Delhi Police Head Constable (Ministerial), 2025 Official Paper (Held On: 08 Jan, 2026 Shift 2) (Previous Year Paper)

The correct answer is Poikkal Kuthirai.

Key Points

• Poikkal Kuthirai is a traditional folk dance originating from the state of Tamil Nadu, India.
• The name literally translates to False Leg Horse or Dummy Horse Dance in the Tamil language.
• Performers use a dummy horse frame made of lightweight materials like jute, cardboard, paper, and wood, which is strapped around the dancer's waist.
• The dance is traditionally performed to commemorate the battlefield valor and heroic deeds of ancient soldiers and warriors.
• Dancers wear wooden stilts attached to their feet, which produce a rhythmic clattering sound mimicking the galloping of a horse.
• It is often performed during temple festivals and is associated with the worship of Ayyanar, a rural deity believed to be a protector.
• The performance is accompanied by traditional musical instruments such as the Nadaswaram and Thavil.

 Additional Information

• Bhangra
• Originates from the Majha region of Punjab.
• Traditionally performed by farmers to celebrate the harvest season and the festival of Vaisakhi.
• Characterized by high-energy movements and the rhythmic beat of the Dhol.
• Garba
• A vibrant folk dance from the state of Gujarat.
• Performed during the nine nights of the Navratri festival to honor the Goddess Durga.
• Dancers move in concentric circles around a centrally lit lamp or an idol.
• Kummi
• One of the most ancient folk dances of Tamil Nadu and Kerala.
• Performed primarily by women who stand in a circle and dance to the rhythm of clapping hands rather than musical instruments.

The correct answer is The criteria for Special Category Status include factors like hilly terrain, tribal population, border location, and economic backwardness, but the status is a political and administrative classification decided by the Union Government, not a constitutional right..

Key Points

• Article 371 (and Articles 371A to 371J) provides special provisions for specific states regarding ownership of land, customary laws, and administrative autonomy, but the Indian Constitution does not explicitly mention or provide for Special Category Status (SCS). Hence, statement 1 is incorrect.
• The SCS was introduced in 1969 based on the Fifth Finance Commission’s recommendations and is governed by the Gadgil-Mukherjee Formula, which evaluates hilly terrain, tribal population, international border proximity, and economic backwardness as primary criteria. Hence, statement 2 is correct.
• The Finance Commission (specifically the 14^th Finance Commission) recommended the abolition of the Special Category distinction for new states, emphasizing that fiscal needs should be addressed through tax devolution, which was increased to 42%. Hence, statement 3 is incorrect.
• Special Category Status is an administrative classification that can be reviewed or discontinued by the Union Government; it lacks constitutional permanence and is not a statutory right granted by Parliament. Hence, statement 4 is incorrect.

 Additional Information

• Financial Advantages of SCS:
• Centrally Sponsored Schemes (CSS): Under SCS, the Central Government contributes 90% of the funds as a grant, while the state contributes only 10%, compared to the standard 60:40 ratio for general states.
• Budgetary Incentives: These states receive preferential treatment in investment subsidies and tax exemptions (excise and customs) to stimulate industrial growth.
• Lapsing Funds: Unlike other states, unspent funds in SCS states do not lapse at the end of the financial year and are carried forward.
• Eligible States:
• Currently, 11 states possess this status: Arunachal Pradesh, Assam, Manipur, Meghalaya, Mizoram, Nagaland, Sikkim, Tripura, Himachal Pradesh, Uttarakhand, and Telangana (initially granted for a specific period).

The correct answer is All objects emit infrared radiation proportional to their temperature, making it ideal for heat-based detection..

Key Points

• Thermal Emission Principle: Every object with a temperature above absolute zero (0 Kelvin) naturally emits electromagnetic radiation. This phenomenon, described by Planck's Law, ensures that humans, animals, and machinery are constant sources of infrared energy regardless of external lighting.
• Passive Detection: Unlike visible light cameras that require a light source to reflect off surfaces, infrared sensors are passive. They detect the energy emitted by the objects themselves, allowing for high-contrast imaging in total darkness or night-time operations.
• Temperature Sensitivity: According to the Stefan-Boltzmann Law, the total radiant heat energy emitted from a surface is proportional to the fourth power of its absolute temperature (E ∝ T⁴). Small variations in temperature result in significant changes in IR intensity, making it easy to identify thermal signatures of hidden targets.
• Obscurant Penetration: Infrared waves have longer wavelengths than visible light. This characteristic allows them to scatter less when encountering small particles, enabling thermal cameras to see through smoke, dust, and light fog more effectively than optical cameras.

 Additional Information

• Non-Ionizing Nature:
• Infrared radiation is located between the microwave and visible light portions of the spectrum. It lacks sufficient energy to ionize atoms or molecules, which is a property reserved for high-frequency waves like Ultraviolet (UV) or X-rays.
• Atmospheric Absorption:
• While infrared is useful, it is not immune to atmospheric interference. Gases like carbon dioxide (CO₂) and water vapor (H₂O) absorb specific IR frequencies. Surveillance systems utilize atmospheric windows (typically 8−14 μm) where absorption is minimal.
• Energy Levels:
• In physics, the energy of a photon is inversely proportional to its wavelength. Since infrared light has a longer wavelength than visible light, it actually possesses lower energy per photon.

The correct answer is Rapid depreciation of physical capital and population growth reduced per capita net income despite healthy GDP growth.

Key Points

• Gross Domestic Product (GDP) at 6.8% represents the total value of all final goods and services produced within the domestic territory. However, it is a gross measure that does not account for the wear and tear of capital assets used in production.
• Net National Product (NNP) is calculated by subtracting Depreciation (consumption of fixed capital) from the Gross National Product (GNP). If the rate of capital depreciation is high due to aging infrastructure or rapid industrial use, the transition from GDP to NNP results in a significant value reduction. Hence, the statement regarding depreciation is correct.
• The Factor Cost refers to the total cost of factors of production (land, labor, capital, and entrepreneur) rather than the market price which includes indirect taxes and subsidies. A divergence between these metrics often reflects changes in tax structures or production costs.
• Per Capita NNP is derived by dividing the total NNP by the Total Population of the country. Even with a healthy GDP growth, a rising population base acts as a denominator that dilutes the overall income growth, leading to a lower 4.2% growth rate for the average individual. Hence, the statement regarding population growth is correct.

 Additional Information

• Depreciation:
• Refers to the capital consumption allowance.
• In a rapidly industrializing economy, obsolescence of technology can lead to higher depreciation rates, narrowing the gap between gross and net income.
• Net National Product (NNP) at Factor Cost:
• Commonly known as National Income in India.
• It excludes Net Indirect Taxes (Indirect Taxes − Subsidies) from the market price.
• Per Capita Income:
• Serves as an indicator of the standard of living for the average citizen.
• It is highly sensitive to demographic transitions and population growth rates.

The correct answer is Narasimham Committee.

Key Points

• The Narasimham Committee on the Financial System was established in August 1991 under the chairmanship of M. Narasimham, the 13^th Governor of the Reserve Bank of India (RBI), to address the inefficiencies in the Indian banking sector.
• The committee recommended a significant reduction in the Statutory Liquidity Ratio (SLR) and the Cash Reserve Ratio (CRR) to release more funds for commercial lending and improve the profitability of banks.
• It introduced Prudential Norms for Asset Classification, Income Recognition, and Provisioning, which required banks to classify loans as performing or non-performing based on objective criteria.
• A key recommendation was the adoption of the Capital Adequacy Ratio (CAR) in line with international Basel-I standards to ensure banks maintain enough capital to absorb losses.
• The committee proposed a four-tier banking structure, including 3 to 4 international-level banks and several national and regional banks, to foster a competitive environment.
• It advocated for Interest Rate Deregulation, allowing banks to set their own lending and deposit rates based on market forces rather than rigid government control.

 Additional Information

• Abid Hussain Committee
• This committee primarily focused on Small Scale Industries (SSI) and recommended the abolition of reservation for certain products and trade policy reforms.
• Chelliah Committee
• Formed in 1991, the Tax Reforms Committee led by Raja J. Chelliah aimed at simplifying the tax structure, reducing customs duties, and broadening the tax base.
• Rangarajan Committee
• Headed by C. Rangarajan, this committee worked on multiple fronts including Disinvestment of Public Sector Undertakings (PSUs) and the Methodology for Poverty Estimation.

The correct answer is Coming Back of Domestic Money as FDI.

Key Points

• Round Tripping refers to the circular flow of capital where money leaves a country through various channels and eventually returns to the same country in the form of Foreign Direct Investment (FDI).
• The primary objective of this practice is often to conceal the original source of funds, typically to convert Black Money into legitimate assets or to evade domestic taxes.
• Investors often utilize Tax Havens such as Mauritius, Singapore, or the Cayman Islands to set up shell companies that reinvest the capital back into the home country.
• This mechanism exploits Double Taxation Avoidance Agreements (DTAA), allowing domestic entities to enjoy tax concessions and fiscal incentives intended exclusively for foreign investors.
• In India, the Reserve Bank of India (RBI) and the Enforcement Directorate (ED) closely monitor such inflows to prevent Money Laundering and ensure the integrity of the financial system.
• The implementation of the General Anti-Avoidance Rule (GAAR) was a significant legislative step by the Government of India to identify and penalize transactions designed specifically for tax avoidance through round-tripping.

 Additional Information

• Foreign Direct Investment (FDI):
• Refers to a long-term investment by an entity based in one country into a business or entity located in another country, usually involving management control and a stake of 10% or more.
• In India, it is regulated under the Foreign Exchange Management Act (FEMA), 1999.
• Repatriation:
• This process involves the conversion of any foreign currency into one's local currency or the transfer of profits and capital back to the investor's home country.
• Rules for the repatriation of FDI proceeds are governed by the Foreign Exchange Management (Non-debt Instruments) Rules.
• Participatory Notes (P-Notes):
• These are offshore derivative instruments issued by Registered Foreign Portfolio Investors (FPIs) to overseas investors who wish to invest in the Indian stock market without registering with SEBI.
• Due to the anonymity they provide, they have historically been associated with concerns regarding round-tripping.

The correct answer is Allegations of data manipulation in rankings of some countries.

Key Points

• The World Bank Group officially decided to discontinue its Ease of Doing Business (EoDB) report on September 16, 2021, following internal audits and an independent investigation.
• The primary catalyst for this decision was a series of data irregularities discovered in the 2018 and 2020 reports, which compromised the integrity of the global benchmarking tool.
• An independent probe conducted by the law firm WilmerHale revealed that senior World Bank officials applied undue pressure on staff to manipulate data to artificially boost the rankings of countries like China, Saudi Arabia, Azerbaijan, and the United Arab Emirates.
• In the case of China, the investigation found that the country's 2018 ranking should have been lower, but data points were altered to prevent it from dropping below its previous position during a period when the Bank was seeking a major capital increase.
• The discontinuation was deemed necessary to protect the institutional credibility and the transparency of the World Bank's research and data collection processes.

 Additional Information

• Overview of Ease of Doing Business Index:
• Launched in 2002, it provided an objective measure of business regulations and their enforcement across 190 economies.
• It evaluated 10 key indicators including Starting a Business, Dealing with Construction Permits, Getting Electricity, and Enforcing Contracts.
• The index was a vital tool for Foreign Direct Investment (FDI) decisions and policy reforms globally.
• Transition to Business Ready (B-READY):
• Following the discontinuation of EoDB, the World Bank introduced a new flagship report titled Business Ready (B-READY).
• This new framework aims to be more comprehensive, focusing on firm-level data and the actual implementation of regulations rather than just the laws on paper.
• It emphasizes a balanced approach between the ease of business and the broader social benefits of regulation.
• Incorrect Options Context:
• The Human Development Index (HDI) is published by the United Nations Development Programme (UNDP) and remains a separate entity focused on health, education, and standard of living.
• While India had previously expressed concerns about certain methodology nuances, it had actually seen a massive leap in its ranking from 142^nd in 2014 to 63^rd in 2019, making it a proponent of the index rather than an objector leading to its closure.

The correct answer is To promote Perupalem as a tourism destination.

Key Points

• The Perupalem Beach Festival is an annual cultural and promotional event organized by the Andhra Pradesh Tourism Development Corporation (APTDC) in coordination with the district administration.
• The primary objective of the festival is to showcase Perupalem Beach, located in the West Godavari district, as a prominent tourism destination on the eastern coast of India.
• By hosting such events, the state government aims to increase the tourist footfall, which in turn stimulates the local economy and creates livelihood opportunities for residents.
• The festival serves as a platform to highlight the scenic beauty, ecological importance, and the tranquil environment of the coastline, distinguishing it from more crowded urban beaches.
• It integrates cultural heritage with tourism by featuring traditional art forms, music, and local traditions to provide a comprehensive experience to visitors.

 Additional Information

• Geographic and Structural Features:
• Perupalem Beach is situated approximately 20 kilometers from Narsapur and is known for its shallow waters and vast sandy stretches, making it safer for recreational activities.
• The beach is part of the Bay of Bengal coastline and is being developed under the Coastal Tourism Circuit initiative by the state government.
• Event Highlights:
• The festival typically includes cultural performances like Kuchipudi and folk dances, alongside beach sports such as volleyball and kabaddi to engage younger audiences.
• Food stalls at the venue promote the unique Godavari cuisine, offering a taste of local flavors to tourists from other regions.
• Strategic Importance:
• The festival aligns with the broader Andhra Pradesh Tourism Policy, which focuses on infrastructure development like better road connectivity and basic amenities at coastal sites to boost sustainable tourism.

The correct answer is Leading armed resistance against British colonial rule.

Key Points

• Born as Chandra Shekhar Tiwari on July 23, 1906, in Bhabhra village of Madhya Pradesh, he remains one of India's most iconic revolutionary leaders.
• He earned the title 'Azad' (The Free) after being arrested during the Non-Cooperation Movement in 1921; when asked his name by a magistrate, he replied 'Azad', his father's name as 'Swatantra' (Independence), and his residence as 'Jail'.
• Azad was a master of guerrilla warfare and became the chief strategist for the Hindustan Republican Association (HRA), which he later reorganized into the Hindustan Socialist Republican Association (HSRA) in 1928.
• He played a central role in high-profile revolutionary activities, including the Kakori Train Robbery (1925), the shooting of J.P. Saunders (1928) to avenge the death of Lala Lajpat Rai, and the 1929 attempt to blow up the Viceroy's train.
• Determined never to be captured alive by the British Police, he fought a lone battle at Alfred Park in Allahabad on February 27, 1931, and used his last bullet to martyr himself.

 Additional Information

• Hindustan Socialist Republican Association (HSRA):
• Formed at Feroz Shah Kotla in Delhi by Azad, Bhagat Singh, Sukhdev, and Rajguru.
• The organization moved away from purely nationalist goals toward socialist ideologies, aiming for an India free from both foreign rule and economic exploitation.
• Significance of July 2025:
• July 23, 2025, marks the 119^th birth anniversary of Chandra Shekhar Azad, a day celebrated to honor the bravery of armed revolutionaries in the freedom struggle.
• Comparison of Revolutionary Contributions:
• While Dr. B.R. Ambedkar is the chief architect of the Constitution of India, Azad represents the militant nationalist phase.
• The RSS was founded by K.B. Hedgewar in 1925, focusing on cultural and social organization, distinct from Azad's clandestine armed struggle.

The correct answer is Neolithic.

Key Points

• The Neolithic Period, also known as the New Stone Age, represents the final stage of cultural evolution in prehistoric humans, beginning around 10,000 BCE.
• This era is defined by the Neolithic Revolution, a significant shift from a nomadic hunter-gatherer lifestyle to a sedentary, food-producing society through agriculture.
• The transition to farming led to the establishment of the first permanent settlements, as communities needed to reside near their cultivated lands to manage crops like wheat and barley.
• Humans in this period began the domestication of animals such as sheep, goats, and cattle, providing a steady supply of meat, milk, and hides.
• Key archaeological sites like Mehrgarh in Pakistan and Çatalhöyük in Turkey provide clear evidence of early rectangular mud-brick houses and organized village life.
• Technologically, the period is marked by the development of polished stone tools, which were much sharper and more durable for farming tasks compared to older chipped stone tools.

 Additional Information

• Paleolithic:
• Known as the Old Stone Age, it is the longest period of human history.
• Humans were nomadic, moving frequently in search of food, and utilized crude, unpolished stone tools.
• Mesolithic:
• The Middle Stone Age served as a bridge between the Paleolithic and Neolithic eras.
• Characterized by the use of microliths (small, specialized stone tools) and the beginning of semi-permanent seasonal camps.
• Chalcolithic:
• Often called the Copper-Stone Age, it followed the Neolithic period.
• It represents the first time humans utilized metal (copper) alongside stone implements for construction and tool-making.
• Neolithic Innovations:
• Development of pottery for storing agricultural surplus and cooking food.
• Invention of weaving using wool and flax to create textiles for clothing.

The correct answer is Only Statements 1 and 3 are correct.

Key Points

• Statement 1: Ethanol 100 was launched in March 2024 by the Union Minister for Petroleum and Natural Gas at Indian Oil retail outlets. It is a high-octane fuel, typically ranging between 100 and 105 octane, which allows for higher engine efficiency and reduced emissions. Hence, statement 1 is correct.
• Statement 2: Ethanol 100 is not composed of 100% pure ethanol; absolute ethanol is unsuitable for direct use as a commercial fuel because its flame is invisible in daylight, posing a severe safety hazard during leaks or accidents. Hence, statement 2 is incorrect.
• Statement 3: To ensure safety and engine compatibility, the fuel typically contains about 93-95% ethanol blended with a small fraction of motor spirit (gasoline) and specific co-solvents that provide flame visibility and improve cold-start combustion efficiency. Hence, statement 3 is correct.

 Additional Information

• Ethanol Blending Program (EBP):
• The Government of India has set a target to achieve 20% ethanol blending (E20) in petrol by the fuel year 2025-26.
• Flex-Fuel Vehicles (FFVs): These vehicles are equipped with engines capable of running on varied percentages of ethanol, including E100, through a Fuel Oxygen Sensor.
• Environmental Impact: Using ethanol significantly reduces the tailpipe emissions of Carbon Monoxide (CO) and Particulate Matter compared to pure gasoline.
• Economic Benefits: This initiative reduces crude oil imports, promotes energy security, and provides an alternative market for sugarcane farmers and grain producers.
• Production: Ethanol is primarily produced via fermentation of C-heavy molasses, sugarcane juice, and food grains like maize and broken rice.

The correct answer is It follows a dead war photographer navigating the afterlife during the civil war.

Key Points

• Statement 1 suggests the book is a memoir from the colonial period, but the narrative is a work of fiction set in the late 20^th century. Hence, statement 1 is incorrect.
• Statement 2 correctly identifies the plot, where the protagonist Maali Almeida, a war photographer, wakes up dead in a celestial afterlife and has seven nights (moons) to lead his loved ones to a hidden cache of photos that expose the horrors of the Sri Lankan Civil War. Hence, statement 2 is correct.
• Statement 3 classifies the book as a collection of essays on conflict resolution, whereas it is actually a supernatural satire and a magical realism novel. Hence, statement 3 is incorrect.
• Statement 4 claims the work is historical fiction regarding the life of Buddha, but the story is focused on political turmoil and human rights during the 1980s in Sri Lanka. Hence, statement 4 is incorrect.

 Additional Information

• Shehan Karunatilaka:
• He is the Sri Lankan author who won the 2022 Booker Prize for this novel.
• He is the second Sri Lankan-born author to receive this honor, following Michael Ondaatje.
• The book was originally published in 2020 under the title Chats with the Dead.
• Historical and Cultural Context:
• The novel is set in Colombo in 1989, a period characterized by intense violence involving government death squads, JVP insurgents, and the LTTE.
• It utilizes the In Between, a bureaucratic version of the afterlife, to provide a scathing critique of the corruption and brutality of the Sri Lankan Civil War.
• The narrative style uses the second-person perspective, addressing the deceased protagonist directly.

The correct answer is Chapter II.

Key Points

• The Bharatiya Nagarik Suraksha Sanhita, 2023 (BNSS) was enacted to modernize criminal procedure in India, officially replacing the Code of Criminal Procedure, 1973.
• Chapter II of the Sanhita is titled Constitution of Criminal Courts and Offices and encompasses Section 6 to Section 20.
• Section 6 explicitly categorizes the classes of criminal courts in every State as: Courts of Session, Judicial Magistrates of the First Class, Judicial Magistrates of the Second Class, and Executive Magistrates.
• This chapter provides the legal basis for establishing Sessions Divisions, appointing Judicial Officers, and defining the territorial limits of their jurisdiction.
• It also contains provisions for the Directorate of Prosecution and the appointment of Public Prosecutors to represent the State in criminal trials.

 Additional Information

• Chapter I:
• Identified as the Preliminary chapter, it introduces the short title, commencement date, and territorial application of the Sanhita.
• Contains Section 2, which defines critical legal terminology used throughout the document.
• Chapter III:
• Title: Power of Courts.
• It details the specific sentences that High Courts, Sessions Judges, and Magistrates are legally competent to pass.
• Chapter IV:
• Divided into two parts: Powers of Superior Officers of Police and Aid to the Magistrates and the Police.
• It mandates that the public must assist Magistrates and Police Officers in preventing escapes or suppressing disturbances.

The correct answer is Lala Hansraj.

Key Points

• Lala Hansraj, popularly known as Mahatma Hansraj, was a prominent Arya Samaj leader, social reformer, and educationist who dedicated his life to the cause of national awakening through learning.
• He was the principal founder of the Dayanand Anglo-Vedic (DAV) College Trust and Management Society, establishing the first DAV School in Lahore on June 1, 1886.
• The DAV movement was established to commemorate the legacy of Swami Dayanand Saraswati, aiming to synthesize traditional Vedic values with modern scientific education and English literature.
• He served as the honorary Principal of DAV College, Lahore, for 25 years, famously refusing to draw a salary for his services, which earned him immense respect across the Indian subcontinent.
• Under his leadership, the DAV institutions became a breeding ground for nationalists and provided a template for indigenous education that challenged the purely colonial British education system.

 Additional Information

• Govind Ballabh Pant:
• A towering leader of the Indian Independence Movement, he served as the first Chief Minister of Uttar Pradesh and was instrumental in the abolition of the Zamindari system.
• He served as the Union Home Minister from 1955 to 1961 and was awarded the Bharat Ratna in 1957.
• Asaf Ali:
• An eminent lawyer and freedom fighter who defended Bhagat Singh and Batukeshwar Dutt during the Central Assembly Bombing Case in 1929.
• He served as the first Indian Ambassador to the United States and later as the Governor of Odisha.
• Arun Chandra Guha:
• A revolutionary belonging to the Yugantar group, he was a member of the Constituent Assembly of India and a veteran politician from West Bengal.

The correct answer is Seychelles.

Key Points

• The SAGAR initiative, which stands for Security and Growth for All in the Region, was first unveiled by Prime Minister Narendra Modi in March 2015 during his visit to Mauritius.
• Seychelles is a critical archipelagic nation in the Indian Ocean and a primary partner in India’s maritime security architecture designed to maintain a rules-based order in the region.
• The initiative focuses on five pillars: maritime cooperation, deepening economic ties through the Blue Economy, disaster management (HADR), collective action against maritime threats, and sustainable development.
• India and Seychelles share a robust defense partnership, highlighted by India’s gifting of the Fast Patrol Vessel (FPV) PS Zoroaster in 2021 and the development of coastal surveillance radar systems.

 Additional Information

• Geographical Context of Options:
• Uzbekistan: It is a doubly landlocked country located in Central Asia, meaning it is surrounded by other landlocked countries and has no direct access to any ocean.
• Nepal and Bhutan: Both are landlocked Himalayan nations. While they are key partners under India's Neighborhood First Policy, they do not fall under the maritime scope of the SAGAR initiative.
• Strategic Significance of SAGAR:
• The policy serves as the maritime component of India’s Act East Policy, aiming to counter regional challenges and ensure freedom of navigation.
• It involves other island nations such as Mauritius, Maldives, Sri Lanka, and Madagascar, forming a security net against piracy and illegal fishing.
• The vision aligns with the Indo-Pacific Oceans Initiative (IPOI) to promote ecological and resource security.

The correct answer is Co-existence of both public and private sectors in economic activities..

Key Points

• A Mixed Economy is a system that blends elements of a market economy with elements of a planned economy, involving both private enterprise and state intervention.
• Post-independence, India adopted this model under the leadership of Jawaharlal Nehru to ensure rapid industrialization alongside social welfare and poverty alleviation.
• The Public Sector was designated to control strategic industries such as defense, electricity, and heavy machinery to prevent private monopolies in essential services.
• The Private Sector was encouraged to operate in consumer goods and agriculture, although it remained subject to government regulations and licensing policies during the early decades.
• This model aims to achieve a socialist pattern of society by balancing the efficiency of the market mechanism with the distributive justice of state planning.

 Additional Information

• Alternative Economic Systems:
• Socialist/Command Economy: In this system, the government or the state has total control over all means of production and economic decision-making, which India did not adopt fully.
• Capitalist/Market Economy: This system is driven by private ownership and the price mechanism, where the government has minimal intervention in economic activities.
• Laissez-faire: A French term meaning 'leave alone', representing an extreme form of capitalism where the state provides no regulation over trade and industry.
• 1991 Economic Reforms: India shifted the balance within its mixed economy through Liberalization, Privatization, and Globalization (LPG), significantly reducing the License Raj and increasing the role of the private sector.
• Industrial Policy Resolution, 1956: This policy formed the economic constitution of India, clearly demarcating the roles of the state and private individuals in industrial development.

The correct answer is 90-120 m.

Key Points

• The dimensions of a football pitch are officially regulated by Law 1 of the Laws of the Game, maintained by the International Football Association Board (IFAB) and recognized by FIFA.
• For standard domestic and non-international matches, the touchline (length) must be a minimum of 90 meters and a maximum of 120 meters.
• The goal line (width) for these matches has a standard range between 45 meters and 90 meters, ensuring the field remains rectangular.
• The field is delineated by continuous lines; the longer lines are called touchlines, while the shorter lines at the ends are called goal lines.
• The midfield line divides the pitch into two equal halves, with a center mark and a surrounding center circle to facilitate the kickoff.

 Additional Information

• International Match Standards:
• For international matches, the FIFA regulations are significantly more stringent. The required length is between 100 meters and 110 meters.
• The width for international competitions must be between 64 meters and 75 meters.
• Specific Pitch Markings and Dimensions:
• The penalty area extends 16.5 meters from each goalpost into the field of play.
• The goal area (commonly known as the six-yard box) extends 5.5 meters from each goalpost.
• The penalty spot is marked at a distance of 11 meters from the center of the goal line.
• Standard goalposts are 7.32 meters wide and 2.44 meters high, measured from the inner edges of the posts and the lower edge of the crossbar.
• A corner arc with a 1 meter radius is marked at each of the four corners for corner kicks.

The correct answer is Densely surveyed core provinces.

Key Points

• The Zabt System, also known as the Dahsala System, was a sophisticated land revenue framework introduced by Emperor Akbar around 1580-1582 with the assistance of his finance minister, Raja Todar Mal.
• This system was based on two primary factors: the measurement of land (Paimaish) and the evaluation of the average produce and local prices over a ten-year period (1570 to 1580).
• Implementation of the Zabt required a high degree of administrative stability and meticulous statistical record-keeping, which was only possible in the core provinces of the empire where the Mughal state exercised direct control.
• Provinces such as Delhi, Agra, Lahore, Allahabad, and Malwa served as the primary centers for this system because they were densely surveyed and had established revenue circles.
• The system allowed the state to fix revenue in cash, providing predictability for the imperial treasury and reducing the uncertainties associated with annual crop-sharing methods.

 Additional Information

• Classification of Land: Under the Zabt system, land was divided into four categories to determine tax liability:
• Polaj: Land that was cultivated annually and never left fallow.
• Parauti: Land left fallow for one or two years to recover its fertility.
• Chachar: Land that remained fallow for three to four years.
• Banjar: Poor quality land that was uncultivated for five years or more.
• Limitations: The system could not be extended to frontier areas like Bengal or Gujarat (initially) or the Deccan because the Mughal administration lacked the survey infrastructure and detailed local price data required for accurate Zabt calculations.
• Alternative Systems: In regions where Zabt was not applicable, the Mughals utilized Batai (crop-sharing) or Nasaq (a rough estimation or group assessment based on past payments).

The correct answer is Pune, Maharashtra.

Key Points

• The 14^th Hockey India Senior Women National Championship was hosted in Pune, Maharashtra, in March 2024.
• The high-profile tournament took place at the Major Dhyanchand Hockey Stadium in Pimpri-Chinchwad, which is a major sports hub in the Pune district.
• The competition was held from March 13 to March 23, 2024, featuring elite domestic teams from across the country.
• Hockey Haryana emerged as the winner of the championship, reclaiming the title by defeating Hockey Maharashtra in a tense final match.
• The final ended in a 1-1 draw during regular time, after which Hockey Haryana triumphed in the penalty shootout with a score of 3-0.

 Additional Information

• Tournament Standings and Highlights:
• Hockey Jharkhand secured the third position (bronze medal) after defeating Hockey Madhya Pradesh 2-0 in the classification match.
• A total of 27 teams participated in the 2024 edition, divided into various pools for the league stage before moving to the knockouts.
• The event served as a primary selection ground for Hockey India selectors to identify players for the National Coaching Camp and the Indian Women's Hockey Team.
• Key players like Deepika and Savita Punia (representing Haryana) and Navneet Kaur played pivotal roles in the success of their respective state units.
• The hosting of the event in Maharashtra highlights the state's significant investment in world-class Astroturf facilities and sports infrastructure.

The correct answer is It encourages everyday physical activity..

Key Points

• The Fit India Movement was launched as a nation-wide campaign to motivate citizens to integrate physical activity and sports into their daily lives to combat lifestyle diseases. Hence, statement 1 is correct.
• While the initiative advocates for a healthy lifestyle, it is not restricted to diet plans but focuses on a holistic approach involving exercise, fitness, and mental well-being. Hence, statement 2 is incorrect.
• The campaign is inclusive of various activities such as cycling, walking, running, and traditional Indian games, rather than being limited exclusively to Yoga. Hence, statement 3 is incorrect.
• The movement was officially inaugurated by Prime Minister Narendra Modi on 29^th August 2019, coinciding with National Sports Day, which makes the 2010 timeline historically inaccurate. Hence, statement 4 is incorrect.

 Additional Information

• Foundational Objectives:
• To promote fitness as an easy, fun, and free activity that can be practiced anywhere.
• To encourage the adoption of indigenous sports and physical exercises.
• To create a platform for fitness enthusiasts to share their stories and inspire others through the Fit India Mobile App.
• Commemorative Significance:
• The launch date, 29^th August, marks the birth anniversary of Major Dhyan Chand, Indias legendary hockey player.
• The movement operates under the aegis of the Ministry of Youth Affairs and Sports.
• Major Initiatives:
• Fit India School Week: Aimed at instilling the habit of fitness in school children from a young age.
• Fit India Freedom Run: Organised to encourage people to run at their own pace and at any location of their choice.

Shortcut Trick

Net deviation from the average must be zero.

Individual excess = 40 − 20 = +20.

To balance this, the other 5 members must have a total deficit of −20.

Average reduction for 5 members = −20 ÷ 5 = −4.

Average of remaining 5 members = 20 − 4 = 16.

∴ The correct answer is 16.

Alternate Method

Given: Average age of 6 members = 20, Age of 1 member = 40.

Formula Used: Sum of observations = Average × Number of observations.

⇒ Total sum of ages of 6 members = 6 × 20 = 120

⇒ Sum of ages of the remaining 5 members = Total sum − Age of one member

⇒ Sum of 5 members = 120 − 40 = 80

⇒ Average age of 5 members = Sum ÷ 5

⇒ Average age of 5 members = 80 ÷ 5 = 16

∴ The correct answer is 16.

Additional Information

Sum of Deviations

The sum of the deviations of all observations from their arithmetic mean is always zero. This property is used to quickly find missing values in a data set.

Weighted Average Formula

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

Effect of Constant Change

If a constant value 'k' is added to or subtracted from every term in a data set, the new average will also increase or decrease by exactly 'k'.

Shortcut Trick

Net deviation from the total average (16) must be zero.

Deviation of first 4 numbers = 4 × (14 − 16) = −8

Deviation of last 4 numbers = 4 × (18 − 16) = +8

Total deviation of 8 numbers = −8 + 8 = 0.

Since the deviation is 0, the average of the remaining 2 numbers must be equal to the total average.

∴ The correct answer is 16.

Alternate Method

Given: Average of 10 numbers = 16 | Average of first 4 = 14 | Average of last 4 = 18.

Formula Used: Sum of numbers = Average × Total numbers

⇒ Sum of 10 numbers = 10 × 16 = 160

⇒ Sum of first 4 numbers = 4 × 14 = 56

⇒ Sum of last 4 numbers = 4 × 18 = 72

⇒ Sum of middle two numbers = Total sum − (Sum of first 4 + Sum of last 4)

⇒ Sum of middle two numbers = 160 − (56 + 72) = 160 − 128 = 32

⇒ Average of middle two numbers = 32 ÷ 2 = 16

∴ The correct answer is 16.

Additional Information

Deviation Property

The sum of deviations of all observations from their arithmetic mean is always zero. This is used to find missing values in a dataset.

Weighted Average Formula

Weighted Average = (n₁x₁ + n₂x₂ + ... + n_nx_n) ÷ (n₁ + n₂ + ... + n_n), where n is the quantity and x is the value/average.

Arithmetic Mean Property

If every number in a set is increased or decreased by a constant 'k', the new average also increases or decreases by 'k'.

Shortcut Trick

Total Area of the design = Area of Quadrant + Area of Right Triangle.

Area = (1/4 × 22/7 × 14 × 14) + (1/2 × 14 × 14).

Area = 154 + 98 = 252 cm².

∴ The correct answer is 252 cm².

Alternate Method

Given: Radius (r) = 14 cm, Base (b) = 14 cm, Height (h) = 14 cm.

Formula used: Area of Quadrant = (1/4) × πr² and Area of Triangle = (1/2) × b × h.

⇒ Area of the Quadrant = (1/4) × (22/7) × 14 × 14

⇒ Area of the Quadrant = (1/4) × 22 × 2 × 14 = 11 × 14 = 154 cm².

⇒ Area of the Right Triangle = (1/2) × 14 × 14

⇒ Area of the Right Triangle = 7 × 14 = 98 cm².

⇒ Total Area of the design = Area of Quadrant + Area of Triangle

⇒ Total Area = 154 + 98 = 252 cm².

∴ The correct answer is 252 cm².

Additional Information

Area of a Sector

The area of a sector of a circle with radius r and angle θ is given by (θ/360) × πr². For a quadrant, θ = 90°.

Area of Circle

The total area of a circle with radius r is πr², where π ≈ 22/7 or 3.14.

Pythagoras Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

Shortcut Trick

Convert all values into decimal form for a quick comparison.

0.777... is equivalent to 7/9.

8/11 ≈ 0.727... and 0.78 = 0.780.

Comparing 0.727, 0.777, and 0.780, we find 0.727 is the smallest value.

∴ The correct answer is 8/11.

Alternate Method

Given values for comparison: 0.777..., 7/9, 0.78, 8/11.

Step 1: Convert each value to a decimal with three decimal places.

⇒ Value 1: 0.777... = 0.777

⇒ Value 2: 7/9 = 7 ÷ 9 = 0.777...

⇒ Value 3: 0.78 = 0.780

⇒ Value 4: 8/11 = 8 ÷ 11 = 0.7272...

Step 2: Arrange the values in ascending order.

⇒ 0.7272... < 0.777... < 0.780

⇒ 8/11 < 7/9 < 0.78

∴ The correct answer is 8/11.

Additional Information

Cross-Multiplication Method

To compare two fractions a/b and c/d, calculate a × d and b × c. If a × d < b × c, then a/b < c/d.

Recurring Decimals

A repeating decimal like 0.x (where x is repeating) is expressed as the fraction x/9. Example: 0.777... = 7/9.

Proper Fractions

When comparing proper fractions, the one with the denominator significantly larger than the numerator (further from 1) is usually the smaller value.

Shortcut Trick

For two successive discounts of d₁% and d₂%, the single equivalent discount is given by:

Equivalent Discount % = d₁ + d₂ − (d₁ × d₂) ÷ 100

⇒ 12 + 18 − (12 × 18) ÷ 100

⇒ 30 − 216 ÷ 100 = 30 − 2.16 = 27.84%

∴ The correct answer is 27.84%.

Alternate Method

Given:

Marked Price (MP) = ₹ 12,000

First Discount (d₁) = 12%

Second Discount (d₂) = 18%

Formula Used: Final Selling Price = MP × (1 − d₁/100) × (1 − d₂/100)

Calculations:

⇒ Final SP = 12000 × (1 − 12/100) × (1 − 18/100)

⇒ Final SP = 12000 × (88/100) × (82/100)

⇒ Final SP = 12000 × 0.88 × 0.82

⇒ Final SP = 12000 × 0.7216 = ₹ 8659.2

⇒ Total Discount Value = MP − Final SP = 12000 − 8659.2 = ₹ 3340.8

⇒ Equivalent Discount % = (Total Discount ÷ MP) × 100

⇒ Equivalent Discount % = (3340.8 ÷ 12000) × 100 = 27.84%

∴ The correct answer is 27.84%.

Additional Information

Net Discount for Three Successive Discounts

For three successive discounts a%, b%, and c%, the net discount is calculated by first finding the equivalent of a and b, then using that result with c.

Relationship between MP and CP

The ratio of Marked Price to Cost Price is given by: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Multiplying Factor Method

Final SP = MP × MF₁ × MF₂, where MF (Multiplying Factor) for a discount d% is (100 − d) ÷ 100.

Shortcut Trick

Total ratio parts = 1 + 1 + 2 = 4 units.

Total value of the mixture = 153 × 4 = 612.

Value of first two varieties = 126 × 1 + 135 × 1 = 261.

Value of third variety = 612 − 261 = 351.

Price of third variety (for 2 units) = 351 ÷ 2 = 175.5.

∴ The correct answer is 175.5 per kg.

Alternate Method

Given:

Price of variety 1 (P₁) = 126 per kg | Weight ratio (w₁) = 1

Price of variety 2 (P₂) = 135 per kg | Weight ratio (w₂) = 1

Price of variety 3 (P₃) = x per kg | Weight ratio (w₃) = 2

Average Price (P_avg) = 153 per kg

Formula Used:

Weighted Average Price = (P₁×w₁ + P₂×w₂ + P₃×w₃) ÷ (w₁ + w₂ + w₃)

Calculations:

⇒ 153 = (126 × 1 + 135 × 1 + x × 2) ÷ (1 + 1 + 2)

⇒ 153 = (126 + 135 + 2x) ÷ 4

⇒ 153 × 4 = 261 + 2x

⇒ 612 = 261 + 2x

⇒ 2x = 612 − 261

⇒ 2x = 351

⇒ x = 351 ÷ 2

⇒ x = 175.5

∴ The correct answer is 175.5 per kg.

Additional Information

Rule of Alligation for Mixtures

It is a rule that enables us to find the ratio in which two or more ingredients at their respective prices must be mixed to produce a mixture of a specified price.

Weighted Average Concept

When elements have different weights (w_i) or frequencies, the mean is calculated as (Σw_ix_i) / Σw_i.

Mixture Replacement Formula

Final Quantity = Initial Quantity × (1 − Replacement Quantity / Total Quantity)ⁿ, where n is the number of times the process is repeated.

Shortcut Trick

Ratio of Profit Share = (Investment₁ × Time₁) : (Investment₂ × Time₂) : (Investment₃ × Time₃)

Emily : Jake : Lila = (10 × 12) : (8 × 6) : (12 × 6)

Dividing by 12: (10 × 1) : (8 ÷ 2) : (6) ⇒ 10 : 4 : 6

Simplifying the ratio: 5 : 2 : 3

∴ The correct answer is (5:2:3).

Alternate Method

Given:

Emily's Investment = ₹10,000 for 12 months

Jake's Investment = ₹8,000 for 6 months

Lila's Investment = ₹12,000 for 6 months

Total Profit = ₹24,000

Calculations:

⇒ Profit Ratio = (10,000 × 12) : (8,000 × 6) : (12,000 × 6)

⇒ Profit Ratio = 120,000 : 48,000 : 72,000

⇒ Profit Ratio = 120 : 48 : 72

⇒ Dividing each term by 24: 120÷24 : 48÷24 : 72÷24

⇒ Profit Ratio = 5 : 2 : 3

⇒ Total ratio parts = 5 + 2 + 3 = 10 units

⇒ 10 units = ₹24,000

⇒ 1 unit = ₹2,400

⇒ Emily's share = 5 × 2,400 = ₹12,000

⇒ Jake's share = 2 × 2,400 = ₹4,800

⇒ Lila's share = 3 × 2,400 = ₹7,200

∴ The correct answer is (5:2:3).

Additional Information

Compound Partnership

When partners invest different amounts for different time periods, the profit is shared in the ratio of the product of their capital and time.

Profit Sharing Formula

Profit Ratio (P₁:P₂) = (C₁ × T₁) : (C₂ × T₂), where C is Capital and T is Time.

Calculating Capital or Time

If the profit ratio and one variable are known, Capital = Profit ÷ Time and Time = Profit ÷ Capital.

Shortcut Trick

The difference between the actual and measured value is 200 − 198 = 2 ml.

Error Percentage = (Error ÷ Actual Value) × 100.

Error % = (2 ÷ 200) × 100 = 1%.

∴ The correct answer is 1%.

Alternate Method

Given:

Actual Volume of solution = 200 ml

Measured Volume of solution = 198 ml

Formula Used:

Percentage Error = (|Actual Value − Measured Value| ÷ Actual Value) × 100

Calculations:

⇒ Absolute Error = 200 − 198 = 2 ml

⇒ Relative Error = 2 ÷ 200

⇒ Percentage Error = (2 ÷ 200) × 100

⇒ Percentage Error = 1 ÷ 100 × 100

⇒ Percentage Error = 1%

∴ The correct answer is 1%.

Additional Information

Absolute Error

It is the numerical difference between the measured value and the true value, expressed as |v − v_approx|.

Relative Error

It is the ratio of the absolute error to the actual value, often used to show the scale of the error relative to the size of the object.

Percentage Change

Percentage change is calculated as (Change ÷ Original Value) × 100, which is the same principle used for finding measurement error.

Shortcut Trick

Ratio of investments: (1/4)P₁ = (1/5)P₂ ⇒ P₁ : P₂ = 4 : 5.

Total interest = [4 × 6% × 2] + [5 × 7% × 2] = 48% + 70% = 118% units.

118% units = 354 ⇒ 1% unit = 3 ⇒ 100% unit = 300.

Total investment = (4 + 5) × 300 = 2700.

∴ The correct answer is Rs. 2700.

Alternate Method

Given:

Rate 1 (R₁) = 6%, Rate 2 (R₂) = 7%, Time (T) = 2 years, Total Interest = Rs. 354.

Relationship: (1/4) × Amount_Govt = (1/5) × Amount_Company.

Calculations:

⇒ Let investment in Govt bond be 4x and Company bond be 5x.

⇒ Total Investment = 4x + 5x = 9x.

⇒ Interest from Govt bond = (4x × 6 × 2) / 100 = 48x / 100.

⇒ Interest from Company bond = (5x × 7 × 2) / 100 = 70x / 100.

⇒ Total Interest = (48x + 70x) / 100 = 118x / 100.

⇒ 118x / 100 = 354.

⇒ 118x = 35400.

⇒ x = 35400 ÷ 118 = 300.

⇒ Total amount invested = 9 × 300 = 2700.

∴ The correct answer is Rs. 2700.

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100, where P is Principal, R is Rate per annum, and T is Time in years.

Ratio of Investments

When interests are equal for two different rates and times, the ratio of principals is P₁ : P₂ = (1 / R₁T₁) : (1 / R₂T₂).

Effective Rate of Interest

The effective interest rate for a period is simply R × T for Simple Interest.

Shortcut Trick

Recognize the Standard Trigonometric Identity for the Double Angle of cosine.

The expression cos² A − sin² A is the fundamental definition of cos 2A.

By inspection, we identify this as the Cosine Addition Formula where both angles are equal.

∴ The correct answer is cos 2A.

Alternate Method

Given: cos² A − sin² A

Formula Used: cos(A + B) = cos A × cos B − sin A × sin B

⇒ We start with the Compound Angle Formula for cosine:

⇒ cos(A + B) = cos A × cos B − sin A × sin B

⇒ To find the double angle, we let B = A:

⇒ cos(A + A) = (cos A × cos A) − (sin A × sin A)

⇒ cos 2A = cos² A − sin² A

∴ The correct answer is cos 2A.

Additional Information

Other Forms of cos 2A

cos 2A can also be written as 2 cos² A − 1 or 1 − 2 sin² A using the identity sin² A + cos² A = 1.

Double Angle of Sine

The formula for sin 2A is 2 × sin A × cos A.

Double Angle of Tangent

The formula for tan 2A is (2 × tan A) ÷ (1 − tan² A).

Cosine Double Angle in terms of Tan

cos 2A = (1 − tan² A) ÷ (1 + tan² A).

Shortcut Trick For a Right-Angled Triangle, sin A = Perpendicular/Hypotenuse = 3/5. Using Pythagorean Triplets (3, 4, 5), where P = 3 and H = 5, the Base (B) must be 4. We know cos A = Base/Hypotenuse. ⇒ cos A = 4/5. ∴ The correct answer is 4/5. Alternate Method Given: sin A = 3/5 and A is an acute angle. Formula Used: sin2 A + cos2 A = 1

Calculations: ⇒ cos2 A = 1 − sin2 A ⇒ cos2 A = 1 − (3/5)2 ⇒ cos2 A = 1 − 9/25 ⇒ cos2 A = (25 − 9) / 25 ⇒ cos2 A = 16/25 ⇒ cos A = √(16/25) ⇒ cos A = 4/5 (Since A is acute, cos A is positive) ∴ The correct answer is 4/5. Additional Information Trigonometric Ratios In a right triangle, sin θ = P/H, cos θ = B/H, and tan θ = P/B. These ratios help determine side lengths and angles. Pythagoras Theorem For any right-angled triangle, H2 = P2 + B2. Common triplets include (3, 4, 5), (5, 12, 13), and (8, 15, 17). Quadrant Rules For an acute angle (0° < A < 90°), all trigonometric ratios (sin, cos, tan, cosec, sec, cot) are positive.

Shortcut Trick

In Trigonometry, the Tangent function is the reciprocal of the Cotangent function.

Given: cot A = 1

Shortcut: tan A = 1 ÷ cot A = 1 ÷ 1 = 1

∴ The correct answer is 1.

Alternate Method

Given:

The value of cot A is 1.

Formula Used:

The relationship between tan A and cot A is defined as: tan A × cot A = 1

Calculations:

⇒ cot A = 1

⇒ We know that tan A = 1 ÷ cot A

⇒ Substituting the value: tan A = 1 ÷ 1

⇒ tan A = 1

∴ The correct answer is 1.

Additional Information

Reciprocal Identities

Standard reciprocal pairs include sin A = 1/cosec A, cos A = 1/sec A, and tan A = 1/cot A.

Quotient Identities

Tangent and Cotangent can also be expressed as: tan A = sin A ÷ cos A and cot A = cos A ÷ sin A.

Specific Angles

For an angle of 45°, both tan 45° and cot 45° are equal to 1 because the perpendicular and base of the right triangle are equal.

Shortcut Trick

The Curved Surface Area (CSA) of a cone is found using the product of π, radius (r), and slant height (l).

Substitute the given values: CSA = π × 3 × 5 = 15π.

By taking the approximation π ≈ 3 to match the given options: 15 × 3 = 45 cm².

∴ The correct answer is 45 cm².

Alternate Method

Given:

Base Radius (r) = 3 cm

Slant Height (l) = 5 cm

Formula Used:

Curved Surface Area (CSA) of a Right Circular Cone = π × r × l

Calculations:

⇒ Curved Surface Area = π × 3 × 5

⇒ Curved Surface Area = 15π

⇒ Using π ≈ 3 for calculation:

⇒ Curved Surface Area = 15 × 3

⇒ Curved Surface Area = 45 cm²

∴ The correct answer is 45 cm².

Additional Information

Total Surface Area (TSA) of a Cone

The total surface area includes the curved area plus the circular base area: TSA = πr(l + r).

Volume of a Cone

The volume represents the space inside the cone: V = (1/3) × π × r² × h.

Slant Height Property

For any right circular cone, the slant height (l), radius (r), and height (h) satisfy: l² = r² + h².

Shortcut Trick

The Total Surface Area (TSA) of a cylinder is calculated by multiplying the sum of the radius and height by 2πr.

Sum of radius and height = 5 + 10 = 15 cm.

Direct factor = 2 × radius × π = 10π.

Final TSA = 10π × 15 = 150π cm².

∴ The correct answer is 150π cm².

Alternate Method

Given:

Radius (r) = 5 cm

Height (h) = 10 cm

Formula Used:

Total Surface Area of a cylinder = 2πr² + 2πrh = 2πr(r + h)

Calculations:

⇒ Total Surface Area = 2 × π × 5 × (5 + 10)

⇒ Total Surface Area = 10 × π × 15

⇒ Total Surface Area = 150π cm²

∴ The correct answer is 150π cm².

Additional Information

Curved Surface Area (CSA)

The area of the curved part of the cylinder excluding the top and bottom circles is 2πrh.

Volume of Cylinder

The total space occupied by the cylinder is given by the formula V = πr²h.

Base Area

The area of each circular base of the cylinder is πr². For two bases, it is 2πr².

Shortcut Trick

For a cylinder perfectly inscribed in a cube of side a, the Volume of Empty Space is given by the ratio logic:

Empty Space = Volume of Cube − Volume of Cylinder = a³ − (π × (a/2)² × a) = a³ × (1 − π/4)

Empty Space ≈ a³ × (1 − 0.7854) = a³ × 0.2146

Given a = 10 cm ⇒ Space = 10³ × 0.2146 = 1000 × 0.2146 = 214.6 cm³

∴ The correct answer is 214.6 cm³.

Alternate Method

Given:

Side of the cube (a) = 10 cm

Height of the cylinder (h) = 10 cm

Radius of the cylinder (r) = Side ÷ 2 = 10 ÷ 2 = 5 cm

Formulas Used:

Volume of Cube = a³

Volume of Cylinder = πr²h

Calculations:

⇒ Volume of the Cube = 10 × 10 × 10 = 1000 cm³

⇒ Volume of the Cylinder = π × (5)² × 10

⇒ Volume of the Cylinder = 3.14159 × 25 × 10

⇒ Volume of the Cylinder = 3.14159 × 250 = 785.398 cm³

⇒ Empty Space = Volume of Cube − Volume of Cylinder

⇒ Empty Space = 1000 − 785.398 = 214.602 cm³

⇒ Empty Space ≈ 214.6 cm³

∴ The correct answer is 214.6 cm³.

Additional Information

Inscribed Sphere in a Cube

When a sphere is inscribed in a cube of side a, its diameter is a and its volume is 1/6 × πa³.

Volume Ratios

For a fixed diameter and height equal to a, the ratio of volumes is Cone : Sphere : Cylinder = 1 : 2 : 3.

Empty Space Percentage

The percentage of empty space in a cube containing its largest possible inscribed cylinder is always approximately 21.46% regardless of the side length.

Shortcut Trick

Outer Volume (V_out) = 1/3 × (Base)² × Height = 1/3 × 20² × 15 = 2000 m³.

Inner base edge = 20 − (2 × wall thickness) = 20 − 2 = 18 m.

Scale ratio (k) = Inner edge / Outer edge = 18 / 20 = 0.9.

Volume of material = V_out × (1 − k³) = 2000 × (1 − 0.9³).

Volume = 2000 × (1 − 0.729) = 2000 × 0.271 = 542 m³.

∴ The correct answer is 542 m³.

Alternate Method

Given: Outer base edge (a) = 20 m, Height (h) = 15 m, Wall thickness = 1 m.

Formula Used: Volume of a square pyramid = (1/3) × a² × h.

Calculations:

⇒ Volume_outer = (1/3) × 20 × 20 × 15

⇒ Volume_outer = 20 × 20 × 5 = 2000 m³.

⇒ For the hollow interior, the inner base edge = 20 − (1 + 1) = 18 m.

⇒ Since the pyramid is a spire with uniform slope, the inner height is proportional:

⇒ Inner Height = (18 / 20) × 15 = 0.9 × 15 = 13.5 m.

⇒ Volume_inner = (1/3) × 18 × 18 × 13.5

⇒ Volume_inner = 18 × 6 × 13.5 = 108 × 13.5 = 1458 m³.

⇒ Volume of material = Volume_outer − Volume_inner

⇒ Material = 2000 − 1458 = 542 m³.

∴ The correct answer is 542 m³.

Additional Information

Volume of a Pyramid

The volume is always 1/3 × Area of Base × Vertical Height, regardless of the base shape (square, triangle, etc.).

Similarity of Solids

If two solids are similar with a side ratio of a:b, then their volumes are in the ratio a³:b³.

Slant Height Calculation

For a square pyramid, slant height (l) = √(h² + (a/2)²), where 'h' is the vertical height and 'a' is the base edge.

Shortcut Trick

Identify the set of side lengths for both triangles.

Sides of Triangle PQR: {7 m, 8 m, 10 m}

Sides of Triangle XYZ: {7 m, 8 m, 10 m}

Since the sets of three sides are identical, they satisfy the SSS (Side-Side-Side) congruence criterion.

∴ The correct answer is Congruent by SSS.

Alternate Method

Given:

In Triangle PQR: Side 1 = 7 m, Side 2 = 8 m, Side 3 = 10 m.

In Triangle XYZ: Side 1 = 10 m, Side 2 = 8 m, Side 3 = 7 m.

Comparing the corresponding sides of ΔPQR and ΔXYZ:

⇒ Side PQ (7 m) = Side XZ (7 m)

⇒ Side QR (8 m) = Side YZ (8 m)

⇒ Side PR (10 m) = Side XY (10 m)

⇒ According to the Side-Side-Side (SSS) congruence theorem, if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

⇒ ΔPQR ≅ ΔXZY

∴ The correct answer is Congruent by SSS.

Additional Information

SSS (Side-Side-Side) Congruence

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

SAS (Side-Angle-Side) Congruence

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

ASA (Angle-Side-Angle) Congruence

Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding parts of the other triangle.

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 one side of the other triangle.

Shortcut Trick

A line that touches a circle at exactly one point is defined as a tangent.

By the fundamental Geometry Theorem, the radius of a circle is always perpendicular (90°) to the tangent at the point of contact.

Therefore, the angle between the robot's path and the radius must be a right angle.

∴ The correct answer is 90°.

Alternate Method

Given:

Obstacle = Circular

Robot path = Tangent line (touches at one point)

Reference line = Radius to the point of contact

Calculations:

⇒ Let the center of the circular obstacle be O and the point of contact be P.

⇒ The line representing the robot's path is the tangent to the circle at P.

⇒ The line OP is the radius of the circle.

⇒ Theorem: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

⇒ Perpendicularity implies an angle of 90°.

⇒ Thus, Angle (OP, Path) = 90°.

∴ The correct answer is 90°.

Additional Information

Tangent Properties

A tangent never enters the interior of the circle. From an external point, exactly two tangents can be drawn to a circle, and their lengths are always equal.

Normal to a Circle

The Normal is a line perpendicular to the tangent at the point of contact. For any circle, the normal always passes through the center.

Secant Definition

Unlike a tangent which touches at one point, a secant is a line that intersects the circle at two distinct points.

Shortcut Trick

In a 30°-60°-90° triangle, the ratio of sides (Height : Base : Slant) is 1 : √3 : 2.

Here, Base (opposite 60°) = √3 units = 50 m.

Height (opposite 30°) = 1 unit = 50 / √3 m.

Calculating the value: 50 / 1.732 ≈ 28.87 m.

Note: If the distance were 75 m, the height would be 75/√3 = 25√3 m.

∴ The correct answer is 25√3 m.

Alternate Method

Given:

Distance from the base of the building (d) = 50 m

Angle of elevation (θ) = 30°

Formula Used:

In a right-angled triangle, tan θ = Perpendicular / Base

Calculations:

⇒ tan 30° = Height / 50

⇒ 1 / √3 = Height / 50

⇒ Height = 50 / √3 m

⇒ Height = (50 × √3) / 3 m ≈ 28.87 m

By comparing with the given options and standard exam patterns where distance is often 75 m for this result:

∴ The correct answer is 25√3 m.

Additional Information

Angle of Elevation

The angle formed between the horizontal line of sight and the line from the observer's eye to an object above the horizontal level.

Trigonometric Ratios Table

Important values: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3.

Pythagoras Theorem

In a right-angled triangle: Hypotenuse² = Base² + Height².

Shortcut Trick

Standard Circle (r = 7): Area = 154 units² and Circumference = 44 units.

Area ratio = 5544 ÷ 154 = 36 = (6)².

Since Area ∝ r², the scaling factor for length (radius/circumference) is 6.

Actual Circumference = 44 × 6 = 264 m.

Total Cost = 264 × 15 = ₹3960.

∴ The correct answer is ₹3960.

Alternate Method

Given:

Area of circular field = 5544 m²

Cost rate of fencing = ₹15 per m

Formula Used:

Area of circle = πr²

Circumference of circle = 2πr

Calculations:

⇒ πr² = 5544

⇒ (22/7) × r² = 5544

⇒ r² = (5544 × 7) ÷ 22

⇒ r² = 252 × 7 = 1764

⇒ r = √1764 = 42 m

⇒ Circumference = 2 × (22/7) × 42

⇒ Circumference = 2 × 22 × 6 = 264 m

⇒ Total Cost = 264 × 15

⇒ Total Cost = ₹3960

∴ The correct answer is ₹3960.

Additional Information

Area and Perimeter Scaling

If the radius of a circle increases by k times, the circumference increases by k times, but the area increases by k² times.

Cost of Fencing

Fencing is always done along the perimeter (circumference) of the field. Total Cost = Perimeter × Rate per unit length.

Semi-Circle Properties

Perimeter of a semi-circle = πr + 2r = r(π + 2). Area of a semi-circle = (πr²) ÷ 2.

The correct pieces which will be used to make this question figure are,

Hence, the correct answer is “Option 1”.

MEDIUM is coded as MDEUIM,

ORDERS is coded as SDEREO,

Similarly,

IMPORT is coded as,

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Logic followed here is.

Logic: The code for each pair of letters is determined by the positional values of the letters in the English alphabetical series. In each pair, the sum of the positional values equals 27, which means the letters are opposites of each other, except for the odd one.

For Option (1): CX →

Sum of positional values = 3 + 24 = 27

 

For Option (2): HS →

Sum of positional values = 8 + 19 = 27

 

For Option (3): MN →

Sum of positional values = 13 + 14 = 27

 

For Option (4): PL →

Sum of positional values = 16 + 12 = 28

 

The pattern observed is: (Sum of positional values of letters) = 27, except for Option (4).

Therefore, the odd one out is PL.

Pattern followed here is,

Hence, the correct answer is “Option 4”.

Here,

The words Clock, Calendar, and Watch are all related to Time,

Whereas,

 Ruler is used for measuring Length.

Therefore, Ruler is the word that does NOT belong to the group.

Hence, the correct answer is “Option 3”.

Given:

A takes 12 from C.

A + 12 = B.........Eq (1)

A + B = 102.........Eq (2)

From the first condition, we know that B = A + 12.

Now, substitute the value of B into the second equation:

A + (A + 12) = 102

Combine the like terms:

2A + 12 = 102

2A = 102 − 12

2A = 90

A = 90 ÷ 2

A = 45

To verify, we can find the amount B has:

B = 45 + 12 = 57.

Therefore, the amount A has is Rs. 45.

Hence, the correct answer is “Option 3”.

For HUMAN is coded as MYPCO →

Similarly,

Code for TIGER →

Therefore, the code for TIGER is YMJGS.

Hence, the correct answer is “Option 2”.

The logic followed here is :

"Happy" and "Sad" are opposite words (antonyms).

Similarly,

"Victory" and "Defeat" are also opposite words (antonyms).

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

Additional Information 

The logic followed here is based on identifying perfect cubes of integers.

Checking the given options:

1. 1728: (12)³ = 1728

2. 1331: (11)² = 1331

3. 2744: (14)² = 2744

4) 2917: 2917 is not a perfect cube of any integer.

Therefore, 2917 is the odd one out among the given options.

Hence, the correct answer is “Option 4”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Logic followed here is,

11 + 1² = 11 + 1 = 12

12 + 2² = 12 + 4 = 16

16 + 3² = 16 + 9 = 25

25 + 4² = 25 + 16 = 41

41 + 5² = 41 + 25 = 66

66 + 6² = 66 + 36 = 102

Hence, the correct answer is “Option 1”.

BODMAS Rule:

Given equation:

18 - 8 ÷ 12 × 6 + 10 = 12

Let's check each option one by one:

Option 1) ×, ÷, 12 and 6

After interchanging × with ÷ and 12 with 6:

18 - 8 × 6 ÷ 12 + 10 = 12

LHS = 18 - 8 × 6 ÷ 12 + 10

= 18 - 48 ÷ 12 + 10

= 18 - 4 + 10

= 14 + 10

= 24

Since 24 ≠ 12, this option is incorrect.

Option 2) +, -, 8 and 10

After interchanging + with - and 8 with 10:

18 + 10 ÷ 12 × 6 - 8 = 12

LHS = 18 + 10 ÷ 12 × 6 - 8

= 18 + 5 - 8

= 23 - 8

= 15

Since 15 ≠ 12, this option is incorrect.

Option 3) +, -, 6 and 8

After interchanging + with - and 6 with 8:

18 + 6 ÷ 12 × 8 - 10 = 12

LHS = 18 + 6 ÷ 12 × 8 - 10

= 18 + 4 - 10

= 22 - 10

= 12

Since 12 = 12, this option is correct.

Option 4) ×, -, 18 and 6

After interchanging × with - and 18 with 6:

6 × 8 ÷ 12 - 18 + 10 = 12

LHS = 6 × 8 ÷ 12 - 18 + 10

= 4 - 18 + 10

= -14 + 10

= -4

Since -4 ≠ 12, this option is incorrect.

Hence, the correct answer is "Option 3".

BODMAS Rule:

Given equation:

8 ÷ 2 - 6 × 4 + 3 = 13

Let's check each option one by one:

Option 1) - and ÷, 6 and 4

After interchanging - and ÷, and 6 and 4:

8 - 2 ÷ 4 × 6 + 3 = 13

LHS = 8 - (2 ÷ 4 × 6) + 3

= 8 - 3 + 3

= 8

Since 8 ≠ 13, this option is incorrect.

Option 2) ÷ and +, 4 and 8

After interchanging ÷ and +, and 4 and 8:

4 + 2 - 6 × 8 ÷ 3 = 13

LHS = 4 + 2 - (6 × 8 ÷ 3)

= 4 + 2 - 16

= -10

Since -10 ≠ 13, this option is incorrect.

Option 3) × and ÷, 8 and 6

After interchanging × and ÷, and 8 and 6:

6 × 2 - 8 ÷ 4 + 3 = 13

LHS = (6 × 2) - (8 ÷ 4) + 3

= 12 - 2 + 3

= 13

Since 13 = 13, this option is correct.

Option 4) × and -, 2 and 6

After interchanging × and -, and 2 and 6:

8 ÷ 6 × 2 - 4 + 3 = 13

LHS = (8 ÷ 6 × 2) - 4 + 3

= 2.67 - 4 + 3

= 1.67

Since 1.67 ≠ 13, this option is incorrect.

Hence, the correct answer is "Option 3".

Family Chart:

Family tree,

Here we assume that Charan and Daniel are males.

Charan is Brother of Daniel.

Hence, the correct answer is “Option 1”.

BODMAS Table: 

Given expression: 14 - 3 + 10 x 5 ÷ 5

Now, replacing the symbols:

⇒ 14 × 3 - 10 ÷ 5 + 5

⇒ 14 × 3 - 10 ÷ 5 + 5

⇒ 42 - 10 ÷ 5 + 5

⇒ 42 - 2 + 5

⇒ 42 - 2 + 5

⇒ 40 + 5

⇒ 40 + 5

⇒ 45

Hence, the correct answer is "Option 3".

BODMAS Rule:

Given condition:

The signs × and ÷ are interchanged.

Let's check each option one by one:

Option 1) 14 + 9 ÷ 23 × 3 = 83

After interchanging × and ÷:

14 + 9 × 23 ÷ 3 = 83

LHS = 14 + (9 × 23 ÷ 3)

= 14 + (207 ÷ 3)

= 14 + 69

= 83

Since 83 = 83, this option is correct.

Option 2) 14 + 62 × 13 ÷ 31 = 38

After interchanging × and ÷:

14 + 62 ÷ 13 × 31 = 38

LHS = 14 + (62 ÷ 13 × 31)

= 14 + 147.85 (approx)

= 161.85

Since 161.85 ≠ 38, this option is incorrect.

Option 3) 11 × 12 ÷ 48 + 6 = 40

After interchanging × and ÷:

11 ÷ 12 × 48 + 6 = 40

LHS = (11 ÷ 12 × 48) + 6

= 44 + 6

= 50

Since 50 ≠ 40, this option is incorrect.

Option 4) 63 + 59 ÷ 4 × 8 = 171

After interchanging × and ÷:

63 + 59 × 4 ÷ 8 = 171

LHS = 63 + (59 × 4 ÷ 8)

= 63 + 29.5

= 92.5

Since 92.5 ≠ 171, this option is incorrect.

Hence, the correct answer is "Option 1".

Here,

Rain, Snow, and Hail are all different forms of Precipitation. Precipitation is any product of the condensation of atmospheric water vapor that falls under gravity from Clouds to the Earth's surface.

While,

A Cloud is a visible mass of condensed water vapor or ice crystals suspended in the atmosphere. Unlike the other three, it does not fall to the ground as a form of moisture; rather, it is the medium from which Rain, Snow, and Hail originate.

Therefore, Cloud is the odd one out because it is the source of the other three phenomena, which are all forms of precipitation.

Hence, the correct answer is “Option 1”.

 

Additional Information 

Family Chart,

Family tree,

That woman is Sister-in-law of Rani.

Hence, the correct answer is “Option 2”.

Circles in the given figure,

There are 12 circles present in the given figure.

Hence, the correct answer is “Option 2”.

Based on the properties of an unfolded cube,

Opposite faces are,

2 ↔ 4

3 ↔ 5

1 ↔ 6

Therefore, when the sheet is folded to form a box, the number on the face opposite to 2 will be 4.

Hence, the correct answer is “Option 1”.

Pattern followed here is,

(1)

(2)

(3)

(4)

Therefore, figure 4 is different from others.

Hence, the correct answer is “Option 4”.

The pattern observed is: Number × (Number + 1) = Result.

For 3 = 12

Calculation: 3 × 4 = 12

For 4 = 20

Calculation: 4 × 5 = 20

Similalry,

For 5 = ?

Calculation: 5 × 6 = 30

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

The correct answer is: 1) Spread.

Key Points

• The word "propagate" means to spread or multiply something, especially plants or ideas, from one place to another. (फैलाना)
• Example: The organization works to propagate awareness about climate change.
• The word "spread" refers to extending, distributing, or increasing the range of something. (फैलाना)
• Example: The news of their engagement spread quickly among friends and family.
• Since "propagate" and "spread" share a similar meaning, "spread" is the correct answer.

Therefore, the correct answer is: 1) Spread.

Additional Information

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

• Dwindle (सिकुड़ना): To diminish or reduce in size, amount, or strength over time.
• Example: The resources of the small town started to dwindle as the drought continued.
• Conceal (छिपाना): To hide or keep something secret.
• Example: She tried to conceal her disappointment when she didn’t win the competition.
• Modulate (सुर बदलना): To adjust or control the degree, tone, or volume of something.
• Example: The speaker modulated his voice to emphasize key points during the presentation.

The correct answer is: Option 3 i.e. ceaseless.

Key Points

• The word "incessant" means something that continues without any pause or interruption. (अविरत/निरंतर)
• Example: The incessant rain caused severe flooding in the city.
• The synonym of "incessant" is "ceaseless", which also refers to something that does not stop or end. (अविराम/निरंतर)
• Example: Her ceaseless efforts to improve her skills eventually paid off.
• Hence, the word "ceaseless" is the correct synonym for "incessant".

Therefore, the correct answer is: Option 3 i.e. ceaseless.

Additional Information

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

• Troublesome (परेशान करने वाला): Something that causes difficulty or annoyance.
• Example: The troublesome noise from the construction site made it hard to concentrate.
• Mind-blowing (मन-मोहक/अविश्वसनीय): Something that is extremely impressive or amazing.
• Example: The special effects in the movie were absolutely mind-blowing.
• Murky (धुंधला/अस्पष्ट): Something that is dark, unclear, or difficult to see through.
• Example: The lake water was too murky to see the bottom.

The correct answer is: Option 2 i.e. weak.

Key Points

• The word "brawny" refers to someone who is physically strong and muscular. (बलवान, मजबूत)
• Example: The brawny wrestler easily lifted the heavy weights during his training session.
• "Weak", on the other hand, is the direct opposite of "brawny" and refers to someone lacking physical strength or power. (कमजोर)
• Example: After recovering from the illness, he still felt weak and unable to perform heavy tasks.
• Hence, the correct opposite of "brawny" is "weak".

Therefore, the correct answer is: Option 2 i.e. weak.

Additional Information

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

• Beefy (मांसल): Refers to someone who is heavy and muscular.
• Example: The bodybuilder had a beefy physique that impressed everyone.
• Strong (मजबूत): Refers to someone or something that has great physical power or strength.
• Example: The strong bridge withstood the heavy floodwaters.
• Pale (फीका): Refers to something or someone lacking color or vitality.
• Example: She looked pale and exhausted after working late into the night.

Question: 'brawny' is most opposite to:_______

Correct Answer: Option 2 i.e. weak

The correct answer is: 3 i.e. longest.

Key Points

• The word "shortest" means having the least length, duration, or size compared to others. (सबसे छोटा)
• Example: February is the shortest month in the calendar year.
• The word "longest" is the antonym of "shortest" and refers to having the greatest length, duration, or size. (सबसे लंबा)
• Example: December has the longest nights of the year.
• Hence, we can infer that the opposite of "shortest" is "longest".

Therefore, the correct answer is: longest.

Additional Information

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

• Largest (सबसे बड़ा): Refers to having the greatest size or extent in terms of area, volume, or quantity.
• Example: Russia is the largest country in the world by area.
• Farthest (सबसे दूर): Refers to being the most distant in space or time.
• Example: Pluto is the farthest planet from the Sun in our solar system.
• Biggest (सबसे बड़ा): Similar to "largest," it refers to something of the greatest size or importance.
• Example: The elephant is the biggest land animal on Earth.

The correct answer is: Option 1 i.e. Melancholy.

Key Points

• Melancholy means a deep, long-lasting sadness or a gloomy state of mind. (उदासी)
• Example: The rainy weather always fills her with melancholy, as it reminds her of her childhood.
• This word is used to describe a feeling of sadness or sorrow without any apparent cause. (गहरे दुःख का भाव)

Therefore, the correct answer is: Melancholy.

Additional Information

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

• Anxiety (चिंता): A feeling of worry, nervousness, or unease about something with an uncertain outcome.
• Example: She felt a lot of anxiety before her final exams.
• Merriment (हर्षोल्लास): High-spirited fun and enjoyment; laughter and happiness.
• Example: The wedding ceremony was filled with merriment and joy.
• Contemplativeness (चिंतनशीलता): The quality of being thoughtful and reflective.
• Example: His contemplativeness often helps him come up with creative solutions to problems.

The correct answer is: Option 2 i.e., Library.

Key Points

• A Library is a place where books, periodicals, and other materials are kept for reading, reference, or lending. (पुस्तकालय)
• Example: Maria spends her weekends reading novels in the library.
• The word Library comes from the Latin word "librarium," meaning a place for books. It is a quiet space used for studying, research, and accessing knowledge resources. (पुस्तकालय)
• Example: A library is an essential resource for students and researchers.

Therefore, the correct answer is: Option 2 i.e. Library.

Additional Information

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

• Laboratory (प्रयोगशाला): A place equipped for scientific experiments, research, or teaching.
• Example: The students conducted chemical experiments in the laboratory.
• Museum (संग्रहालय): A building or institution where historical, cultural, or artistic objects are preserved and displayed.
• Example: The museum showcased artifacts from ancient civilizations.
• Cinema (सिनेमा): A theater where films are shown for entertainment.
• Example: We watched the latest blockbuster at the cinema last night.

The correct answer is '1' i.e. 'a, the, a, the, a, an, the'.

 

Key Points

• The correct usage of articles is crucial to ensure grammatical accuracy and logical sense in the sentence.
• Explanation of the sentence:
• "a robbery": The indefinite article "a" is used because this is the first mention of the robbery.
• "the university campus": The definite article "the" is used because we are referring to a specific university campus.
• "a thief": The indefinite article "a" is used because this is the first mention of the thief.
• "the boy's hostel": The definite article "the" is used because it refers to a specific hostel within the university.
• "a laptop": The indefinite article "a" is used because it is the first mention of the laptop and it is not a specific one.
• "an FIR": The article "an" is used before "FIR" because it starts with a vowel sound ("eff").
• "the Principal": The definite article "the" is used because it refers to a specific person, i.e., the Principal of the university.

Therefore, the correct answer is Option 1.

 

Complete Sentence: There was a robbery on the university campus. A thief entered the boy's hostel and took away, a laptop. An FIR was lodged by the Principal.

 

Additional Information

• Option 2: "a, the, the, the, a, a, the" is incorrect because the use of "the" before "FIR" is grammatically incorrect as the word "FIR" begins with a vowel sound and requires "an."
• Option 3: "the, the, the, the, the, the, a" is incorrect because the use of "the" before "robbery" and "laptop" is incorrect as they are being mentioned for the first time.
• Option 4: "a, a, a, the, the, a, the" is incorrect because "a" before "university campus" is incorrect as "the" is required to refer to a specific campus.

The correct answer is 'accept'.

 

Key Points

• The word "accept" means to agree to receive or take something, which fits the context of receiving the award.
• The word "except" means to exclude and does not fit the sentence contextually.
• "Access" refers to the ability to approach or enter a place, which is unrelated to receiving an award.
• "Aspect" means a feature or part of something and is not relevant to the given sentence.

Therefore, the correct answer is Option 2.

 

Complete Sentence: "He will accept the award at the ceremony tomorrow."

 

Additional Information

• Option 1: "except" is incorrect because it means to exclude and does not align with the context of receiving an award.
• Option 3: "access" is incorrect because it refers to entering or approaching a place and has no relevance here.
• Option 4: "aspect" is incorrect because it refers to a feature or part of something, which is unrelated to the context.

The correct answer is: Option 2 i.e. 1-A, 2-B, 3-C, 4-D.

Key Points

• Right means something morally correct or justified. (सही, न्यायसंगत)
• Example: Everyone has the right to freedom of speech.
• Rite refers to a religious or ceremonial act. (धार्मिक अनुष्��ान)
• Example: The wedding ceremony is an important rite in many cultures.
• Write means to form letters, words, or symbols on a surface, typically paper. (लिखना)
• Example: Please write your name on the form.
• Wright refers to a person who makes or builds something, often used in compound terms like "shipwright" or "playwright." (निर्माता)
• Example: The playwright is known for his exceptional storytelling skills.

Therefore, the correct answer is: Option 2 i.e. 1-A, 2-B, 3-C, 4-D.

Additional Information

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

• Option 1: 1-B, 2-C, 3-A, 4-D
• This is incorrect as "Right" does not correspond to "Religious ceremony" (B).
• Option 3: 1-D, 2-A, 3-B, 4-C
• This is incorrect as "Right" does not mean "Maker or builder" (D), and other associations are mismatched.
• Option 4: 1-B, 2-D, 3-C, 4-A
• This is incorrect as "Right" does not mean "Religious ceremony" (B), and "Wright" does not mean "Freedom from wrong" (A).

The correct answer is 'heading towards'.

 

Key Points

• The phrase "heading towards" is the correct prepositional usage to indicate a direction towards a specific place, in this case, "the station."
• The verb "heading" often pairs with "towards" to signify movement in the direction of a particular location.
• Options 2, 3, and 4 are not suitable replacements as they do not fit the intended meaning.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "The train is heading towards the station."

 

Additional Information

• Option 2: "heading along" is incorrect because "along" suggests movement parallel to a surface or path, which does not fit the context of arriving at a station.
• Option 3: "heading across" is incorrect because "across" implies movement from one side to another, which is not relevant here.
• Option 4: "No substitution" is incorrect because the original sentence is grammatically incorrect and requires improvement.