mandapa (half hall), maha-mandapa (great hall), or nata-mandapa (dance hall).
• Mandapas are a common feature of Hindu, Jain, and Buddhist temples across India, showcasing the architectural and artistic heritage of these traditions.

Additional Information

• Key Features of Mandapas:
• Mandapas are usually supported by a series of pillars, which are often elaborately carved with figures of deities, celestial beings, and floral designs.
• They are typically open or semi-open structures, allowing natural light and ventilation into the space.
• In larger temples, the mandapa may have a raised platform for conducting rituals and accommodating worshippers.
• Architectural Significance:
• The mandapa represents the intermediate space between the outer world and the sanctum, symbolizing the spiritual journey of devotees.
• In South Indian temples (Dravidian style), mandapas are often adorned with monolithic sculptures and serve as venues for temple festivals and ceremonies.
• In North Indian temples (Nagara style), the mandapa often has a shikhara (tower) above it, adding to the grandeur of the structure.
• Other Key Architectural Elements in Indian Temples:
• Garbhagriha: The innermost sanctum where the presiding deity is enshrined.
• Shikhara/Vimana: The tower or spire above the sanctum, symbolizing Mount Meru.
• Gopuram: The monumental gateway in South Indian temples.
• Pradakshina Patha: The circumambulatory path around the sanctum for devotional walks.
• Examples of Famous Temples with Mandapas:
• Brihadeshwara Temple, Tamil Nadu: Features a massive mandapa with intricate carvings.
• Sun Temple, Konark, Odisha: The mandapas here depict the chariot wheels of the Sun God.
• Meenakshi Temple, Madurai: Known for its thousand-pillar mandapa with exquisite sculptures.

Important Points

• Option 1 - Gateway Tower: This refers to the Gopuram in South Indian temple architecture, which serves as the entrance gate to the temple complex.
• Option 2 - Outer Boundary Wall: Temples often have a fortified prakaras (enclosure wall) to demarcate the sacred space.
• Option 4 - Water Tank: Many Indian temples have a temple tank or pond, often used for ritual purification.
• Each of these elements is significant but distinct from the role and structure of a mandapa in traditional Indian temples.

The correct answer is Rumtek Monastery.

Key Points

• Rumtek Monastery, located near Gangtok, the capital of Sikkim, is the largest and most famous monastery in the region.
• It was originally built in the 16th century by the 9th Karmapa Wangchuk Dorje, later renovated by the 16th Karmapa Rangjung Rigpe Dorje in the 1960s.
• This monastery serves as the seat of the Karma Kagyu lineage, one of the oldest schools of Tibetan Buddhism.
• Rumtek Monastery is renowned for its colorful murals, sacred thangkas (scroll paintings), and intricate architectural designs inspired by Tibetan Buddhist traditions.
• The monastery is famous for hosting the annual Chaams (mask dances), which are vibrant and culturally significant events depicting Buddhist stories and teachings.
• It is surrounded by serene landscapes and offers stunning views of the mountains, attracting visitors and devotees from around the world.

Additional Information

• Pemayangtse Monastery:
• Located in Pelling, Sikkim, this monastery is one of the oldest in the state, established in the 17th century.
• It follows the Nyingma sect of Tibetan Buddhism and is famous for its wooden structure depicting the heavenly palace of Guru Rinpoche.
• Enchey Monastery:
• Situated in Gangtok, this monastery belongs to the Nyingma sect and was constructed in the 19th century.
• It is known for its sacred significance and hosts vibrant festivals like Chaam dances during January.
• Tashiding Monastery:
• Located near Yuksom, Tashiding Monastery is considered one of the holiest sites in Sikkim.
• It follows the Nyingma tradition and is famous for its sacred water festival, Bumchu.
• Significance of Monasteries in Sikkim:
• Monasteries serve as centers for Buddhist learning, meditation, and rituals.
• They preserve Tibetan art, culture, and traditions, making them significant landmarks for cultural tourism.
• Sikkim is home to over 200 monasteries, many of which are centuries old.

Important Points

• Buddhist Festivals:
• The monasteries of Sikkim host various festivals like Losar (Tibetan New Year), Saga Dawa, and Chaams (mask dances), which are deeply rooted in Buddhist traditions.
• These festivals attract devotees and tourists, offering insight into Buddhist spirituality and cultural richness.
• Architectural Style:
• Monasteries in Sikkim exhibit Tibetan architectural styles, featuring intricate woodwork, vibrant murals, and sacred objects like prayer wheels and flags.
• They are often located in scenic areas, symbolizing peace and harmony.
• Cultural Tourism:
• Sikkim’s monasteries play a vital role in promoting cultural and spiritual tourism, contributing to the state's economy.
• Visitors can engage in meditation retreats, learn about Buddhism, and participate in local festivals.

The correct answer is David Diop.

Key Points

• David Diop won the International Booker Prize in 2021 for his novel At Night All Blood is Black.
• The book was translated from French to English by Megan McDowell, and the prize is awarded jointly to the author and translator.
• At Night All Blood is Black is a profound exploration of themes such as war, trauma, and brotherhood, set during World War I.
• The novel received critical acclaim for its lyrical prose, emotional depth, and depiction of the psychological effects of war.
• David Diop is a French author of Senegalese descent, and this recognition highlights the growing diversity in global literature.

Additional Information

• International Booker Prize:
• The prize is awarded annually for the best book translated into English and published in the UK or Ireland.
• It celebrates both the author and translator, with the £50,000 prize split equally between them.
• The prize aims to promote international literature and encourage translations of works from diverse languages.
• David Diop:
• Born in 1966, David Diop is a French writer and professor of literature.
• His novel At Night All Blood is Black was inspired by accounts of African soldiers who fought for France during World War I.
• Diop's work often explores themes of identity, history, and the human condition.
• At Night All Blood is Black:
• The novel tells the story of a Senegalese soldier in the French army who struggles with guilt and grief after losing his best friend in battle.
• It delves into the psychological toll of war and the cultural tensions faced by African soldiers in Europe.
• The book has been praised for its poetic language and powerful portrayal of wartime experiences.
• Other Notable Winners:
• Olga Tokarczuk won the prize in 2018 for her novel Flights.
• Jokha Alharthi won in 2019 for her novel Celestial Bodies, becoming the first Arabic-language author to win the prize.
• Mariana Enriquez, though nominated, has not won the prize yet.

Important Points

• Translation in Literature:
• Translation plays a critical role in making global literature accessible to wider audiences.
• It allows readers to engage with diverse cultural perspectives and literary traditions.
• The International Booker Prize emphasizes the importance of translators in the literary world.
• Prominent Themes in At Night All Blood is Black:
• War: The novel vividly depicts the horrors of war and its impact on soldiers' mental health.
• Brotherhood: The protagonist’s relationship with his fallen friend drives the narrative.
• Identity: It explores the cultural and racial challenges faced by African soldiers in a European army.
• Impact of the Prize:
• Winning the International Booker Prize brings global recognition to authors and translators.
• It often leads to increased readership and translations of their works into other languages.
• The prize contributes to the promotion of global literary diversity.

The correct answer is Eldhose Paul.

Key Points

• Eldhose Paul became the first Indian to win a gold medal in triple jump at the Commonwealth Games (CWG) 2022 held in Birmingham.
• He achieved this historic milestone on August 7, 2022, with a best jump of 17.03 meters, showcasing exceptional skill and determination.
• Paul's victory marked a significant achievement for Indian athletics as it was the first-ever gold medal in triple jump at the Commonwealth Games.
• His gold medal performance led to a double podium finish for India, with Abdulla Aboobacker securing the silver medal in the same event.
• The win highlighted India's growing dominance in athletics on the global stage, especially in field events.

Additional Information

• Commonwealth Games 2022:
• The 2022 Commonwealth Games were held in Birmingham, England, from July 28 to August 8, 2022.
• India sent a 215-member contingent to compete in 16 sports, winning a total of 61 medals (22 gold, 16 silver, and 23 bronze).
• Eldhose Paul:
• Born in Kerala, India, Eldhose Paul is a professional athlete specializing in the triple jump.
• He is part of the Indian Navy and has represented India in multiple international athletics events.
• Paul's performance at CWG 2022 was a result of years of rigorous training and dedication.
• Triple Jump:
• The triple jump is a track and field event where athletes perform a hop, step, and jump into a sandpit.
• The event requires a combination of speed, strength, and technique to achieve maximum distance.
• India has been gaining recognition in this discipline, with athletes like Eldhose Paul and Abdulla Aboobacker making significant contributions.
• Other Indian Achievements at CWG 2022:
• Murali Sreeshankar: Won a silver medal in the men's long jump event, making history as India's first medalist in the discipline at CWG.
• Avinash Sable: Secured a silver medal in the 3000m steeplechase, breaking the Kenyan dominance in the event.
• Neeraj Chopra: Although absent in CWG 2022 due to injury, he remains an inspiration in Indian athletics with his Olympic gold in javelin throw.

Important Points

• India's Performance in Athletics:
• India has been steadily improving in athletics, with athletes excelling in both track and field events on the global stage.
• Other notable field event athletes include Neeraj Chopra, Annu Rani, and Tajinderpal Singh Toor.
• Significance of CWG 2022:
• The event provided a platform for Indian athletes to showcase their talent and gain international recognition.
• India's successes in disciplines like weightlifting, wrestling, and badminton further solidified its position as a sporting powerhouse.

The correct answer is The Subsidiary Alliance system had which of the following conditions for the allied Indian rulers?.

Key Points

• Statement 1: They were allowed to maintain their own independent armies. This statement is incorrect as the Subsidiary Alliance system required allied Indian rulers to disband their independent armies and instead rely on British forces for defense.
• Statement 2: They had to keep a British Resident in their court. This statement is correct. Under the Subsidiary Alliance, the allied Indian rulers were required to maintain a British Resident at their court to oversee administrative matters and safeguard British interests.
• Statement 3: They were free to enter into alliances with other Indian rulers without British consent. This statement is incorrect. The system explicitly prohibited allied Indian rulers from entering into diplomatic or military alliances with other rulers without British approval.
• Statement 4: They were not required to pay any revenue to the British. This statement is incorrect. The allied rulers had to pay a subsidy or revenue to the British for the maintenance of the British troops stationed within their territories.
• Correct Answer: The correct condition under the Subsidiary Alliance was that allied Indian rulers had to keep a British Resident in their court (Statement 2).

Additional Information

• Subsidiary Alliance System:
• The Subsidiary Alliance system was introduced by Lord Wellesley, the Governor-General of India from 1798 to 1805, as part of British expansionist policies in India.
• It was designed to establish British dominance over Indian states without direct annexation, enabling the British to control the political and military affairs of allied states.
• Allied rulers under the Subsidiary Alliance system had to accept the presence of British troops within their territories.
• They were required to pay a financial subsidy to the British for maintaining these troops, which often led to financial strain on the allied states.
• Key Features of Subsidiary Alliance:
• Allied rulers had to disband their independent armies and rely on British forces for protection against external and internal threats.
• The British Resident stationed at the ruler's court acted as a political agent and monitored the ruler's actions to ensure alignment with British policies.
• Allied rulers were prohibited from entering into alliances or engaging in diplomatic relations with other states without British approval.
• The system often resulted in the erosion of sovereignty and autonomy of Indian rulers, making them dependent on British support.
• Examples of States under Subsidiary Alliance:
• Hyderabad: The Nizam of Hyderabad was among the first rulers to accept the Subsidiary Alliance in 1798.
• Mysore: After the defeat of Tipu Sultan in the Fourth Anglo-Mysore War, Mysore was brought under the Subsidiary Alliance in 1799.
• Awadh: The Nawab of Awadh signed the Subsidiary Alliance in 1801, leading to significant British control over the region.

Important Points

• Consequences of Subsidiary Alliance:
• The system led to the loss of sovereignty and independence of Indian states, turning them into British dependencies.
• It facilitated the expansion of British influence and control over Indian territories without direct annexation.
• The financial burden of maintaining British troops often led to economic decline and political instability in allied states.
• Many Indian rulers resented the system, considering it an infringement on their autonomy and dignity.
• Historical Context:
• The Subsidiary Alliance system played a crucial role in the establishment of British dominance in India during the late 18th and early 19th centuries.
• It was an essential component of British imperial policies aimed at controlling Indian territories through indirect means.
• The system laid the foundation for subsequent British annexations and consolidation of power in India.

The correct answer is It is admissible only if the original is lost, destroyed, or unavailable for valid reasons.

Key Points

• Secondary evidence refers to a reproduction or substitution of original documents, such as photocopies, scanned documents, or certified copies, which can be admitted in court under specific conditions.
• According to the BSA, 2023, secondary evidence is admissible only when the original document is proven to be lost, destroyed, or unavailable for valid and reasonable reasons.
• Such evidence must satisfy the court's conditions of authenticity and reliability before being admitted as valid proof.
• Secondary evidence is not preferred over primary evidence, as primary evidence (original documents) is always prioritized in legal proceedings due to its higher authenticity.
• The rule ensures that secondary evidence is used only as a last resort when all efforts to produce the original have been exhausted.

Additional Information

• Primary Evidence:
• It refers to the original document itself, presented in its original form.
• Under the law, primary evidence is considered the best evidence and is always given preference in court.
• Examples include original contracts, deeds, or physical copies of signed agreements.
• Admissibility of Secondary Evidence:
• Secondary evidence is only admissible under the following conditions:
• The original is lost or destroyed.
• The original is in possession of a third party who refuses to produce it despite legal notices.
• The original is in a location inaccessible due to valid reasons, such as being in a foreign jurisdiction.
• Examples include certified copies, duplicates, or digitally scanned versions of documents.
• Legal Principles:
• The principle of best evidence ensures that the original document is presented whenever possible to avoid manipulation or misrepresentation.
• Secondary evidence is subjected to rigorous scrutiny to verify its accuracy and genuineness.
• Examples of Secondary Evidence Usage:
• A photocopy of a lost will submitted as evidence after proving the original was destroyed in an accident.
• Scanned images of contracts used in cases where the originals are retained by an inaccessible party.

Important Points

• Option 1: "It is always preferred over primary evidence" - This is incorrect as primary evidence is always preferred over secondary evidence in legal proceedings.
• Option 3: "It must be printed in color only" - This is incorrect because there is no legal requirement for secondary evidence to be in color.
• Option 4: "It cannot be used in criminal cases" - This is incorrect as secondary evidence can be used in criminal cases provided it meets the admissibility requirements.

The correct answer is AP Singh.

Key Points

• AP Singh was commissioned into the fighter stream of the Indian Air Force (IAF) in December 1984, making him a significant figure in the Indian Air Force's history.
• He has had a distinguished career in the IAF, holding key operational and administrative positions during his tenure.
• As a fighter pilot, he has been part of several critical missions, contributing to the defense and operational strategies of the Indian Air Force.
• His leadership and expertise in the fighter stream have earned him numerous accolades and recognition within the armed forces.
• AP Singh’s commissioning in December 1984 aligns with the timeline mentioned in the question, confirming him as the correct answer.

Additional Information

• Indian Air Force (IAF):
• The Indian Air Force is the air arm of the Indian Armed Forces, established on 8 October 1932.
• It plays a crucial role in securing Indian airspace and conducting aerial warfare during conflicts.
• The IAF is one of the largest and most advanced air forces in the world.
• Fighter Stream:
• The fighter stream of the IAF is responsible for conducting offensive and defensive aerial operations.
• It includes aircraft like Sukhoi Su-30MKI, Mirage-2000, Tejas, MiG-29, and Rafale, which are used for air-to-air combat, ground attacks, and strategic missions.
• Fighter pilots undergo rigorous training to handle these sophisticated aircraft and engage in high-pressure situations.
• Commissioning into IAF:
• Commissioning is the process by which individuals are officially inducted into the armed forces as officers.
• In the IAF, officers are commissioned through academies such as the National Defence Academy (NDA), Air Force Academy (AFA), or via other direct entry schemes.
• During commissioning, officers are assigned to various streams like fighter, transport, or helicopter based on their aptitude and training.
• Distinguished Air Chiefs:
• Over the years, the IAF has seen several notable Air Chiefs who contributed to the modernization and operational readiness of the force.
• Leaders like RKS Bhadauria, B S Dhanoa, and Vivek Ram Chaudhari have played key roles in enhancing the capabilities of the IAF.

Important Points

• RKS Bhadauria: He was the 26th Chief of Air Staff and played a key role in the induction of the Rafale fighter jets into the IAF.
• B S Dhanoa: Known for his leadership during the 2016 surgical strikes and the Balakot airstrikes.
• Vivek Ram Chaudhari: Current Chief of Air Staff (as of 2023) with significant contributions to operational readiness and strategic planning.

The correct answer is There is clear evidence for the practice of Sati..

Key Points

• The worship of Pashupati: The Harappan civilization practiced religious rituals, and seals depicting a male deity resembling Lord Shiva, referred to as "Pashupati," have been found. These depictions suggest the worship of a male deity in Harappan culture. Hence, this statement is correct.
• Women wearing ornaments: Archaeological evidence, such as figurines and jewelry, confirms that women in the Harappan civilization wore ornaments made of gold, silver, copper, and bronze. These artifacts highlight the advanced craftsmanship of the Harappans. Hence, this statement is correct.
• Practice of Sati: There is no evidence to suggest that the Harappan civilization practiced Sati. Sati, the ritual of a widow immolating herself on her husband's funeral pyre, emerged much later in Indian history and is associated with a different cultural context. Hence, this statement is incorrect.
• Main crops grown: Wheat and barley were indeed the primary crops cultivated by the Harappans. Evidence from granaries and other agricultural artifacts confirms their reliance on these crops for sustenance. Hence, this statement is correct.

Additional Information

• Harappan Civilization Overview:
• The Harappan civilization, also known as the Indus Valley Civilization, flourished between 2600 BCE to 1900 BCE in the northwestern regions of South Asia.
• It spanned modern-day Pakistan and parts of northwestern India, with prominent cities like Harappa, Mohenjo-Daro, Lothal, and Dholavira.
• Religious Practices:
• The Harappans worshipped natural elements, animals, and male and female deities. The "Pashupati seal" suggests the worship of a proto-Shiva figure.
• Terracotta figurines and seals also indicate the worship of Mother Goddess, symbolizing fertility.
• Jewelry and Ornaments:
• Harappan craftsmanship was highly advanced, evident in gold, silver, and copper ornaments. Beads, bangles, and necklaces were common among women and men.
• Such ornaments were often traded, highlighting the civilization's commercial prowess.
• Agriculture:
• The Harappans were skilled agriculturalists, cultivating crops like wheat, barley, peas, and sesame.
• They used advanced irrigation techniques and plowed fields using oxen, as evidenced by terracotta models of plows.

Important Points

• Absence of Sati Practice:
• The Harappan civilization's burial practices included extended burials, pot burials, and wooden coffins. These were devoid of rituals like Sati, which became prominent in later periods.
• Sati is historically linked to the post-Vedic and medieval period in India, primarily among specific communities.
• Trade and Economy:
• The Harappans engaged in trade with Mesopotamia and other regions, exchanging goods like cotton, metals, and ornaments.
• Seals and scripts found at Harappan sites point to a well-organized economic system.
• Architectural Advancements:
• Harappan cities were characterized by grid layouts, advanced drainage systems, and public baths, showcasing their expertise in urban planning.
• Structures like the Great Bath of Mohenjo-Daro highlight their architectural prowess and cultural significance.

The correct answer is Both 1 and 2.

Key Points

• Statement 1: The Himalayan belt of India consists of copper, zinc, cobalt, and lead.
• The Himalayan region is rich in mineral resources like copper, zinc, lead, cobalt, and other metallic minerals.
• This is due to the geological structure and tectonic activities in the region, which have resulted in the formation of mineral-rich zones. Hence, this statement is correct.
• Statement 2: Most of the building stones, such as granite, marble, and gypsum, are found in Rajasthan.
• Rajasthan is well-known for its vast reserves of building stones like granite, marble, sandstone, and gypsum.
• The state contributes significantly to India's production of these materials and is often referred to as the hub for marble and sandstone mining. Hence, this statement is correct.
• As both statements are correct, the correct answer is Both 1 and 2.

Additional Information

• Mineral Resources in the Himalayan Belt:
• The Himalayan region, due to its complex geological structure, is rich in metallic minerals like copper, lead, zinc, and cobalt.
• Some parts of the Himalayan belt are also known for the presence of mica, gypsum, and other non-metallic minerals.
• These resources play a key role in the industrial development of the region, especially in states like Himachal Pradesh, Uttarakhand, and Jammu & Kashmir.
• Building Stones in Rajasthan:
• Rajasthan is India's largest producer of marble, contributing significantly to both domestic use and export.
• The state is also rich in granite, which is used extensively for construction and decorative purposes.
• Gypsum, another important resource found in Rajasthan, is used in the production of cement, plaster, and other construction materials.
• Key regions in Rajasthan for mineral extraction include Kishangarh, Makrana, and Udaipur.
• Importance of Minerals in India:
• India is rich in mineral diversity, which contributes to its economic development.
• Minerals like iron ore, coal, bauxite, and limestone are critical for industries like steel, power, and cement.
• The country is also a significant producer of mica, manganese, and chromite.
• Geological Factors:
• The geological structure of India, including its Precambrian rocks, Gondwana formations, and the Himalayan orogeny, has contributed to the rich distribution of minerals.
• Regions like the Aravalli range (Rajasthan) and the Vindhyan system are known for their mineral wealth.

The correct answer is 2, 3, and 4 only.

Key Points

• Statement 1: For the initial two stages of the demographic cycle, a high fertility rate and death rate would result in high population growth.
  

This statement is incorrect. In the first two stages of the demographic transition, while both fertility and death rates are high, population growth remains low due to the balance between the two. Only in the latter part of the second stage does population growth increase due to a decline in mortality while fertility remains high.

• Statement 2: In the third stage, both fertility and mortality factors would decline significantly.
  

This statement is correct. The third stage is characterized by a significant decline in both fertility and mortality rates, leading to a slowing of population growth.

• Statement 3: The demographic transition theory does not explicitly take into account the migration factor.
  

This statement is correct. The theory primarily focuses on birth and death rates and their impact on population growth, excluding migration as a variable in its framework.

• Statement 4: Social and cultural factors can greatly affect the population, which can impact what the theory predicts.
  

This statement is correct. Social and cultural factors such as traditions, education, and economic conditions can influence fertility and mortality rates, thereby affecting the outcomes predicted by the demographic transition theory.

• Hence, the correct answer is 2, 3, and 4 only.

Additional Information

• Demographic Transition Theory:
• The theory describes the transition of a population from high birth and death rates to low birth and death rates as a country develops economically.
• It is divided into four stages: High Stationary, Early Expanding, Late Expanding, and Low Stationary.
• The theory was developed based on observations of demographic changes in Western countries during the Industrial Revolution.
• Stages of Demographic Transition:
• Stage 1: High birth and death rates lead to a stable and low population growth.
• Stage 2: Death rates decline due to better healthcare and sanitation, while birth rates remain high, resulting in rapid population growth.
• Stage 3: Birth rates begin to decline due to societal changes such as urbanization and education, causing population growth to slow down.
• Stage 4: Both birth and death rates are low, leading to stable or even declining population growth.
• Factors Excluded from the Theory:
• Migration is not considered a factor in the demographic transition theory, despite its impact on population size and structure.
• External factors like wars, pandemics, or government policies are also not included in the theory.
• Impact of Social and Cultural Factors:
• Social norms, traditions, and cultural values can influence fertility rates significantly.
• Economic conditions such as poverty or wealth also impact birth and death rates.
• Government initiatives like family planning programs can accelerate or decelerate demographic transitions.

The correct answer is Agra Gharana.

Key Points

• The Agra Gharana traces its lineage back to the dhrupad tradition, one of the oldest forms of Indian classical music. It is directly influenced by the techniques and aesthetics of dhrupad singing.
• The gharana emphasizes razakhani and nomtom alap, which are stylistic features derived from the dhrupad tradition, showcasing its strong connection to the genre.
• The founder of the Agra Gharana, Haji Sujan Khan, was deeply rooted in the dhrupad style. His descendants further developed the gharana by incorporating khayal and other contemporary styles.
• Agra Gharana is known for its robust voice culture and the ability to blend elements of dhrupad with khayal singing, maintaining the discipline and purity of the tradition.
• Its compositions often include long and intricate alap (improvisations) and layakari (rhythmic interplay), hallmarks of the dhrupad tradition.

Additional Information

• Gwalior Gharana:
• The Gwalior Gharana is the oldest khayal gharana but does not have direct roots in the dhrupad tradition.
• Founded by Natthan Khan and Haddu Khan, it focuses on simplicity and melody in its compositions, prioritizing clear enunciation of lyrics and raga development.
• It emphasizes the use of taans (fast melodic patterns) and bol-baant (syllabic rhythm patterns).
• Jaipur-Atrauli Gharana:
• This gharana is known for its complex and intricate raga structures but is not directly influenced by the dhrupad tradition.
• Founded by Alladiya Khan, it specializes in rare ragas and emphasizes perfect intonation and elaborate improvisation.
• The gharana uniquely combines academic rigor with aesthetic appeal.
• Rampur-Sahaswan Gharana:
• This gharana emphasizes the purity of ragas and is known for the clarity and precision of its compositions.
• It was founded by Inayat Hussain Khan but does not have direct ties to the dhrupad tradition.
• The Rampur-Sahaswan style incorporates elements of both khayal and thumri singing.
• Characteristics of Dhrupad:
• Dhrupad is the oldest surviving genre of Hindustani classical music, originating in medieval India.
• It emphasizes spiritual and meditative elements, with compositions focusing on devotional themes.
• Key features include nomtom alap (rhythmic syllables) and intricate rhythmic patterns.
• It uses a deep and resonant voice and prioritizes purity of notes and ragas.

Important Points

• The Agra Gharana is a unique blend of dhrupad and khayal styles, showcasing a transition from ancient to modern musical traditions.
• It focuses on voice modulation, intricate improvisations, and rhythmic play, preserving the essence of dhrupad while embracing the dynamism of khayal.
• Other gharanas such as Gwalior, Jaipur-Atrauli, and Rampur-Sahaswan have their distinct styles but lack direct influence from the dhrupad tradition.

The correct answer is Only 1 is Correct.

Key Points

• Statement 1: A team gaining ball possession must attempt a shot within 24 seconds, or it results in a shot clock violation.
  
• This statement is correct. In basketball, the shot clock rule enforces that a team must take a shot within a stipulated time (24 seconds in professional games, such as the NBA). This ensures the game remains fast-paced and competitive.
• Statement 2: A disqualification foul is awarded only when a player accumulates five personal fouls.
  
• This statement is incorrect. The disqualification foul criteria depend on the competition. For example, in the NBA, players are disqualified after six personal fouls, while in FIBA (International Basketball Federation), it is five personal fouls.
• Statement 3: Reverse spin dribble is a defensive maneuver used exclusively for ball interception.
  
• This statement is incorrect. A reverse spin dribble is an offensive technique used by players to evade defenders and maintain possession, not a defensive maneuver.

Additional Information

• Shot Clock Rule:
• The shot clock in basketball is a timer designed to speed up the game by requiring teams to attempt a field goal within a specific time.
• In the NBA, the shot clock is 24 seconds, while in NCAA basketball (college-level), it is 30 seconds.
• If the offensive team fails to attempt a shot within the time limit, it results in a "shot clock violation," and possession is handed over to the opposing team.
• Personal Fouls and Disqualification:
• A personal foul is a breach of the rules that involves illegal contact with an opponent.
• In the NBA, players are disqualified upon committing their sixth personal foul. In FIBA rules, the limit is five personal fouls.
• Disqualification fouls can also occur for unsportsmanlike or flagrant behavior, depending on the referee's judgment.
• Reverse Spin Dribble:
• The reverse spin dribble is an advanced dribbling technique where the player pivots and uses a spin motion to change direction.
• This maneuver is used to evade defenders and create space for a shot or pass.
• It is an offensive skill and has no application in defense or ball interception.

Important Points

• Basketball Rules:
• Basketball has two main governing bodies: the NBA (National Basketball Association) and FIBA (International Basketball Federation). Rules may differ slightly between the two.
• The game is played with two teams of five players each, aiming to score points by shooting the ball through the opponent's hoop.
• Fouls and Violations:
• Common fouls include personal fouls, technical fouls, and flagrant fouls.
• Violations like traveling, double dribbling, and the shot clock violation disrupt the flow of the game and result in turnovers.
• Skills and Techniques:
• Players use various offensive skills, including dribbling, shooting, and passing, to outmaneuver their opponents.
• Defensive skills include blocking, stealing, and positioning to disrupt the opponent's plays.

The correct answer is One-fifth of war booty and hidden wealth.

Key Points

• Khums is an Islamic tax, which literally means "one-fifth." It refers to the obligation of Muslims to pay 20% of certain types of wealth.
• Khums is primarily applied to war booty and hidden wealth discovered unexpectedly, such as treasures found underground. It is considered a mandatory tax under Islamic law.
• This tax is divided into two equal parts: one part goes to the Imam or religious leader, and the other part is distributed among needy categories such as orphans, the poor, and travelers.
• In the context of medieval Islamic states, Khums served as a crucial source of revenue for the ruler and the state, supporting both governance and religious functions.
• The concept of Khums is derived from the Quran, specifically from Surah Al-Anfal (8:41), which mentions that one-fifth of the spoils of war belongs to Allah, the Prophet, his relatives, orphans, and the needy.

Additional Information

• Islamic Taxation System:
• Islamic taxation includes various types of obligatory payments such as Zakat, Khums, and Jizya, each serving distinct purposes in society.
• Zakat is a mandatory charitable contribution, typically 2.5% of a Muslim's savings, aimed at helping the poor and needy.
• Jizya is a tax imposed on non-Muslim subjects of an Islamic state as a form of protection and exemption from military duties.
• Ushr refers to a tax on agricultural produce, generally set at 10% of the harvest.
• Historical Context of Khums:
• In medieval Islamic states, Khums was particularly significant during wars and conquests, as it applied to the spoils of war.
• It was one of the mechanisms to ensure the equitable distribution of wealth among the community while funding administrative and religious responsibilities.
• The tax facilitated the functioning of Islamic governance and supported the spread of Islam during the medieval period.
• Application of Khums:
• Khums is obligatory upon all Muslims under specific conditions. For example, it applies to war booty, discovered treasures, certain types of earnings, and unused savings after expenses.
• In the Shiite tradition, Khums also extends to net earnings after deducting necessary expenses, making it a broader form of taxation.
• Comparison with Other Taxes:
• Unlike Zakat, which is a fixed annual obligation, Khums is situational, depending on the acquisition of specific types of wealth.
• It is distinct from Jizya, which is levied on non-Muslims, and Ushr, which is tied to agricultural produce.

Important Points

• Historical Example: The implementation of Khums was observed during the early Islamic caliphates, where it played a significant role in the redistribution of wealth obtained from conquests.
• Modern Practice: In contemporary times, Khums is primarily observed among Shiite Muslims, with specific guidelines provided by religious scholars and leaders.
• Quranic Basis: The concept of Khums is rooted in Islamic scripture, ensuring its significance in Islamic jurisprudence and theology.
• Role in Islamic Society: Khums contributes to social welfare and religious activities, emphasizing the importance of wealth redistribution in Islam.
• Administration: Historically, the collection and distribution of Khums were managed by the ruler or religious authorities, ensuring adherence to Islamic principles.

The correct answer is Bhubaneswar, Odisha.

Key Points

• The Yonex-Sunrise 47th Inter State - Inter Zonal & Junior National Badminton Championships 2024 was held in Bhubaneswar, Odisha, a city well-known for hosting major sporting events and promoting badminton at the grassroots level.
• Bhubaneswar is a key hub for sports in India, with infrastructure such as Kalinga Stadium, which frequently hosts national and international sporting events.
• The event featured participation from various state and zonal teams across India, bringing together young badminton players to compete at a high level of intensity and skill.
• This championship is vital for nurturing and identifying future badminton talents in India, contributing to the development of the sport nationally. Yonex-Sunrise brand, a globally renowned sports equipment company, sponsors this prestigious badminton event, ensuring high standards for both players and the audience.

Additional Information

• Badminton Championships:
• The Junior National Badminton Championships are organized annually by the Badminton Association of India (BAI).
• The championships are divided into Inter-State and Inter-Zonal categories, where players represent their states or zones in team events.
• The championship aims to foster competitive spirit among young players and provide a platform for budding talents to showcase their skills.
• These events are crucial for selecting players for international tournaments like the Thomas Cup, Uber Cup, and Sudirman Cup.
• Importance of Bhubaneswar in Sports:
• Bhubaneswar has emerged as a sports capital of India, hosting prominent events like the Hockey World Cup and Asian Athletics Championships.
• The city has world-class facilities like the Kalinga Stadium, which is equipped to host multiple sports, including badminton, hockey, and athletics.
• Government initiatives and investments have transformed Bhubaneswar into a hub for sports training and development.
• Yonex-Sunrise Partnership:
• Yonex-Sunrise is a major sponsor of badminton in India and has been instrumental in supporting tournaments and providing premium equipment to players.
• The brand sponsors several national and international badminton tournaments, contributing to the sport's growth globally.
• Yonex-Sunrise's involvement ensures high-quality standards for equipment, promoting better performance for athletes.
• Badminton in India:
• Badminton is one of the most popular sports in India, with players like P.V. Sindhu, Saina Nehwal, and Kidambi Srikanth achieving international acclaim.
• India has a strong presence in badminton globally, with significant performances in tournaments like the Olympics, World Championships, and BWF tournaments.
• Grassroots initiatives and championships like this one are vital for nurturing young talent and ensuring India's continued success in the sport.

Important Points

• Badminton Association of India (BAI):
• BAI is the governing body for badminton in India, responsible for organizing tournaments and developing the sport at all levels.
• It conducts championships such as the National Badminton Championships and provides training opportunities to players.
• Development of Sports in Odisha:
• The Odisha government has invested heavily in sports infrastructure, making the state a hub for national and international events.
• Initiatives like the Odisha Sports Development Fund have boosted sports development and athlete training.
• Key Achievements:
• India's badminton players have consistently won medals in global events, including Olympic bronze and silver medals.
• Events like the Junior National Championships are instrumental in identifying talents who can represent India on the international stage.

The correct answer is Helium.

Key Points

• An alpha particle consists of two protons and two neutrons, which is the same as the nucleus of a helium atom. Hence, the correct answer is helium.
• In the process of alpha decay, an unstable nucleus emits an alpha particle to achieve a more stable state, reducing its atomic number by 2 and mass number by 4.
• The emitted alpha particle is positively charged because it contains two protons but no electrons.
• Alpha decay typically occurs in heavy elements like uranium, thorium, or radium, where the nucleus has excess energy or is unstable due to its large size.
• The process of alpha emission decreases the element's position on the periodic table by two places, transforming it into a different element.

Additional Information

• Alpha Decay Process:
• Alpha decay is a type of radioactive decay in which an unstable atomic nucleus releases an alpha particle.
• The general representation of alpha decay is: Parent Nucleus → Daughter Nucleus + Alpha Particle (He²⁺).
• For example, Uranium-238 undergoes alpha decay to form Thorium-234: U-238 → Th-234 + He²⁺.
• Characteristics of Alpha Particles:
• Alpha particles are large and heavy compared to other types of radioactive emissions like beta particles or gamma rays.
• They have low penetration power and can be stopped by a sheet of paper or human skin.
• Due to their high mass and charge, alpha particles are highly ionizing, meaning they can cause significant damage to biological tissues if ingested or inhaled.
• Comparison with Other Particles:
• Hydrogen: A hydrogen atom consists of one proton and one electron, and it is unrelated to alpha decay.
• Lithium: Lithium is a light element with three protons and is not emitted during alpha decay.
• Deuterium: Deuterium is a heavy isotope of hydrogen with one proton and one neutron, also unrelated to alpha decay.
• Applications of Alpha Particles:
• Alpha particles are used in smoke detectors and certain types of cancer treatments, such as targeted alpha therapy (TAT).
• They are also employed in scientific research to study atomic structures and nuclear reactions.
• Important Examples of Alpha-Emitting Elements:
• Uranium (U): A well-known radioactive element undergoing alpha decay.
• Radium (Ra): Known for its use in early medical treatments and its radioactive properties.
• Polonium (Po): A highly radioactive element used in some industrial applications.

The correct answer is Jharkhand.

Key Points

• Jhumair is a popular folk dance that originates from the state of Jharkhand, India.
• This dance form is predominantly performed by the tribal communities of Jharkhand and is deeply rooted in their cultural traditions.
• Jhumair is primarily performed during festivals, social gatherings, and special occasions such as marriages or harvest celebrations.
• The dance is accompanied by traditional musical instruments like drums (dhol), nagara, and flute, which enhance its rhythmic and vibrant appeal.
• It is characterized by graceful movements and is performed in groups, often symbolizing unity and joy within the community.

Additional Information

• Jhumair's Cultural Significance:
• It is not just a dance but a means of storytelling, where performers depict themes of love, nature, and daily life.
• The dance is often performed in a circle, symbolizing harmony and equality within the community.
• Jhumair is an expression of gratitude towards nature and a celebration of life.
• Other Folk Dances of Jharkhand:
• Chhau Dance: A semi-classical dance form that incorporates martial arts and is performed during festivals like Chaitra Parva.
• Paika Dance: A traditional war dance performed with swords and shields, symbolizing valor.
• Santhal Dance: Performed by the Santhal tribe, it is a celebration of nature, harvest, and community spirit.
• Comparison with Other States:
• Odisha: Known for dances like Odissi (classical) and Sambalpuri (folk).
• West Bengal: Famous for dances like Baul and Raibeshe.
• Gujarat: Renowned for Garba and Dandiya Raas, which are associated with Navratri celebrations.
• Role of Folk Dances in India:
• Folk dances like Jhumair play a vital role in preserving the cultural heritage of India.
• They serve as a medium for cultural exchange and help in uniting diverse communities.
• These dances are often tied to seasonal or agricultural cycles, reflecting the deep connection between people and nature.

Important Points

• Traditional Instruments: Instruments like mandar, dhol, and flute play a crucial role in enhancing the appeal of Jhumair.
• Community Participation: Both men and women actively participate in this dance, showcasing gender equality in cultural practices.
• Preservation Efforts: With modernization, initiatives have been taken to document and promote such folk traditions to prevent their decline.
• UNESCO Recognition: Some Indian folk dances, including Chhau from neighboring regions, have gained global recognition, inspiring efforts to preserve dances like Jhumair.

The correct answer is World Bank.

Key Points

• The Logistics Performance Index (LPI) is a biennial index published by the World Bank. It was first introduced in 2007.
• The LPI measures the ease and efficiency of logistics in a country, providing a global benchmark for logistics and trade facilitation performance.
• The index evaluates countries based on six key components: Customs performance, infrastructure quality, ease of arranging shipments, quality of logistics services, tracking & tracing, and timeliness.
• In the 2023 edition, the LPI ranked 139 countries, using data collected through surveys of logistics professionals and quantitative data from global supply chains.
• The LPI is considered a critical tool for policymakers to identify areas of improvement in their trade logistics and supply chain management processes.

Additional Information

• World Bank:
• The World Bank was founded in 1944 and is headquartered in Washington, D.C., United States.
• Its primary mission is to provide financial and technical assistance to developing countries for development projects such as infrastructure, healthcare, and education.
• It comprises five institutions, the most notable being the International Bank for Reconstruction and Development (IBRD) and the International Development Association (IDA).
• In the context of the LPI, the World Bank aims to enhance global trade efficiency and support countries in improving their trade logistics capabilities.
• Other Options Explained:
• IMF (International Monetary Fund): The IMF primarily focuses on economic stability, exchange rates, and global monetary cooperation. It does not publish indices related to logistics.
• WTO (World Trade Organization): The WTO deals with the rules of trade between nations and resolving trade disputes, not specific logistics performance indices.
• UNCTAD (United Nations Conference on Trade and Development): UNCTAD works on trade and development issues, particularly for developing nations, but does not publish the LPI.
• Components of LPI:
• Customs: Efficiency and effectiveness of customs clearance processes.
• Infrastructure: Quality of trade and transport infrastructure.
• Ease of arranging shipments: Competitiveness of prices for international shipments.
• Logistics quality: Competence and quality of logistics services.
• Tracking & tracing: Ability to track and trace consignments.
• Timeliness: Frequency of shipments reaching their destination within the scheduled or expected delivery time.
• Important Points:
• The LPI is based on a combination of both qualitative and quantitative data, making it a unique and comprehensive measurement tool.
• Top-performing countries in the LPI typically include nations with advanced infrastructure and streamlined customs processes, such as Germany, Singapore, and Sweden.
• Developing nations use the LPI as a benchmark to identify and address weaknesses in their logistics systems.

The correct answer is Only Statement 1 is correct.

Key Points

• Statement 1: Income tax and dividends from Public Sector Undertakings (PSUs) are classified as revenue receipts in the government budget because they are recurring incomes for the government without creating any liabilities. Hence, statement 1 is correct.
• Statement 2: Disinvestment in PSUs is classified as a capital receipt in the government budget, not a revenue receipt. This is because disinvestment involves the sale of government assets, which is a one-time transaction and leads to a reduction in government assets rather than generating recurring income. Hence, statement 2 is incorrect.
• Revenue Receipts: These include income earned by the government through taxation (like income tax, GST, etc.) and non-tax revenues (like dividends from PSUs, interest on loans given by the government, etc.). They do not lead to an increase in liabilities or a decrease in assets.
• Capital Receipts: These involve transactions that lead to either an increase in liabilities (like borrowing) or a decrease in assets (like disinvestment or sale of government property).
• Classification of Receipts: The distinction between revenue receipts and capital receipts is crucial in government budgeting as it helps in understanding the government’s financial health and sustainability of income sources.

Additional Information

• Revenue Receipts:
• These are non-redeemable and do not involve any repayment of liabilities.
• Examples include tax revenues (like corporate tax, income tax, excise duty, customs duty) and non-tax revenues (like interest, dividends, and profits from PSUs).
• Revenue receipts are used to meet the day-to-day expenses of the government such as administrative costs, salaries, subsidies, and welfare programs.
• Capital Receipts:
• These include borrowings, disinvestment, sale of government properties, and loans received from foreign governments or financial institutions.
• Capital receipts lead to either an increase in liabilities (like loans) or a decrease in assets (like disinvestment).
• Examples include market borrowings, disinvestment proceeds, recovery of loans, and external assistance.
• Disinvestment in PSUs:
• The government sells its stake in Public Sector Undertakings (PSUs) to private entities or the public to raise funds.
• Disinvestment is categorized as a capital receipt because it involves selling government assets.
• It is a part of the government’s economic policies to reduce fiscal deficits and promote private investment.
• Importance of Budget Classification:
• Helps in understanding the government’s fiscal position and its ability to generate sustainable income.
• Aids policymakers in allocating resources efficiently and ensuring balanced growth.
• Ensures transparency and accountability in government financial management.

Important Points

• Income Tax: A major source of revenue receipts, it is levied on individuals and corporations based on their income levels.
• Dividends from PSUs: These are profits distributed by government-owned enterprises to the government, categorized as non-tax revenue.
• Disinvestment Objectives: Includes raising funds, reducing fiscal deficit, and improving efficiency in PSUs through private ownership.
• Budget 2023-24 Example: In the Union Budget 2023-24, the government emphasized non-tax revenue sources such as dividends and interest to meet fiscal goals.
• Fiscal Deficit: Understanding revenue and capital receipts is crucial for calculating fiscal deficit, which reflects the gap between total revenue and total expenditure.

The correct answer is Andhra Pradesh.

Key Points

• Alluri Sitarama Raju was a prominent freedom fighter who led the Rampa Rebellion in the 1920s, a tribal uprising against British rule. The rebellion took place in the regions that now form part of modern-day Andhra Pradesh.
• The rebellion primarily occurred in the Godavari Agency area, which is located in the Eastern Ghats. This area was heavily populated by tribal communities.
• Alluri Sitarama Raju mobilized the tribal population against the oppressive policies of the British, especially against the Forest Act, which restricted the rights of the tribals to use forest resources.
• His leadership in guerrilla warfare strategies against the British made him a revered figure among the tribal communities and earned him the nickname "Manyam Veerudu" (Hero of the Jungle).
• The rebellion ended in 1924 when Alluri Sitarama Raju was captured and executed by the British, but his legacy continues to inspire freedom movements and tribal rights advocacy.

Additional Information

• Rampa Rebellion:
• The rebellion occurred in the 1922-1924 period and was centered in the Rampa region of the Godavari districts in Andhra Pradesh.
• It was a tribal revolt against British colonial oppression, particularly against the restrictions imposed by the Madras Forest Act of 1882.
• The act limited the tribals' access to the forest, which was their primary source of livelihood, pushing them into hardship and poverty.
• Alluri Sitarama Raju:
• Born on 4th July 1897, in Pandrangi village in the Visakhapatnam district of Andhra Pradesh.
• He was inspired by the ideals of the Indian freedom struggle and was deeply moved by the plight of tribal communities under British rule.
• His leadership in armed rebellion against the British made him a folk hero among tribals.
• He was captured and executed by the British in 1924, but his efforts laid the groundwork for future tribal movements.
• Impact of the Forest Act:
• The Madras Forest Act restricted the usage of forest resources, including grazing, collecting firewood, and hunting, which were integral to the tribal way of life.
• The act alienated the tribal communities from their traditional lands and pushed them into economic distress, leading to widespread resentment.
• This resentment culminated in revolts like the Rampa Rebellion, which aimed to restore tribal rights and autonomy.
• Guerrilla Warfare Strategy:
• Alluri Sitarama Raju adopted guerrilla warfare tactics to fight against the British forces.
• He led surprise attacks on British police stations, seized arms, and disrupted their administration in the tribal areas.
• His deep knowledge of the terrain and support from tribal communities made these tactics highly effective.

Important Points

• Legacy: Alluri Sitarama Raju is remembered as a symbol of tribal resistance and patriotism. His life and sacrifices continue to inspire movements advocating for tribal rights and environmental protection.
• Recognition: The Indian government has honored his contributions by naming institutions and projects after him, such as the Alluri Sitarama Raju University.
• Regional Significance: The rebellion is seen as a pivotal moment in the history of Andhra Pradesh and is celebrated annually in the region.
• Tribal Movements: The Rampa Rebellion is part of a larger context of tribal uprisings during British rule, such as the Santhal Rebellion and Munda Rebellion, highlighting the widespread discontent among indigenous communities.

The correct answer is Poverty reduction and modernization.

Key Points

• The Sixth Five-Year Plan (1980-85) was focused on achieving poverty reduction and modernization of industries in India. It aimed to improve the living standards of people and ensure balanced economic development.
• The plan emphasized the importance of economic self-reliance and targeted reducing the percentage of people living below the poverty line through employment generation and rural development.
• Key sectors prioritized under this plan included agriculture, energy, industry, and human resource development, which were seen as critical for modernization and sustainable growth.
• The government introduced several schemes and programs to foster rural development, including Integrated Rural Development Programme (IRDP) and National Rural Employment Programme (NREP).
• The Sixth Plan also emphasized technological upgradation and modernization in industries to make them more competitive globally. This was aimed at reducing dependency on imports and achieving self-reliance.

Additional Information

• Integrated Rural Development Programme (IRDP):
• Launched in 1980, the IRDP aimed to provide employment opportunities and improve the quality of life in rural areas by offering productive assets to the poor.
• The program targeted individuals below the poverty line, including small farmers, landless laborers, and rural artisans.
• National Rural Employment Programme (NREP):
• Introduced during the Sixth Plan, this program focused on creating employment opportunities in rural areas through labor-intensive projects like road construction, irrigation, and afforestation.
• The program also aimed at improving rural infrastructure to support economic development.
• Modernization of Industries:
• The Sixth Plan promoted the adoption of modern technologies to enhance industrial efficiency and productivity.
• It aimed at reducing import dependency and fostering self-reliance in key sectors like energy, steel, and engineering goods.
• Poverty Reduction:
• The Sixth Plan sought to reduce the percentage of people living below the poverty line from 48% to 30% by the end of the plan period.
• This was to be achieved through a combination of employment generation, rural development, and targeted welfare programs.

Important Points

• Planning Commission: The Sixth Plan was prepared and implemented by the Planning Commission of India, which has since been replaced by NITI Aayog in 2015.
• Self-Reliance: A key feature of the Sixth Plan was its focus on achieving economic self-reliance through domestic production and reduced import dependency.
• Achievements: The Sixth Plan successfully achieved a growth rate of 5.4%, exceeding its target of 5.2%, and made significant contributions to poverty alleviation and industrial modernization.
• Legacy: The initiatives introduced during this period laid the foundation for several future programs and policies aimed at rural development and poverty reduction in India.

The correct answer is Budhu Bhagat.

Key Points

• Budhu Bhagat was a prominent tribal leader who mobilized the tribal peasantry in the Chotanagpur region during the Kol Revolt of 1831-1832.
• The Kol Revolt was an uprising led by the Kol tribal community against British exploitation, oppressive revenue policies, and the encroachment of their lands.
• Budhu Bhagat became the face of the resistance, organizing the tribal peasants to fight against the colonial forces and their local collaborators, including zamindars.
• The movement was marked by guerrilla warfare tactics, with tribal warriors attacking British establishments and symbols of exploitation in the Chotanagpur Plateau.
• The revolt was eventually suppressed by the British, but it highlighted the growing discontent among tribal communities regarding colonial policies. Hence, statement 1 is correct.

Additional Information

• Kol Revolt (1831-1832):
• The Kol Revolt was primarily triggered by the exploitation of tribal communities, including high land taxes, forced labor, and the loss of their ancestral lands.
• It was a significant uprising that involved various tribal groups, including the Kols, Mundas, and Oraons.
• The revolt spread across regions of modern-day Jharkhand and parts of Bihar, impacting British administrative control in these areas.
• Key Tribal Leaders:
• Budhu Bhagat: Known for his leadership during the Kol Revolt in Chotanagpur.
• Raghunath Mahato: Initiated a farmers' revolt against forced taxation but was not part of the Kol Revolt. Statement 2 is incorrect.
• Raghoji Bhangre: Led uprisings in Maharashtra against colonial forces but had no connection to the Kol Revolt. Statement 3 is incorrect.
• Tantiya Tope: Played a significant role in the 1857 Rebellion alongside Rani Laxmibai, but was not involved in tribal uprisings like the Kol Revolt. Statement 4 is incorrect.
• Geographical Context:
• The Kol Revolt was concentrated in the Chotanagpur Plateau, which is rich in mineral resources and has historically been home to tribal communities.
• British exploitation of these resources and imposition of zamindari systems disrupted the traditional tribal way of life.
• Impact of the Kol Revolt:
• Although the revolt was suppressed, it forced the British to reconsider their revenue and administrative policies in tribal regions.
• The uprising laid the foundation for subsequent tribal revolts, such as the Munda Rebellion (1899-1900) led by Birsa Munda.

Important Points

• Tribal Movements in India:
• Tribal revolts were often triggered by the loss of autonomy, exploitation by landlords, and oppressive colonial policies.
• Prominent uprisings include the Santal Rebellion (1855-1856), the Munda Rebellion (1899-1900), and the Chuar Revolt (1767-1809).
• These movements were typically localized but were critical in shaping the narrative of resistance against colonial rule.
• Role of Tribal Leaders:
• Tribal leaders like Budhu Bhagat, Birsa Munda, and Sidu-Kanhu became symbols of resistance and are still revered as heroes in their communities.
• They played an essential role in mobilizing tribal populations and preserving their cultural identity in the face of external threats.

The correct answer is A is true but R is false.

Key Points

• Assertion (A): Globalization has led to increased outsourcing of services to India.
• Globalization has allowed companies to transcend geographic boundaries, leading to outsourcing as a cost-effective strategy.
• India has become a preferred outsourcing destination due to its large pool of skilled professionals, especially in sectors like IT and customer service.
• The availability of English-speaking professionals and advancements in technology have further boosted India's position in global outsourcing.
• Hence, Assertion (A) is correct.
• Reason (R): India offers high-cost, low-skill services to foreign companies.
• This statement is incorrect because India is known for offering low-cost, high-skill services, particularly in areas such as IT, software development, and business process outsourcing.
• India's services are competitively priced and backed by skilled professionals, making it an attractive destination for outsourcing.
• Examples include the IT hubs of Bengaluru, Hyderabad, and Pune, which cater to high-end technological services.
• Hence, Reason (R) is false.
• Correct Analysis:
• While Assertion (A) is true, Reason (R) does not correctly explain or align with the assertion.
• The outsourcing boom is driven by India's capabilities in delivering cost-effective and high-quality services, not by low-skill services.

Additional Information

• Globalization and Outsourcing:
• Globalization has enabled businesses to access resources and talent from across the world.
• India has emerged as a leading hub for outsourcing, especially in Information Technology Enabled Services (ITES), customer support, and software development.
• Companies like TCS, Infosys, and Wipro are global leaders in outsourcing solutions.
• Foreign companies outsource to India to reduce costs while ensuring high-quality output.
• Factors Contributing to India's Outsourcing Strength:
• Cost Advantage: Labor costs in India are significantly lower compared to developed nations.
• Skilled Workforce: India boasts a large pool of highly educated professionals, particularly in STEM fields.
• Technology and Infrastructure: With advancements in IT infrastructure, India provides seamless services to global clients.
• Language Proficiency: English proficiency among Indian professionals makes communication with global clients easier.
• Common Outsourced Services:
• IT Services: Software development, cloud computing, and cybersecurity.
• Customer Support: Call centers and live chat support services.
• Business Process Outsourcing (BPO): Data entry, payroll processing, and financial services.
• KPO (Knowledge Process Outsourcing): Legal services, market research, and analytics.
• Examples of Global Outsourcing to India:
• Microsoft and IBM have major operations in India for software development.
• Amazon outsources customer support and IT services to Indian professionals.
• Google has research and development centers in Bengaluru and Hyderabad.

Important Points

• Historical Background: The outsourcing trend began in the 1990s, driven by advancements in IT and the liberalization of India's economy.
• IT Sector Contribution: The IT sector contributes significantly to India's GDP, and outsourcing plays a key role in this growth.
• Challenges in Outsourcing: Despite its advantages, outsourcing faces challenges such as data security concerns and cultural differences.
• Future Trends: With emerging technologies like AI and blockchain, India's outsourcing industry is evolving to handle more complex and high-value tasks.

Shortcut Trick

Apply the BODMAS sequence directly to the expression:

⇒ √(7 × 447 ÷ 21 + 73 − 26)

⇒ √(447 ÷ 3 + 73 − 26)

⇒ √(149 + 73 − 26) = √196 = 14

∴ The correct answer is 14.

Alternate Method

Given:

Expression: √(7 × 447 ÷ 21 + 73 − 26)

Concept Used:

BODMAS Rule: Solve in the order of Brackets, Of, Division, Multiplication, Addition, Subtraction.

Calculations:

⇒ √(7 × 447 ÷ 21 + 73 − 26)

First, calculate the division and multiplication parts together:

⇒ 7 × (447 / 21)

⇒ (7 / 21) × 447

⇒ (1 / 3) × 447

⇒ 149

Substitute this value back into the original expression:

⇒ √(149 + 73 − 26)

Next, perform the addition:

⇒ √(222 − 26)

Finally, perform the subtraction and find the square root:

⇒ √(196)

⇒ 14

∴ The correct answer is 14.

Additional Information

BODMAS Rule

It dictates the proper sequence of operations in any mathematical expression: Brackets, Order (powers/roots), Division, Multiplication, Addition, and Subtraction.

Fraction Simplification Trick

When dividing and multiplying simultaneously, combining them as a single fraction (a × b / c) allows you to cancel common factors easily before doing large multiplication.

Common Square Roots

Memorizing squares of numbers up to 30 significantly speeds up simplification. For instance, knowing that 14² = 196 and 15² = 225 saves manual calculation time.

Shortcut Trick

When the Principal is constant, Simple Interest (SI) is directly proportional to (Rate × Time).

Effective Rate percentage for Case 1 = 5% × 4 = 20%

Effective Rate percentage for Case 2 = 7% × 6 = 42%

Since 20% corresponds to ₹500, then 42% will correspond to (500 ÷ 20) × 42.

New Simple Interest = 25 × 42 = ₹1050.

∴ The correct answer is ₹1,050.

Alternate Method

Given:

SI₁ = ₹500

T₁ = 4 years, R₁ = 5% per annum

T₂ = 6 years, R₂ = 7% per annum

Formula Used:

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

Principal (P)

4 years @ 5% p.a. R × T = 20%

SI = ₹500

Principal (P)

6 years @ 7% p.a. R × T = 42%

SI = ₹1050

Calculation:

Using the given data for Case 1 to find the Principal (P):

⇒ 500 = (P × 5 × 4) ÷ 100

⇒ 500 = (P × 20) ÷ 100

⇒ P = (500 × 100) ÷ 20

⇒ P = ₹2500

Now, finding the Simple Interest for Case 2 using the same Principal:

⇒ SI₂ = (2500 × 7 × 6) ÷ 100

⇒ SI₂ = 25 × 42

⇒ SI₂ = ₹1050

∴ The correct answer is ₹1,050.

Additional Information

Proportionality of Simple Interest

When the principal amount is kept constant, simple interest becomes strictly proportional to the product of Rate (R) and Time (T). Formula ratio form: SI₁ ÷ SI₂ = (R₁ × T₁) ÷ (R₂ × T₂).

Total Amount in Simple Interest

The total amount (A) after simple interest is accrued is given by A = P + SI = P(1 + (R × T) ÷ 100).

Difference between CI and SI for 2 Years

For any given principal P and rate R% per annum, the difference between Compound Interest and Simple Interest strictly for a 2-year period is D = P(R ÷ 100)².

Shortcut Trick

When the same distance is covered at speeds S₁ and S₂ with total time T, Distance (D) = T × (S₁ × S₂) ÷ (S₁ + S₂)

Given, S₁ = 25 kmph, S₂ = 4 kmph, T = 5 hours 48 mins = 29/5 hours.

⇒ D = (29/5) × (25 × 4) ÷ (25 + 4)

⇒ D = (29/5) × (100/29)

⇒ D = 100 ÷ 5 = 20 km.

∴ The correct answer is 20 km.

Alternate Method

Start End

Bike: 25 kmph

Walk: 4 kmph

Distance = D

Total Time = 5 hr 48 min

Given:

Speed of bike (S₁) = 25 kmph

Speed while walking (S₂) = 4 kmph

Total journey time (T) = 5 hours 48 minutes

Formula Used:

Time = Distance ÷ Speed

Calculations:

⇒ Total time (T) = 5 + (48 ÷ 60) hours = 5 + 4/5 = 29/5 hours

⇒ Let the one-way distance be D km.

⇒ Time taken by bike = D / 25 hours

⇒ Time taken walking = D / 4 hours

⇒ Total Time = (D / 25) + (D / 4) = 29/5

⇒ (4D + 25D) ÷ 100 = 29/5

⇒ 29D / 100 = 29/5

⇒ D / 100 = 1/5

⇒ D = 100 ÷ 5 = 20

∴ The correct answer is 20 km.

Additional Information

Average Speed

When a person covers a certain distance at speed x and returns the same distance at speed y, the average speed for the whole journey is (2xy) ÷ (x + y).

Proportionality of Speed and Time

For a fixed distance, speed is inversely proportional to time. If the ratio of speeds is a : b, then the ratio of time taken will be b : a.

Relative Speed

If two objects move in opposite directions at speeds S₁ and S₂, their relative speed is S₁ + S₂. If moving in the same direction, it is |S₁ − S₂|.

Shortcut Trick

For a cliff of height h and two points on opposite sides with elevation angles θ₁ and θ₂, the distance d is:

d = h(cot θ₁ + cot θ₂)

Given d = 200 m, θ₁ = 30°, θ₂ = 45°

200 = h(cot 30° + cot 45°) = h(√3 + 1)

h = 200 ÷ (√3 + 1) = 100(√3 − 1) m

∴ The correct answer is 100(√3 − 1) m.

Alternate Method

Given:

Distance between points A and B = 200 m

Angle of elevation from point A = 30°

Angle of elevation from point B = 45°

Formula Used:

tan θ = Perpendicular ÷ Base

Calculations:

30°

45°

C A B D h h√3 h

200 m

Let the height of the cliff be CD = h and distance AD = x.

Then, distance BD = 200 − x.

In right-angled ΔACD:

⇒ tan 30° = CD ÷ AD

⇒ 1 ÷ √3 = h ÷ x

⇒ x = h√3

In right-angled ΔBCD:

⇒ tan 45° = CD ÷ BD

⇒ 1 = h ÷ (200 − x)

⇒ 200 − x = h

Substituting the value of x:

⇒ 200 − h√3 = h

⇒ h + h√3 = 200

⇒ h(√3 + 1) = 200

⇒ h = 200 ÷ (√3 + 1)

Rationalising the denominator by multiplying the numerator and denominator by (√3 − 1):

⇒ h = [200 × (√3 − 1)] ÷ [(√3 + 1) × (√3 − 1)]

⇒ h = 200(√3 − 1) ÷ (3 − 1)

⇒ h = 200(√3 − 1) ÷ 2

⇒ h = 100(√3 − 1) m

∴ The correct answer is 100(√3 − 1) m.

Additional Information

Points on the Same Side of a Tower

If both observation points are on the same side of a tower of height h with angles θ₁ and θ₂ (where θ₁ > θ₂), the distance between them is d = h(cot θ₂ − cot θ₁).

Angle of Elevation vs Depression

The angle of elevation of a point from an observer is geometrically equal to the angle of depression of the observer from that point, forming alternate interior angles.

Standard Trigonometric Ratios

Frequently used values in heights and distances are: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3. They represent the direct ratio of perpendicular height to base distance.

Shortcut Trick

Volume of a cuboid = Length × Breadth × Height = 350 cm³

Given Breadth = 7 cm, so Length × Height = 350 ÷ 7 = 50

Since Length = 2 × Height (H), we have 2H × H = 50 ⇒ 2H² = 50 ⇒ H² = 25 ⇒ H = 5 cm.

Therefore, Length = 2 × 5 = 10 cm.

∴ The correct answer is 10 cm × 7 cm × 5 cm.

Alternate Method

Given:

Volume of the cuboid = 350 cm³

Breadth (B) = 7 cm

Length (L) = 2 × Height (H)

Formula Used:

Volume of a cuboid = L × B × H

L = 10 cm H = 5 cm B = 7 cm Cuboid Volume = 350 cm³

Calculations:

⇒ Volume = (2H) × 7 × H

⇒ 350 = 14H²

⇒ H² = 350 ÷ 14

⇒ H² = 25

⇒ H = 5 cm

⇒ Length (L) = 2 × 5 = 10 cm

⇒ Dimensions = 10 cm × 7 cm × 5 cm

∴ The correct answer is 10 cm × 7 cm × 5 cm.

Additional Information

Surface Area of a Cuboid

Total Surface Area (TSA) = 2(LB + BH + HL). Lateral Surface Area (LSA) = 2H(L + B).

Diagonal of a Cuboid

The length of the longest rod that can be placed in a cuboid is given by its diagonal formula: √(L² + B² + H²).

Cube Properties

A cube is a special cuboid where L = B = H = a. Its Volume = a³ and Total Surface Area = 6a².

Shortcut Trick

Profit ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

Ratio (P : Q) = (8000 × 12) : (12000 × 7)

Ratio (P : Q) = 96000 : 84000 = 8 : 7

Total profit ratio parts = 8 + 7 = 15 parts

Q's share = (7 / 15) × 6800 ≈ Rs. 3173.33

∴ The correct answer is Rs. 3173.33.

Alternate Method

Given:

P's initial investment = Rs. 8,000

Investment duration for P = 12 months

Q's joining investment = Rs. 12,000

Investment duration for Q = 12 − 5 = 7 months

Total annual profit = Rs. 6,800

Partner PRs. 8,000× 12 months= 96k unitsRatio : 8Partner QRs. 12,000× 7 months= 84k unitsRatio : 7Total Profit = Rs. 6800

Formula Used:

Profit Ratio = (Capital of A × Time of A) : (Capital of B × Time of B)

Calculations:

⇒ Profit ratio of P to Q = (8000 × 12) : (12000 × 7)

⇒ Profit ratio = 96000 : 84000

⇒ Profit ratio = 96 : 84

Dividing the ratio by 12:

⇒ Profit ratio (P : Q) = 8 : 7

⇒ Total profit units = 8 + 7 = 15 units

⇒ Q's share in profit = (7 / 15) × Total Profit

⇒ Q's share = (7 / 15) × 6800

⇒ Q's share = 47600 / 15

⇒ Q's share = 3173.33

∴ The correct answer is Rs. 3173.33.

Additional Information

Compound Partnership

When partners invest different capital amounts for different time periods, the profit is divided in the ratio of the product of their capital and time: Profit Ratio = C₁T₁ : C₂T₂.

Joining Mid-Way

If a business profit is evaluated annually (12 months) and a partner joins after 't' months, their active period for generating profit is calculated as (12 − t) months.

Sleeping Partner vs Active Partner

An active partner manages the business and usually receives a fixed salary or a specific percentage of profit prior to general division. A sleeping partner only invests capital and receives profit strictly according to the investment ratio.

Shortcut Trick

Sum of exterior angles of any regular polygon is always 360°.

Therefore, Sum of interior angles = 6 × 360° = 2160°.

Since each internal triangle contributes 180°, number of triangles = 2160° ÷ 180° = 12.

Number of sides = Number of triangles + 2 = 12 + 2 = 14 sides.

Number of diagonals = Sides × (Sides − 3) ÷ 2 = 14 × 11 ÷ 2 = 77.

∴ The correct answer is 77 diagonals.

Alternate Method

Given:

Sum of the interior angles of a regular polygon = 6 × Sum of its exterior angles

Sum of Interior Angles = 6 × 360°

Interior Angle

Exterior Angle

Polygon Inside

Formulas Used:

Sum of exterior angles of a polygon = 360°

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

Number of diagonals in an n-sided polygon = n(n − 3) ÷ 2

Calculations:

⇒ Sum of exterior angles = 360°

⇒ Sum of interior angles = 6 × 360° = 2160°

⇒ (n − 2) × 180° = 2160°

⇒ n − 2 = 2160° ÷ 180°

⇒ n − 2 = 12

⇒ n = 14

The regular polygon has 14 sides.

⇒ Number of diagonals = 14 × (14 − 3) ÷ 2

⇒ Number of diagonals = 14 × 11 ÷ 2 = 154 ÷ 2 = 77

∴ The correct answer is 77 diagonals.

Additional Information

Interior Angle of a Regular Polygon

Each interior angle of a regular polygon with n sides is calculated as: [(n − 2) × 180°] ÷ n.

Exterior Angle of a Regular Polygon

Each exterior angle of a regular polygon is calculated as: 360° ÷ n. The sum of an interior angle and its corresponding straight-line exterior angle is always 180°.

Number of Diagonals

A diagonal is a line segment connecting two non-adjacent vertices. The total number of diagonals in an n-sided polygon is given by the exact formula: n(n − 3) ÷ 2.

Shortcut Trick

Let the Cost Price (CP) be 100x. Since markup is 40%, Marked Price (MP) = 140x.

Selling Price (SP) after 25% discount on MP = 140x × 0.75 = 105x.

Profit = SP − CP = 105x − 100x = 5x.

Given 5x = Rs. 75 ⇒ x = 15.

∴ The correct answer is Rs. 1500.

Alternate Method

Given:

Markup % = 40%

Discount % = 25%

Profit = Rs. 75

Formula Used:

Marked Price (MP) = CP × (100 + Markup %) ÷ 100

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

Markup: +40%

Discount: -25%

CP = 100x

SP = 105x

MP = 140x

Profit: +5x

Profit (5x) = Rs. 75 ⇒ x = 15

Calculations:

⇒ Let the Cost Price (CP) be 100x.

⇒ Marked Price (MP) = 100x + (40 ÷ 100) × 100x = 140x

⇒ Discount given on MP = 25% of 140x = 35x

⇒ Selling Price (SP) = MP − Discount = 140x − 35x = 105x

⇒ Profit = SP − CP = 105x − 100x = 5x

⇒ We are given that Profit = Rs. 75

⇒ 5x = 75

⇒ x = 15

⇒ Cost Price (CP) = 100 × 15 = Rs. 1500

∴ The correct answer is Rs. 1500.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP), never on the Cost Price. The formula for actual SP is: SP = MP × (1 − Discount / 100).

Successive Discounts

If two successive discounts of a% and b% are offered, the equivalent single discount percentage is given by: (a + b − a × b ÷ 100)%.

Direct Relation between CP and MP

A very useful trick for quick calculations: The ratio of Cost Price to Marked Price is exactly CP / MP = (100 − Discount %) / (100 + Profit %).

Shortcut Trick

Since the area of the plot is 625 m² (a perfect square), we consider it a square plot.

Side of the square plot = √625 = 25 m.

A 1 m wide path outside increases the side by 2 m (1 m on each opposite side).

New side of the boundary = 25 + 2 = 27 m.

Total area including the path = 27² = 729 m².

∴ The correct answer is 729 m².

Alternate Method

Area = 625 m² Side = 25 m

1 m

1 m

27 m

Given:

Area of the plot = 625 m²

Width of the footpath (w) = 1 m

Formula Used:

Area of square = (Side)²

Outer side = Inner side + 2 × Width of path

Calculation:

⇒ Side of the square plot (a) = √625 = 25 m

⇒ The 1 m wide footpath surrounds the plot uniformly.

⇒ Total side length including the path = a + 2w = 25 + 2 × 1

⇒ Outer side = 27 m

⇒ Total area including the footpath = (27)²

⇒ Total area = 729 m²

∴ The correct answer is 729 m².

Additional Information

Area of Path Outside a Square/Rectangle

When a path of width 'w' is built completely outside a shape, its length and breadth both increase by 2w. For a square of side 'a', Area of path = 4w(a + w).

Area of Path Inside a Square/Rectangle

When a path of width 'w' is built completely inside a shape, its interior length and breadth both decrease by 2w. For a square of side 'a', Area of path = 4w(a − w).

Intersecting Paths (Cross Path)

If two perpendicular paths of width 'w' run parallel to the length and breadth through the center of a rectangular plot, Area of path = w(L + B − w).

Shortcut Trick

Old ratio → R : B : G = 4 : 5 : 6 and New ratio → R : B : G = 2 : 5 : 7

Since the blue ratio part is 5 in both cases, no scaling of the ratios is needed.

Decrease in red ratio parts = 4 − 2 = 2 parts, which corresponds to the 6 red balls removed.

⇒ 1 ratio part = 6 ÷ 2 = 3 balls.

⇒ Original red balls = 4 parts = 4 × 3 = 12 balls.

∴ The correct answer is 12 balls.

Alternate Method

Given:

Initial ratio of Red : Blue : Green = 4 : 5 : 6

Let the original number of balls be:

⇒ Red = 4x

⇒ Blue = 5x

⇒ Green = 6x

After the modifications, the new quantities become:

⇒ Red = 4x − 6

⇒ Blue = 5x (remains unchanged)

⇒ Green = 6x + 3

The new ratio is given as 2 : 5 : 7.

Ratio Change Tracking

Original

Red: 4x

Blue: 5x

Green: 6x

− 6

No change

• 3

New

Red: 2y

Blue: 5y

Green: 7y

Since Blue is constant, 5x = 5y ⇒ x = y

Calculations:

Comparing the new quantities of Red and Blue balls to their ratio:

⇒ (4x − 6) / 5x = 2 / 5

Cross-multiplying the equation:

⇒ 5 × (4x − 6) = 2 × 5x

⇒ 20x − 30 = 10x

⇒ 10x = 30

⇒ x = 3

Verifying this using the Green and Blue balls ratio:

⇒ (6x + 3) / 5x = 7 / 5

⇒ 30x + 15 = 35x

⇒ 5x = 15 ⇒ x = 3 (Verified)

Calculating the original number of Red balls:

⇒ 4x = 4 × 3 = 12

∴ The correct answer is 12 balls.

Additional Information

Compound Ratio

When two or more ratios are multiplied together, it is called a compound ratio. For ratios a:b and c:d, the compound ratio is (a × c) : (b × d).

Duplicate & Triplicate Ratios

The duplicate ratio of a:b is a² : b², and the triplicate ratio is a³ : b³. Similarly, the sub-duplicate ratio is √a : √b.

Componendo and Dividendo

If a/b = c/d, then according to the rule of componendo and dividendo, (a + b) / (a − b) = (c + d) / (c − d). This property is highly useful for simplifying fraction equations directly.

Shortcut Trick

Let speeds be 4, 5, 6 and each equal distance be their LCM, 60 units. (Lowest speed = 4)

Total Distance = 3 × 60 = 180 units.

Total Time = (60 ÷ 4) + (60 ÷ 5) + (60 ÷ 6) = 15 + 12 + 10 = 37 units.

Average Speed = Total Distance ÷ Total Time = 180 ÷ 37.

Required Ratio = Average Speed ÷ Lowest Speed = (180 ÷ 37) ÷ 4 = 45:37.

∴ The correct answer is 45:37.

Alternate Method

Given:

A train covers 3 equal distances at speeds in the ratio 4:5:6.

Formula Used:

Average Speed = Total Distance ÷ Total Time

Time = Distance ÷ Speed

Distance = D Distance = D Distance = D

Speed = 4x Speed = 5x Speed = 6x

Time = D/4x Time = D/5x Time = D/6x

Journey of 3 Equal Distances

Calculations:

⇒ Let the 3 equal distances be D, D, and D. Total distance = 3D.

⇒ Let the respective speeds be 4x, 5x, and 6x. The lowest speed is 4x.

⇒ Total Time = (D ÷ 4x) + (D ÷ 5x) + (D ÷ 6x)

⇒ Total Time = (15D + 12D + 10D) ÷ 60x

⇒ Total Time = 37D ÷ 60x

⇒ Average Speed = Total Distance ÷ Total Time

⇒ Average Speed = 3D ÷ (37D ÷ 60x)

⇒ Average Speed = (3D × 60x) ÷ 37D = 180x ÷ 37

⇒ Required Ratio = Average Speed : Lowest Speed

⇒ Required Ratio = (180x ÷ 37) : 4x

⇒ Required Ratio = 180 : (37 × 4) = 180 : 148

⇒ Required Ratio = 45 : 37

∴ The correct answer is 45:37.

Additional Information

Average Speed for Two Equal Distances

When a person travels two equal distances at speeds x and y, the Average Speed = 2xy ÷ (x + y).

Average Speed for Three Equal Distances

When a person travels three equal distances at speeds x, y, and z, the Average Speed = 3xyz ÷ (xy + yz + zx).

Relative Speed

For two bodies moving in opposite directions, Relative Speed = S₁ + S₂. For bodies moving in the same direction, Relative Speed = |S₁ − S₂|.

Shortcut Trick

Price drops by 20% (1÷5), so Price ratio (Original : Reduced) = 5 : 4

Quantity is inversely proportional to price, so Quantity ratio = 4 : 5

Increase in quantity ratio = 5 − 4 = 1 unit → 5 kg

Original quantity = 4 units = 4 × 5 = 20 kg

Original price = Total Expenditure ÷ Original Quantity = 200 ÷ 20 = Rs. 10

∴ The correct answer is Rs. 10.

Alternate Method

Given:

Total expenditure = Rs. 200

Reduction in price = 20%

Extra quantity purchased = 5 kg

Formula Used:

Expenditure = Price × Quantity

Price Ratio Quantity Ratio

Original Reduced

5

4

4

5

+1 Unit = 5 kg

Original Qty = 4 × 5 = 20 kg → Original Price = 200 ÷ 20 = Rs. 10

Calculations:

⇒ Let the original price be Rs. x per kg.

⇒ Original quantity = 200 ÷ x

⇒ Reduced price = x − 20% of x = 0.8x

⇒ New quantity = 200 ÷ 0.8x = 250 ÷ x

⇒ Difference in quantity = New quantity − Original quantity

⇒ (250 ÷ x) − (200 ÷ x) = 5

⇒ 50 ÷ x = 5

⇒ x = 10

∴ The correct answer is Rs. 10.

Additional Information

Direct Formula for Reduced Price

Reduced Price = (Reduction % ÷ 100) × (Total Amount ÷ Extra Quantity).

Direct Formula for Original Price

Original Price = [Reduction % ÷ (100 − Reduction %)] × (Total Amount ÷ Extra Quantity).

Inverse Proportion Rule

When the total expenditure remains constant, the Price of an item is inversely proportional to its Consumption Quantity (P ∝ 1 ÷ Q).

Shortcut Trick

Using the deviation method for averages:

New Average = Old Average + (Total Deviation ÷ Total Days)

Deviation on Saturday = 45° C − 40° C = +5° C

New Average = 40 + (5 ÷ 6) = 40 + 0.833 = 40.83° C

∴ The correct answer is 40.83° C.

Alternate Method

Given:

Average temperature from Monday to Friday (5 days) = 40° C

Temperature on Saturday = 45° C

Formula Used:

Average = Sum of all observations ÷ Total number of observations

Mon to Fri (5 days) Avg = 40° C

Saturday 40° C base

+5° C

Distribute +5° C among all 6 days

New Average = 40 + (5 ÷ 6) = 40.83° C

Calculations:

⇒ Total temperature from Monday to Friday = 5 × 40 = 200° C

⇒ Total temperature from Monday to Saturday = 200 + 45 = 245° C

⇒ Total number of days = 6

⇒ Average temperature for 6 days = 245 ÷ 6 = 40.833...° C

⇒ Average temperature ≈ 40.83° C

∴ The correct answer is 40.83° C.

Additional Information

Net Deviation Method

New Average = Assumed Average + (Total Deviation ÷ Total Number of Items). This trick easily solves complex average problems without large multiplications.

Weighted Average

Used when combining groups of different sizes. Formula: A_w = (N₁A₁ + N₂A₂) ÷ (N₁ + N₂).

Replacement in Averages

If a new value replaces an old one, New Value = Old Value + (Increase in Average × Total Items).

Shortcut Trick

Discount percentage is the ratio of discount given to the original marked price.

Discount fraction = 150 ÷ 1200 = 1 ÷ 8

Converting the fraction directly to percentage gives exactly 12.5%.

∴ The correct answer is 12.5%.

Alternate Method

Given:

Original Price (Marked Price) = Rs. 1200

Discount offered = Rs. 150

Formula Used:

Discount % = (Discount ÷ Marked Price) × 100

Marked Price = ₹1200 (100%)

Selling Price = ₹1050

₹150

Discount % (To Find)

Calculations:

⇒ Discount % = (150 ÷ 1200) × 100

⇒ Discount % = (15 ÷ 120) × 100

⇒ Discount % = (1 ÷ 8) × 100

⇒ Discount % = 100 ÷ 8 = 12.5%

∴ The correct answer is 12.5%.

Additional Information

Marked Price (MP)

It is the original or printed price of an item. All discounts are strictly calculated on the Marked Price unless specified otherwise.

Selling Price (SP) after Discount

The final price at which an item is sold. It is calculated as SP = MP − Discount, or SP = MP × (1 − d ÷ 100).

Successive Discounts

If two consecutive discounts of a% and b% are offered, the single equivalent discount percentage is given by (a + b − ab ÷ 100)%.

Common Fractional Equivalents

1 ÷ 8 = 12.5% | 1 ÷ 4 = 25% | 3 ÷ 8 = 37.5% | 5 ÷ 8 = 62.5%

Shortcut Trick

Cost Price can be calculated directly by subtracting both the Discount and the Profit from the Marked Price.

CP = MP − Discount − Profit

CP = 720 − 144 − 36

CP = 720 − 180 = 540

∴ The correct answer is Rs. 540.

Alternate Method

Given:

Marked Price (MP) = Rs. 720

Discount = Rs. 144

Profit = Rs. 36

CP = ?

SP = 576

MP = 720

• 36 (Profit)

− 144 (Discount)

Total Difference = 144 + 36 = 180

Price Relation Concept

Formula Used:

Selling Price (SP) = Marked Price − Discount

Cost Price (CP) = Selling Price − Profit

Calculation:

⇒ SP = 720 − 144 = 576

⇒ CP = 576 − 36 = 540

∴ The correct answer is Rs. 540.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP) before any transaction takes place. Selling Price = MP × (1 − Discount% ÷ 100).

Profit & Loss

Profit or Loss is always evaluated based on the initial Cost Price (CP) of the article. Selling Price = CP × (1 + Profit% ÷ 100).

Markup Percentage

Markup is the additional amount added directly to the Cost Price in order to set the Marked Price. Markup% = (MP − CP) ÷ CP × 100.

Shortcut Trick

When equal distances are covered at two different speeds x and y, the average speed = (2 × x × y) ÷ (x + y)

Here, x = 50 km/h and y = 25 km/h

Average Speed = (2 × 50 × 25) ÷ (50 + 25)

⇒ Average Speed = 2500 ÷ 75 = 100 ÷ 3 = 33.33 km/h

∴ The correct answer is 33.33 km/h.

Alternate Method

Given:

Distance 1 (D₁) = 100 km, Speed 1 (S₁) = 50 km/h

Distance 2 (D₂) = 100 km, Speed 2 (S₂) = 25 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

Time = Distance ÷ Speed

100 km @ 50 km/h 100 km @ 25 km/h

Time = 2 hours Time = 4 hours

Total: 200 km in 6 hours

Calculations:

⇒ Time taken for the first 100 km (T₁) = 100 ÷ 50 = 2 hours

⇒ Time taken for the next 100 km (T₂) = 100 ÷ 25 = 4 hours

⇒ Total Distance = 100 + 100 = 200 km

⇒ Total Time = 2 + 4 = 6 hours

⇒ Average Speed = 200 ÷ 6 = 100 ÷ 3

⇒ Average Speed = 33.33 km/h

∴ The correct answer is 33.33 km/h.

Additional Information

Average Speed for Unequal Distances

When distances covered are unequal, you must use the basic formula: Average Speed = Total Distance ÷ Total Time. You cannot simply average the speeds.

Average Speed for Three Equal Distances

If a journey is divided into three equal parts covered at speeds x, y, and z, the average speed is (3 × x × y × z) ÷ (xy + yz + zx).

Relative Speed Concept

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂). When they move in the same direction, it is their difference (S₁ − S₂).

Shortcut Trick

Using the chain rule formula: M₁ × D₁ × W₂ = M₂ × D₂ × W₁

⇒ 66 × 79 × (1 / 11) = 6 × D₂ × 1

⇒ 6 × 79 = 6 × D₂

⇒ D₂ = 79

∴ The correct answer is 79 days.

Alternate Method

Given:

Number of women initially (M₁) = 66

Number of days taken initially (D₁) = 79

Number of women later (M₂) = 6

Work to be completed later = 1 / 11 of the total work

Method Used:

Total Work = Efficiency × Time (Assuming the efficiency of 1 woman is 1 unit/day)

Calculations:

⇒ Total work completed by 66 women = 66 × 79 = 5214 units

⇒ Work to be completed by 6 women = 1 / 11 of Total work

⇒ Required work = 5214 ÷ 11 = 474 units

⇒ Efficiency of 6 women = 6 units/day

⇒ Number of days required = Required work ÷ Efficiency

⇒ Days = 474 ÷ 6 = 79

∴ The correct answer is 79 days.

Additional Information

MDH Rule (Chain Rule)

Used to compare two different groups working on a project: (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂.

Work and Efficiency

Efficiency is inversely proportional to the time taken to complete a given amount of work. Total Work = Efficiency × Time.

Combined Work Rule

If person A takes x days and person B takes y days, their combined work per day is (1/x + 1/y).

Shortcut Trick

Given the ratio of Length to Width = 4 : 1

Perimeter in ratio units = 2 × (4 + 1) = 10 units

Actual perimeter is 100 cm, so 10 units = 100 cm ⇒ 1 unit = 10 cm

Therefore, Length = 40 cm and Width = 10 cm

Area = 40 × 10 = 400 cm²

∴ The correct answer is 400 cm².

Alternate Method

Given:

Perimeter of the rectangle = 100 cm

Length (L) = 4 × Width (W)

Formula Used:

Perimeter = 2 × (L + W)

Area = L × W

Length = 4W Width = W Perimeter = 100 cm Area = 400 cm²

Calculations:

⇒ 2 × (4W + W) = 100

⇒ 2 × 5W = 100

⇒ 10W = 100

⇒ W = 10 cm

⇒ L = 4 × 10 = 40 cm

⇒ Area = 40 × 10 = 400 cm²

∴ The correct answer is 400 cm².

Additional Information

Properties of a Rectangle

In a rectangle, opposite sides are parallel and equal in length. Furthermore, all four interior angles are exactly 90°.

Diagonal of a Rectangle

The length of a diagonal divides the rectangle into two right-angled triangles. It can be found using Pythagoras theorem: d = √(L² + W²).

Perimeter and Area Relation

For a given fixed perimeter, a square (where length equals width) will always enclose the maximum possible area among all rectangular shapes.

Shortcut Trick

Let x = tanθ. Using standard trigonometric double angle identities:

Given sinA = 2x / (1 + x²) = 2tanθ / (1 + tan²θ) = sin(2θ)

⇒ A = 2θ

We need to find tanA = tan(2θ) = 2tanθ / (1 − tan²θ)

Substituting x = tanθ back into the formula, we directly get tanA = 2x / (1 − x²).

∴ The correct answer is 2x/(1−x²).

Alternate Method

Given:

sinA = 2x / (1 + x²)

Formula Used:

sinA = Perpendicular / Hypotenuse

tanA = Perpendicular / Base

Base = √(Hypotenuse² − Perpendicular²)

AP = 2xB = 1 − x²H = 1 + x²

Calculations:

⇒ Perpendicular (P) = 2x

⇒ Hypotenuse (H) = 1 + x²

⇒ Base (B) = √((1 + x²)² − (2x)²)

⇒ Base (B) = √(1 + x⁴ + 2x² − 4x²)

⇒ Base (B) = √(1 + x⁴ − 2x²)

⇒ Base (B) = √((1 − x²)²)

⇒ Base (B) = 1 − x²

⇒ tanA = P / B = 2x / (1 − x²)

∴ The correct answer is 2x/(1−x²).

Additional Information

Trigonometric Double Angle Formulas

Formulas linking half angles with tangency: sin(2A) = 2tanA / (1 + tan²A), cos(2A) = (1 − tan²A) / (1 + tan²A), and tan(2A) = 2tanA / (1 − tan²A).

Algebraic Pythagorean Triplets

Just like numbers (3, 4, 5), an algebraic triplet such as (2x, 1 − x², 1 + x²) always forms the sides of a right-angled triangle since (2x)² + (1 − x²)² = (1 + x²)².

Basic Trigonometric Ratios

Remember the basic trigonometric acronym SOH CAH TOA: sinθ = Perpendicular / Hypotenuse, cosθ = Base / Hypotenuse, and tanθ = Perpendicular / Base.

Shortcut Trick

Using the weighted average method for replaced mixtures:

Net Alcohol % = [ (Remaining Vol × Old %) + (Replaced Vol × New %) ] ÷ Total Vol

Net Alcohol % = [ (90 × 30) + (30 × 50) ] ÷ 120

Net Alcohol % = (2700 + 1500) ÷ 120 = 4200 ÷ 120 = 35%

∴ The correct answer is 35%.

Alternate Method

Given:

Total volume of mixture = 120 L

Original alcohol concentration = 30%

Volume of mixture replaced = 30 L

Alcohol concentration in new liquid = 50%

Formula Used:

Alligation Ratio: (w₁ ÷ w₂) = (x₂ − m) ÷ (m − x₁)

Where w₁, w₂ are weights, x₁, x₂ are percentages, and m is the mean percentage.

Alligation Method 30% (Leftover) 50% (New added)

x%

50 − x 3 Ratio (90L) x − 30 1 Ratio (30L)

Calculations:

⇒ Remaining volume of original mixture = 120 − 30 = 90 L

⇒ Volume of new liquid added = 30 L

⇒ Ratio of quantities (w₁ : w₂) = 90 : 30 = 3 : 1

⇒ Let the concentration of the resulting mixture be x%.

⇒ Applying Alligation (from the diagram):

⇒ (50 − x) ÷ (x − 30) = 3 ÷ 1

⇒ 50 − x = 3 × (x − 30)

⇒ 50 − x = 3x − 90

⇒ 3x + x = 50 + 90

⇒ 4x = 140

⇒ x = 35%

∴ The correct answer is 35%.

Additional Information

Replacement Method

When a fraction of a mixture is replaced by another substance, the concentration of the left-over original mixture remains unchanged before mixing.

Rule of Alligation

It gives the ratio in which two ingredients at given percentages must be mixed to produce a mixture of a desired percentage.

Weighted Average

The combined percentage of two groups mixed in a ratio w₁ : w₂ is (w₁x₁ + w₂x₂) ÷ (w₁ + w₂).

Shortcut Trick

To convert an angle from degrees to radians, multiply the given angle by π / 180.

⇒ Radian measure = 270 × (π / 180)

⇒ Radian measure = 3π/2

∴ The correct answer is 3π/2 radians.

Alternate Method

Given:

Angle = 270°

Formula Used:

Angle in radians = Angle in degrees × (π / 180°)

0° / 360°90°180°270°270°= 3π/2

Calculations:

⇒ Angle in radians = 270 × (π / 180)

⇒ Angle in radians = (270 / 180) × π

⇒ Angle in radians = (3 / 2) × π

⇒ Angle in radians = 3π/2

∴ The correct answer is 3π/2 radians.

Additional Information

Degrees to Radians Conversion

To convert an angle from degrees to radians, you need to multiply the angle by π / 180.

Radians to Degrees Conversion

To convert an angle from radians to degrees, you need to multiply the angle by 180 / π.

Common Standard Angles

30° = π/6 | 45° = π/4 | 60° = π/3 | 90° = π/2 | 180° = π | 360° = 2π

Shortcut Trick

In trigonometry, if the sine of one angle equals the cosine of another, the angles are complementary.

Mathematically, if sin A = cos B, then A + B = 90°.

Given that sin x = cos y and cos x = sin y.

Directly applying the complementary angle property, we get x + y = 90°.

∴ The correct answer is 90°.

Alternate Method

Given:

⇒ sin x = cos y

⇒ cos x = sin y

Formula Used:

⇒ cos θ = sin(90° − θ)

Calculations:

From the first equation:

⇒ sin x = sin(90° − y)

Equating the angles on both sides:

⇒ x = 90° − y

⇒ x + y = 90°

This relationship natively forms the acute angles of a right-angled triangle where the sum of non-right angles is always 90°.

x

y

A B C

Right Triangle: sin x = cos y ⇒ x + y = 90°

∴ The correct answer is 90°.

Additional Information

Complementary Angles in Trigonometry

When the sum of two angles is 90°, they are defined as complementary. Their trigonometric co-functions perfectly mirror each other: sin(90° − θ) = cos θ, tan(90° − θ) = cot θ, and sec(90° − θ) = cosec θ.

Pythagorean Trigonometric Identities

The primary fundamental identities are: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Sum and Difference Formulas

sin(A ± B) = sin A × cos B ± cos A × sin B
cos(A ± B) = cos A × cos B ∓ sin A × sin B