SSC CGL 2025 (Held On: 21 Sept, 2025 Shift 2) (Previous Year Paper)

Thus, option 4 is exactly the same as the one given.

Hence, the correct answer is "Option 4".

BODMAS Rule:

Given equation: 14 - 7 × 30 ÷ 10 + 4 = 54

Let's check each option one by one

1. • and -

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

⇒ 14 + 7 × 30 ÷ 10 − 4 = 54

⇒ 14 + 7 × 3 − 4 = 54

⇒ 14 + 21 − 4 = 54

⇒ 35 − 4 = 54

⇒ 31 ≠ 54

⇒ LHS ≠ RHS

2. × and -

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

⇒ 14 × 7 − 30 ÷ 10 + 4 = 54

⇒ 14 × 7 − 3 + 4 = 54

⇒ 98 − 3 + 4 = 54

⇒ 102 − 3 = 54

⇒ 99 ≠ 54

⇒ LHS ≠ RHS

3. • and ÷

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

⇒ 14 ÷ 7 × 30 − 10 + 4 = 54

⇒ 2 × 30 − 10 + 4 = 54

⇒ 60 − 10 + 4 = 54

⇒ 64 − 10 = 54

⇒ 54 = 54

⇒ LHS = RHS

4. ÷ and ×

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

⇒ 14 − 7 ÷ 30 × 10 + 4 = 54

⇒ 14 − 0.23 × 10 + 4 = 54

⇒ 14 − 2.3 + 4 = 54

⇒ 18 − 2.3 = 54

⇒ 15.67 ≠ 54

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

BODMAS Rule:

I. 27 ÷ 3 - 18 × 3 + 9 = 24

Interchanging the given two signs + and ÷, we get:

⇒ 27 + 3 − 18 × 3 ÷ 9 = 24

⇒ 27 + 3 − 18 × (1/3) = 24

⇒ 27 + 3 − 6 = 24

⇒ 30 − 6 = 24

⇒ 24 = 24

⇒ LHS = RHS

II. 12 ÷ 8 × 12 + 16 - 7 = 19

Interchanging the given two signs + and ÷, we get:

⇒ 12 + 8 × 12 ÷ 16 − 7 = 19

⇒ 12 + 8 × (3/4) − 7 = 19

⇒ 12 + 6 − 7 = 19

⇒ 18 - 7 = 19

⇒ 11 ≠ 19

⇒ LHS ≠ RHS

Thus, only II is not correct.

Hence, the correct answer is "Option 4".

Family Chart:

Given: A is the mother of B. B is the sister of C. 

Thus, A is mother of C.

Hence, the correct answer is "Option 3".

Family Chart:

Given: P is the brother of Q. Q is the sister of R. R is the father of S.

Thus, P is Uncle of S.

Hence, the correct answer is "Option 4".

Given: A student fails to submit assignments repeatedly.

Course of Action:

1. Give extra time and counseling - Follows (This is a reasonable and constructive step. The student may be facing academic or personal difficulties. Providing counseling and some additional time can help understand the reason and improve the student’s performance.) 2. Suspend the student - Does not follow (This is a very strict action and should usually be taken only after other corrective measures fail. Immediate suspension without trying to help the student first may not be appropriate.)

Thus, only 1 follows.

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

Given: P1*, Q2*, R3*, S4*, T5*, E6*, V7*, W8*, X9*

The logic followed here is:

Thus, E6* is the odd one out.

Hence, the correct answer is "Option 3".

Statement:

Some pens are pencils. All pencils are stationary. No stationary is electronic.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some pens are not electronic. - Follows (Because Some pens are pencils,  All pencils are stationary and No stationary is electronic, which means some pens that are stationary are not electronic.)

II. Some stationary are pens. - Follows (Because Some pens are pencils. All pencils are stationary, which means some stationary are pens.)

Thus, both I and II follow.

Hence, the correct answer is "Option 3".

Given Word: PREACHER

Let's check each option one by one:

1. TEACH → PREACHER → It cannot be formed as T is missing.
2. TOUCH → PREACHER → It cannot be formed as T, O, U is missing.
3. CHAR → PREACHER → It can be formed
4. CREATE → PREACHER → It cannot be formed as T is missing.

Thus, CHAR can be formed using the letters of the word PREACHER.

Hence, the correct answer is "Option 3".

Given: _ABLE, _LIKELY, _BALANCE

Now, let's check each option one by one:

1. IN → INABLE, INLIKELY, INBALANCE

All three words become meaningless.

2. UN → UNABLE, UNLIKELY, UNBALANCE

All three words become meaningful.

3. RE → REABLE, RELIKELY, REBALANCE

All three words become meaningless.

4. DE → DEABLE, DELIKELY, DEBALANCE

All three words become meaningless.

Thus, UN can complete all three words meaningfully.

Hence, the correct answer is "Option 2".

Given:

"check list has been generated" is written as"jo ke al si ha",

"His idea has check" is written as "of al fu ha",

"number in check list" is written as "ha ya go ke".

"His number generated there" is written as "ya si fu xo"

Thus,  'My number has been generated' is written as 'jo si ya al ne'.

Hence, the correct answer is "Option 3".

The position and positional values or English Alphabets are:

Given: ARB, BSC, CTD, DUE, ?

The logic followed here is:

Thus, EVF comes next.

Hence, the correct answer is "Option 3".

Given:

1. Razia Sultana – She was a queen/ruler of the Delhi Sultanate.
2. Rani Durgavati – She was a queen and ruler of Gondwana.
3. Rani Lakshmibai – She was the queen of Jhansi and a warrior ruler.
4. Sarojini Naidu – She was a freedom fighter, poet, and political leader, not a queen.

The first three were women rulers/queens, while Sarojini Naidu was a freedom fighter, poet, and political leader.

Hence, the correct answer is "Option 4".

The position and positional values or English Alphabets are:

Given: ACE, BDF, CEG, ?

The logic followed here is:

Thus, DFH can replace the question mark (?) in the following series.

Hence, the correct answer is "Option 1".

Given:

Original price = ₹2000

Discount = 15%

VAT = 10%

Formula used:

Discounted price = MP − Discount

Final price = Discounted price + VAT

Calculation:

Discount = 2000 × 15 ÷ 100 = 300

Price after discount = 2000 − 300 = 1700

VAT = 1700 × 10 ÷ 100 = 170

Final amount = 1700 + 170 = 1870

∴ Net amount paid = ₹1870.

Given: If 9 @ 3 = 108 and 10 @ 2 = 80, what is 7 @ 1?

The logic followed here is:

Logic: a @ b = a × b × 4

9 @ 3 = 108 → 9 × 3 × 4 = 108

10 @ 2 = 80 → 10 × 2 × 4 = 80

Similarly,

7 @ 1? → 7 × 1 × 4 = 28

Thus 7 @ 1 is related to 28.

Hence, the correct answer is "Option 3".

Situation: While walking to the office, you witness a road accident.

1. Ignore and move ahead

This is irresponsible. In an emergency, ignoring the situation may delay help for the injured person.

2. Call emergency services and inform traffic police

This is the most appropriate and responsible action. Informing emergency services ensures that medical help and authorities arrive quickly.

3. Wait until someone else helps

This shows a lack of responsibility. Immediate action is important in accident situations.

4. Post it on social media

This does not help the victim and may violate privacy. The priority should be assistance, not publicity.

Thus, 'Call emergency services and inform traffic police' is what I will do.

Hence, the correct answer is "Option 2".

BODMAS Rule:

Decoding the given information:

Let's check each option one by one: 

1. 6 + 3 - 2 x 1 = 19

After replacing the symbols by their meaning, we get:

⇒ 6 × 3 + 2 - 1 = 19

⇒ 18 + 2 - 1 = 19

⇒ 20 - 1 = 19

⇒ 19 = 19

⇒ LHS = RHS

2. 8 - 4 x 2 + 1 = 10

After replacing the symbols by their meaning, we get:

⇒ 8 + 4 - 2 × 1 = 10

⇒ 8 + 4 - 2 = 10

⇒ 12 - 2 = 10

⇒ 10 = 10

⇒ LHS = RHS

3. 5 + 2 x 4 - 3 = 11

After replacing the symbols by their meaning, we get:

⇒ 5 × 2 - 4 + 3 = 11

⇒ 10 - 4 + 3 = 11

⇒ 13 - 4 = 11

⇒ 9 ≠ 11

⇒ LHS ≠ RHS

4. 10 x 3 - 5 + 2 = 17

After replacing the symbols by their meaning, we get:

⇒ 10 - 3 + 5 × 2 = 17

⇒ 10 - 3 + 10 = 17

⇒ 20 - 3 = 17

⇒ 17 = 17

⇒ LHS = RHS

Thus, equation 3 is incorrect after applying these symbol transformations.

Hence, the correct answer is "Option 3".

Given: You are a nurse in an emergency ward. A patient arrives with severe chest pain. 

1. Call the doctor immediately. - Follows

Reason: Severe chest pain in an emergency ward can indicate a life-threatening condition such as a heart attack (myocardial infarction). In such situations, immediate medical attention is critical. A nurse’s first priority is to ensure that the patient receives urgent medical evaluation and treatment. Therefore, the nurse should alert the doctor immediately so that proper diagnosis and emergency treatment can begin.

2. Check patient's insurance - Does not follows
   

Reason: Administrative tasks are not a priority during a medical emergency.

3. Fill out admission form - Does not follows
   

Reason: Documentation can be completed later after the patient is stabilized.

4. Contact the family - Does not follows

Reason: Informing family members is important but not the first step in an emergency.

Thus, 'Call the doctor immediately' is what a Nurse should do first.

Hence, the correct answer is "Option 1".

Given: 144, 121, 100, 81, ?, 49

The logic followed here is:

Thus, 64 will come at the place of question mark.

Hence, the correct answer is "Option 1".

BODMAS Rule:

Given: 3 * 4 # 2 @ 5

Now replacing the symbol by their meaning, we get:

= 3 + 4 × 2 − 5 

= 3 + 8 − 5 

= 11 − 5 

= 6

Thus, the value of the expression is 6.

Hence, the correct answer is "Option 2".

Statements: Some keys are locks. Some locks are doors.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some keys are doors. - False (There is no definite relation between keys and doors, it can be possible but it is not definite)

II. All locks being keys is a possibility. - True (because, some keys are locks, it implies that all locks being key is a possibility).

Thus, only Conclusion II follows.

Hence, the correct answer is "Option 1".

Given: 'LION' is coded as '12-9-15-14'.

Similarly,

Thus, 'NOIL' will be coded as '14-15-9-12'.

Hence, the correct answer is "Option 4".

Given: 3, 6, 18, 72, 360, ?

The logic followed here is:

Thus, 2160 will come in the place of ?.

Hence, the correct answer is "Option 3".

Given: 5, 9, 27, 31, 94, 97, 292

The logic followed here is:

Thus, '94, 292' is the incorrect combination.

Hence, the correct answer is "Option 4".

The correct answer is Indian Space Research Organization.

Key Points

• Indian Space Research Organization (ISRO) is the national space agency of India, responsible for the planning, execution, and development of space exploration and satellite programs.
• It was established in 1969 by Dr. Vikram Sarabhai, who is considered the father of the Indian space program.
• ISRO operates under the Department of Space, which comes directly under the Prime Minister of India. Its headquarters is located in Bengaluru, Karnataka.
• The main objective of ISRO is to develop space technology and its application for various national tasks, such as communication, weather forecasting, navigation, and Earth observation.
• ISRO is globally recognized for its cost-effective space missions, such as the Mars Orbiter Mission (MOM), also known as Mangalyaan, which made India the first Asian nation to reach Mars and the first nation globally to do so in its maiden attempt.

Additional Information

• Option 1: Indian Scientific Research Organization
• This is an incorrect option. The name does not correspond to any existing scientific organization in India.
• While scientific research is a focus of various institutions in India, ISRO is specifically dedicated to space exploration and technology development.
• Option 3: Indian Satellite Rocket Organization
• This is an incorrect option. ISRO is not limited to satellite and rocket development but encompasses broader aspects of space technology and its applications.
• Although ISRO is known for its successful launch vehicles such as the PSLV (Polar Satellite Launch Vehicle) and GSLV (Geosynchronous Satellite Launch Vehicle), its scope extends beyond this.
• Option 4: International Space Research Organization
• This is also incorrect. ISRO is a national agency of India, not an international organization.
• However, ISRO collaborates with various international space agencies such as NASA, ESA, and Roscosmos for research and missions.
• ISRO’s Achievements:
• Successful launch of Chandrayaan-1, India’s first lunar probe, in 2008.
• Launch of Mangalyaan (Mars Orbiter Mission) in 2013, making India the first Asian country to reach Mars.
• Development of NavIC, India’s own navigation system, comparable to GPS.
• GSLV Mk III’s successful launch, which is capable of carrying heavier payloads and was used for the Chandrayaan-2 mission in 2019.
• Future Missions:
• Planned launch of Gaganyaan, India’s first manned space mission.
• Development of a reusable launch vehicle to reduce the cost of space missions.

The correct answer is Bypassing Pakistan for trade with Afghanistan.

Key Points

• Chabahar Port is strategically located on the southeastern coast of Iran, providing India with a direct route to Afghanistan and Central Asia, bypassing Pakistan. This is especially critical for enhancing India-Afghanistan trade relations.
• India has invested significantly in the development of Chabahar Port, as it provides access to the landlocked countries of Central Asia through the International North-South Transport Corridor (INSTC), avoiding reliance on Pakistani routes.
• The port serves as a gateway for India to counter China’s influence in the region, particularly in the context of China’s partnership with Pakistan on the Gwadar Port, which is part of the China-Pakistan Economic Corridor (CPEC).
• It facilitates the transportation of goods to Afghanistan, including humanitarian aid, ensuring uninterrupted trade and strengthening India’s geopolitical influence in the region.
• Chabahar Port plays a critical role in India’s strategic objectives, enabling it to establish a foothold in the energy-rich regions of the Middle East and Central Asia while circumventing political and logistical challenges posed by Pakistan.

Additional Information

• Chabahar Port:
• Located in the Sistan-Baluchistan Province of Iran, it is the country’s only oceanic port situated on the Gulf of Oman and provides direct access to the Indian Ocean.
• India has invested in the development of the port under a bilateral agreement signed in May 2016 between India, Iran, and Afghanistan.
• The port consists of two terminals, Shahid Beheshti and Shahid Kalantari, with the former being developed by India.
• It is a vital component of the International North-South Transport Corridor (INSTC), aimed at connecting India with Central Asia and Russia via Iran.
• Strategic Significance:
• The port strengthens India’s presence in the region and reduces its dependency on Pakistan for accessing Afghanistan and Central Asia.
• It serves as a counterbalance to China’s influence in the region, particularly through its investments in Pakistan’s Gwadar Port.
• It supports India’s energy security by facilitating trade routes to resource-rich countries in Central Asia and the Middle East.
• Comparison with Gwadar Port:
• Gwadar Port, located in Pakistan, is just 70 km away from Chabahar Port and is a part of China’s Belt and Road Initiative (BRI).
• While Gwadar is operated by China, Chabahar is being developed with India’s investment, symbolizing strategic competition between the two nations.
• Unlike Gwadar, Chabahar provides direct access to Afghanistan without passing through Pakistan, making it highly beneficial for India’s regional trade and security interests.
• India-Afghanistan Trade:
• India has utilized the Chabahar Port to send shipments of wheat and other aid to Afghanistan, bypassing Pakistan’s restrictions.
• This trade route has significantly boosted India’s economic and diplomatic ties with Afghanistan and Central Asian countries.
• The port has also facilitated the opening of new markets for Indian goods in Central Asia and beyond.

Important Points

• Option 1: Access to the Persian Gulf:
• While Chabahar Port is located near the Persian Gulf, its primary importance lies in providing access to Afghanistan and Central Asia, not just the Gulf. Hence, this is not the correct option.
• Option 2: Connecting India to the Mediterranean Sea:
• The port does not directly connect India to the Mediterranean Sea. The INSTC primarily links India to Central Asia and Russia. Hence, this option is incorrect.
• Option 4: Enhancing Iran's naval capabilities:
• While the development of Chabahar Port may indirectly benefit Iran’s naval capabilities, this is not its primary strategic significance for India. Hence, this option is incorrect.
• Option 5: No option:
• This is not a valid option as the primary strategic importance of Chabahar Port lies in bypassing Pakistan for trade with Afghanistan. Hence, this option is not correct.

The correct answer is Meghalaya.

Key Points

• Traditional Archery Competitions: Meghalaya is renowned for its traditional archery competitions, locally known as "Teer." These competitions are deeply rooted in the culture of the Khasi tribe.
• Unique Format: Teer is not just a sport but also a form of legalized gambling in Meghalaya. Participants bet on the number of arrows that will hit the target during the competition.
• Daily Events: The competitions are conducted daily at designated "Teer counters" across the state, where people can place bets. The results are announced later in the evening.
• Cultural Significance: Teer holds immense cultural importance and is considered a traditional pastime in the region, reflecting the indigenous practices of the local communities.
• Government Regulation: Teer is regulated under the Meghalaya Amusement and Betting Tax Act, ensuring legal oversight of the activity.

Additional Information

• History of Teer: Teer originated as a traditional form of archery practiced by the Khasi tribe in Meghalaya. Over time, it evolved into a structured activity with betting elements.
• Legal Framework: The Meghalaya government legalized Teer betting through the Meghalaya Amusement and Betting Tax Act, making it a regulated form of gambling unique to the state.
• Betting System: Participants bet on two rounds of archery: the first round involves 50 archers shooting 30 arrows each, while the second round includes 20 arrows per archer. The winning numbers are derived from the total number of arrows hitting the target.
• Economic Impact: Teer betting has become a significant economic activity in Meghalaya, providing employment opportunities and generating revenue for the state government.
• Cultural Festivals: Archery competitions are often part of traditional festivals and celebrations in Meghalaya, showcasing the skill and heritage of the local communities.

Important Points

• Distinct from Other States: While archery is practiced in various forms across India, the unique betting system and cultural integration make Teer exclusive to Meghalaya.
• Tourist Attraction: Teer competitions attract tourists interested in experiencing the rich cultural heritage of Meghalaya and its unique traditions.
• Social Interaction: Teer serves as a social gathering point for locals, fostering community bonds and celebrating their cultural identity.
• Other States: Kerala, Rajasthan, and Tamil Nadu do not have similar traditional archery competitions or legal betting systems like Teer.

The correct answer is Mumbai.

Key Points

• The 2018 Intercontinental Cup final was held at the Mumbai Football Arena, located in Andheri, Mumbai.
• India's national football team, led by Sunil Chhetri, emerged victorious in the final, defeating Kenya 2-0.
• Sunil Chhetri, India's all-time leading goal scorer, played a pivotal role in the tournament by scoring both goals in the final match.
• The Intercontinental Cup was organized as a preparatory tournament for the Indian team ahead of the 2019 AFC Asian Cup.
• The Mumbai Football Arena is known for hosting several football events and has become a hub for Indian football matches, owing to its modern facilities and central location.

Additional Information

• Sunil Chhetri:
• Sunil Chhetri is considered one of India's greatest football players and has captained the national team in numerous tournaments.
• As of 2018, he is the third-highest active international goal scorer in the world, behind Cristiano Ronaldo and Lionel Messi.
• Chhetri’s performance in the 2018 Intercontinental Cup was instrumental in India's success, as he scored crucial goals throughout the tournament.
• Mumbai Football Arena:
• The Mumbai Football Arena is part of the Andheri Sports Complex and has hosted various national and international football events.
• It is renowned for its vibrant atmosphere, with passionate fans supporting the Indian football team during crucial matches.
• The arena has a seating capacity of approximately 7,000 spectators, making it an intimate venue for high-energy games.
• 2018 Intercontinental Cup:
• The tournament featured four teams: India, Kenya, New Zealand, and Chinese Taipei.
• The event was organized to provide competitive exposure to the Indian team ahead of the 2019 AFC Asian Cup.
• India won the tournament, showcasing significant improvement in their gameplay under coach Stephen Constantine.
• Kenya’s Performance:
• Kenya was the runner-up in the tournament, losing to India in the final.
• Their team showcased strong defensive capabilities but struggled to counter India’s offensive strategies led by Sunil Chhetri.

Important Points

• Sunil Chhetri’s Milestone:
• During the tournament, Sunil Chhetri equaled and later surpassed the international goal tally of Argentine superstar Lionel Messi, highlighting his prolific scoring ability.
• Chhetri’s performance earned him widespread recognition and boosted Indian football’s profile globally.
• Venue Selection:
• The choice of the Mumbai Football Arena as the venue was strategic, considering its modern facilities and strong football fanbase in Mumbai.
• The compact stadium ensured an electrifying atmosphere, contributing to the players’ morale during the matches.
• Impact on Indian Football:
• The victory in the Intercontinental Cup was a significant morale booster for the Indian football team ahead of the 2019 AFC Asian Cup.
• The tournament helped improve India’s FIFA ranking and showcased the growing potential of Indian football on the international stage.

The correct answer is Introduction of virtual court hearings.

Key Points

• The Bharatiya Nyaya Sanhita, introduced as a replacement for the Indian Penal Code (IPC), includes provisions aimed at modernizing the judicial process in India.
• A significant reform under the Bharatiya Nyaya Sanhita is the introduction of virtual court hearings, which ensures that judicial processes can continue seamlessly using technology.
• Virtual hearings allow litigants, lawyers, and judges to participate in court proceedings without being physically present, thereby reducing delays and improving accessibility, particularly during emergencies like the COVID-19 pandemic.
• These hearings are conducted using secure digital platforms to maintain the integrity and confidentiality of the judicial process.
• The reform emphasizes efficiency, transparency, and accessibility by leveraging technology to reduce pendency in courts and make justice delivery more effective.

Additional Information

• Digital Reforms for Courts:
• The Indian judiciary has been adopting digital reforms such as the e-Courts Mission Mode Project, which aims to computerize courts and enhance their functioning.
• Virtual court hearings are part of this broader initiative, enabling remote access and reducing the time taken for proceedings.
• Such reforms promote a paperless environment, improving efficiency and reducing costs.
• Impact of Virtual Hearings:
• Virtual hearings have made justice delivery more inclusive by allowing individuals from remote and rural areas to participate in proceedings without incurring significant travel expenses.
• They are particularly beneficial for cases involving environmental disasters, pandemics, or other emergencies.
• Other Proposed Reforms Under Bharatiya Nyaya Sanhita:
• The Bharatiya Nyaya Sanhita emphasizes streamlining procedures, such as fast-tracking cases and introducing time limits for specific processes.
• The focus on using digital evidence highlights the importance of technology in modern justice delivery.
• Technological Integration in Judiciary:
• Besides virtual hearings, the judiciary is exploring the use of tools like Artificial Intelligence (AI) for case management and legal research.
• Other technological advancements include online case filing, digital case records, and e-payment systems for court fees.

Important Points

• Comparison of Other Options:
• No trials allowed: This is not a reform under Bharatiya Nyaya Sanhita. Trials remain an integral part of the judicial process.
• Online registration for judges: While technology is used for administrative tasks, this specific option is not directly related to the reforms under Bharatiya Nyaya Sanhita.
• Abolition of police reports: This is incorrect as police reports (FIRs) are a critical part of the criminal justice system in India.
• Examples of Virtual Hearings:
• During the COVID-19 pandemic, the Supreme Court and several High Courts in India conducted virtual hearings to ensure continuity in justice delivery.
• Countries like the United States and the United Kingdom have also adopted virtual court systems to modernize their judiciary.

The correct answer is Rajneet Kohli.

Key Points

• Rajneet Kohli was appointed as the Executive Director of Foods at Hindustan Unilever Limited (HUL) in March 2025.
• Hindustan Unilever Limited (HUL) is one of India’s largest fast-moving consumer goods (FMCG) companies, and the Foods category is a significant segment of its business operations.
• Rajneet Kohli is a seasoned professional with years of experience in the FMCG sector, having held leadership positions in reputed organizations before joining HUL.
• The appointment of Kohli is part of HUL’s strategic focus on strengthening its food business, which includes brands in segments like packaged foods, beverages, and culinary products.
• This development aligns with HUL’s plans to enhance its market share and expand its footprint in the rapidly growing Indian packaged food industry.

Additional Information

• Hindustan Unilever Limited (HUL):
• HUL is an Indian subsidiary of the British company Unilever, which has a legacy of over 80 years in the Indian market.
• The company operates in various sectors, including personal care, home care, and foods & beverages.
• HUL’s popular food brands include Kissan, Knorr, Brooke Bond, and Lipton, among others.
• The Foods and Refreshments segment contributes significantly to HUL’s overall revenue and growth in the Indian market.
• Rajneet Kohli’s Professional Background:
• Rajneet Kohli has extensive experience in managing brands and driving growth in the consumer goods industry.
• He has held senior management roles, contributing to product innovation, strategic planning, and market expansion in the FMCG domain.
• Indian Packaged Food Industry:
• The Indian packaged food market is rapidly growing, driven by changing lifestyles, urbanization, and increasing health-consciousness among consumers.
• By 2025, the Indian packaged food market is projected to grow at a compound annual growth rate (CAGR) of around 10-12%.
• Major players in this market include HUL, Nestle, ITC, Britannia, and Parle Products.
• HUL’s Strategy for Growth:
• HUL is focusing on strengthening its premium product portfolio, including health and wellness products, to cater to a growing consumer base.
• Investments in R&D and marketing are being ramped up to maintain HUL’s competitive edge in the food and beverage sector.
• HUL’s commitment to sustainable business practices has further enhanced its reputation in the market.

Important Points

• Leadership in the Indian FMCG Sector:
• HUL has consistently been a market leader in the FMCG sector in India, leveraging its strong distribution network and innovative product portfolio.
• Appointments like that of Rajneet Kohli aim to further solidify HUL’s position in the highly competitive food category.
• HUL’s focus on consumer-centric solutions and sustainable practices sets it apart in the industry.
• FMCG Industry in India:
• The Indian FMCG market is projected to grow at a CAGR of around 14% during the 2022-2027 period, driven by increasing disposable incomes and demand for high-quality products.
• Food and beverages account for a significant share of the FMCG market, with companies introducing innovative and health-focused products to meet consumer preferences.

The correct answer is Arches, domes, and rock carvings.

Key Points

• Kangra Fort's architectural grandeur: The fort is renowned for its majestic arches, domes, and rock carvings, which depict exquisite craftsmanship and contribute significantly to its visual appeal.
• Arches: The intricately designed arches within the fort serve both structural and aesthetic purposes, symbolizing the Indo-Islamic architectural style prevalent during the era of its construction.
• Domes: The fort features elegantly crafted domes, which add to its monumental appearance and showcase the influence of Mughal architecture.
• Rock carvings: The walls and gateways of Kangra Fort are adorned with intricate rock carvings, reflecting the artistic and cultural heritage of ancient India.
• Strategic location: Built on a steep hill overlooking the Ban Ganga and Majhi rivers, the fort's design and structural elements emphasize its defensive and aesthetic significance.

Additional Information

• History: Kangra Fort, located in Himachal Pradesh, is one of the oldest forts in India. It was built by the Royal Rajput family of Kangra, the Katoch dynasty, and has a history dating back to more than 4,000 years.
• Religious significance: The fort houses ancient temples, including the Laxmi Narayan Temple and Ambika Devi Temple, which are adorned with artistic carvings and hold religious importance.
• Defensive architecture: The fort's design incorporates features such as high ramparts, multiple gateways, and narrow passageways, ensuring its defense against invaders.
• Tourist attraction: Kangra Fort is a popular tourist destination due to its historical significance, architectural beauty, and panoramic views of the surrounding valleys.
• Preservation: The fort is maintained by the Archaeological Survey of India (ASI), ensuring its legacy for future generations.

Important Points

• Option 1: Wooden sculptures: Wooden sculptures are not a feature of Kangra Fort. The fort is primarily built using stone, showcasing rock carvings instead. Hence, this option is incorrect.
• Option 2: Colorful glass windows: While colorful glass windows are associated with other architectural styles, they are not significant elements of Kangra Fort's design. Hence, this option is incorrect.
• Option 4: Painted ceilings and tiled floors: Kangra Fort does not have painted ceilings or tiled floors as key architectural features. Its focus is on stone structures and carvings. Hence, this option is incorrect.
• Option 3: Arches, domes, and rock carvings: These are integral elements of Kangra Fort's architecture, contributing to its historical and visual magnificence. Hence, this option is correct.

The correct answer is Dramatic retelling of Salhesh legends by a Bhagat and Manarias.

Key Points

• The Festival of Salhesh is a significant cultural event celebrated primarily by the Dalit communities in Mithila, a region spanning parts of Bihar and Nepal.
• The festival is centered around the worship and celebration of Salhesh, a folk hero and deity revered for his bravery and justice.
• A distinct feature of this festival is the dramatic retelling of Salhesh legends, performed by a Bhagat (folk storyteller or bard) and the Manarias (a group of performers who enact the tales).
• These performances typically include musical narratives, dance, and theatrics to bring the stories of Salhesh to life, making them a vibrant cultural expression of the community.
• This oral tradition not only preserves the folk tales of Salhesh but also strengthens the cultural identity and unity of the community that celebrates the festival.

Additional Information

• Salhesh as a Folk Hero:
• Salhesh is a cultural hero and a symbol of social justice and equality, particularly for the Dalit communities in the Mithila region.
• He is often depicted as a protector of the downtrodden, and his tales resonate deeply with values of courage and fairness.
• Role of Bhagat and Manarias:
• The Bhagat serves as the storyteller, narrating the legends of Salhesh with great passion and devotion.
• The Manarias complement the narration by performing dramatic enactments that include costumes, props, and traditional Mithila music and dance forms.
• Importance of Oral Traditions:
• Oral traditions like the dramatic retelling of Salhesh legends play a crucial role in preserving and transmitting cultural heritage across generations.
• They serve as a medium of education, entertainment, and community bonding.
• Comparison with Other Options:
• Option 1: Harvest ceremonies involving animal sacrifice are not specific to the Festival of Salhesh but are seen in various other cultural practices in Mithila. Hence, this option is incorrect.
• Option 3: Buddhist chants invoking Salhesh are not a part of this festival, as Salhesh is not associated with Buddhism. Hence, this option is incorrect.
• Option 4: Sword dances performed by women warriors are not a feature of this festival. Such performances are more common in tribal and warrior communities. Hence, this option is incorrect.

Important Points

• Cultural Significance: Festivals like the Festival of Salhesh are not just religious events but also social occasions that reinforce community ties and shared identity.
• Geographical Context: The Mithila region, known for its rich cultural heritage, encompasses parts of Bihar in India and southern Nepal.
• Representation through Art: The legends of Salhesh are also depicted in Mithila paintings, a traditional art form of the region.
• Community Involvement: The festival sees active participation from all sections of the community, making it a collective celebration of their cultural roots.

The correct answer is Allahabad Pillar Inscription of Samudragupta.

Key Points

• The Allahabad Pillar Inscription is one of the most important literary sources for the Gupta period. It provides detailed information about the reign of Samudragupta, one of the greatest rulers of the Gupta Empire.
• It was composed by Harisena, the court poet and minister of Samudragupta, and is written in Sanskrit using the Brahmi script.
• The inscription glorifies the achievements, conquests, and administrative policies of Samudragupta, describing him as a great warrior, statesman, and patron of arts and culture.
• The Allahabad Pillar Inscription is located on a pillar at Kausambi (near Allahabad) and is a crucial source for understanding the political and military history of the Gupta Empire.
• It also mentions the extent of Samudragupta's empire, including his campaigns across northern and southern India, and his relations with other rulers and kingdoms.

Additional Information

• Nasik Prashasti of Gautamiputra Satakarni:
• The Nasik Prashasti was issued by Gautamiputra Satakarni, a ruler of the Satavahana dynasty. It provides information about his military achievements and administrative policies.
• It is an inscription found in the Nasik caves and predates the Gupta period, making it unrelated to the literary sources of the Gupta era.
• Aihole Inscription of Pulakeshin II:
• The Aihole inscription was issued by Pulakeshin II, a ruler of the Chalukya dynasty. It describes his conquests and achievements.
• It belongs to the early medieval period and is not connected to the Gupta period.
• Hathigumpha Inscription of Kharavela:
• The Hathigumpha inscription is attributed to Kharavela, a ruler of the Kalinga dynasty. It is engraved on a rock near Bhubaneswar, Odisha.
• This inscription predates the Gupta period and describes the achievements of Kharavela, making it unrelated to Gupta literary sources.
• Samudragupta's Significance:
• Samudragupta is often referred to as the Napoleon of India due to his extensive military campaigns and ability to establish a vast empire.
• The Gupta Empire under Samudragupta witnessed significant advancements in art, culture, and administration, earning it the title of the Golden Age of India.
• The Allahabad Pillar Inscription is a primary source for understanding the extent of his empire, which stretched from the Himalayas to the southern tip of India.

Important Points

• Gupta Period: The Gupta Empire (circa 320-550 CE) is known for its contributions to literature, science, mathematics, astronomy, and art. The Allahabad Pillar Inscription is a testament to its historical richness.
• Samudragupta's Conquests: The inscription mentions his conquests over numerous kingdoms, including northern India and parts of southern India, showcasing his military prowess.
• Court Poet Harisena: Harisena's composition of the inscription highlights the importance of royal patronage of literature and scholarship during the Gupta era.
• Political History: The inscription serves as a valuable resource for reconstructing the political and military history of ancient India during the Gupta reign.

The correct answer is Swapnil Kusale.

Key Points

• Swapnil Kusale won the bronze medal in the 50m Rifle 3 Position Men's event at the Paris 2024 Olympics, marking a historic achievement as the first Indian to secure a medal in this shooting event.
• The 50m Rifle 3 Position is a highly technical shooting event where athletes compete in three positions: kneeling, prone, and standing, testing both precision and endurance.
• Swapnil Kusale's victory was a result of consistent performance, including high scores across all three positions, showcasing his mastery in rifle shooting.
• This achievement holds immense significance for India's Olympic shooting history, demonstrating the growth of the sport in the country and inspiring future generations of Indian shooters.
• The medal win also reflects the success of government-backed sports initiatives and training programs aimed at nurturing shooting talent in India.

Additional Information

• 50m Rifle 3 Position Event:
• In the 50m Rifle 3 Position event, shooters fire at a target from a distance of 50 meters in three positions: kneeling, prone, and standing.
• Each shooter competes in a total of 120 shots, divided into 40 shots per position.
• The event demands a high level of mental focus, physical stability, and technical precision.
• India's Shooting Achievements:
• India has been steadily advancing in shooting sports at the international level, with shooters like Abhinav Bindra and Rahi Sarnobat earning accolades.
• Abhinav Bindra is India's first individual gold medalist in shooting at the 2008 Beijing Olympics.
• Indian shooters regularly perform well in events such as the ISSF World Cup and Asian Games.
• Swapnil Kusale - Profile:
• Swapnil Kusale is a professional shooter representing India in rifle shooting events.
• He has competed in various national and international championships, earning recognition for his consistent performances.
• His success at the Paris 2024 Olympics highlights his dedication to the sport and his ability to perform under pressure.
• Shooting Federations and Support:
• The National Rifle Association of India (NRAI) oversees shooting sports in India, ensuring athletes receive proper training and resources.
• Government programs like Target Olympic Podium Scheme (TOPS) and Khelo India provide financial and infrastructural support to athletes.
• These initiatives have played a crucial role in enhancing India's performance at global shooting events.

Important Points

• Key Characteristics of Rifle Shooting:
• Requires precise body control and steady breathing to maintain focus and accuracy.
• Modern rifles are equipped with advanced features like adjustable stocks and sophisticated sights for enhanced precision.
• Shooting events are governed by the International Shooting Sport Federation (ISSF), which sets rules and standards for competitions.
• Olympics and Indian Shooting:
• India's participation in shooting at the Olympics began in the 20th century, with notable improvements in recent decades.
• Indian shooters have earned medals in both rifle and pistol categories, showcasing versatility.
• The success of athletes like Swapnil Kusale highlights India's growing dominance in international shooting competitions.

The correct answer is Option 1.

Key Points

• Statement 1: Qutub-ud-din Aibak established the Slave Dynasty after the death of Mohammad Ghori. This statement is correct.
• Qutub-ud-din Aibak was a former slave of Muhammad Ghori, who later rose to power after Ghori's death in 1206.
• He laid the foundation of the Slave Dynasty (also known as the Mamluk Dynasty), which was the first dynasty of the Delhi Sultanate.
• He was known for his contribution to architecture, including the construction of the famous Qutub Minar in Delhi.
• Statement 2: The Delhi Sultanate began with the rule of Balban, one of the notable rulers of the Khalji dynasty. This statement is incorrect.
• The Delhi Sultanate began with the Slave Dynasty and not the Khalji dynasty.
• Ghiyasuddin Balban was indeed a notable ruler, but he belonged to the Slave Dynasty, not the Khalji Dynasty.
• The Khalji Dynasty succeeded the Slave Dynasty and was established by Jalal-ud-din Khalji in 1290.
• Thus, only Statement 1 is correct, making Option 1 the correct answer.

Additional Information

• Qutub-ud-din Aibak:
• He was the founder of the Delhi Sultanate and the Slave Dynasty.
• Aibak ruled from 1206 to 1210 and was succeeded by his son-in-law Iltutmish.
• He is credited with initiating the construction of the Qutub Minar and building the Quwwat-ul-Islam Mosque.
• Delhi Sultanate:
• The Delhi Sultanate was established in 1206 and lasted until 1526.
• It comprised five dynasties: Slave (Mamluk), Khalji, Tughlaq, Sayyid, and Lodi.
• Each dynasty contributed to the political, cultural, and architectural development of the Indian subcontinent.
• Khalji Dynasty:
• The Khalji Dynasty began in 1290 with Jalal-ud-din Khalji.
• It is known for its expansionist policies under rulers like Alauddin Khalji.
• Alauddin Khalji is famous for his successful military campaigns and administrative reforms.
• Ghiyasuddin Balban:
• Balban was a prominent ruler of the Slave Dynasty and reigned from 1266 to 1287.
• He is known for consolidating the Sultanate, strengthening the administration, and promoting the concept of divine kingship.
• Balban introduced the Persian court practices of sijda (prostration) and paibos (kissing of feet) to emphasize the authority of the Sultan.

Important Points

• The Slave Dynasty is also referred to as the Mamluk Dynasty, as its rulers were initially slaves who rose to power.
• The Delhi Sultanate was known for its architectural contributions, including the construction of mosques, forts, and minarets.
• The Khalji and Tughlaq dynasties played a significant role in expanding the Sultanate's territorial boundaries.
• The Sultanate's rulers introduced administrative reforms and promoted Persian culture in India.

The correct answer is working hours of women and children.

Key Points

• The Factory Act of 1881 was introduced during British rule in India to regulate working conditions in factories, particularly focusing on the working hours of women and children.
• The Act limited the number of working hours for children under the age of 12 to 9 hours per day, aiming to prevent exploitation and ensure their welfare.
• It also mandated that children working in factories were to receive four holidays in a month and adequate rest intervals during work hours.
• For women, the Act aimed to regulate working hours to ensure they were not subjected to long or harsh working hours, which could negatively impact their health and family responsibilities.
• The Factory Act of 1881 was significant because it marked the beginning of legislative efforts to regulate labor conditions in India, paving the way for future labor reforms.

Additional Information

• Important Provisions of Factory Act 1881:
• The Act was introduced by the British government as a response to social reform efforts aimed at improving labor conditions.
• It was applicable to factories employing 100 or more workers, focusing on industries where exploitation of labor was rampant.
• The Act mandated the provision of ventilation, lighting, and sanitary conditions in factories to improve worker health.
• It required factory owners to maintain records of child workers to ensure compliance with age and working hour restrictions.
• Subsequent Developments:
• The Factory Act of 1891 further enhanced the provisions of the 1881 Act by reducing working hours for children and introducing restrictions on night work for women.
• Later, the Indian Factories Act of 1948 replaced earlier legislations and introduced comprehensive measures for labor welfare, including safety, working conditions, and health regulations.
• Impact on Labor Welfare:
• The Factory Act of 1881 was the first step toward improving labor conditions in India, though its scope was limited to specific industries and regions.
• It raised awareness of the need for labor laws in India and led to increased focus on worker rights and welfare in subsequent decades.
• Similar Laws in Other Countries:
• In England, the Factory Acts of the 19th century aimed to improve working conditions, especially for women and children, setting an example for India.
• Other countries, such as the United States, also passed labor laws during the Industrial Revolution to regulate working hours and ensure safety in factories.

Important Points

• Historical Context: The Factory Act of 1881 was introduced during the tenure of Lord Ripon, who is known for his reform-oriented policies in India.
• Age Restrictions: The Act defined a child worker as someone under the age of 12 years, marking an early attempt to regulate child labor.
• Industrial Revolution Influence: The Act was inspired by similar labor laws enacted in Britain during the Industrial Revolution.
• Social Impact: While the Act was limited in scope, it marked an important step toward addressing labor exploitation and improving working conditions in colonial India.

The correct answer is Only statement 1 is correct.

Key Points

• Statement 1: The book "India on Our Minds" offers an insightful analysis of India's economic growth and social challenges. This statement is correct as the book focuses on examining India's advancements in economic sectors and the hurdles faced in addressing socio-economic disparities. It provides a detailed and analytical overview of India's transformation in various domains. Hence, statement 1 is correct.
• Statement 2: The book is a fictional novel about India's freedom struggle. This statement is incorrect as "India on Our Minds" is a non-fictional work that delves into India's contemporary socio-economic landscape rather than being a historical or fictional account of the freedom struggle. Hence, statement 2 is incorrect.
• Given the nature of the book and its analytical insights, it is evident that it is not a fictional novel. It is recognized for its contribution to understanding India's growth trajectory and challenges.
• The book is an important resource for individuals interested in India's current status in global economics and its socio-political challenges. It provides a platform for critical analysis and debate regarding India's progress and future potential.
• Hence, the correct answer is "Only statement 1 is correct."

Additional Information

• Focus of "India on Our Minds":
• The book examines India's economic growth in the context of global markets and its role as a key player in the global economy.
• It provides an analysis of social challenges such as poverty, inequality, and access to education and healthcare.
• It discusses the implications of India's policies and reforms on its citizens and on the global stage.
• India's Economic Growth:
• India has emerged as the world's fifth-largest economy in terms of nominal GDP and third-largest by purchasing power parity (PPP).
• The country has seen significant growth in sectors such as technology, manufacturing, and services.
• Despite this growth, challenges such as income inequality and rural-urban disparities persist.
• Social Challenges in India:
• India faces challenges in providing universal access to quality education and healthcare.
• Issues such as gender inequality and lack of infrastructure in rural areas affect development.
• Efforts such as the National Education Policy (NEP) 2020 and Ayushman Bharat aim to address these challenges.
• Importance of Non-fictional Analysis:
• Non-fictional works like "India on Our Minds" provide a factual and analytical perspective on contemporary issues.
• They serve as valuable resources for policymakers, researchers, and students interested in India's socio-economic landscape.

Important Points

• Other Books on India's Socio-economic Landscape:
• "India After Gandhi" by Ramachandra Guha: Covers India's political history and socio-economic developments after independence.
• "The Invention of India" by Shashi Tharoor: Explores India's history, culture, and contributions to the global stage.
• "Why Nations Fail" by Daron Acemoglu and James Robinson: Includes references to India's development challenges in the context of global economic history.
• Key Reports and Indices:
• Human Development Index (HDI): India ranked 132nd in the 2022 report, highlighting areas for improvement in education, health, and income.
• Global Hunger Index (GHI): India's ranking reflects ongoing challenges in eradicating hunger and malnutrition.
• Ease of Doing Business Report: India has made significant progress, ranking 63rd in the 2020 report, up from 142nd in 2014.

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

Key Points

• Assertion (A): The retreating monsoon winds are associated with dry weather and clear skies in northern India.
• This statement is correct. During the retreating monsoon phase (typically from October to November), the southwest monsoon winds withdraw from the Indian subcontinent.
• As the moist monsoon winds retreat, they no longer bring rainfall to northern India, leading to clear skies and dry weather conditions.
• Reason (R): During the retreating monsoon, the low-pressure area over the northern plains is replaced by a high-pressure system.
• This statement is also correct. As the monsoon withdraws, the low-pressure system that dominated during the rainy season dissipates, and a high-pressure system takes its place.
• The high-pressure system results in subsidence of air, which suppresses cloud formation, causing clear skies and dry conditions.
• Explanation: The Reason (R) correctly explains the Assertion (A).
• The retreating monsoon is characterized by the withdrawal of moist winds and the establishment of high-pressure systems in northern India, resulting in clear skies and dry weather.
• This phenomenon marks the transition from the monsoon season to the winter season in India.

Additional Information

• Retreating Monsoon:
• The retreating monsoon occurs during October and November, marking the transition from the rainy season to winter in India.
• It is characterized by the withdrawal of the southwest monsoon winds and the establishment of dry, northeast trade winds.
• The retreating monsoon is most prominent in regions like North India, the Western Ghats, and Tamil Nadu, where it often brings light showers.
• High-Pressure Systems:
• A high-pressure system forms when air converges aloft and descends, causing subsidence (downward movement of air).
• This results in clear skies, low humidity, and dry weather, typical of post-monsoon conditions in northern India.
• Impact on Tamil Nadu:
• While northern India experiences dry weather during the retreating monsoon, Tamil Nadu receives significant rainfall due to the northeast monsoon winds.
• This phenomenon is known as the northeast monsoon season, which is crucial for agricultural activities in Tamil Nadu.
• Climatological Significance:
• The retreating monsoon period is critical for the onset of the Rabi crop season in India, as the dry weather provides favorable conditions for sowing.
• This period also marks the beginning of a reduction in humidity and a gradual drop in temperatures in northern India.

Important Points

• Weather Patterns: The retreating monsoon is marked by clear skies, reduced rainfall, and cooler nights, especially in northern and central India.
• Seasonal Transition: This phase represents a transition from the wet monsoon season to the dry winter season, with significant changes in wind patterns and atmospheric pressure.
• Regional Variations: While northern and central India experience dry weather, southern states like Tamil Nadu benefit from the northeast monsoon, which brings rainfall.
• Temperature Changes: The retreating monsoon is often accompanied by a drop in night temperatures, leading to a cooler climate in many regions.

The correct answer is Money Bill.

Key Points

• A Money Bill is a type of bill in the Indian Parliament that exclusively deals with matters specified in Article 110 of the Constitution of India.
• It includes provisions for the imposition, abolition, remission, alteration, or regulation of any tax or revenue collection.
• Under Article 110, a bill is classified as a Money Bill if it deals with:
• The imposition or abolition of taxes.
• The custody and withdrawal of money from the Consolidated Fund of India or the Contingency Fund of India.
• The appropriation of money out of the Consolidated Fund.
• A Money Bill can only be introduced in the Lok Sabha, not in the Rajya Sabha.
• After being passed by the Lok Sabha, the Rajya Sabha can only suggest amendments, which the Lok Sabha may accept or reject. The Rajya Sabha cannot reject or amend a Money Bill without the concurrence of the Lok Sabha.

Additional Information

• Ordinary Bill:
• An Ordinary Bill is a regular bill that deals with any matter other than financial matters specified under Article 110.
• It can be introduced in either the Lok Sabha or the Rajya Sabha.
• It requires the approval of both houses and has no special financial provisions.
• Private Bill:
• A Private Bill is introduced by a private member (a Member of Parliament who is not a minister).
• It deals with public interest issues but is rarely passed in the Indian Parliament.
• Constitutional Amendment Bill:
• It is introduced to amend the provisions of the Constitution of India under Article 368.
• It requires a special majority in both houses of Parliament and, in some cases, the ratification of half of the state legislatures.
• Procedure for a Money Bill:
• The Speaker of the Lok Sabha decides whether a bill is a Money Bill or not, and the decision is final.
• After passage in the Lok Sabha, the Money Bill is sent to the Rajya Sabha, which must return it within 14 days.
• If the Rajya Sabha fails to return the bill within 14 days, it is deemed to have been passed by both houses in the form in which it was passed by the Lok Sabha.

Important Points

• Article 110: It lays down the definition of a Money Bill in the Indian Constitution.
• Role of the Speaker: The Speaker of the Lok Sabha has the final authority to decide whether a bill is a Money Bill or not.
• Exclusive Introduction: Money Bills can only be introduced in the Lok Sabha on the recommendation of the President of India.
• Examples: The Finance Bill and the Appropriation Bill are types of Money Bills.

The correct answer is Is a scalar quantity, dependent on the axis.

Key Points

• The moment of inertia of a rigid body is a measure of its resistance to angular acceleration when a torque is applied about an axis.
• Moment of inertia is a scalar quantity and depends on the distribution of mass in the rigid body and the specific axis about which it is being calculated.
• It is calculated mathematically as the integral of mass elements multiplied by the square of their perpendicular distances from the axis of rotation (I = ∫r² dm).
• The value of the moment of inertia changes based on the geometry, shape, and orientation of the body relative to the axis. For example, the moment of inertia of a rod about its center is different from that about one of its ends.
• Hence, the moment of inertia is a scalar quantity, but it is dependent on the axis.

Additional Information

• Definition of Moment of Inertia:
• The moment of inertia represents the rotational equivalent of mass in linear motion. It quantifies how the mass is distributed relative to the axis of rotation.
• Its SI unit is kg.m², and it is always a positive scalar quantity.
• Factors Affecting Moment of Inertia:
• Mass Distribution: The farther the mass is from the axis, the greater the moment of inertia.
• Axis of Rotation: The axis's location and orientation significantly affect the value of the moment of inertia. For example, a uniform disc has different moments of inertia when rotated about its central axis and its diameter.
• Shape and Geometry: The shape (sphere, cylinder, rod, etc.) of the object influences its moment of inertia.
• Applications of Moment of Inertia:
• It is crucial in mechanical systems involving rotation, such as flywheels and turbines.
• In the design of vehicles, it helps determine the stability and control of rotating components like wheels and propellers.
• It is also used in structural engineering to analyze beams and other elements subject to torque or rotational forces.
• Parallel and Perpendicular Axis Theorems:
• Parallel Axis Theorem: If the moment of inertia of a body about an axis passing through its center of mass is known, the moment of inertia about any parallel axis can be calculated as I = I_cm + Md², where d is the distance between the axes.
• Perpendicular Axis Theorem: For a planar body, the moment of inertia about an axis perpendicular to the plane is the sum of the moments of inertia about two mutually perpendicular axes in the plane.

Important Points

• Moment of Inertia for Common Shapes:
• Thin Rod: About an axis through the center and perpendicular to its length: I = (1/12)ML².
• Solid Sphere: About its diameter: I = (2/5)MR².
• Solid Cylinder: About its central axis: I = (1/2)MR².
• Hollow Cylinder: About its central axis: I = MR².
• The moment of inertia is an integral property that underpins key concepts in rotational dynamics, such as angular momentum and torque.
• It is not a vector quantity but a scalar, although its influence is directional based on the axis of rotation.
• Understanding the moment of inertia is essential in designing efficient mechanical systems and analyzing rotational motion in physics.

The correct answer is 12.

Key Points

• The Universal Immunisation Programme (UIP) is one of the largest public health programs globally, aimed at reducing child mortality and morbidity due to vaccine-preventable diseases in India.
• Under UIP, 12 diseases are covered for free immunization nationally and sub-nationally. These include:
• Tuberculosis (BCG vaccine)
• Diphtheria, Pertussis, and Tetanus (DPT vaccine)
• Polio (OPV/IPV)
• Measles and Rubella (MR vaccine)
• Hepatitis B
• Japanese Encephalitis (JE vaccine) in endemic districts
• Haemophilus Influenzae Type B (HiB) (as Pentavalent vaccine)
• Rotavirus
• Pneumococcal Conjugate Vaccine (PCV)
• Measles second dose
• The program was initiated in 1985 and has expanded significantly over the years to include newer vaccines and reach remote areas.
• The Ministry of Health and Family Welfare oversees the UIP, ensuring vaccine availability and distribution across the country.
• India has achieved several milestones under UIP, such as the eradication of Polio and significant reductions in diseases like Measles and Neonatal Tetanus.

Additional Information

• History of UIP:
• Launched in 1985, replacing the Expanded Programme on Immunisation (EPI), which began in 1978.
• Initially targeted six diseases: Tuberculosis, Diphtheria, Pertussis, Tetanus, Poliomyelitis, and Measles.
• Gradual expansion brought in vaccines like Hepatitis B, Japanese Encephalitis, and Pentavalent vaccine.
• Implementation:
• Vaccination is provided through a network of primary health centers (PHCs), sub-centers, and Anganwadi workers.
• Emphasis is placed on reaching remote and underserved areas to reduce disparities in immunization coverage.
• Significant Achievements:
• India was declared Polio-free in 2014, a significant milestone under UIP.
• Reduction in Measles-related mortality by >50% due to improved vaccine coverage.
• Successful introduction of new vaccines like Rotavirus and Pneumococcal Conjugate Vaccine (PCV).
• Challenges:
• Vaccine hesitancy due to misinformation and cultural barriers.
• Maintaining the cold chain for vaccine storage, especially in remote regions.
• Ensuring equitable distribution and addressing logistical issues.
• Future Goals:
• Achieving universal immunization coverage under the Mission Indradhanush.
• Strengthening surveillance systems to monitor vaccine-preventable diseases.
• Introducing newer vaccines to address emerging health concerns.

Important Points

• Mission Indradhanush:
• Launched in December 2014 to accelerate the reach of UIP.
• Aimed at vaccinating all children under 2 years and pregnant women against vaccine-preventable diseases.
• Focus on 201 high-priority districts and states with low immunization coverage.
• Cold Chain Management:
• Essential for maintaining vaccine potency.
• India has over 27,000 cold chain points to store and distribute vaccines.
• Incorporation of technologies like solar-powered cold chain equipment to improve efficiency.
• New Vaccine Introduction:
• Rotavirus Vaccine: Prevents severe diarrheal diseases in infants.
• Pneumococcal Conjugate Vaccine: Addresses pneumonia and meningitis caused by pneumococcal bacteria.
• Human Papillomavirus (HPV) Vaccine: Proposed for introduction to combat cervical cancer.

The correct answer is India slipped in its global rank.

Key Points

• The Global Gender Gap Report is published annually by the World Economic Forum (WEF), which measures gender equality across four key dimensions: economic participation and opportunity, educational attainment, health and survival, and political empowerment.
• India has seen a slip in its global rank in recent editions of the report, indicating a widening gender gap in areas such as workforce participation, political representation, and educational equality.
• As per the latest trends, India’s performance has been particularly poor in economic participation and opportunity, where the gap between men and women has widened due to low female workforce participation and unequal pay.
• In the health and survival category, India continues to struggle due to issues such as sex ratio imbalances and access to healthcare for women.
• The decline in rank reflects broader systemic issues, including social norms, cultural barriers, and the impact of economic disruptions like the COVID-19 pandemic, which disproportionately affected women.

Additional Information

• Global Gender Gap Report:
• The report was first introduced by the World Economic Forum (WEF) in 2006 and aims to benchmark progress toward gender equality worldwide.
• The index ranks countries based on their performance across four dimensions: economic participation, educational attainment, health and survival, and political empowerment.
• In recent years, countries like Iceland, Finland, and Norway have consistently ranked at the top due to their progressive policies and cultural acceptance of gender equality.
• India's Position:
• In the 2023 edition of the report, India ranked 127th out of 146 countries, showing a decline from previous years.
• India’s economic participation and opportunity score remains low, mainly due to limited access to leadership roles and unequal pay.
• India’s political empowerment score is relatively better, attributed to the representation of women in the Lok Sabha and state assemblies.
• Impact of COVID-19:
• The COVID-19 pandemic exacerbated existing inequalities, pushing more women out of the workforce and increasing unpaid caregiving responsibilities.
• Many women in India faced challenges such as job losses, reduced income, and limited access to healthcare and education.
• Government Initiatives:
• India has launched several schemes to bridge the gender gap, such as Beti Bachao Beti Padhao, Mahila-E-Haat, and Stand-Up India.
• Programs focusing on education, entrepreneurship, and healthcare aim to empower women and reduce disparities.

Important Points

• Key Challenges:
• India’s low female labor force participation rate remains a major challenge in achieving gender equality.
• Persistent issues such as gender-based violence, discrimination, and patriarchal norms hinder progress.
• Lack of access to education and healthcare in rural areas disproportionately affects women and widens the gender gap.
• Recommendations:
• Promote policies that encourage women’s economic participation, such as flexible work arrangements and skill development programs.
• Increase investments in healthcare and education for women, especially in rural and underserved areas.
• Strengthen legal frameworks to address gender-based violence and workplace discrimination.

The correct answer is Revenue Budget.

Key Points

• Revenue Budget refers to the government’s accounting of its revenue receipts (both tax and non-tax) and the expenditure met from this revenue.
• It includes all recurring income sources such as tax revenues (e.g., income tax, GST, corporate tax) and non-tax revenues (e.g., dividends from public sector enterprises, interest receipts).
• The revenue budget details the government’s recurring expenditures on areas such as administration, subsidies, pensions, interest payments, and defense expenditure.
• When revenue receipts exceed revenue expenditure, it results in a Revenue Surplus. Conversely, when the expenditure surpasses receipts, it leads to a Revenue Deficit.
• It differs from the Capital Budget, which deals with long-term investments and liabilities, focusing on creating assets like infrastructure.

Additional Information

• Capital Budget:
• Deals with the government’s revenue from loans, borrowings, and the creation of assets like roads, schools, and hospitals.
• Includes capital receipts (e.g., loans, recovery of loans, disinvestment) and capital expenditure (e.g., infrastructure development).
• Finance Budget:
• It refers to the overall annual financial statement presented in Parliament, containing details of both revenue and capital budgets.
• It is an umbrella term encompassing all aspects of the government’s financial planning.
• Expenditure Budget:
• It is a part of the Union Budget that provides a detailed account of the government’s expenditure for the fiscal year.
• It is divided into revenue expenditure and capital expenditure.
• Revenue Receipts:
• Comprises tax revenues (e.g., GST, customs duties) and non-tax revenues (e.g., dividends, interest receipts).
• These receipts do not lead to an increase in liabilities or a reduction in assets.
• Revenue Expenditure:
• Includes day-to-day operational expenses such as salaries, subsidies, and interest payments.
• Unlike capital expenditure, it does not result in the creation of assets or reduction of liabilities.

Important Points

• Key Differences between Revenue and Capital Budget:
• Revenue Budget: Focuses on recurring income and expenditure, does not create assets.
• Capital Budget: Focuses on long-term investments, asset creation, and liabilities.
• Revenue Deficit: Occurs when revenue expenditure exceeds revenue receipts, indicating a shortfall in meeting day-to-day expenses.
• Budget Presentation: In India, the Union Budget is presented annually by the Finance Minister, as mandated under Article 112 of the Indian Constitution.
• Key Components of Union Budget: Revenue Budget, Capital Budget, Finance Bill, and Appropriation Bill.
• Fiscal Responsibility: The Fiscal Responsibility and Budget Management (FRBM) Act guides the government to reduce fiscal deficits and ensure fiscal discipline.

The correct answer is Only 1 correct.

Key Points

• Statement 1: Jhumar is indeed a harvest dance of Jharkhand. It is performed in linked rows, with the accompaniment of traditional musical instruments like the mandar and nagara drums. The dance is closely associated with the celebration of nature and agricultural prosperity. Hence, statement 1 is correct.
• Statement 2: The claim that women alone perform the Mardani variant wielding swords is inaccurate. Jhumar primarily involves men and women dancing together in harmony, and there is no specific "Mardani" variant where women perform with swords. Hence, statement 2 is incorrect.
• The Jhumar dance is performed during festive and social occasions, often marking the end of the harvest season. It is a vibrant expression of joy and community bonding.
• The dance is characterized by graceful movements, rhythmic footwork, and the use of traditional costumes, which adds to the cultural richness of the performance.
• Therefore, only statement 1 is correct.

Additional Information

• Jhumar Dance:
• Jhumar is a traditional folk dance of the tribal communities in Jharkhand, Odisha, and parts of West Bengal.
• The name "Jhumar" is derived from the rhythmic movements and the "jhumming" sound created during the performance.
• It is performed primarily during harvest festivals or other significant celebrations, symbolizing gratitude to nature.
• Musical Instruments:
• The performance is accompanied by traditional instruments such as mandar, nagara, and dhol.
• These instruments create a rhythmic and energetic ambiance, elevating the spirit of the dance.
• Tribal Communities:
• Jhumar is primarily performed by tribal communities such as the Santhals, Oraons, and Mundas.
• The dance reflects their cultural identity and their deep connection with nature and agriculture.
• Variants of Jhumar:
• Jhumar has several regional variations, such as the Chotanagpur Jhumar and the Bengal Jhumar, each with distinct styles and musical accompaniments.
• However, none of these variants specifically involve women wielding swords.

Important Points

• Costumes:
• Performers wear traditional costumes, often featuring bright colors and intricate embroidery.
• Women typically wear sarees, while men don dhotis and turbans.
• Social Significance:
• The dance fosters a sense of community and unity among the participants.
• It serves as a medium for storytelling and preserving cultural heritage.
• Cultural Representation:
• Jhumar is not just a dance form but also a representation of the tribal way of life.
• It emphasizes values like harmony, gratitude, and celebration.

The correct answer is Assam.

Key Points

• Kanaklata Barua was a courageous young female revolutionary who actively participated in India’s freedom struggle during the Quit India Movement.
• She was born on 22 December 1924, in the village of Bohgaon, located in Assam. Her early life was marked by a strong sense of patriotism and social awareness.
• During the Quit India Movement in 1942, Kanaklata Barua, along with other protesters, attempted to hoist the Indian National Flag at the local police station in Gohpur, Assam.
• On 20 September 1942, while leading a procession of unarmed protesters, Kanaklata was shot dead by the police. Her act of bravery and sacrifice made her a symbol of courage and patriotism in the Indian freedom struggle.
• The state of Assam honors her memory, and she is widely regarded as a martyr who fought for India's independence.

Additional Information

• Quit India Movement (1942):
• The Quit India Movement was launched on 8 August 1942, under the leadership of Mahatma Gandhi, to demand an end to British rule in India.
• It is also known as the August Kranti Movement.
• The movement called for mass protests, strikes, and civil disobedience across India, with the slogan "Do or Die."
• It faced severe repression from the British government, including arrests of leaders and violent crackdowns on protesters.
• Role of Women in the Freedom Struggle:
• Women like Kanaklata Barua, Rani Lakshmibai, Aruna Asaf Ali, and Sarojini Naidu played pivotal roles in India’s independence movement.
• They participated in marches, protests, and revolutionary activities, often risking their lives for the cause of freedom.
• Their contributions highlighted the critical role of women in shaping India’s socio-political landscape.
• Assam in the Freedom Struggle:
• The state of Assam was an active participant in the Indian freedom movement, with notable leaders like Gopinath Bordoloi and Kanaklata Barua.
• It witnessed significant protests during the Quit India Movement, including the hoisting of the tricolor in defiance of British authorities.
• Many freedom fighters from Assam sacrificed their lives, earning the state a prominent place in India’s independence history.
• Legacy of Kanaklata Barua:
• Kanaklata is remembered as a young martyr who symbolized the courage and determination of India’s youth during the freedom struggle.
• In her honor, several institutions, roads, and awards in Assam and other parts of India bear her name.
• She continues to inspire generations with her patriotism and bravery.

Important Points

• Significance of the Indian National Flag:
• During the freedom struggle, hoisting the Indian National Flag was a powerful act of defiance against British rule.
• It symbolized the aspirations of freedom fighters and united people under the common goal of independence.
• Young Martyrs in India’s Freedom Struggle:
• Kanaklata Barua was among several young martyrs who sacrificed their lives for India’s independence, including Khudiram Bose and Bhagat Singh.
• Their sacrifices serve as a reminder of the youthful energy and determination that fueled India’s freedom movement.

The correct answer is 12 years old.

Key Points

• Baji Raut was a 12-year-old boy from Odisha who became a martyr in India’s freedom struggle.
• He was shot dead by the British police for refusing to ferry them across the Brahmani River to pursue freedom fighters.
• Baji Raut was a member of the Banara Satyagraha, which was a movement opposing British colonial rule in Odisha.
• Despite his young age, Baji Raut displayed immense courage and refused to assist the British police, knowing the consequences.
• His sacrifice is remembered as an act of bravery and patriotism, symbolizing the resistance of ordinary Indians, including children, against colonial oppression.

Additional Information

• Baji Raut’s Background:
• He was born into a poor family in the village of Nilakanthapur in Odisha.
• His father was a boatman, and Baji followed in his footsteps, working as a ferryman on the Brahmani River.
• Incident Details:
• In 1938, during the Prajamandal Movement, the British police were chasing freedom fighters who had taken refuge across the Brahmani River.
• Baji Raut, upon realizing the police intentions, refused to ferry them across the river, despite threats.
• He was shot dead along with other volunteers, making him one of the youngest martyrs in India’s freedom struggle.
• Legacy:
• Baji Raut’s heroism is celebrated in Odisha and across India as an example of selfless sacrifice for the nation.
• Several monuments and schools in Odisha have been named after him to honor his contribution.
• Prajamandal Movement:
• This movement was a significant part of India’s freedom struggle, focused on opposing the British rule in princely states.
• It aimed to organize protests against the oppressive policies of feudal rulers and the British administration.

Important Points

• Youngest Martyrs:
• Baji Raut is regarded as one of the youngest martyrs in India’s history, symbolizing the involvement of people from all walks of life and age groups in the freedom struggle.
• Other young martyrs include Khudiram Bose, who was executed at the age of 18 for his role in revolutionary activities.
• Role of Odisha in Freedom Struggle:
• Odisha played a significant role in India’s independence movement, with movements like the Quit India Movement and the Prajamandal Movement.
• Leaders such as Gopabandhu Das and Harekrushna Mahatab contributed immensely to the struggle against colonial rule.

The correct answer is Yamuna River.

Key Points

• The National Mission for Clean Ganga (NMCG) aims to rejuvenate the Ganga River and its tributaries by addressing pollution, ecological restoration, and sustainable river management.
• In 2025, the Yamuna River, a major tributary of the Ganga, was added to the 'National Aquatic Ecosystem Restoration Mission' to enhance its ecological health and tackle severe pollution issues.
• The Yamuna River is the second-largest tributary of the Ganga, flowing through states like Uttarakhand, Haryana, Uttar Pradesh, and Delhi, making it crucial for urban and rural water needs.
• The inclusion of the Yamuna River under the mission aligns with the government’s commitment to addressing pollution hotspots, including industrial effluents and untreated sewage, particularly in urban areas like Delhi and Agra.
• Several restoration efforts under NMCG include bioremediation, afforestation, public awareness campaigns, and infrastructure development for sewage treatment plants (STPs) along the Yamuna basin.

Additional Information

• National Mission for Clean Ganga (NMCG):
• NMCG is implemented under the Ministry of Jal Shakti and was launched in 2014 as part of the government’s flagship Namami Gange Programme.
• Its primary objectives include pollution abatement, river rejuvenation, biodiversity conservation, and public participation.
• The program focuses on sustainable development approaches, including industrial regulation and urban wastewater management.
• Yamuna River:
• The Yamuna originates from the Yamunotri Glacier in Uttarakhand and flows for approximately 1,376 km before merging with the Ganga in Prayagraj, Uttar Pradesh.
• It is heavily polluted, particularly in urban areas like Delhi, due to untreated sewage, industrial discharges, and agricultural runoff.
• Efforts to clean the river include the Yamuna Action Plan, initiated in 1993 with Japanese aid, which focuses on sewage treatment and reducing pollution.
• Other Tributaries under NMCG:
• Several other tributaries like the Ghaghara, Gandak, and Son Rivers are already part of the mission, addressing pollution and restoration issues.
• The inclusion of tributaries ensures a holistic approach to cleaning the entire Ganga basin.
• Pollution Challenges:
• Major pollution sources include urban wastewater, agricultural runoff, and industrial effluents.
• Efforts like setting up sewage treatment plants (STPs) and promoting zero liquid discharge (ZLD) principles are crucial for controlling pollution levels.

Important Points

• Namami Gange Programme:
• Launched in June 2014 with an allocation of Rs. 20,000 crore, it is one of the most comprehensive river rejuvenation programs globally.
• The program focuses on cleaning the Ganga River, afforestation, industrial effluent monitoring, and developing riverfronts.
• Role of State Governments:
• State governments play a critical role by implementing sewage management infrastructure and enforcing pollution control regulations.
• They also engage local communities and stakeholders for better implementation of river restoration projects.
• Public Participation:
• Public awareness campaigns, including the involvement of NGOs, schools, and local bodies, are pivotal for the success of restoration programs.
• Initiatives like Ganga Utsav and river walks aim to educate citizens about the importance of river conservation.

The correct answer is To keep production under government control.

Key Points

• The Industrial Policy Resolution (IPR) of 1956 was a landmark in India’s economic policy, laying the foundation of a mixed economy where both the public and private sectors could co-exist under state regulation.
• The government introduced licensing even for expansion of private industries to maintain control over production capacity and ensure that resources were allocated based on national priorities.
• The licensing system aimed to regulate the growth of certain industries, ensuring that they aligned with the development goals of the government, such as equitable distribution of resources and prevention of monopolies.
• This measure was implemented to ensure that the private sector did not dominate critical industries and that the state maintained a significant role in economic planning and resource allocation.
• The focus was particularly on industries considered critical for national development, such as steel, heavy machinery, and defense, which were placed under stringent control to meet long-term goals.

Additional Information

• Industrial Policy Resolution (IPR) of 1956:
• The IPR 1956 categorized industries into three schedules:
• Schedule A: Industries exclusively reserved for the public sector, such as defense and atomic energy.
• Schedule B: Industries where both the public and private sectors could operate, but the government took an active role.
• Schedule C: Industries left to the private sector but regulated by the government through licensing.
• The policy emphasized the importance of the public sector in commanding the economy and achieving socialist-inspired goals of equitable distribution of wealth.
• Objectives of Licensing:
• To prevent excessive concentration of economic power in a few hands and ensure balanced regional development.
• To prioritize the allocation of resources to industries crucial for the country’s development, such as infrastructure and heavy industries.
• To regulate production to meet domestic demands and prevent overproduction or underproduction in specific sectors.
• Impact of Licensing:
• The licensing system led to the emergence of the License Raj, where businesses had to obtain multiple clearances and approvals, often leading to inefficiencies and corruption.
• While the system aimed to ensure equitable growth, it also hindered innovation and competitiveness in the private sector.
• The government retained significant control over industrial growth, aligning production with its planned economic goals.
• Alternatives to Licensing:
• In the 1991 economic reforms, the government dismantled the License Raj, allowing industries to grow freely with fewer restrictions.
• This liberalization policy aimed to boost economic efficiency, innovation, and competitiveness in the global market.

Important Points

• Option 1: To promote export competition: This is incorrect. Licensing was not aimed at promoting exports but at regulating industrial growth domestically.
• Option 3: To prevent technological innovation: This is incorrect. Licensing was not intended to hinder innovation but to ensure government control over critical industries.
• Option 4: To encourage luxury production: This is incorrect. The focus was on essential industries, not luxury goods, to meet the developmental needs of the country.

The correct answer is 4) 2 and 3.

Key Points

• Article 263 of the Constitution of India empowers the President, not Parliament, to establish the Inter-State Council. Hence, statement 1 is incorrect.
• The Inter-State Council is tasked with investigating and discussing subjects of common interest between states or between the Union and states. It also makes recommendations for better coordination of policy and action on such subjects. Hence, statement 2 is correct.
• The composition of the Inter-State Council includes the Prime Minister as the Chairperson, Union Ministers, and Chief Ministers of states. It is structured to ensure representation from all levels of government. Hence, statement 3 is correct.
• The Council's role is consultative, and it does not have adjudicatory or binding decision-making power over inter-state disputes.
• Article 263 does not mandate the creation of an Inter-State Council but leaves it to the discretion of the President, based on the necessity for coordination and cooperation.

Additional Information

• Constitutional Provision (Article 263):
• Article 263 of the Constitution provides for the establishment of an Inter-State Council to serve as a platform for discussion and resolution of disputes between states or between states and the Union.
• The article outlines three main purposes of the council: investigating inter-state disputes, discussing subjects of common interest, and making recommendations for coordination of policy and action.
• The Council is consultative in nature and does not have binding authority.
• Composition of the Inter-State Council:
• The Prime Minister serves as the Chairperson of the Council.
• Other members include Chief Ministers of all states, Administrators of Union Territories, and Union Ministers as designated by the Prime Minister.
• Inter-State Council's Functions:
• Facilitates coordination between states and the Union in areas of mutual interest.
• Provides recommendations for better policy implementation and dispute resolution.
• Investigates and discusses specific issues referred to it by the President.
• Significance of the Council:
• Helps in promoting cooperative federalism by providing a platform for dialogue between states and the Union.
• Addresses administrative and legislative challenges in a non-adjudicative manner.
• Encourages harmonization of policies across states for common goals such as economic growth and social development.
• Historical Context:
• The Inter-State Council was established in 1990 by a Presidential Order based on the recommendations of the Sarkaria Commission.
• The Sarkaria Commission emphasized the need for such a forum to improve Centre-State and inter-state relations.

Important Points

• Role of the Inter-State Council: It is purely advisory in nature and does not have the power to adjudicate disputes or enforce its recommendations.
• Sarkaria Commission: Recommended the establishment of the Inter-State Council to address Centre-State and inter-state conflicts and enhance cooperative federalism.
• Article 262 vs. Article 263: While Article 262 deals with the adjudication of inter-state water disputes, Article 263 focuses on a consultative mechanism for broader inter-state issues.
• Cooperative Federalism: The council is an essential mechanism for fostering dialogue and collaboration between states and the Union, promoting the ideal of cooperative federalism enshrined in the Constitution.

Shortcut Trick

Solve the denominator directly: 24² + 6² − 144 = 576 + 36 − 144 = 468.

Convert the decimal numerator to an integer with a negative power of 10: 0.01404 = 1404 × 10⁻⁵.

Divide the converted numerator by the denominator: 1404 ÷ 468 = 3.

Combine with the power of 10 to get the final result: 3 × 10⁻⁵.

∴ The correct answer is 3 × 10⁻⁵.

Alternate Method

Given:

Expression = 0.01404 ÷ (24² + 6² − 144)

Calculations:

⇒ First, simplify the terms inside the parentheses (denominator).

⇒ 24² = 576

⇒ 6² = 36

⇒ Denominator = 576 + 36 − 144

⇒ Denominator = 612 − 144 = 468

⇒ Substitute the simplified denominator back into the expression.

⇒ Expression = 0.01404 ÷ 468

⇒ To make the division easier, write 0.01404 as an integer multiplied by a base of 10.

⇒ 0.01404 = 1404 × 10⁻⁵

⇒ Expression = (1404 × 10⁻⁵) ÷ 468

⇒ Expression = (1404 ÷ 468) × 10⁻⁵

⇒ Expression = 3 × 10⁻⁵

∴ The correct answer is 3 × 10⁻⁵.

Additional Information

BODMAS Rule

Simplification problems strictly follow the BODMAS order: Brackets, Orders (powers/roots), Division/Multiplication, and Addition/Subtraction.

Decimal to Exponent Conversion

A decimal number can be seamlessly converted to an integer by multiplying it with a negative power of 10 that perfectly matches the number of decimal places shifted (e.g., 0.01404 = 1404 × 10⁻⁵).

Algebraic Identity Application

The denominator pattern in the expression resembles the partial factor (a² + b² − ab), which inherently stems from the sum of cubes formula: a³ + b³ = (a + b)(a² − ab + b²).

Shortcut Trick

If a sum becomes n times in t years at compound interest, it becomes n^m times in m × t years.

Here, the sum becomes 2 times in 4 years.

We need to find the time for the sum to become 8 times itself.

8 can be written as 2³ (so m = 3).

Time required = 3 × 4 = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given:

A sum invested at compound interest doubles itself in 4 years.

Formula Used:

A = P(1 + R/100)^T

0 yrs P

4 yrs 2P

8 yrs 4P

12 yrs 8P

×2

×2

×2

Calculations:

⇒ 2P = P(1 + R/100)⁴

⇒ 2 = (1 + R/100)⁴

Let the sum become 8 times in T years.

⇒ 8P = P(1 + R/100)^T

⇒ 8 = (1 + R/100)^T

We know that 8 can be written as 2³:

⇒ 2³ = (1 + R/100)^T

Substitute the value of 2 from the first equation:

⇒ ((1 + R/100)⁴)³ = (1 + R/100)^T

⇒ (1 + R/100)¹² = (1 + R/100)^T

Comparing the exponents on both sides:

⇒ T = 12

∴ The correct answer is 12 years.

Additional Information

Simple vs Compound Interest

Simple Interest grows by adding a constant amount each year, whereas Compound Interest grows by multiplying a constant factor each year.

Compound Interest Formula

Amount A = P(1 + R/100)ⁿ and CI = A − P, where P is the principal sum, R is the rate of interest, and n is the time period.

Rule of 72

The Rule of 72 is a quick mental math shortcut to estimate the number of years required to double your money at a given annual compound interest rate (Years ≈ 72 ÷ Rate).

Shortcut Trick

Every Whole number is automatically an Integer, a Rational number, and a Real number.

The set of Whole numbers is {0, 1, 2, 3, ...}.

We need a non-zero number, which eliminates 0.

Among the given options, only 1 is a non-zero whole number.

∴ The correct answer is 1.

Alternate Method

Given:

Sets to check: Whole, Integer, Rational, and Real numbers.

Condition: The number must be non-zero.

Definitions:

⇒ Whole numbers = {0, 1, 2, 3, ...}

⇒ Integers = {..., −2, −1, 0, 1, 2, ...}

⇒ Rational numbers = Numbers of the form p/q (where q ≠ 0).

⇒ Real numbers = All rational and irrational numbers.

Checking the Options:

⇒ Option 1: 1 is non-zero. It is a Whole number, Integer, Rational (1/1), and Real. (Satisfies all)

⇒ Option 2: 0 is a Whole number, but the question asks for a non-zero number. (Rejected)

⇒ Option 3: −1 is an Integer but NOT a Whole number. (Rejected)

⇒ Option 4: √2 is a Real number but NOT a Whole, Integer, or Rational number. (Rejected)

∴ The correct answer is 1.

Additional Information

Natural Numbers

Counting numbers starting from 1 are called Natural numbers (N = {1, 2, 3, 4, ...}). They do not include 0, fractions, or decimals.

Irrational Numbers

Numbers that cannot be written as a simple fraction p/q. Their decimal expansions are non-terminating and non-repeating. Examples: √2, π, e.

Prime Numbers

Natural numbers greater than 1 that have exactly two distinct positive divisors: 1 and themselves. Examples: 2, 3, 5, 7, 11.

Shortcut Trick

To directly find the speed in km/h, calculate distance over time and multiply by the conversion factor (18 ÷ 5).

Speed = (300 ÷ 24) × (18 ÷ 5)

Speed = 12.5 × 3.6 = 45 km/h

∴ The correct answer is 45 km/h.

Alternate Method

Given:

Distance covered by the athlete = 300 m

Time taken = 24 seconds

Formula Used:

Speed = Distance ÷ Time

Speed in km/h = Speed in m/s × (18 ÷ 5)

Start Finish Distance = 300 m  A   Time = 24 s Speed = ? km/h

Calculations:

⇒ Speed in m/s = 300 ÷ 24

⇒ Speed = 12.5 m/s

⇒ Speed in km/h = 12.5 × (18 ÷ 5)

⇒ Speed in km/h = 2.5 × 18

⇒ Speed = 45 km/h

∴ The correct answer is 45 km/h.

Additional Information

Speed Conversion Factors

To convert speed from m/s to km/h, always multiply by 18 ÷ 5. Conversely, to convert from km/h to m/s, multiply by 5 ÷ 18.

Average Speed

When an object travels equal distances at two different speeds S₁ and S₂, the average speed for the entire journey is given by (2 × S₁ × S₂) ÷ (S₁ + S₂).

Relative Speed

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

Shortcut Trick

According to the given condition, directly equate the volume and surface area of the sphere:

⇒ (4/3)πr³ = 4πr²

⇒ r/3 = 1 (Canceling 4πr² from both sides)

⇒ r = 3

∴ The correct answer is 3 units.

Alternate Method

Given:

Volume of the sphere = Surface area of the sphere

Formula Used:

Volume of a sphere = (4/3)πr³

Surface Area of a sphere = 4πr²

 O r Volume = Surface Area

Calculation:

According to the given condition:

⇒ (4/3) × π × r³ = 4 × π × r²

⇒ (4/3) × r³ = 4 × r²

⇒ (1/3) × r = 1 (Since radius r ≠ 0, we can divide both sides by 4r²)

⇒ r = 3 × 1

⇒ r = 3 units

∴ The correct answer is 3 units.

Additional Information

Volume of a Hemisphere

When a sphere is divided into two equal parts, each part is called a hemisphere. Volume = (2/3)πr³

Curved Surface Area (CSA) of a Hemisphere

The surface area of the curved surface only, excluding the flat circular top. CSA = 2πr²

Total Surface Area (TSA) of a Hemisphere

Includes the curved surface area plus the area of the flat circular base (πr²). TSA = 3πr²

Shortcut Trick

Convert time directly to hours: 48 minutes = 48 ÷ 60 = 4/5 hours.

Speed = Distance ÷ Time

Speed = 7.2 ÷ (4/5) = 7.2 × 5/4 = 9 km/h.

∴ The correct answer is 9 km/h.

Alternate Method

Start End Distance = 7.2 km Time = 48 minutes Speed = ? km/h

Given:

Distance = 7.2 km

Time = 48 minutes

Formula Used:

Speed = Distance ÷ Time

Calculations:

⇒ First, convert time from minutes to hours to match the required speed unit (km/h).

⇒ Time = 48 ÷ 60 hours

⇒ Time = 0.8 hours

⇒ Speed = 7.2 ÷ 0.8

⇒ Speed = 72 ÷ 8

⇒ Speed = 9 km/h

∴ The correct answer is 9 km/h.

Additional Information

Conversion of Speed Units

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

Average Speed

Average Speed is calculated as the total distance traveled divided by the total time taken (Total Distance ÷ Total Time).

Relative Speed

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

Shortcut Trick

Profit ratio is directly proportional to (Capital × Time).

Ratio of X : Y : Z = (50 × 12) : (100 × 12) : (150 × 6)

Ratio = 600 : 1200 : 900 = 2 : 4 : 3

Total profit = 2 + 4 + 3 = 9 parts = Rs. 90,000 ⇒ 1 part = Rs. 10,000

Difference in earnings of Z and X = 3 − 2 = 1 part.

∴ The correct answer is Rs. 10,000.

Alternate Method

Given:

Investment by X = Rs. 50,000

Investment by Y = Rs. 1,00,000

Investment by Z = Rs. 1,50,000

Total Profit at year-end = Rs. 90,000

Formula Used:

Profit Ratio = (C₁ × T₁) : (C₂ × T₂) : (C₃ × T₃)

X 50k 12 mths Ratio: 2 Y 100k 12 mths Ratio: 4 Z 150k 6 mths Ratio: 3 Diff (Z − X) = 3 − 2 = 1 part

Calculations:

⇒ Time period for X = 12 months

⇒ Time period for Y = 12 months

⇒ Z joined after 6 months, so Time period for Z = 12 − 6 = 6 months

⇒ Profit Ratio (X : Y : Z) = (50,000 × 12) : (1,00,000 × 12) : (1,50,000 × 6)

⇒ Ratio = 6,00,000 : 12,00,000 : 9,00,000

⇒ Dividing each term by 3,00,000 ⇒ Ratio = 2 : 4 : 3

⇒ Total profit parts = 2 + 4 + 3 = 9 parts

⇒ 9 parts = Rs. 90,000

⇒ 1 part = 90,000 ÷ 9 = Rs. 10,000

⇒ Profit share of X = 2 × 10,000 = Rs. 20,000

⇒ Profit share of Z = 3 × 10,000 = Rs. 30,000

⇒ Difference (Z − X) = 30,000 − 20,000 = Rs. 10,000

∴ The correct answer is Rs. 10,000.

Additional Information

Compound Partnership

When partners invest different capital amounts for different time durations, the profit is divided in the ratio of the product of their respective capital and time period: (C₁ × T₁ : C₂ × T₂).

Joining Mid-Way

If a partner joins the business later in the year, their effective time period is calculated by subtracting their joining time from the total business duration. Here, Z joined after 6 months, so the effective active time was 12 − 6 = 6 months.

Active vs Sleeping Partner

A partner who physically manages the business is called an active or working partner. They often receive a fixed salary or commission from the net profit before the remaining amount is distributed among all partners based on their capital ratios.

Shortcut Trick

Total parts in ratio = 2 + 3 + 4 = 9 parts.

Value of 9 parts = ₹9000 ⇒ 1 part = ₹1000.

Difference in ratio (Highest − Lowest) = 4 − 2 = 2 parts.

Difference amount = 2 × 1000 = ₹2000.

∴ The correct answer is ₹2000.

Alternate Method

Given:

Total prize amount = ₹9000

Ratio of shares of three friends = 2 : 3 : 4

2 Parts 3 Parts 4 Parts Total Prize = ₹9000 (9 Parts) Lowest Highest Difference = 4 − 2 = 2 Parts

Calculations:

Let the shares of the three friends be 2x, 3x, and 4x respectively.

⇒ Total sum = 2x + 3x + 4x = 9x

⇒ We are given that the total sum is ₹9000.

⇒ 9x = 9000

⇒ x = 9000 ÷ 9 = 1000

⇒ The highest share = 4x = 4 × 1000 = 4000

⇒ The lowest share = 2x = 2 × 1000 = 2000

⇒ Difference = 4000 − 2000 = 2000

∴ The correct answer is ₹2000.

Additional Information

Compound Ratio

The ratio of the product of the antecedents to that of the consequents of two or more given ratios is called the compound ratio. If a:b and c:d are two ratios, their compound ratio is (a × c):(b × d).

Duplicate & Triplicate Ratios

The duplicate ratio of a:b is a²:b². The triplicate ratio of a:b is a³:b³.

Proportion Rule

An equality of two ratios is called a proportion. If a:b = c:d, then a, b, c, and d are in proportion. The fundamental rule is: Product of extremes = Product of means (a × d = b × c).

Shortcut Trick

Let the base and height of the triangle be 5x and 4x respectively.

Area = (1 ÷ 2) × Base × Height = (1 ÷ 2) × 5x × 4x = 10x².

Given Area = 160 cm² ⇒ 10x² = 160 ⇒ x² = 16 ⇒ x = 4.

Base = 5 × 4 = 20 cm, and Height = 4 × 4 = 16 cm.

∴ The correct answer is 20 cm and 16 cm.

Alternate Method

Given:

Ratio of base to height = 5 : 4

Area of the triangular flag = 160 cm²

Formula Used:

Area of a Triangle = (1 ÷ 2) × Base × Height

Base = 5x Height = 4x Area = 160 sq cm Base = 20 cm, Height = 16 cm

Calculations:

⇒ Let the base of the triangle be 5x.

⇒ Let the height of the triangle be 4x.

⇒ Area = (1 ÷ 2) × (5x) × (4x)

⇒ 160 = 10x²

⇒ x² = 160 ÷ 10

⇒ x² = 16

⇒ x = √16 = 4

⇒ Base = 5 × 4 = 20 cm

⇒ Height = 4 × 4 = 16 cm

∴ The correct answer is 20 cm and 16 cm.

Additional Information

Area of an Equilateral Triangle

For a triangle with all three sides equal to a, Area = (√3 ÷ 4) × a².

Heron's Formula

For a triangle with side lengths a, b, and c, Area = √[s(s − a)(s − b)(s − c)], where s = (a + b + c) ÷ 2.

Right-Angled Triangle

Area = (1 ÷ 2) × Base × Perpendicular. The sides satisfy the Pythagorean theorem: Hypotenuse² = Base² + Perpendicular².

Shortcut Trick

Fractional equivalent of 8% = 8/100 = 2/25

Multiplying factor for 2 years = (1 + 2/25)² = (27/25)² = 729/625

Here, 729 units represent the current population and 625 units represent the past population.

⇒ 729 units = 58320 ⇒ 1 unit = 80

⇒ Past Population = 625 × 80 = 50000

∴ The correct answer is 50000.

Alternate Method

Given:

Current Population = 58,320

Annual increase rate (R) = 8%

Time (T) = 2 years

Formula Used:

Current Population = P × (1 + R/100)^T

Past (P) Year 1 58,320        + 8% + 8% Population Growth over 2 Years P × 1.08 × 1.08 = 58,320

Calculations:

Let the population 2 years ago be P.

⇒ 58320 = P × (1 + 8/100)²

⇒ 58320 = P × (108/100)²

⇒ 58320 = P × (27/25)²

⇒ 58320 = P × (729/625)

⇒ P = 58320 × (625/729)

⇒ P = 80 × 625

⇒ P = 50000

∴ The correct answer is 50000.

Additional Information

Population Decrease (Depreciation)

If the population decreases by R% annually, the population after T years is P × (1 − R/100)^T.

Successive Percentage Change

If a value undergoes two successive percentage changes of A% and B%, the net percentage change is given by: Net Change = A + B + (A × B)/100.

Population After n Years vs n Years Ago

Population after n years = P × (1 + R/100)ⁿ. Population n years ago = P ÷ (1 + R/100)ⁿ.

Shortcut Trick

Overall profit percentage = (100 ÷ 5000) × 100 = +2%

By Alligation, ratio of profit to loss investment = (2 − (−5)) : (10 − 2) = 7 : 8

Total investment parts = 7 + 8 = 15 parts

Investment in profit item = (7 ÷ 15) × 5000 ⇒ 35000 ÷ 15 = 2333.33

∴ The correct answer is Rs. 2,333.33.

Alternate Method

Given:

Total Investment = Rs. 5000

Profit on 1st item = 10%

Loss on 2nd item = 5%

Net profit = Rs. 100

Formula Used:

Net Profit = (Profit on 1st item) − (Loss on 2nd item)

 Profit Item Loss Item  +10%  −5%  +2%  7  8 Ratio = 7 : 8

Calculations:

Let the investment in the profit-making item be x.

⇒ Investment in the loss-making item = 5000 − x

⇒ Profit from 1st item = 10% of x = 0.10x

⇒ Loss from 2nd item = 5% of (5000 − x) = 0.05 × (5000 − x)

⇒ Net profit = 0.10x − 0.05 × (5000 − x)

⇒ 100 = 0.10x − 250 + 0.05x

⇒ 100 + 250 = 0.15x

⇒ 350 = 0.15x

⇒ x = 350 ÷ 0.15

⇒ x = 35000 ÷ 15

⇒ x = 7000 ÷ 3 ≈ 2333.33

∴ The correct answer is Rs. 2,333.33.

Additional Information

Alligation Method

Used to find the ratio in which two components at given prices/percentages are mixed to produce a mixture at a target value. The components are subtracted diagonally with respect to the overall mixture average.

Overall Profit/Loss Percentage

Net Profit % = (Net Profit ÷ Total CP) × 100. It combines individual profits and losses across parts of an investment.

Profit and Loss Basics

Profit occurs when Selling Price > Cost Price. Loss occurs when Cost Price > Selling Price. Both values are fundamentally calculated on the initial Cost Price or Investment.

Shortcut Trick

For questions where groups work as 'OR', Time = Given Days ÷ [(M_and ÷ M_or) + (W_and ÷ W_or)]

Time = 70 ÷ [(5 ÷ 5) + (12 ÷ 12)]

Time = 70 ÷ (1 + 1) = 70 ÷ 2

Time = 35 days

∴ The correct answer is 35 Days.

Alternate Method

Given:

Time taken by a group of 5 men = 70 days

Time taken by a group of 12 women = 70 days

Formula Used:

Efficiency = Total Work ÷ Time Taken

Calculations:

⇒ Let the total work be the LCM of given days (70, 70) = 70 units.

⇒ Efficiency of 5 men = 1 unit/day

⇒ Efficiency of 12 women = 1 unit/day

⇒ Combined efficiency of (5 men + 12 women) = 1 + 1 = 2 units/day.

⇒ Time taken by 5 men and 12 women together = Total Work ÷ Combined Efficiency

⇒ Required Time = 70 ÷ 2 = 35 days.

∴ The correct answer is 35 Days.

Additional Information

OR - AND Concept

When a task is done by 'x' men OR 'y' women in D days, the time taken by 'a' men AND 'b' women together directly uses the formula: D ÷ [(a ÷ x) + (b ÷ y)].

Total Work Equivalence

Total Work = Men × Days. Equating different groups (M₁ × D₁ = M₂ × D₂) helps in finding individual efficiency ratios.

Efficiency and Time Relationship

Time taken to complete a task is inversely proportional to the working efficiency. Increasing efficiency reduces the time proportionately.

Shortcut Trick

Using the unitary method, we can first find the number of bottles filled in 1 minute.

Bottles filled per minute = 120 ÷ 6 = 20 bottles.

Bottles filled in 14 minutes = 20 × 14 = 280 bottles.

∴ The correct answer is 280 milk bottles.

Alternate Method

Given:

Initial work (W₁) = 120 bottles

Initial time (T₁) = 6 minutes

New time (T₂) = 14 minutes

Formula Used:

Using the chain rule for direct proportion: W₁ / T₁ = W₂ / T₂

6 minutes × 20 (Rate) 120 bottles 14 minutes × 20 (Rate) 280 bottles

Calculations:

⇒ 120 / 6 = W₂ / 14

⇒ 20 = W₂ / 14

⇒ W₂ = 20 × 14

⇒ W₂ = 280

∴ The correct answer is 280 milk bottles.

Additional Information

Direct Proportion

When two quantities increase or decrease together, they are in direct proportion. The ratio of their values remains constant: X₁ / Y₁ = X₂ / Y₂.

Inverse Proportion

When one quantity increases while the other decreases, they are in inverse proportion. Their product remains constant: X₁ × Y₁ = X₂ × Y₂.

Unitary Method

A technique to solve proportion problems by first finding the value of a single unit, and then multiplying that rate to find the required proportional value.

Shortcut Trick

Average weight of the two removed boxes = (21 + 10) ÷ 2 = 15.5 kg.

If the average of the removed items is exactly equal to the original average of the group, the new average remains unchanged.

Since the removed boxes have the same average as the whole group, there is 0 net deviation.

∴ The correct answer is 15.5 kg.

Alternate Method

Given:

Average weight of 10 boxes = 15.5 kg

Weight of the heaviest box = 21 kg

Weight of the lightest box = 10 kg

Formula Used:

Sum of observations = Average × Number of observations

Total 10 boxes = 155 kg (15.5 kg/box)  10 kg  Remaining 8 boxes (124 kg)  21 kg    New Average = 124 ÷ 8 = 15.5 kg

Calculations:

⇒ Total weight of 10 boxes = 10 × 15.5 = 155 kg

⇒ Total weight of the heaviest and lightest boxes = 21 + 10 = 31 kg

⇒ Weight of the remaining 8 boxes = 155 − 31 = 124 kg

⇒ Average weight of the remaining boxes = 124 ÷ 8

⇒ Average weight = 15.5 kg

∴ The correct answer is 15.5 kg.

Additional Information

Net Deviation Method

If the average of a sub-group removed from a total group is perfectly equal to the original average, the new average remains unchanged.

Combined Average

When combining two separate groups, the combined average is represented by: (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Replacement in Average

New value = Old value + (Number of items × Change in average). A positive change means the incoming item is heavier.

Shortcut Trick

Initial acid percentage in the mixture = (2 / 5) × 100 = 40%

Fraction of original mixture remaining = (150 − 30) / 150 = 120 / 150 = 4 / 5

Since the removed part is replaced by pure water, the acid concentration reduces proportionally.

Final acid percentage = Initial % × Fraction remaining = 40% × (4 / 5) = 32%

∴ The correct answer is 32%.

Alternate Method

Given:

Total initial volume of mixture = 150 litres

Ratio of acid to water = 2 : 3

Amount of mixture replaced with water = 30 litres

      150 Litres Ratio 2:3 Acid: 60L Water: 90L  − 30L Mixture  + 30L Water  150 Litres Acid: 48L Water: 102L Acid = 32%

Calculations:

⇒ Quantity of acid initially = [2 / (2 + 3)] × 150 = (2 / 5) × 150 = 60 litres

⇒ When 30 litres of mixture is removed, the acid removed proportionally = (2 / 5) × 30 = 12 litres

⇒ Remaining acid in the mixture = 60 − 12 = 48 litres

⇒ Total volume after replacing with 30 litres of water remains 150 litres

⇒ Percentage of acid in final mixture = (Remaining Acid / Total Volume) × 100

⇒ Percentage of acid = (48 / 150) × 100 = 32%

∴ The correct answer is 32%.

Additional Information

Successive Replacement Formula

If a vessel contains V litres of pure liquid, and R litres are repeatedly removed and replaced with another liquid n times, the remaining pure liquid = V × (1 − R/V)ⁿ.

Alligation Rule

Ratio of quantities = (Cheaper quantity / Dearer quantity) = (Price of dearer − Mean price) / (Mean price − Price of cheaper). This easily computes mixture proportions.

Concentration in Mixtures

When two mixtures of volumes V₁ and V₂ with concentrations C₁ and C₂ are mixed, the final concentration is (C₁V₁ + C₂V₂) ÷ (V₁ + V₂).

Shortcut Trick

Convert all heights to cm: 0.8 m = 80 cm and 1.2 m = 120 cm.

Volume of top part = Length × Width × Height = 40 × 30 × 80 = 96,000 cm³ = 96 L.

Volume of bottom part = Base Area × Height = 60 × 120 = 7,200 cm³ = 7.2 L.

Total Volume = 96 L + 7.2 L = 103.2 L.

∴ The correct answer is 103.2 L.

Alternate Method

Given:

Base dimensions of the top rectangular prism = 40 cm × 30 cm

Height of the top rectangular prism = 0.8 m = 80 cm

Base area of the bottom triangular prism = 60 cm²

Height of the bottom triangular prism = 1.2 m = 120 cm

Formula Used:

Volume of a rectangular prism = Length × Width × Height

Volume of any prism = Base Area × Height

1 Liter (L) = 1,000 cm³

Top Part (Rectangular Prism) Base = 40 × 30 cm, Height = 80 cm Volume = 96,000 cu cm = 96 L Bottom Part (Triangular Prism) Base Area = 60 sq cm, Height = 120 cm Volume = 7,200 cu cm = 7.2 L Total Volume = 96 L + 7.2 L = 103.2 L

Calculations:

⇒ Volume of the top rectangular part = 40 × 30 × 80

⇒ Volume of the top rectangular part = 96,000 cm³

⇒ Convert top part to liters: 96,000 ÷ 1000 = 96 L

⇒ Volume of the bottom triangular part = 60 × 120

⇒ Volume of the bottom triangular part = 7,200 cm³

⇒ Convert bottom part to liters: 7,200 ÷ 1000 = 7.2 L

⇒ Total capacity of the water tank = 96 L + 7.2 L = 103.2 L

∴ The correct answer is 103.2 L.

Additional Information

Volume of a Prism

The volume of any prism is calculated by the product of its uniform base area and its height (V = Base Area × Height), regardless of the geometric shape of its base.

Important Volume Conversions

1 m³ = 1,000 Liters and 1 Liter = 1,000 cm³. By relation, 1 m³ equals 1,000,000 cm³.

Composite Solids

The total volume of a composite figure is simply the direct sum of the volumes of its individual 3D components without any geometric loss.

Shortcut Trick

The standard trigonometric identity is cosec²A = 1 + cot²A.

Substitute cotA = x + (1/x) directly into the formula.

cosec²A = 1 + [x + (1/x)]²

cosec²A = 1 + x² + (1/x²) + 2

cosec²A = x² + (1/x²) + 3

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

Alternate Method

Given:

cotA = x + (1/x)

Formula Used:

cosec²A − cot²A = 1

(a + b)² = a² + b² + 2ab

Calculations:

⇒ cosec²A = 1 + cot²A

⇒ cosec²A = 1 + [x + (1/x)]²

⇒ cosec²A = 1 + x² + (1/x)² + 2 × x × (1/x)

⇒ cosec²A = 1 + x² + (1/x²) + 2

⇒ cosec²A = x² + (1/x²) + 3

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

Additional Information

Pythagorean Trigonometric Identities

• sin²θ + cos²θ = 1

• sec²θ − tan²θ = 1

• cosec²θ − cot²θ = 1

Reciprocal Trigonometric Identities

• sinθ = 1 ÷ cosecθ

• cosθ = 1 ÷ secθ

• tanθ = 1 ÷ cotθ

Standard Algebraic Identity

• (a + b)² = a² + b² + 2ab

Shortcut Trick

The slope of a straight line passing through any two given points is calculated directly by the ratio of the change in y to the change in x.

Slope = Change in y ÷ Change in x

Slope = (−7 − 5) ÷ (4 − (−2))

Slope = −12 ÷ 6 = −2

∴ The correct answer is −2.

Alternate Method

Given:

Coordinates of the first point: (x₁, y₁) = (−2, 5)

Coordinates of the second point: (x₂, y₂) = (4, −7)

Formula Used:

Slope (m) = (y₂ − y₁) ÷ (x₂ − x₁)

X Y O Δx = 6 Δy = −12 (−2, 5) (4, −7) m = −12 ÷ 6 = −2

Calculations:

⇒ m = (−7 − 5) ÷ (4 − (−2))

⇒ m = −12 ÷ (4 + 2)

⇒ m = −12 ÷ 6

⇒ m = −2

∴ The correct answer is −2.

Additional Information

Equation of a Line (Two-Point Form)

The equation of a straight line passing through (x₁, y₁) and (x₂, y₂) is given by y − y₁ = m(x − x₁), where m is the slope.

Parallel and Perpendicular Lines

Two lines are considered parallel if their slopes are equal (m₁ = m₂) and perpendicular if the product of their slopes is −1 (m₁ × m₂ = −1).

Distance Formula

The straight-line distance between two points (x₁, y₁) and (x₂, y₂) is d = √[(x₂ − x₁)² + (y₂ − y₁)²].

Shortcut Trick

The points A(3, 0), B(0, 4) and Origin O(0, 0) form a right-angled triangle.

The minimum distance from the origin to the line segment AB is simply the altitude drawn to the hypotenuse.

Altitude (h) = (Base × Perpendicular) ÷ Hypotenuse

Here, Base = 3, Perpendicular = 4, Hypotenuse = √(3² + 4²) = 5.

h = (3 × 4) ÷ 5 = 12 ÷ 5 = 2.4

∴ The correct answer is 2.4 units.

Alternate Method

Given:

Origin O = (0, 0), Point A = (3, 0) and Point B = (0, 4)

Formula Used:

Area of right-angled triangle = 1/2 × base × height

Hypotenuse = √(base² + height²)

         O(0, 0) A(3, 0) B(0, 4)  3 4 AB = 5  h  h = (3 × 4) ÷ 5 = 2.4 units

Calculations:

⇒ OA = 3 units and OB = 4 units

⇒ In ΔOAB, Hypotenuse AB = √(OA² + OB²)

⇒ AB = √(3² + 4²) = √(9 + 16) = √25 = 5 units

⇒ The minimum distance from origin O to line AB is the perpendicular altitude (h) from O to AB.

⇒ Area of ΔOAB = 1/2 × base × height = 1/2 × OA × OB

⇒ Area of ΔOAB = 1/2 × 3 × 4 = 6 sq. units

⇒ Using AB as the base, Area of ΔOAB = 1/2 × AB × h

⇒ 1/2 × 5 × h = 6

⇒ 5 × h = 12

⇒ h = 12 ÷ 5 = 2.4 units

∴ The correct answer is 2.4 units.

Additional Information

Perpendicular Distance from Origin

The perpendicular distance from the origin (0, 0) to any straight line given by the equation ax + by + c = 0 is determined using the formula d = |c| ÷ √(a² + b²).

Altitude to Hypotenuse

In any right-angled triangle with base 'a', perpendicular 'b' and hypotenuse 'c', the length of the altitude drawn to the hypotenuse is h = (a × b) ÷ c.

Line Intercept Form

The standard equation of a straight line making an x-intercept 'a' and a y-intercept 'b' on the coordinate axes is x/a + y/b = 1.

Shortcut Trick

Identify the position of the given equal parts in △LMN and △OPQ:

1. ∠L = ∠O (Angle)
2. LM = OP (Included Side)
3. ∠M = ∠P (Angle)

Since the equal side is positioned exactly between the two equal angles, the triangles are congruent by the ASA (Angle-Side-Angle) rule.

∴ The correct answer is ASA.

Alternate Method

Given:

⇒ In △LMN and △OPQ, ∠L = ∠O, LM = OP, and ∠M = ∠P

L M N O P Q

Step-by-step Proof:

⇒ ∠L = ∠O (Given equal angles)

⇒ LM = OP (Given equal included sides)

⇒ ∠M = ∠P (Given equal angles)

⇒ When two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, the two triangles are defined as congruent.

⇒ Therefore, by the Angle-Side-Angle (ASA) property, △LMN ≅ △OPQ.

∴ The correct answer is ASA.

Additional Information

SAS (Side-Angle-Side) Congruence

Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and included angle of the other.

SSS (Side-Side-Side) Congruence

Two triangles are congruent if all three sides of one triangle are respectively equal to the three sides of the other.

AAS (Angle-Angle-Side) Congruence

Two triangles are congruent if any two angles and a non-included side of one are equal to the corresponding parts of the other.

RHS (Right Angle-Hypotenuse-Side) Congruence

Two right-angled triangles are congruent if the hypotenuse and one side of one triangle are equal to the hypotenuse and corresponding side of the other.

Shortcut Trick

For a surd of the form √(a − 2√b), find two numbers whose sum is a and product is b.

Since 6 + 5 = 11 and 6 × 5 = 30, we get √(11 − 2√30) = √6 − √5.

Its reciprocal is 1/(√6 − √5), which simplifies to its conjugate √6 + √5.

Substituting back: (√6 − √5) − (√6 + √5) = −2√5.

∴ The correct answer is −2√5.

Alternate Method

Given:

Expression = √(11 − 2√30) − 1/√(11 − 2√30)

Formula Used:

a² + b² − 2ab = (a − b)²

(a − b)(a + b) = a² − b²

Calculations:

⇒ Let us simplify the root term √(11 − 2√30).

⇒ We know that 11 = 6 + 5 and 30 = 6 × 5.

⇒ 11 − 2√30 = 6 + 5 − 2√(6 × 5)

⇒ 11 − 2√30 = (√6)² + (√5)² − 2(√6)(√5)

⇒ 11 − 2√30 = (√6 − √5)²

⇒ Taking the square root, √(11 − 2√30) = √6 − √5

⇒ Now, find the value of the reciprocal 1/√(11 − 2√30):

⇒ 1/(√6 − √5)

⇒ Rationalizing by multiplying the numerator and denominator by (√6 + √5):

⇒ (√6 + √5) / [(√6 − √5)(√6 + √5)]

⇒ (√6 + √5) / [(√6)² − (√5)²]

⇒ (√6 + √5) / (6 − 5) = √6 + √5

⇒ Substitute these values back into the original expression:

⇒ Expression = (√6 − √5) − (√6 + √5)

⇒ Expression = √6 − √5 − √6 − √5

⇒ Expression = −2√5

∴ The correct answer is −2√5.

Additional Information

Square Root of a Surd

To find the square root of a surd in the form (x ± 2√y), find two numbers 'a' and 'b' such that a + b = x and a × b = y. The simplified square root is √a ± √b.

Rationalization

The process of eliminating surds from the denominator by multiplying the numerator and denominator by its conjugate. The conjugate of √a − √b is √a + √b.

Algebraic Identity

Difference of squares: (a − b)(a + b) = a² − b², which is frequently used to simplify surd denominators during rationalization.