Delhi Police Head Constable (Ministerial), 2025 Official Paper (Held On: 12 Jan, 2026 Shift 2) (Previous Year Paper)

The correct answer is Mesolithic.

Key Points

• The Mesolithic Age, also known as the Middle Stone Age, served as a transitional phase between the Paleolithic and Neolithic periods, dating roughly from 10,000 BC to 6,000 BC in the Indian context.
• The hallmark of this period is the production of Microliths, which are very small stone tools ranging from 1 cm to 5 cm in length, typically made of materials like chert, agate, and carnelian.
• These microliths were often geometric in shape (trapezes, lunates, triangles) and were used as components for composite tools such as spearheads and arrowheads, reflecting an advancement in hunting technology.
• This era witnessed the earliest signs of domestication of animals in India. Excavations at Bagor in Rajasthan and Adamgarh in Madhya Pradesh provide significant zooarchaeological evidence of domesticated cattle, sheep, and goats.
• The period coincided with the onset of the Holocene epoch, characterized by a warmer and more humid climate, which led to a proliferation of flora and fauna and encouraged humans to move into new ecological niches.

 Additional Information

• Paleolithic:
• Characterized by the use of large, unpolished stone tools like hand-axes, choppers, and cleavers.
• Humans were primarily hunter-gatherers and lived in a nomadic state during the Pleistocene ice age.
• Neolithic:
• Defined by the beginning of sedentary life, systematic agriculture, and the production of polished stone tools.
• Introduction of pottery and the wheel occurred during this phase, with key sites like Mehrgarh and Burzahom.
• Chalcolithic:
• This was the Copper-Stone Age, marking the first use of metal (copper) alongside stone tools.
• It saw the emergence of organized rural settlements and distinct ceramic traditions like the Malwa and Jorwe cultures.

The correct answer is War goddess who resisted state power.

Key Points

• Sammakka is a legendary tribal deity of the Koya community, primarily worshipped in the state of Telangana. Her significance is deeply rooted in historical resistance against the Kakatiya dynasty during the 13th century.
• In tribal belief systems, she is revered as a war goddess who led a fierce rebellion against King Pratapa Rudra to protest the imposition of tributes and taxes on the forest-dwelling tribes during a period of severe famine and drought.
• Unlike many mainstream deities, Sammakka is a human-turned-goddess whose divinity stems from her military valor and her ultimate sacrifice for the socio-economic rights and dignity of her people.
• She represents the spirit of defiance against centralized state authority, serving as a symbol of tribal autonomy and the preservation of indigenous ways of life against external administrative intrusion.
• The legendary battle occurred at Medaram, where she and her daughter Saralamma fought the royal armies, eventually disappearing into the forest, leaving behind only a casket of vermillion.

 Additional Information

• Medaram Jatara:
• Known as the Sammakka Saralamma Jatara, it is the largest tribal congregation in the world, celebrated biennially in the Mulugu district.
• It was declared a State Festival by the Government of Telangana and is characterized by the absence of permanent temples or idols, using bamboo poles and vermillion to represent the deities.
• Koya Tribe:
• The Koyas are an indigenous community settled in the Godavari river basin across Telangana, Andhra Pradesh, and Chhattisgarh.
• Their culture is noted for the Gondi language influence and the performance of the Permakore dance during the festival.
• Historical Context:
• The Kakatiya Empire was a major South Indian power with its capital at Warangal. The conflict with Sammakka highlights early tensions between agrarian empires and forest societies regarding resource management.

The correct answer is The Delimitation Commission’s orders are final and binding, cannot be challenged in any court, and are implemented as per the schedule laid down in the delimitation order..

Key Points

• Under Article 329(a) of the Constitution of India, the validity of any law relating to the delimitation of constituencies or the allotment of seats to such constituencies cannot be called into question in any court. This grants the Commission's orders immunity from judicial review to prevent delays in the electoral cycle. Hence, statement 1 is incorrect.
• The Delimitation Commission is a statutory body constituted by the Central Government under the Delimitation Commission Act, enacted under Article 82. It is not a permanent constitutional body appointed every 5 years; it is set up following census operations as directed by Parliament. Hence, statement 2 is incorrect.
• The orders of the Commission have the force of law and are published in the Gazette of India. These orders cannot be modified by the President, Parliament, or any State Legislature. They take effect from a date specified by the President and are final. Hence, statement 3 is correct.
• While maintaining a uniform population-to-seat ratio is a goal, the Commission must also consider geographical compactness, physical features, administrative boundaries, and public convenience. Furthermore, it specifically reserves seats for Scheduled Castes and Scheduled Tribes based on population density in specific areas. Hence, statement 4 is incorrect.

 Additional Information

• Composition and Scope:
• The Commission consists of three members: a retired Supreme Court Judge (Chairperson), the Chief Election Commissioner, and the State Election Commissioner of the respective state.
• The 84th Amendment Act of 2001 froze the number of seats in the Lok Sabha and State Assemblies based on the 1971 census until the first census after 2026.
• The 87th Amendment Act of 2003 provided for the delimitation of constituencies based on the 2001 Census without changing the total number of seats.
• The primary objective of delimitation is to ensure one vote, one value by creating equal population segments across constituencies.

The correct answer is The funding for MGNREGA is shared equally between the Central and State Governments, with States responsible for wage payments.

Key Points

• The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA), enacted in September 2005, legally guarantees at least 100 days of wage employment in a financial year to every rural household whose adult members volunteer to do unskilled manual work. Hence, statement 1 is correct.
• The Act contains a statutory provision for the payment of an unemployment allowance if the applicant is not provided with work within 15 days of applying for employment. Hence, statement 2 is correct.
• The list of permissible works under Schedule I of the Act includes water conservation, afforestation, desilting of tanks, and creating infrastructure for agriculture and livestock. Hence, statement 3 is correct.
• The Central Government bears 100% of the unskilled wage cost and 75% of the material and semi-skilled/skilled wage cost, while State Governments contribute 25% of the material cost and pay the unemployment allowance. Hence, statement 4 is incorrect.

 Additional Information

• Core Objectives:
• To enhance livelihood security and create durable assets like wells, ponds, and roads in rural areas.
• To reduce rural-to-urban migration by providing local employment opportunities during lean agricultural seasons.
• Administrative Framework:
• Gram Panchayats are responsible for planning, implementing, and monitoring the works.
• The Social Audit mechanism is mandatory under the Act to ensure transparency and accountability in fund utilization.
• Priority is given to women, ensuring that at least one-third of the total beneficiaries are female workers.
• Constitutional Basis:
• It aligns with Article 41 of the Directive Principles of State Policy, which directs the State to secure the Right to Work.

The correct answer is Eskers are sinuous ridges of stratified sand and gravel deposited by subglacial meltwater streams flowing within ice tunnels, serving as evidence of former glacial drainage patterns.

Key Points

• Statement 1 describes these features as steep-sided ridges composed of till formed by subaerial erosion. In reality, eskers are glacio-fluvial landforms consisting of stratified drift (sorted layers) rather than unsorted glacial till. Hence, statement 1 is incorrect.
• Statement 2 correctly identifies eskers as sinuous ridges of stratified sand and gravel. These are deposited by subglacial meltwater streams flowing through ice tunnels or tubes at the base of stagnant or retreating glaciers. They act as a blueprint for reconstructing paleo-drainage systems. Hence, statement 2 is correct.
• Statement 3 attributes the formation of eskers to wind action and loess deposits. Loess is an aeolian (wind-blown) silt deposit, whereas eskers are exclusively water-laid features found within glacial environments. Hence, statement 3 is incorrect.
• Statement 4 links eskers to lateral morainic deposition and the maximum extent of a glacier. Lateral moraines form at the glacier margins from debris falling off the ice, while eskers are internal depositional features. Hence, statement 4 is incorrect.

 Additional Information

• Characteristics of Eskers:
• They typically range from a few meters to over 30 meters in height and can extend for hundreds of kilometers, often appearing as railway embankments across the landscape.
• The sediments are well-sorted due to the action of high-velocity meltwater flowing under hydrostatic pressure.
• Eskers usually run parallel to the direction of ice flow.
• Other Glacial Landforms:
• Kames: These are irregularly shaped mounds or isolated hills of stratified drift deposited in crevasses or depressions on the melting ice surface.
• Drumlins: These are asymmetrical, canoe-shaped hills composed of till that indicate the direction of ice movement.
• Moraines: These are accumulations of unstratified debris (till) deposited directly by the ice at its edges (lateral) or terminus (terminal/end).

The correct answer is Mosquito repellant creams provide a physical barrier preventing mosquitoes from biting by forming a thick layer on the skin..

Key Points

• DEET (N,N-Diethyl-meta-toluamide) is the most common active ingredient in repellents; it works by binding to odorant-binding proteins and olfactory receptors in mosquitoes, confusing their ability to detect human attractants like carbon dioxide and lactic acid. Hence, statement 1 is correct.
• Repellent creams do not act as a mechanical or physical barrier like a suit of armor; instead, they function biochemically by creating a vapor zone that deters insects or masks the host. The thickness of the application does not prevent bites through physical obstruction. Hence, statement 2 is incorrect.
• Natural repellents, such as citronella oil, lemon eucalyptus, and neem oil, are volatile organic compounds that mask human scents. They disrupt the mosquito's chemotaxis, making it difficult for the insect to lock onto a target. Hence, statement 3 is correct.
• The duration of protection is influenced by the concentration of the active ingredient, the formulation type (aerosol vs. cream), and environmental variables such as ambient temperature, wind speed, and the user's perspiration rate. Hence, statement 4 is correct.

 Additional Information

• Chemical Repellents:
• Picaridin: A synthetic compound resembling the natural compound piperine found in plants that produce black pepper; it is effective against various arthropods.
• IR3535: A synthetic amino acid derivative that is structurally similar to the naturally occurring amino acid beta-alanine.
• Biological Mechanisms:
• Mosquitoes use sensilla located on their antennae and maxillary palps to detect chemical signatures.
• Kairomones: These are the chemical signals emitted by humans that mosquitoes track to find blood meals.
• Permethrin: Unlike skin-applied creams, this is a contact insecticide used on fabrics that kills mosquitoes upon contact.

The correct answer is Sundar Pichai.

Key Points

• Sundar Pichai, born in Madurai, Tamil Nadu, is the Chief Executive Officer of Alphabet Inc. and its subsidiary Google.
• He earned his degree from IIT Kharagpur in Metallurgical Engineering before pursuing an M.S. from Stanford University and an MBA from the Wharton School of the University of Pennsylvania.
• Joining Google in 2004, he played a critical role in the development of the Google Chrome browser and overseen the Android operating system's growth.
• He was appointed CEO of Google in 2015 and later became the CEO of Alphabet Inc. in 2019, following the reorganization of the company.
• Under his guidance, Google has transitioned to an AI-first company, launching advanced Large Language Models (LLMs) like Gemini and integrating Artificial Intelligence across its global product ecosystem.

 Additional Information

• Satya Nadella:
• He serves as the Executive Chairman and CEO of Microsoft, taking over in 2014.
• He is widely credited with shifting Microsoft's focus toward Cloud Computing and the Azure platform.
• Arvind Krishna:
• He is the Chairman and CEO of IBM (International Business Machines Corporation).
• He was the principal architect of the Red Hat acquisition, the largest in IBM's history, focusing on Hybrid Cloud technology.
• Parag Agrawal:
• An Indian-origin executive who served as the CEO of Twitter from November 2021 until the company was acquired by Elon Musk in October 2022.
• He previously held the position of Chief Technology Officer (CTO) at the social media giant.

The correct answer is Focus on Bay of Bengal regional cooperation.

Key Points

• BIMSTEC acts as a natural platform to fulfill India's primary foreign policy objectives, specifically the Act East Policy and Neighborhood First Policy, by linking South Asian and Southeast Asian economies.
• The Bay of Bengal is a geostrategically vital maritime zone, housing roughly 22% of the world population, making regional cooperation essential for India’s maritime security and blue economy interests.
• India has shifted its focus to BIMSTEC as a more viable alternative for regional integration due to the persistent stagnation of SAARC, caused largely by bilateral tensions and cross-border terrorism.
• The organization facilitates the development of India's North-Eastern states by promoting connectivity projects that provide landlocked areas access to Bay of Bengal ports via Bangladesh and Myanmar.
• India leads the Security pillar within BIMSTEC, which includes cooperation on counter-terrorism, transnational crime, and disaster management, reinforcing India's role as a Net Security Provider in the Indian Ocean Region.

 Additional Information

• BIMSTEC Foundation and Membership:
• Established on June 6, 1997, through the Bangkok Declaration.
• It comprises seven members: Bangladesh, Bhutan, India, Myanmar, Nepal, Sri Lanka, and Thailand.
• The Secretariat is located in Dhaka, Bangladesh.
• Strategic Infrastructure Projects:
• The Kaladan Multi-Modal Transit Transport Project connects the eastern Indian seaport of Kolkata with Sittwe seaport in Myanmar.
• The India-Myanmar-Thailand Trilateral Highway is a landmark project aimed at boosting land connectivity and trade with ASEAN nations.
• Economic Significance:
• Member states have a combined GDP of over 3.5 trillion USD.
• The proposed BIMSTEC Free Trade Area (FTA) aims to enhance intra-regional trade by reducing tariff and non-tariff barriers.

The correct answer is Bombay.

Key Points

• In 1924, the first multi-sport event in India was organized under the Olympic format, known then as the Indian Olympic Games. This event was critical for aligning Indian sports with the standards set by the International Olympic Committee (IOC).
• The city of Bombay served as the administrative and organizational heart of this movement, led by influential figures like Sir Dorabji Tata and Dr. A.G. Noehren, who sought to professionalize Indian athletics.
• The primary objective of the 1924 games was to identify and select talented athletes to represent India at the Paris 1924 Summer Olympics, marking a significant milestone in India's participation in global sports.
• The success of this event influenced the future sports structure by necessitating a permanent governing body, which eventually led to the official formation of the Indian Olympic Association (IOA) in 1927.
• This structure facilitated the transition of these games into what we now recognize as the National Games of India, a name officially adopted during the 9th edition held in 1940.

 Additional Information

• Lahore:
• While the organizational impetus came from the Bombay Olympic Association, early editions of the All-India Olympic Games were also hosted in Lahore, making it a key historical site for pre-independence sports.
• Delhi:
• The capital city later became a pivotal hub for international sports, famously hosting the inaugural Asian Games in 1951 and several subsequent editions of the National Games.
• Kolkata:
• Known as the sports capital of India, it hosted the games in 1938 and has consistently been a major center for the development of football and track-and-field events.
• Sir Dorabji Tata:
• As the founding President of the IOA, his personal funding and vision were instrumental in sending the first organized Indian contingent to the 1920 Antwerp Olympics, three years before the formal national structure was established.

The correct answer is 1980.

Key Points

• The Indian women's hockey team made its historic debut at the Olympic Games in 1980, held in Moscow, Soviet Union.
• The 1980 Moscow Olympics was a landmark event as it featured the inaugural competition for women's field hockey in the history of the Summer Olympics.
• The Indian squad was led by captain Rupa Saini and delivered a commendable performance by finishing fourth in the overall standings among the six competing nations.
• The tournament followed a round-robin format where India competed against Zimbabwe, Czechoslovakia, the Soviet Union, Austria, and Poland.
• Although they narrowly missed a podium finish, this qualification established the foundation for women's field hockey in the Indian sporting landscape.

 Additional Information

• Evolution of the Indian Women's Hockey Team in the Olympics:
• After the 1980 appearance, the team faced a long gap of 36 years before qualifying for the 2016 Rio Olympics.
• At the 2020 Tokyo Olympics (held in 2021), the team achieved its best modern-day result by reaching the semi-finals for the first time.
• During the Tokyo Games, the team defeated Australia in the quarter-finals, eventually finishing fourth under the captaincy of Rani Rampal and coach Sjoerd Marijne.
• The International Hockey Federation (FIH) governs the qualification process, which has shifted from invitational formats to performance-based Olympic Qualifiers and Continental Championships.
• In the 1980 edition, Zimbabwe claimed the first-ever Gold Medal in women's Olympic hockey, a victory that remains one of the greatest upsets in the sport.

The correct answer is All of the above.

Key Points

• Cash Reserve Ratio (CRR) refers to the specific percentage of Net Demand and Time Liabilities (NDTL) that commercial banks are mandated to maintain as cash reserves with the Reserve Bank of India (RBI). When the RBI increases the CRR, banks are required to park a larger portion of their deposits with the central bank, which directly reduces the loanable funds available for credit creation, thereby leading to a significant decrease in the money supply. Hence, statement 1 is correct.
• The increase in CRR acts as a part of a contractionary monetary policy or dear money policy. As the liquidity in the banking system tightens, the scarcity of funds typically pushes up the interest rates in the economy. In the framework of the money market, this tightening of credit conditions often aligns with an adjustment where the demand for money (liquidity preference) shifts or the cost of acquiring money increases. Hence, statement 2 is correct.
• A higher CRR is primarily utilized as a tool to curb inflationary pressures. By reducing the liquidity available with banks and the public, it lowers aggregate demand and consumption spending. This reduction in the overall demand for goods and services helps in stabilizing the price levels and leads to a decrease in inflation. Hence, statement 3 is correct.

 Additional Information

• Cash Reserve Ratio (CRR) Details:
• It is governed under the provisions of Section 42(1) of the Reserve Bank of India Act, 1934.
• Banks do not receive any interest from the RBI on the amount maintained as CRR, making it a non-interest-earning asset for commercial banks.
• Unlike Statutory Liquidity Ratio (SLR), which can be maintained in the form of gold or government securities, CRR must be kept strictly in cash.
• The Monetary Policy Committee (MPC) reviews the CRR periodically to manage price stability and support economic growth objectives.

The correct answer is They appear on the maṇḍapa roof and continue the Ajanta mural tradition.

Key Points

• The Badami Cave temples, located in the Bagalkot district of Karnataka, represent the finest examples of Chalukyan architecture and art from the 6th century CE.
• Cave 3, popularly known as the Vishnu Cave, is the largest and most ecologically significant cave in the complex, featuring an inscription by the Chalukya King Mangalesha dated to 578 CE.
• The murals in this cave are primarily found on the soffits of the brackets and the vaulted roof of the maṇḍapa (the assembly hall), depicting various divine and courtly scenes.
• Art historians note that these paintings serve as a critical link in Indian art history, as they continue the Ajanta mural tradition while introducing a more stylized and elongated human form characteristic of the southern schools.
• The technique used at Badami is similar to the tempera or fresco-secco method seen at Ajanta, where pigments were applied over a lime plaster surface.

 Additional Information

• Chronological Context:
• The Badami Chalukyas ruled the Deccan region between the 6th and 8th centuries CE, long before the rise of the Imperial Cholas in the 9th-12th centuries.
• The Chola dynasty is famous for the Brihadisvara Temple murals, which are distinct in style and period from the Early Western Chalukyan works.
• Thematic Differences:
• While Cave 4 at Badami is dedicated to Jainism and contains images of Mahavira and other Tirthankaras, Cave 3 is exclusively Vaishnavite, focusing on incarnations such as Varaha, Narasimha, and Trivikrama.
• The murals in Cave 3 are monumental wall paintings and are not considered miniature paintings, which became a dominant style much later in Indian history during the Medieval period.

The correct answer is To monitor Earth's surface changes and ecosystem disturbances.

Key Points

• NISAR (NASA-ISRO Synthetic Aperture Radar) is a landmark joint mission between the United States (NASA) and India (ISRO), designed to observe Earth's most complex processes.
• The primary objective is to study Earth's surface changes, specifically measuring movements as small as centimeters to monitor tectonic deformation, volcanic activity, and landslides.
• It is equipped to monitor ecosystem disturbances by tracking changes in biomass, carbon storage, and vegetation health, providing insights into the impacts of climate change.
• The mission focuses on the cryosphere, observing the movement and melting of ice sheets and glaciers in Antarctica and the Arctic to predict sea-level rise.
• NISAR utilizes a 12-day repeat cycle, mapping the entire globe consistently to provide high-resolution data for geohazards and natural resource management.

 Additional Information

• Dual-Band Radar Technology: This is the first satellite mission to use two different radar frequencies, the L-band (1.25 GHz) provided by NASA and the S-band (3.2 GHz) provided by ISRO.
• L-band SAR: Capable of penetrating thick forest canopies to study the ground beneath, essential for measuring seismic strain.
• S-band SAR: Targeted at coastal processes, soil moisture, and agricultural monitoring.
• Mission Hardware: NASA is providing the L-band SAR, a high-rate communication subsystem, and a 12-meter deployable mesh reflector; ISRO is providing the spacecraft bus, the S-band SAR, and the GSLV Mark II launch vehicle.
• Global Impact: The data will be open-access, supporting global efforts in disaster management, groundwater depletion analysis, and sustainable agriculture.
• Launch Site: The satellite is scheduled for launch from the Satish Dhawan Space Centre in Sriharikota.

The correct answer is Heavy and Basic Industries.

Key Points

• During India's initial planning phase, specifically starting with the Second Five-Year Plan (1956-1961), the government adopted the Mahalanobis Model, which prioritized heavy and basic industries to foster self-reliance.
• The Industrial Policy Resolution of 1956 served as the blueprint for this era, granting the Public Sector a lead role in the commanding heights of the economy, including sectors like iron and steel, heavy machinery, and chemicals.
• Massive capital investments were directed toward establishing Public Sector Undertakings (PSUs), such as the Bhilai, Rourkela, and Durgapur Steel Plants, to create an industrial base for future growth.
• This strategy was rooted in Import Substitution Industrialization (ISI), aimed at reducing dependence on foreign capital goods and building a robust domestic manufacturing infrastructure.
• The growth during the 1950s to the 1980s was characterized by state-led development where basic industries provided the necessary inputs for other sectors of the national economy.

 Additional Information

• Sectoral Comparisons:
• Information Technology (IT): This sector only gained momentum after the Economic Reforms of 1991 and the subsequent globalization of the Indian economy; it was not a priority during the early planning years.
• Fast-Moving Consumer Goods (FMCG): Growth in this sector was restricted during the License Raj era (pre-1990s) as the government discouraged luxury consumption in favor of capital formation.
• Tourism and Hospitality: These were considered tertiary services and received relatively low public sector outlay compared to the primary focus on structural industrialization.
• First Five-Year Plan: Unlike the heavy industry focus of the second plan, the First Plan (1951-1956) primarily targeted agricultural development and irrigation projects.

The correct answer is Mahmud Gawan's assassination weakened the Sultanate.

Key Points

• The Bahmani Sultanate was established in 1347 by Ala-ud-Din Bahman Shah (Hasan Gangu) as an independent kingdom after revolting against Muhammad bin Tughluq of the Delhi Sultanate. Hence, statement 1 is incorrect.
• Mahmud Gawan served as the Prime Minister and Vakil-us-Sultanat under three kings; his execution in 1481 due to conspiracies by rival factions (Deccanis) led to the loss of central authority and the fragmentation of the state. Hence, statement 2 is correct.
• The capital of the kingdom was initially established at Gulbarga (Ahsanabad) but was shifted to Bidar in 1424 during the reign of Ahmad Shah I Wali for better strategic control and climate. Hence, statement 3 is incorrect.
• The Sun Temple at Konark was commissioned by King Narasimhadeva I of the Eastern Ganga Dynasty in the 13th century, long before the Bahmani rise. Hence, statement 4 is incorrect.

 Additional Information

• Mahmud Gawan:
• He was a brilliant administrator and military strategist who successfully captured Goa and Dabhol.
• He established the famous Madrasa of Mahmud Gawan in Bidar, which was a significant center for Islamic learning.
• He introduced administrative reforms by dividing the kingdom into eight provinces (tarafs) to curb the power of local governors.
• Decline and Legacy:
• Internal strife between Afagis (foreigners) and Deccanis (local nobles) triggered the eventual collapse.
• The empire eventually split into the five Deccan Sultanates: Adil Shahi (Bijapur), Nizam Shahi (Ahmednagar), Imad Shahi (Berar), Qutb Shahi (Golconda), and Barid Shahi (Bidar).

The correct answer is 1, 2 and 3 are correct.

Key Points

• The Sri-khol, often referred to simply as the Khol, is a traditional terracotta two-sided drum originating from Bengal and Assam. It is fundamentally linked to the Gaudiya Vaishnava tradition and serves as the primary rhythmic accompaniment for Kirtan (devotional chanting) and Gayan-Bayan. Hence, statement 1 is correct.
• The Ektara is a primitive one-stringed instrument used by wandering bards and mystics across the Indian subcontinent. It is the signature musical tool of the Baul community of Bengal, used to provide a rhythmic drone that complements their spiritual and philosophical songs. Hence, statement 2 is correct.
• The Dhol is a versatile barrel-shaped drum found in various regional variations; among the Rabha tribe of the Northeast, it is an essential percussion instrument used during traditional War Dances (like the Nak-kati) and agricultural festivals to provide high-energy beats. Hence, statement 3 is correct.

 Additional Information

• Musical Traditions and Instruments:
• Sri-khol: Constructed from clay or terracotta, its body is wider in the middle with two leather-bound heads. It was historically popularized by the saint Chaitanya Mahaprabhu in the 15th century.
• Baul Singing: This is a unique folk tradition recognized by UNESCO as a Masterpiece of the Oral and Intangible Heritage of Humanity. The music emphasizes the internal search for the 'Man of the Heart' (Moner Manush).
• Rabha Tribe: An Indo-Mongoloid community primarily residing in Assam, Meghalaya, and West Bengal. Their cultural performances often feature the Kram (drum), Badungduppa (bamboo instrument), and the Dhol to narrate tales of valor and harvest.
• Kirtan: A form of Bhakti yoga involving call-and-response chanting, which attained peak popularity during the Bhakti Movement in medieval India.

The correct answer is A-2, B-1, C-3.

Key Points

• Arjuna Award: Instituted in 1961, this award recognizes sportspersons for their outstanding performance in various sports and games at the international level over a period of four years. It includes a bronze statue of Arjuna, a certificate, and a cash prize. Hence, Arjuna Award matches with Outstanding Performance.
• Dronacharya Award: Named after the legendary guru from the Mahabharata, this honor was introduced in 1985 to provide Coach Recognition. It is given to instructors who have demonstrated excellence in training athletes to achieve podium finishes at prestigious events like the Olympics and World Championships. Hence, Dronacharya Award matches with Coach Recognition.
• Khel Ratna Award: Officially the Major Dhyan Chand Khel Ratna Award, it is considered the Top Sporting Honor in India. Established in 1991-92, it is conferred upon athletes for the most spectacular and outstanding performance over a four-year cycle. Hence, Khel Ratna Award matches with Top Sporting Honor.

 Additional Information

• National Sports Awards: These awards are administered by the Ministry of Youth Affairs and Sports, Government of India.
• National Sports Day: The awards are typically presented by the President of India on August 29 every year, marking the birth anniversary of hockey wizard Major Dhyan Chand.
• Renaming History: The Khel Ratna was formerly named after Rajiv Gandhi but was renamed in 2021 to honor Major Dhyan Chand.
• First Recipient: The first Khel Ratna was awarded to the legendary Chess Grandmaster Viswanathan Anand.
• Dhyan Chand Award: Distinct from the Khel Ratna, there is also a Dhyan Chand Award for Lifetime Achievement in Sports and Games, instituted in 2002.

The correct answer is Acute balance of payments crisis.

Key Points

• By July 1991, India faced a severe Balance of Payments (BoP) crisis where the foreign exchange reserves dropped to approximately $1.2 billion, sufficient to fund only about two weeks of essential imports.
• The Gulf War (1990-91) played a critical role by triggering a sharp rise in global crude oil prices and causing a massive decline in remittances from Indian workers stationed in the Middle East.
• Internal economic instability was marked by a high fiscal deficit of nearly 8.4% of GDP and a double-digit inflation rate peaking at 16.7%, which collapsed international investor confidence in the Indian economy.
• To prevent a sovereign default, the Reserve Bank of India (RBI) was forced to pledge 47 tonnes of gold with the Bank of England and 20 tonnes with the Union Bank of Switzerland to secure emergency credit.

 Additional Information

• New Economic Policy (NEP) 1991:
• Launched under Prime Minister P.V. Narasimha Rao and Finance Minister Dr. Manmohan Singh, the reforms introduced the LPG model: Liberalization, Privatization, and Globalization.
• The International Monetary Fund (IMF) and the World Bank provided a $7 billion bailout package contingent upon India implementing structural adjustments to open its domestic market.
• Context of Other Options:
• Trade Surplus: This was absent in 1991; India suffered from a chronic trade deficit due to high dependency on petroleum imports and low export competitiveness.
• High Agricultural Output: While the Green Revolution improved food security, it could not offset the macroeconomic imbalance caused by industrial stagnation and debt.
• Booming Exports: India’s share in global trade was less than 0.5% in 1991, hindered by the restrictive License-Permit Raj system.

The correct answer is UNDP Human Development Report.

Key Points

• The Human Development Index (HDI) is a statistical tool used to measure a country's overall achievement in its social and economic dimensions, released annually by the United Nations Development Programme (UNDP).
• The concept was developed in 1990 by Pakistani economist Mahbub ul Haq and Indian Nobel laureate Amartya Sen to shift the focus of development from purely economic metrics like GDP to human-centric progress.
• The index is calculated using three fundamental dimensions: Long and healthy life (Life expectancy at birth), Knowledge (Mean and expected years of schooling), and A decent standard of living (GNI per capita at Purchasing Power Parity).
• The Human Development Report (HDR) serves as a critical global benchmark, ranking nations like India into categories ranging from Very High to Low human development based on their composite scores.

 Additional Information

• UNDP Subsidiary Indices:
• The report also features the Inequality-adjusted HDI (IHDI), which adjusts the HDI score based on the level of inequality within a country's population.
• Other key metrics include the Gender Inequality Index (GII) and the Multidimensional Poverty Index (MPI), which provide deeper insights into societal disparities.
• Other International Organizations:
• The World Bank primarily publishes the World Development Report and focused on the Ease of Doing Business index (now discontinued), which assesses the regulatory environment for businesses.
• The World Health Organization (WHO) focuses on global health statistics and policy, such as the World Health Statistics report, rather than integrated human development rankings.

The correct answer is 0 kg.

Key Points

• A photon is defined as an elementary particle that serves as the quantum of the electromagnetic field, representing the smallest discrete amount of electromagnetic radiation such as light, X-rays, and radio waves.
• In the Standard Model of particle physics, the rest mass (also known as invariant mass) of a photon is exactly zero. This property distinguishes it from matter particles like electrons or protons.
• According to Albert Einstein’s Special Theory of Relativity, any particle with a non-zero rest mass would require infinite energy to reach the speed of light (approximately 299,792,458 m/s). Since photons always travel at this speed in a vacuum, they must possess zero rest mass.
• While they lack mass, photons possess energy and momentum. The energy of a photon is directly proportional to its electromagnetic frequency, expressed by the equation ( E = hf ), where h is Planck’s constant.
• The momentum of a photon is given by the relation ( p = E/c ), allowing light to exert radiation pressure on surfaces despite having no mass.

 Additional Information

• Comparison with other physical constants:
• 9.1 × 10⁻³¹ kg: This is the approximate rest mass of an electron, which is the lightest stable subatomic particle with a negative charge.
• 1.6 × 10⁻¹⁹: This numerical value is associated with the elementary charge (measured in Coulombs), representing the magnitude of electric charge carried by a single proton or electron.
• Wave-Particle Duality: Photons demonstrate both wave-like behavior (such as interference and refraction) and particle-like behavior (such as the photoelectric effect).
• Force Carrier: The photon is the gauge boson that mediates the electromagnetic force, one of the four fundamental forces of nature.

Shortcut Trick

Volume of Cone = (1/3) × π × r² × h

⇒ 1232 = (1/3) × (22/7) × r² × 24

⇒ 1232 = 8 × (22/7) × r²

⇒ 154 = (22/7) × r² ⇒ r² = 7 × 7 = 49

⇒ r = 7 cm

∴ The correct answer is 7 cm.

Alternate Method

Given:

Volume (V) of the right circular cone = 1232 cm³

Height (h) of the cone = 24 cm

Formula Used:

Volume of a right circular cone = (1/3) × π × r² × h

Calculations:

⇒ 1232 = (1/3) × (22/7) × r² × 24

⇒ 1232 = (22/7) × r² × 8

⇒ r² = (1232 × 7) / (22 × 8)

⇒ r² = (154 × 7) / 22

⇒ r² = 7 × 7

⇒ r² = 49

⇒ r = √49 = 7 cm

∴ The correct answer is 7 cm.

Additional Information

Slant Height (l)

The relationship between slant height (l), height (h), and radius (r) is l = √(h² + r²).

Curved Surface Area (CSA)

The Curved Surface Area of a cone is given by the formula π × r × l.

Total Surface Area (TSA)

The Total Surface Area of a cone is π × r × (l + r), which includes the base area πr².

Shortcut Trick

Direct Formula for Volume of a Pyramid = (1÷3) × Base Area × Vertical Height

Base Area (Square) = side² = 10 × 10 = 100 cm²

Volume = (1÷3) × 100 × 12 = 100 × 4 = 400 cm³

∴ The correct answer is 400 cm³.

Alternate Method

Given:

Base side (a) = 10 cm

Vertical height (h) = 12 cm

Step 1: Calculate the Area of the Square Base.

⇒ Base Area = side × side

⇒ Base Area = 10 cm × 10 cm = 100 cm²

Step 2: Calculate the Volume of the Pyramid using the standard formula.

⇒ Volume = (1÷3) × Base Area × Height

⇒ Volume = (1÷3) × 100 × 12

⇒ Volume = 100 × 4

⇒ Volume = 400 cm³

∴ The correct answer is 400 cm³.

Additional Information

Slant Height of a Square Pyramid

The slant height (l) is the distance from the apex to the midpoint of a base edge: l = √(h² + (a÷2)²).

Lateral Surface Area (LSA)

The LSA of a square pyramid is the sum of areas of its four triangular faces: LSA = 2 × a × l (where l is slant height).

Total Surface Area (TSA)

The TSA includes the base area and the lateral area: TSA = a² + 2 × a × l.

General Pyramid Volume

For any pyramid (triangular, hexagonal, etc.), the volume is always (1÷3) × Area of the Base × Vertical Height.

Shortcut Trick

The Incenter is the point where the internal angle bisectors of a triangle intersect.

By geometric definition, the internal bisectors of any triangle (Acute, Right, or Obtuse) must stay within the boundaries of the triangle.

Since all three bisectors are internal, their point of concurrency must lie inside the triangle.

Thus, Assertion (A) is true, and Reason (R) provides the fundamental logic for it.

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

Alternate Method

Given: A triangle with its angle bisectors and incenter.

Property: The Incenter (I) is equidistant from all sides of the triangle, serving as the center of the Incircle.

⇒ Assertion (A): The incenter is the center of the largest circle that can fit inside the triangle.

⇒ Reason (R): This point is generated by the intersection of internal angle bisectors.

⇒ Since internal bisectors begin at the vertices and extend into the interior, they must meet inside.

⇒ Both statements are conceptually accurate and linked.

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

Additional Information

Incenter and Inradius

The radius of the incircle (r) is calculated as Area (A) ÷ Semi-perimeter (s).

Points Always Inside

The Centroid and the Incenter are the only two major centers that always lie inside any triangle.

Points That Can Be Outside

The Circumcenter and Orthocenter lie outside in an obtuse-angled triangle and on the boundary in a right-angled triangle.

Equilateral Triangle Special Case

In an equilateral triangle, the Centroid, Incenter, Orthocenter, and Circumcenter all coincide at the same point.

Shortcut Trick

Net profit for distribution = 80% of 48,000 = ₹38,400.

Modified profit sharing ratio P : Q : R = 6 : 7 : (9 ÷ 2) = 6 : 7 : 4.5.

Total ratio parts = 6 + 7 + 4.5 = 17.5.

Q share = (7 ÷ 17.5) × 38,400 = (2 ÷ 5) × 38,400 = ₹15,360.

∴ The correct answer is ₹15,360.

Alternate Method

Given:

Investment ratio of P, Q, and R = 6 : 7 : 9

Total Profit = ₹48,000

Reinvestment = 20%

Condition: R is a silent partner, so he gets only 50% of his investment-based share.

Formula Used:

Profit Share = (Individual Ratio ÷ Total Ratio) × Distributed Profit

Calculations:

⇒ Amount to be distributed = 48,000 − (20% of 48,000)

⇒ Amount to be distributed = 48,000 − 9,600 = ₹38,400

⇒ Effective Profit Ratio P : Q : R = 6 : 7 : (9 ÷ 2)

⇒ P : Q : R = 6 : 7 : 4.5 = 12 : 14 : 9

⇒ Sum of ratios = 12 + 14 + 9 = 35

⇒ Q share = (14 ÷ 35) × 38,400

⇒ Q share = (2 ÷ 5) × 38,400

⇒ Q share = 2 × 7,680 = ₹15,360

∴ The correct answer is ₹15,360.

Additional Information

Partnership Profit Sharing

Profit is divided based on the product of Capital and Time. Ratio = (C₁ × T₁) : (C₂ × T₂).

Active vs Silent Partner

An active partner manages the business, while a silent (sleeping) partner only provides capital and may receive a different share as per the agreement.

Reserve Fund / Reinvestment

If a portion of the profit is reinvested or kept as a reserve, it must be subtracted from the Gross Profit before calculating individual shares.

Shortcut Trick

Apply the Alligation Rule to find the required ratio of the two fertilizers.

Higher concentration (40%) and Lower concentration (25%) are mixed to get 30%.

Ratio = (Mean − Lower) : (Higher − Mean)

Ratio = (30 − 25) : (40 − 30) = 5 : 10 = 1 : 2

∴ The correct answer is 1 : 2.

Alternate Method

Given:

Nitrogen percentage in Fertilizer 1 = 40%

Nitrogen percentage in Fertilizer 2 = 25%

Desired Mean Mixture concentration = 30%

Formula Used:

Quantity of Cheaper / Quantity of Dearer = (CP of Dearer − Mean Price) / (Mean Price − CP of Cheaper)

Calculations:

⇒ Let the quantity of Fertilizer 1 be Q₁ and Fertilizer 2 be Q₂.

⇒ By Rule of Alligation:

⇒ Q₁ : Q₂ = (30 − 25) : (40 − 30)

⇒ Q₁ : Q₂ = 5 : 10

⇒ Q₁ : Q₂ = 1 : 2

∴ The correct answer is 1 : 2.

Additional Information

Weighted Average Formula

The mean concentration (C_m) can also be calculated as (n₁c₁ + n₂c₂) ÷ (n₁ + n₂), where n is the quantity and c is the concentration.

Mixture Replacement Rule

If a quantity x is removed from a container of volume V and replaced with water n times, the final concentration is Initial × (1 − x/V)ⁿ.

Alligation for Three Components

For three ingredients, pair them (Cheaper with Mean and Dearer with Mean) and sum the respective ratio parts.

Shortcut Trick

Identify the decimal part: 0.625 is a known multiple of 0.125 (1/8).

Since 0.125 = 1/8, then 0.625 = 5 × 0.125 = 5/8.

The total value is 3 + 5/8.

Convert mixed fraction to improper: (3 × 8 + 5) / 8 = 29/8.

∴ The correct answer is 29/8.

Alternate Method

Given: Current level = 3.625 times the base level.

To convert a decimal to a fraction, divide by the power of 10 corresponding to the decimal places.

⇒ 3.625 = 3625/1000

⇒ Dividing numerator and denominator by 5: 725/200

⇒ Dividing numerator and denominator by 5: 145/40

⇒ Dividing numerator and denominator by 5: 29/8

∴ The correct answer is 29/8.

Additional Information

Conversion of Decimal to Fraction

Count the number of digits after the decimal point and place the number over 10 raised to that power (e.g., 0.abc = abc/1000).

Standard Fraction to Decimal Table (Base 8)

1/8 = 0.125 | 3/8 = 0.375 | 5/8 = 0.625 | 7/8 = 0.875. Remembering these helps in fast calculation.

Improper Fraction

An improper fraction has a numerator larger than the denominator. It can be written as a mixed number: 29/8 = 3 5/8.

Shortcut Trick

Recognize the Pythagorean triplet (3, 4, 5) where tan θ = Perpendicular / Base = 3/4.

Here, Perpendicular (P) = 3 and Base (B) = 4, so the Hypotenuse (H) must be 5.

The ratio for sin θ is defined as Perpendicular / Hypotenuse.

By direct substitution: sin θ = 3/5.

∴ The correct answer is 3/5.

Alternate Method

Given: tan θ = 3/4

Formula Used: tan θ = Perpendicular (P) / Base (B) and sin θ = Perpendicular (P) / Hypotenuse (H)

Calculations:

⇒ Let Perpendicular (P) = 3k and Base (B) = 4k

⇒ According to Pythagoras Theorem: H² = P² + B²

⇒ H² = (3k)² + (4k)²

⇒ H² = 9k² + 16k² = 25k²

⇒ H = √(25k²) = 5k

⇒ sin θ = P / H = 3k / 5k

⇒ sin θ = 3/5

∴ The correct answer is 3/5.

Additional Information

Trigonometric Identities

The fundamental identity relates sine and cosine as: sin²θ + cos²θ = 1.

Common Pythagorean Triplets

Standard sets of integers that satisfy a² + b² = c² include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Ratio Relations

tan θ can also be expressed as sin θ / cos θ. Since tan θ = 3/4 and sin θ = 3/5, then cos θ must be 4/5.

Shortcut Trick

Use the direct relationship between arc length, radius, and angle in radians.

Formula: Radius = Arc Length ÷ Angle (in radians)

Radius = 44 ÷ 4 = 11 cm

∴ The correct answer is 11 cm.

Alternate Method

Given:

Length of the arc (s) = 44 cm

Central angle (θ) = 4 radians

Formula Used:

The arc length (s) of a circle is given by: s = r × θ

Where 'r' is the radius and 'θ' is the angle in radians.

Calculations:

⇒ s = r × θ

⇒ 44 = r × 4

⇒ r = 44 ÷ 4

⇒ r = 11 cm

∴ The correct answer is 11 cm.

Additional Information

Area of Sector

The area of a circular sector is given by A = (1/2) × r² × θ, where θ is in radians.

Radian to Degree Conversion

To convert an angle from radians to degrees, multiply by (180/π). 1 radian ≈ 57.3°.

Arc Length in Degrees

If the angle is given in degrees, the arc length formula is s = (θ/360) × 2πr.

Shortcut Trick

Use the Trigonometric Identity for Complementary Angles: cot(90° − θ) = tan θ.

Given that tan θ = 1.

Directly substituting the value, we get cot(90° − θ) = 1.

∴ The correct answer is 1.

Alternate Method

Given: tan θ = 1

Formula Used: tan θ = Opposite / Adjacent and cot(90° − θ) = tan θ

⇒ tan θ = 1

⇒ Since tan 45° = 1, we have θ = 45°

⇒ Now, find cot(90° − θ)

⇒ cot(90° − 45°) = cot 45°

⇒ cot 45° = 1

∴ The correct answer is 1.

Additional Information

Complementary Angle Identities

Trigonometric ratios of complementary angles follow: sin(90°−θ) = cosθ, sec(90°−θ) = cosecθ, and tan(90°−θ) = cotθ.

Reciprocal Identities

The tangent and cotangent functions are reciprocals: cot θ = 1 / tan θ.

Standard Trigonometric Values at 45°

For an angle of 45°, both tan 45° and cot 45° are equal to 1, while sin 45° and cos 45° are both 1/√2.

Shortcut Trick

Initial total parts = 5 (Milk) + 3 (Water) = 8 parts.

Total solution = 56 L ⇒ 8 parts = 56 L ⇒ 1 part = 7 L.

Since Water remains constant (3 parts), compare Milk parts.

Milk increase = 7 parts − 5 parts = 2 parts.

Quantity of milk to be added = 2 parts × 7 L = 14 L.

∴ The correct answer is 14 L.

Alternate Method

Given: Total solution = 56 L, Initial Ratio (M:W) = 5:3, Final Ratio (M:W) = 7:3.

Formula Used: Ratio = Quantity of Milk ÷ Quantity of Water.

⇒ Quantity of milk = (5 / (5+3)) × 56 = (5/8) × 56 = 35 L

⇒ Quantity of water = 56 − 35 = 21 L

⇒ Let the quantity of milk added be x litres.

⇒ New quantity of milk = (35 + x) L

⇒ (35 + x) / 21 = 7 / 3

⇒ 3 × (35 + x) = 7 × 21

⇒ 105 + 3x = 147

⇒ 3x = 147 − 105 = 42

⇒ x = 42 ÷ 3 = 14 L

∴ The correct answer is 14 L.

Additional Information

Ratio Balancing

When one component in a mixture is added or removed, the other component remains constant. Scale the ratios so that the constant component has the same number of units in both ratios.

Alligation Rule

Used to find the proportion in which two ingredients are mixed to produce a mixture of a desired price or concentration: (Cheaper quantity) ÷ (Dearer quantity) = (d − m) ÷ (m − c).

Concentration of Milk

Concentration % = (Quantity of Milk ÷ Total Volume) × 100. In this case, initial concentration was 62.5% and final concentration is 70%.

Shortcut Trick

Rate 20% = 1/5 ⇒ Multiplier = 6/5

Amount after 2 years = 68,000 × (6/5) × (6/5) = 68,000 × 1.44 = ₹97,920

New Sum after adding ₹16,000 = 97,920 + 16,000 = ₹1,13,920

Final Amount after 1 more year = 1,13,920 × (6/5) = 1,13,920 × 1.2 = ₹1,36,704

∴ The correct answer is Rs. 1,36,704.

Alternate Method

Given: Initial Principal (P₁) = ₹68,000, Rate (R) = 20%, Time (t₁) = 2 years, Addition = ₹16,000, Time (t₂) = 1 year.

Formula: Amount (A) = P(1 + R/100)ⁿ

Calculation for the first 2 years:

⇒ Amount (A₁) = 68,000 × (1 + 20/100)²

⇒ A₁ = 68,000 × (1.2)²

⇒ A₁ = 68,000 × 1.44 = ₹97,920

Total amount after adding more money:

⇒ New Principal (P₂) = 97,920 + 16,000 = ₹1,13,920

Calculation for the 3rd year:

⇒ Final Amount = 1,13,920 × (1 + 20/100)¹

⇒ Final Amount = 1,13,920 × 1.2 = ₹1,36,704

∴ The correct answer is Rs. 1,36,704.

Additional Information

Compound Interest Formula

Amount A = P(1 + R/100)ⁿ, where P is Principal, R is Rate, and n is time in years. Compound Interest CI = A − P.

Effective Rate for 2 Years

If the rate is R% for two years, the effective compound interest rate is (R + R + R²/100)%. For 20%, it is 20 + 20 + 4 = 44%.

Successive Growth

Compound interest is an example of successive percentage growth. When additional capital is added, the new sum becomes the principal for the subsequent period.

Shortcut Trick

Angle between tangents from an external point and the angle subtended by the chord at the center are supplementary.

∠AOC + ∠ABC = 180^o

⇒ ∠AOC = 180^o − 50^o

⇒ ∠AOC = 130^o

∴ The correct answer is 130^o.

Alternate Method

Given: ∠ABC = 50^o, where AB and BC are tangents to the circle with center O.

Formula: Sum of angles in a quadrilateral is 360^o and the radius is perpendicular to the tangent at the point of contact.

Step-by-step Calculation:

⇒ In quadrilateral OABC, OA ⊥ AB and OC ⊥ BC (Radius ⊥ Tangent property)

⇒ ∠OAB = 90^o and ∠OCB = 90^o

⇒ ∠OAB + ∠ABC + ∠OCB + ∠AOC = 360^o

⇒ 90^o + 50^o + 90^o + ∠AOC = 360^o

⇒ 230^o + ∠AOC = 360^o

⇒ ∠AOC = 360^o − 230^o

⇒ ∠AOC = 130^o

∴ The correct answer is 130^o.

Additional Information

Tangent Properties

Tangents drawn from an external point to a circle are equal in length (AB = BC).

Angle at Circumference

The angle subtended by a chord at the center is double the angle subtended by it at any point on the remaining part of the circle.

Alternate Segment Theorem

The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Shortcut Trick

Apply the Tangent-Secant Theorem: PQ² = PR × PS

Given PQ = 16 cm and PR = 8 cm.

16² = 8 × PS ⇒ 256 = 8 × PS ⇒ PS = 32 cm.

Chord RS = PS − PR = 32 − 8 = 24 cm.

∴ The correct answer is 24 cm.

Alternate Method

Given: Length of tangent PQ = 16 cm, length of external secant segment PR = 8 cm.

Formula Used: When a tangent and a secant are drawn from an external point to a circle, the square of the tangent length is equal to the product of the secant length and its external segment length (PQ² = PR × PS).

Calculations:

⇒ Let the length of the chord RS be x cm.

⇒ Total length of secant PS = PR + RS = 8 + x.

⇒ According to the theorem: PQ² = PR × PS

⇒ 16² = 8 × (8 + x)

⇒ 256 = 8(8 + x)

⇒ 256 ÷ 8 = 8 + x

⇒ 32 = 8 + x

⇒ x = 32 − 8

⇒ x = 24 cm.

∴ The correct answer is 24 cm.

Additional Information

Intersecting Chords Theorem

If two chords AB and CD intersect at point P inside a circle, then PA × PB = PC × PD.

Two Secants Theorem

If two secants PAB and PCD are drawn from an external point P, then PA × PB = PC × PD.

Tangent-Radius Property

A tangent at any point of a circle is perpendicular to the radius through the point of contact (OQ ⊥ PQ).

Shortcut Trick

Investment ratio Arun : Bablu : Chandan = 24 : 16 : 40 = 3 : 2 : 5.

Bablu commission = 30% of ₹75,000 = ₹22,500.

Remaining profit = 70% of 75,000 = ₹52,500.

Bablu's share from remaining = (2 ÷ 10) × 52,500 = ₹10,500.

Total share = 22,500 + 10,500 = ₹33,000.

∴ The correct answer is ₹33,000.

Alternate Method

Given:

Investment of Arun = ₹2,40,000

Investment of Bablu = ₹1,60,000

Investment of Chandan = ₹4,00,000

Working Partner Commission = 30%

Total Profit = ₹75,000

Formula: Profit Share Ratio = Ratio of Capitals × Time Period

⇒ Ratio of Capitals = 2,40,000 : 1,60,000 : 4,00,000

⇒ Ratio = 24 : 16 : 40 = 3 : 2 : 5

⇒ Bablu's Commission = (30 ÷ 100) × 75,000 = ₹22,500

⇒ Remaining Profit = 75,000 − 22,500 = ₹52,500

⇒ Total Ratio Parts = 3 + 2 + 5 = 10

⇒ Bablu's Profit Share = (2 ÷ 10) × 52,500 = ₹10,500

⇒ Bablu's Total Share = Commission + Profit Share

⇒ Total Share = 22,500 + 10,500 = ₹33,000

∴ The correct answer is ₹33,000.

Additional Information

Working vs Sleeping Partner

A Working Partner manages the business and receives a salary or commission, while a Sleeping Partner only invests capital and shares profit/loss.

Partnership Profit Distribution

Profit is distributed in the ratio of (Capital₁ × Time₁) : (Capital₂ × Time₂) after deducting any fixed commissions or salaries.

Commission Calculation

Commission is usually calculated on the Gross Profit unless the question specifies it is on the net profit after such commission.

Shortcut Trick

Initial Loss = 15% → Selling Price (SP₁) = 100% − 15% = 85%

Required Gain = 15% → Required Selling Price (SP₂) = 100% + 15% = 115%

Using the unitary method: If 85% corresponds to ₹85,000, then 115% corresponds to:

Required SP = (85,000 ÷ 85) × 115 = 1,000 × 115 = ₹1,15,000

∴ The correct answer is ₹1,15,000.

Alternate Method

Given:

First Selling Price (SP₁) = ₹85,000

Loss percentage (L%) = 15%

Desired Gain percentage (G%) = 15%

Formula Used:

Cost Price (CP) = [SP × 100] ÷ [100 − Loss%]

New Selling Price (SP₂) = [CP × (100 + Gain%)] ÷ 100

Calculations:

⇒ Cost Price (CP) = (85,000 × 100) ÷ (100 − 15)

⇒ CP = (85,000 × 100) ÷ 85

⇒ CP = 1,000 × 100 = ₹1,00,000

Now, to find the new selling price for a 15% gain:

⇒ SP₂ = [1,00,000 × (100 + 15)] ÷ 100

⇒ SP₂ = [1,00,000 × 115] ÷ 100

⇒ SP₂ = 1,000 × 115 = ₹1,15,000

∴ The correct answer is ₹1,15,000.

Additional Information

Cost Price and Selling Price Relationship

When there is a profit, SP = CP + Profit. When there is a loss, SP = CP − Loss. Profit or Loss is always calculated on the Cost Price (CP).

Successive Percentage Formula

If an item is sold at a loss of L% and we need a gain of G%, the ratio of the two selling prices is (100 − L) : (100 + G).

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount. The final Profit% depends on both the markup and the discount given.

Shortcut Trick

Apply the Tangent-Secant Theorem: PB² = PC × PA.

24² = 16 × PA ⇒ 576 = 16 × PA ⇒ PA = 36 cm.

Since PA = PC + AC, then AC = 36 − 16 = 20 cm.

∴ The correct answer is 20 cm.

Alternate Method

Given:

Length of tangent PB = 24 cm

Length of external secant segment PC = 16 cm

Formula Used:

For a circle, when a tangent and a secant are drawn from an external point P, the property is: PB² = PC × PA

⇒ PA = PC + AC

⇒ PB² = PC × (PC + AC)

⇒ 24² = 16 × (16 + AC)

⇒ 576 = 16 × (16 + AC)

⇒ 16 + AC = 576 ÷ 16

⇒ 16 + AC = 36

⇒ AC = 36 − 16

⇒ AC = 20 cm

∴ The correct answer is 20 cm.

Additional Information

Tangent-Secant Theorem

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment part.

Secant-Secant Theorem

When two secant segments are drawn to a circle from an external point P, the product of the lengths of one secant segment and its external part equals the product of the other: PA × PB = PC × PD.

Intersecting Chords Theorem

If two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other: PA × PB = PC × PD.

Shortcut Trick

Ratio of radius (r) to height (h) = 4 : 5.

Let r = 4x and h = 5x.

Volume ∝ r² × h ⇒ 4² × 5 = 80 units³.

80 × (22/7) × x³ = 86,240 ⇒ x³ = (86,240 × 7) ÷ (80 × 22) = 343.

x = √³343 = 7 ⇒ Height (h) = 5 × 7 = 35 cm.

∴ The correct answer is 35 cm.

Alternate Method

Given:

Volume of cylinder (V) = 86,240 cm³

Ratio of radius (r) and height (h) = 4 : 5

Formula Used:

Volume of cylinder (V) = πr²h

Calculations:

⇒ Let radius (r) = 4x and height (h) = 5x.

⇒ 86,240 = (22/7) × (4x)² × (5x)

⇒ 86,240 = (22/7) × 16x² × 5x

⇒ 86,240 = (22/7) × 80x³

⇒ x³ = (86,240 × 7) ÷ (22 × 80)

⇒ x³ = 1078 × 7 ÷ 22

⇒ x³ = 49 × 7

⇒ x³ = 343

⇒ x = 7

⇒ Height of cylinder (h) = 5x = 5 × 7 = 35 cm.

∴ The correct answer is 35 cm.

Additional Information

Curved Surface Area of Cylinder

The Curved Surface Area (CSA) is given by 2πrh, where r is the radius and h is the height.

Total Surface Area of Cylinder

The Total Surface Area (TSA) includes the CSA and the areas of the two circular bases: TSA = 2πr(h + r).

Base Area of Cylinder

The area of the circular base is calculated using the formula A = πr².

Shortcut Trick

Initial classrooms = 20 − 4 = 16

Initial students = 16 × 40 = 640

Current students = 20 × 35 = 700

New students = 700 − 640 = 60

∴ The correct answer is 60 students.

Alternate Method

Given:

Initial students per room = 40

Final students per room = 35

Final classrooms = 20

New classrooms added = 4

Calculations:

⇒ Total original classrooms = Final classrooms − Added classrooms

⇒ Original classrooms = 20 − 4 = 16

⇒ Total original students = 16 × 40 = 640

⇒ Total current students = 20 × 35 = 700

⇒ Number of new students = Total current students − Total original students

⇒ New students = 700 − 640 = 60

∴ The correct answer is 60 students.

Additional Information

Total Value Formula

The total number of items is always the product of the number of groups and the average per group: Total = Count × Average.

Weighted Average Logic

When two groups are combined, the new average is (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is the quantity and x is the value per unit.

Change in Total

To find the addition or removal of members, subtract the initial total from the final total.

Shortcut Trick

Expand (3 + 4√7)² using the identity (a + b)²: 9 + 112 + 24√7 = 121 + 24√7.

By comparing coefficients of √7, we find k = 24.

Substitute k in the expression: ((24 + 2)²) ÷ 36 = 26² ÷ 6².

Simplify the ratio: (26/6)² = (13/3)².

∴ The correct answer is (13/3)².

Alternate Method

Given: (3 + 4√7)² = 121 + k√7

Formula Used: (a + b)² = a² + b² + 2ab

⇒ (3)² + (4√7)² + 2 × 3 × 4√7 = 121 + k√7

⇒ 9 + 112 + 24√7 = 121 + k√7

⇒ 121 + 24√7 = 121 + k√7

⇒ k√7 = 24√7

⇒ k = 24

Now, substitute the value of k in ((k + 2)²) / 36:

⇒ ((24 + 2)²) ÷ 36

⇒ (26)² ÷ 36

⇒ 676 ÷ 36

⇒ (13 × 13 × 4) ÷ (9 × 4)

⇒ 169 ÷ 9

⇒ (13/3)²

∴ The correct answer is (13/3)².

Additional Information

Square of a Binomial

The expansion follows the standard algebraic identity (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Comparison of Surds

For rational numbers a, b, c, d and irrational √x, if a + b√x = c + d√x, then the rational parts (a = c) and irrational coefficients (b = d) must be equal.

Power Rules

The property (x/y)ⁿ = xⁿ / yⁿ allows simplifying squared fractions by reducing the base before or after squaring.

Shortcut Trick

Simplify the fraction directly: 1080 ÷ 360 = 3.

Rewrite the base 6: 3⁴ × 2⁵ × 3 = 3⁵ × 2⁵ = (3 × 2)⁵ = 6⁵.

Comparing powers of 6: p = 5.

Evaluate the expression: 5² − 5(5) + 1 = 25 − 25 + 1 = 1.

Since 1 is neither prime nor composite, the result is determined.

∴ The correct answer is Neither a prime nor a composite number.

Alternate Method

Given: (3⁴ × 2⁵ × 1080) / 360 = 6^p

Formula Used: a^m × aⁿ = a^m+n; aⁿ × bⁿ = (ab)ⁿ; If a^x = a^y, then x = y.

⇒ (3⁴ × 2⁵ × (1080 ÷ 360)) = 6^p

⇒ 3⁴ × 2⁵ × 3¹ = 6^p

⇒ 3^{(4 + 1)} × 2⁵ = 6^p

⇒ 3⁵ × 2⁵ = 6^p

⇒ (3 × 2)⁵ = 6^p

⇒ 6⁵ = 6^p

⇒ p = 5

Now, finding the value of p² − 5p + 1:

⇒ 5² − 5(5) + 1

⇒ 25 − 25 + 1

⇒ 1

Analysis of result: The number 1 is neither a prime number (it has only one factor) nor a composite number (it does not have more than two factors).

∴ The correct answer is Neither a prime nor a composite number.

Additional Information

Definition of 1

The number 1 is the multiplicative identity. It is excluded from the definitions of both prime and composite numbers because prime numbers must have exactly two distinct factors.

Prime and Composite Numbers

Prime numbers are natural numbers greater than 1 with exactly two factors (1 and itself). Composite numbers are natural numbers greater than 1 that have more than two factors.

Exponent Rules

The Power of a Product Rule states that (ab)ⁿ = aⁿ × bⁿ. This is essential for solving equations where bases can be broken into prime factors.

Checking all the options

(1) 12, 01, 34, 04 → H, B, T, E

(2) 11, 02, 34, 01 → G, C, T, B

(3) 44, 00, 33, 04 → Y, A, S, E

(4) 12, 00, 34, 04 → H, A, T, E

Hence, the correct answer is “Option 4”.

The unfolded appearance after the cut is,

Hence, the correct answer is “Option 4”.

Let us check the other options:

Option (1): 98, 67, 34, 41, 66 → P, D, C, C, E

Option (2): 23, 00, 99, 12, 30 → P, B, D, E, E 

Option (3): 98, 20, 22, 41, 97 → P, L, A, C, E

Option (4): 67, 43, 59, 99, 78 → D, A, T, D, E

Hence, the correct answer is “Option 3”.

APPLE is coded as ZNMHZ →

Similarly,

let's find the code for LEMON:

Hence, the correct answer is “Option 1”.

Here

3125 = 5⁵ (In this case, the base 5 is a prime number.)

4 = 2² (In this case, the base 2 is a prime number.)

27 = 3³ (In this case, the base 3 is a prime number.)

256 = 4⁴ (In this case, the base 4 is a composite number (not a prime number).

Hence, the correct answer is “Option 3”.

<br> <br>

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Here,

Hence, the correct answer is “Option 3”.

​Here,

The letters F, K, and Z are all formed using exactly 3 straight lines.

While,

 

The letter E is formed using 4 straight lines (1 vertical and 3 horizontal).

Therefore, the odd one out is E.

Hence, the correct answer is “Option 1”.

Triangles in the given figure,

There are 12 triangles present in the given figure.

Hence, the correct answer is “Option 1”.

Triangles in the given figure,

There are 16 triangles in the given figure.

Hence, the correct answer is “Option 3”.

Family chart:

Family tree,

H is Uncle of A.

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Hence, the correct answer is “Option 1”.

Opposite pairs of unfolded dice,

 Opposite to 

 Opposite to 

 Opposite to 

Option (1): 

→ Can not be formed as opposite pair are adjacent pair to each other.

Option (2): 

 → Can not be formed as opposite pair are adjacent pair to each other.

Option (3): 

 → Can not be formed as opposite pair are adjacent pair to each other.

Option (4): 

 → Can be formed as opposite pair are not adjacent pair to each other.

Hence, the correct answer is “Option 4”.

Logic followed here is,

(1 × 7) + 2 = 7 + 2 = 9

(9 × 7) + 2 = 63 + 2 = 65

(65 × 7) + 2 = 455 + 2 = 457

(457 × 7) + 2 = 3100 + 2 = 3201

Hence, the correct answer is “Option 3”.

Knife is related to Cut →

A Knife is a tool specifically used for the action of Cutting.

Similarly,

Spoon is to, 

A Spoon is a tool specifically used for the action of Eating.

Hence, the correct answer is “Option 1”.

Here,

Dog, Cat, and Lion belong to the same group (Mammals),

<br>

Whereas,

 Eagle belongs to a different group (Birds).

Therefore, the different one is Eagle.

Hence, the correct answer is “Option 1”.

Here,

2, 5, and 11 are Prime Numbers.

While,

44 is a Composite Number.

Therefore, the number 44 is not like the others.

Hence, the correct answer is “Option 4”.

<br> <br>

Pattern followed here is,

Hence, the correct answer is “Option 3”.

BODMAS Table: 

Given equation: 45 ÷  5 + 12 − 8 = ?

Applying the BODMAS rule:

⇒ 45 ÷ 5 + 12 − 8 = ?

⇒ 45 ÷  5 + 12 − 8 = ?

⇒ 9 + 12 − 8 = ?

⇒ 21 − 8 = ?

⇒ 13

Hence, the correct answer is “Option 2”.

BODMAS Table: 

Given equation: 9 × 4 ÷ 3 = ?

⇒ 9 × 4 ÷ 3 = ?

⇒ 36 ÷ 3 = ?

⇒ 12.

Hence, the correct answer is "Option 1".

BODMAS Table: 

Given expression: 18 % 3 # 5 @ 2 * 4 = ?

<br>

Now, replacing the symbols:

⇒ 18 ÷ 3 + 5 - 2 × 4 = ?

⇒ 18 ÷ 3 + 5 - 2 × 4 = ?

⇒ 6 + 5 - 2 × 4 = ?

⇒ 6 + 5 - 8 = ?

⇒ 6 + 5 - 8 = ?

⇒ 11 - 8 = ?

⇒ 3.

Hence, the correct answer is "Option 4".

BODMAS Table: 

Given equation: 18 % 3 # 4 = ?

<br>

Now, replacing the symbols:

⇒ 18 ÷ 3 - 4 = ?

⇒ 18 ÷ 3 - 4 = ?

⇒ 6 - 4 = ?

⇒ 2.

Hence, the correct answer is "Option 3".

Given:

Total number of men = 8

Age of the man who left = 30 years

Average age increase = 2 years

Calculations:

⇒ Total increase in the sum of ages = Number of men × Increase in average

⇒ Total increase = 8 × 2 = 16 years

Since the average increased, the new man must be older than the man he replaced.

⇒ Age of new man = Age of outgoing man + Total increase

⇒ Age of new man = 30 + 16

⇒ Age of new man = 46 years

Hence, the correct answer is “Option 3”.

The number of cubes in the given figure is shown below:

The number of cubes in the given figure is → (4 × 5 × 5)   = 100

And,

15 cubes in right side column.

Total cubes = 100 + 15 = 115

Hence, the correct answer is “Option 2”.

Family Chart:

Family tree,

That woman is Sister of Ravi.

Hence, the correct answer is “Option 1”.

The correct answer is: 3) Military supplies.

Key Points

• The word "materiel" refers to military equipment, supplies, and resources used by armed forces. (सैन्य सामग्री)
• Example: The troops were well-equipped with the materiel needed for the mission.
• "Military supplies" is the correct synonym for "materiel" as it specifically refers to the equipment and resources used in military operations. (सैन्य आपूर्ति)
• Example: The military base received a fresh shipment of military supplies last week.
• Hence, the term "military supplies" is the most appropriate match for the word "materiel."

Therefore, the correct answer is: 3) Military supplies.

Additional Information

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

• Fabric (कपड़ा): A material made by weaving or knitting fibers together.
• Example: The tailor used a soft fabric to make the dress.
• Military clothing (सैन्य वस्त्र): Uniforms and attire worn by military personnel.
• Example: The soldiers were dressed in standard military clothing for the parade.
• Soldiers (सैनिक): Members of an army who serve and fight in wars.
• Example: The soldiers demonstrated great bravery on the battlefield.

The correct answer is: 3) Remedy.

Key Points

• The word "Panacea" refers to a solution or remedy for all difficulties or diseases. (सर्वरोग नाशक)
• Example: Many believed that the new policy would serve as a panacea for the economic crisis.
• The correct word "Remedy" means a treatment or solution for a problem or disease. (उपाय या उपचार)
• Example: The doctor prescribed a herbal remedy for her cough.
• Hence, "remedy" is a synonym for "panacea" as both refer to solutions or cures.

Therefore, the correct answer is: 3) Remedy.

Additional Information

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

• Unhappy (असंतुष्ट): Feeling or showing sorrow; not satisfied.
• Example: She was unhappy with the outcome of her exam.
• Ill-will (शत्रुता): Hostile feelings or intentions.
• Example: There was ill-will between the two rival teams during the match.
• Readymade (तैयार): Something made for immediate use or consumption.
• Example: He bought a readymade suit for the wedding.

The correct answer is: Option 4 i.e. gullible.

Key Points

• The word "astute" means having or showing the ability to accurately assess situations or people and turn this to one's advantage. (चतुर, चालाक)
• Example: He was astute enough to recognize the potential of the new business opportunity.
• The word "gullible" means easily deceived or tricked because of being too trusting. (भोला-भाला, आसानी से धोखा खा लेने वाला)
• Example: The scam targeted gullible people who believed the fake promises of huge returns.
• The opposite of "astute" (intelligent and perceptive) is "gullible" (easily fooled or naive).

Therefore, the correct answer is: Option 4 i.e. gullible.

Additional Information

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

• Distraught (व्याकुल): Deeply upset and agitated.
• Example: She was distraught after hearing about the accident.
• Savvy (समझदार): Having practical understanding or knowledge.
• Example: He is a savvy investor who knows how to make the most of his money.
• Adroit (कुशल): Skillful and clever, especially in using the hands or mind.
• Example: She is adroit at handling difficult negotiations.

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

Key Points

• The word "lucid" means something that is clear, easily understood, or expressed in a way that makes sense. (स्पष्ट)
• Example: The teacher gave a lucid explanation of the complex topic, which helped the students understand it easily.
• "Ambiguous" refers to something that is unclear, open to more than one interpretation, or not easily understood. It is the opposite of "lucid." (अस्पष्ट)
• Example: His statement was so ambiguous that nobody could figure out what he really meant.
• Hence, we can infer that the opposite of 'lucid' is 'ambiguous.'

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

Additional Information

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

• Dreadful (भयानक): Something that is extremely bad, unpleasant, or causing great fear.
• Example: The dreadful news of the disaster left everyone in shock.
• Inconspicuous (अगोचर): Something that is not easily noticeable or does not attract attention.
• Example: She wore inconspicuous clothes to blend in with the crowd.
• Dull (मंद): Something that is boring, not interesting, or lacking brightness.
• Example: The lecture was so dull that half the audience fell asleep.

The correct answer is: 3) Conversational narcissist.

Key Points

• A Conversational narcissist is a person who always redirects the focus of a conversation towards themselves, often ignoring or minimizing others' contributions. (वार्तालाप का स्वार्थी व्यक्ति)
• Example: Every time someone shares a story, she interrupts with a similar story about herself, proving she's a conversational narcissist.
• In the given sentence, the definition matches the behavior of a conversational narcissist, making it the most appropriate answer.

Therefore, the correct answer is: Conversational narcissist.

Additional Information

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

• Philanthropist (परोपकारी): A person who seeks to promote the welfare of others, especially by donating money to good causes.
• Example: The philanthropist donated millions to support education for underprivileged children.
• Legalise (कानूनी बनाना): To make something legal or lawful by passing a law.
• Example: The government decided to legalise the use of e-scooters on public roads.
• Eccentric (अजीब): A person who behaves in a way that is unconventional or slightly strange.
• Example: His eccentric habits, like wearing mismatched shoes, always drew attention.

The correct answer is: Option 1, i.e., Author.

Key Points

• The word "Author" refers to a person who writes books, articles, or other written works as a profession or for publication. (लेखक)
• Example: J.K. Rowling is a famous author known for writing the Harry Potter series.
• Authors are creative thinkers who often express their thoughts, stories, or knowledge in written form. (लेखक अपने विचार और कहानियाँ लिखित रूप में व्यक्त करते हैं।)

Therefore, the correct answer is: Author.

---

Additional Information

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

• Editor (संपादक): A person who prepares written material for publication by correcting, condensing, or modifying it.
• Example: The editor suggested changes to improve the article's clarity.
• Poet (कवि): A person who composes poetry.
• Example: William Wordsworth is a celebrated poet known for his romantic poems.
• Publisher (प्रकाशक): A person or company that prepares and issues books, journals, or other works for sale.
• Example: The publisher released the new edition of the novel last week.

The correct answer is Option 2.

 

Key Points

• The error lies in the phrase "to crossing", which is grammatically incorrect.
• After the infinitive marker "to", the verb must be in its base form (infinitive), not the gerund/participle form.
• Thus, the correct usage is "to cross" instead of "to crossing".
• Therefore, the error is located in part B of the sentence.

Therefore, the correct answer is B.

 

Correct Sentence: "She was attempting to cross the road but was scared as there was heavy traffic."

 

Additional Information

• A: "She was attempting" – This part is grammatically correct and requires no changes.
• C: "but was scared" – This part is grammatically correct and requires no changes.
• D: "as there was heavy traffic." – This part is grammatically correct and requires no changes.
• No error – This would be the correct option if there were no mistakes in the sentence, but there is an error in part B.

The correct answer is: Option 4 i.e. She doesn't want to lose her keys.

Key Points

• The word "lose" means to fail to keep something or to be deprived of something. (खो देना)
• Example: Be careful not to lose your wallet while traveling.
• The word "loose" means not tight or not firmly fixed in place. (ढीला)
• Example: The shirt is too loose and doesn’t fit me properly.
• In the given sentence, the context is about not wanting to misplace or lose keys, so the correct word is "lose".

Therefore, the correct answer is: She doesn't want to lose her keys.

Additional Information

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

• Option 1: He will loose the game if he's not careful.
• Explanation: The word "loose" (ढीला) is incorrectly used here. The correct word should be "lose" (खो देना) since the sentence is about losing a game.
• Corrected Sentence: He will lose the game if he's not careful.
• Option 2: Please lose your grip.
• Explanation: While grammatically correct, this sentence is contextually odd. It implies someone is being asked to let go intentionally, which is uncommon.
• Example: Please loosen (ढीला करें) your grip on the rope for better comfort.
• Option 3: The knot is too loss to hold.
• Explanation: The word "loss" (हानि) is incorrectly used here. The correct word should be "loose" (ढीला).
• Corrected Sentence: The knot is too loose to hold.

The correct answer is Option 3.

 

Key Points

• The primary grammatical issue in the sentence is the improper use of the preposition 'to' to describe a span of time.
• The word 'during' is a preposition used to indicate that something happens throughout the course or duration of a specific period.
• Since the 'holiday season' refers to a continuous time period, 'during' is the most appropriate choice to show that the shop will be open throughout that duration.
• The phrase 'during the holiday season' ensures the sentence is idiomatic and grammatically accurate.

Therefore, the correct answer is Option 3.

 

Correct Sentence: 'Will your shop remain open during the holiday season?'

 

Additional Information

• At the holiday season: While 'at' can be used for specific points in time or specific holidays (e.g., 'at Christmas'), it is less common than 'during' when referring to a 'season' which implies a length of time.
• Into the holiday season: This implies a movement or progression from a prior time towards or inside the start of the season, which does not fit the context of staying open throughout the period.
• No substitution: This is incorrect because the original preposition 'to' usually indicates a direction or a limit (e.g., Monday to Friday) rather than duration within a single period.

The correct answer is Option 1.

 

Key Points

• The adjective conscious is idiomatically followed by the preposition of when it refers to being aware of something.
• The phrase conscious of is the standard grammatical construction used to indicate that someone is noticing or realizing a particular fact or feeling.
• While conscious about is sometimes used in informal speech, conscious of is the preferred and correct form in formal English and competitive exams.
• Thus, the underlined part should be replaced with conscious of to improve the sentence.

Therefore, the correct answer is conscious of.

 

Correct Sentence: 'She was conscious of her appearance throughout the event.'

 

Additional Information

• conscious with: This is a grammatically incorrect combination; the preposition with does not pair with conscious in this context.
• conscious to: This is generally incorrect for expressing awareness of a noun (like appearance). While one might be conscious to the fact that..., conscious of remains the standard for awareness of things.
• No substitution: This is incorrect because the original preposition about is less standard than of in this grammatical structure.

The correct answer is Option 2.

 

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "The citizens elected the philanthropist as the president of the municipal corporation."
• To convert to passive voice: Place the object "the philanthropist" at the beginning.
• Change the active verb form "elected" (simple past) to "was elected" (simple past passive).
• Add the preposition "by" followed by the original subject "the citizens."
• Ensure the complement "as the president of the municipal corporation" remains unchanged for clarity.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "The philanthropist was elected as the president of the municipal corporation by the citizens."

 

Additional Information

• Option 1: "The philanthropist had been elected as the president of the municipal corporation by the citizens." – Incorrect tense (past perfect passive instead of simple past).
• Option 3: "The philanthropist was being elected as the president of the municipal corporation by the citizens." – Incorrect tense (past continuous passive).
• Option 4: "The philanthropist had been elected the president of the municipal corporation by the citizens." – Incorrect tense (past perfect passive).

The correct answer is Option 2.

 

Key Points

• Active voice structure: The subject performs the action on the object.
• In the passive voice, the sentence is: "The employees were asked to submit their reports on time."
• Identify the implied subject/agent: "Someone" (since the doer is not specified).
• Change the passive verb "were asked" (past simple passive) to "asked" (past simple active).
• Retain the object "the employees" and the infinitive phrase "to submit their reports on time."

Therefore, the correct answer is Option 2.

 

Correct Sentence: "Someone asked the employees to submit their reports on time."

 

Additional Information

• Option 1: "The employees asked to submit their reports on time." – Incorrect, removes the agent and changes meaning.
• Option 3: "The employees were asking to submit their reports on time." – Incorrect tense and meaning.
• Option 4: "Someone ask to submit their reports on time to the employees." – Incorrect verb form ("ask" instead of "asked").

The correct answer is Option 2.

 

Key Points

• Active voice structure: The subject performs the action on the object.
• In the passive voice, the sentence is: "The children were promised a trip to the zoo by their parents."
• Identify the subject/agent: "Their parents."
• Change the passive verb "were promised" (past simple passive) to "promised" (past simple active).
• Retain the object "the children" and the complement "a trip to the zoo."

Therefore, the correct answer is Option 2.

 

Correct Sentence: "Their parents promised the children a trip to the zoo."

 

Additional Information

• Option 1: "Their parents promise the children a trip to the zoo." – Incorrect tense (present simple instead of past simple).
• Option 3: "Their parents had promised the children a trip to the zoo." – Incorrect tense (past perfect instead of past simple).
• Option 4: "Their parents have promised the children a trip to the zoo." – Incorrect tense (present perfect instead of past simple).

The correct answer is Option 3.

 

Key Points

• Indirect Speech: Mohan asked why the vase had been moved from its original place.
• Key Conversions:
• "was moved" becomes "had been moved"
• Past tense passive in direct speech shifts to past perfect passive in indirect speech.
• Reporting verb:
• Direct: "said"
• Converted to: "asked" because the sentence is interrogative.
• Word Order:
• Indirect questions use statement order: "why the vase had been moved" (not "why had the vase been moved").
• Punctuation and Format:
• No quotation marks in indirect speech.
• Sentence flows naturally with reporting verb + indirect clause.

Therefore, the correct answer is Option 3.

 

Correct Sentence: Mohan asked why the vase had been moved from its original place.

 

Additional Information

• Option 1: "Mohan said that why the vase was moved..."
• Incorrect because "said that why" is ungrammatical.
• Tense not shifted correctly ("was moved" → "had been moved").
• Option 2: "Mohan asked that why had the vase moved..."
• Incorrect word order ("why had the vase moved").
• Suggests active voice instead of passive.
• Option 4: "Mohan asked why had the vase been moving..."
• Incorrect tense and aspect ("been moving" = continuous, not passive).
• Word order error again.

The correct answer is Option 3.

 

Key Points

• Indirect Speech: Roma said that she was feeling very excited to speak in the conference the following day.
• Key Conversions:
• "I am feeling" → "she was feeling"
• Present continuous tense changes to past continuous in indirect speech.
• Pronoun "I" changes to "she" to match the subject Roma.
• "tomorrow" → "the following day"
• Time reference shifts appropriately in indirect narration.
• Verb form:
• "to speak" remains unchanged as the infinitive verb form is correct.
• Punctuation and Format:
• No quotation marks in indirect speech.
• Sentence flows naturally with reporting verb + indirect clause.

Therefore, the correct answer is Option 3.

 

Correct Sentence: Roma said that she was feeling very excited to speak in the conference the following day.

 

Additional Information

• Option 1: "Roma said that she had been feeling very excited..."
• Incorrect tense shift: "had been feeling" suggests past perfect continuous, which is unnecessary here.
• Option 2: "Roma said that she was feeling very excited to spoke..."
• Grammatical error: "to spoke" is incorrect; should be "to speak".
• Option 4: "Roma said that she had been feeling very excited to be speaking..."
• Incorrect tense and aspect: "had been feeling... to be speaking" changes the meaning and introduces unnecessary complexity.

The correct answer is 'with'.

 

Key Points

• The word dissatisfied is an adjective used to describe a feeling of unhappiness or lack of contentment.
• In English, the adjective dissatisfied is most commonly followed by the preposition 'with' when referring to the person or thing that is causing the dissatisfaction.
• The phrase 'dissatisfied with' is a standard collocation used to indicate displeasure regarding a specific situation or outcome, such as the team's performance.

Therefore, the correct answer is Option 4.

 

Complete Sentence: 'The manager is dissatisfied with the team's performance this quarter.'

 

Additional Information

• Option 1: 'on' is incorrect as it is generally used for surfaces, days, or specific topics, but does not collocate with dissatisfied.
• Option 2: 'at' is incorrect; while we might be 'angry at' or 'annoyed at' a situation, dissatisfied exclusively takes 'with'.
• Option 3: 'of' is incorrect as it typically indicates origin, possession, or composition, and is not the correct preposition for this context.

The correct answer is Option 4.

 

Key Points

• Indirect Speech: She exclaimed that it was an incredibly beautiful evening.
• Direct Speech Conversion: She said, "What an incredibly beautiful evening it is!"
• Key Conversions:
• "it was" → "it is"
• In direct speech, the speaker expresses the feeling in the present moment, so "was" shifts to "is".
• Exclamatory form:
• The reporting verb "exclaimed" requires an exclamatory sentence in direct speech.
• Hence, "What an incredibly beautiful evening it is!" correctly conveys the emotion.
• Punctuation:
• Exclamation mark (!) is essential to reflect the tone of "exclaimed".

Therefore, the correct answer is Option 4.

 

Correct Sentence: She said, "What an incredibly beautiful evening it is!"

 

Additional Information

• Option 1: "She said, 'Wasn't it an incredibly beautiful evening?'"
• Incorrect because it changes the statement into a question.
• Option 2: "She exclaimed, 'It was an incredibly beautiful evening.'"
• Grammatically correct but lacks the exclamatory form; tone is flat.
• Option 3: "She said, 'What an incredibly beautiful evening it was!'"
• Incorrect tense: "was" instead of "is". Does not match the present emotional expression in direct speech.

The correct answer is option 3.

Key Points

• The word "Consistently" is spelled correctly and means "in a steady and reliable manner."
• Among the given options, "Consistently" is the only correct spelling that matches the definition provided.
• Examples of the word in use:
• She performs consistently well in her exams.
• The manager consistently supports his team in challenging situations.

Additional Information

• Incorrect Spellings:
• Consistintly: This is an incorrect spelling as it adds an extra "i" after "t."
• Consistantly: This is another common error where "a" is incorrectly used instead of "e."
• Consissisntly: This is a completely incorrect spelling with multiple errors.
• Correct Usage: Always ensure that "Consistently" is spelled with "e" after "t" and without any additional letters.

The correct answer is 'Initial'.

 

Key Points

• The passage mentions “preliminary reports” about the aircraft crash.
• The word “preliminary” refers to something that occurs at an early stage, before final confirmation.
• Thus, “Initial” is the most appropriate synonym, as it conveys the idea of first or early findings.
• Other options (“Final”, “Unimportant”, “Accurate”) do not match the contextual meaning of “preliminary”.

Therefore, the correct answer is 'Option 2'.

 

Complete Passage: Ahmedabad witnessed a tragic incident yesterday when a small passenger aircraft crashed shortly after take-off from the city's domestic airport. According to (1) preliminary reports, the plane was en route to Jaipur and was carrying two crew members and six passengers. Eyewitnesses described hearing an unusually loud noise before the aircraft descended rapidly and collided with an open field on the city's outskirts. Emergency services arrived within minutes, and rescue teams worked tirelessly to pull survivors from the wreckage. Sadly, three passengers lost their lives, while the remaining survivors sustained injuries of varying severity. Hospitals in the area quickly activated emergency protocols to provide urgent medical care.

 

Additional Information

• Final: Opposite of preliminary; refers to the last stage, not the first.
• Unimportant: Incorrect, as preliminary reports are significant early findings.
• Accurate: Preliminary reports may or may not be accurate; accuracy is determined later.

The correct answer is 'Blocked and restricted from access'.

 

Key Points

• In the passage, investigators ensured the crash site was “cordoned off” to preserve evidence.
• The phrase “cordoned off” means an area is blocked, sealed, or restricted so that unauthorized people cannot enter.
• Thus, “Blocked and restricted from access” is the closest meaning in this context.
• Other options like “Decorated with ribbons”, “Opened for visitors”, and “Cleaned thoroughly” do not fit the usage in the passage.

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: Investigators from the Directorate General of Civil Aviation have been deployed to determine the cause of the crash. Early speculation points to a possible mechanical failure, though officials emphasize that it is too soon to draw conclusions. The site has been (2) cordoned off to preserve evidence, and a detailed examination of the aircraft's flight data recorder will be conducted.

 

Additional Information

• Decorated with ribbons: Refers to ornamentation, not restriction.
• Opened for visitors: Opposite meaning; cordoned off prevents entry.
• Cleaned thoroughly: Refers to sanitation, not blocking access.

The correct answer is 'When'.

 

Key Points

• The sentence is: “Ahmedabad witnessed a tragic incident yesterday ____(3) a small passenger aircraft crashed shortly after take-off…”
• The blank requires a connector that introduces the time of the incident.
• “When” correctly conveys the idea that the tragic incident occurred at the time the aircraft crashed.
• Other options do not fit: “Where” indicates place, “Which” introduces a relative clause, and “While” indicates simultaneity but does not match the context.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: Ahmedabad witnessed a tragic incident yesterday (3) when a small passenger aircraft crashed shortly after take-off from the city's domestic airport. According to preliminary reports, the plane was en route to Jaipur and was carrying two crew members and six passengers...

 

Additional Information

• Where: Refers to location, not time.
• Which: Used for relative clauses, not suitable here.
• While: Suggests simultaneity, but the sentence is about a specific time of occurrence.

The correct answer is 'Arrived'.

 

Key Points

• The sentence is: “Emergency services ____(4) within minutes, and rescue teams worked tirelessly to pull survivors from the wreckage.”
• The context clearly refers to a past event (the aircraft crash in Ahmedabad).
• Therefore, the correct verb form must be in the past tense: “Arrived”.
• Other options are incorrect: “Arrives” (present tense), “Arriving” (present participle, grammatically unsuitable here), “Have arrived” (present perfect, does not match the simple past narrative).

Therefore, the correct answer is 'Option 3'.

 

Complete Passage: Ahmedabad witnessed a tragic incident yesterday when a small passenger aircraft crashed shortly after take-off from the city's domestic airport. According to preliminary reports, the plane was en route to Jaipur and was carrying two crew members and six passengers. Eyewitnesses described hearing an unusually loud noise before the aircraft descended rapidly and collided with an open field on the city's outskirts. Emergency services (4) arrived within minutes, and rescue teams worked tirelessly to pull survivors from the wreckage...

 

Additional Information

• Arrives: Present tense, does not fit the past narrative.
• Arriving: Present participle, grammatically incorrect in this sentence.
• Have arrived: Present perfect tense, inconsistent with the simple past narration of the passage.

The correct answer is 'About'.

 

Key Points

• The sentence is: “This accident has prompted renewed discussions ____(5) aviation safety standards and the importance of stringent maintenance checks for smaller aircraft.”
• The correct preposition here is “About” because discussions are held regarding or concerning a subject.
• “About” fits naturally with “aviation safety standards,” making the sentence grammatically and contextually correct.
• Other options do not fit: “Under” suggests authority or control, “At” indicates location/time, and “By” indicates agency or means — none align with the intended meaning.

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: This accident has prompted renewed discussions (5) about aviation safety standards and the importance of stringent maintenance checks for smaller aircraft. While air travel remains statistically safer than road transport, incidents like this serve as a sobering reminder of the risks involved...

 

Additional Information

• Under: Implies being controlled or governed, not suitable here.
• At: Refers to a place or time, incorrect in this context.
• By: Indicates agency or means, not appropriate for “discussions.”

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

Key Points

• The word "Vituperative" means harsh, bitter, or abusive language used to criticize someone or something. (कटु/गाली-गलौज भरा)
• Example: His vituperative comments during the debate offended many participants.
• The correct spelling of the word in the context of the sentence is "Vituperative". This word emphasizes the act of making caustic or abusive remarks. (गाली-गलौज भरा)
• Example: The politician's vituperative speech targeted his opponents directly.

Therefore, the correct answer is: Option 2 - Vituperative.

Additional Information

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

• Vittuperative (गलत वर्तनी): This is an incorrect spelling of "Vituperative" and does not have any meaning.
• Vitupirative (गलत वर्तनी): This is also an incorrect spelling of "Vituperative" and does not carry any meaning.
• Vituparative (गलत वर्तनी): This is another incorrect spelling of "Vituperative" and is meaningless.

The correct answer is option 1, i.e., Ophthalmologist.

Key Points

• The word Ophthalmologist refers to a medical specialist in the branch of medicine concerned with the study and treatment of disorders and diseases of the eye.
• The correct spelling is Ophthalmologist, which comes from the Greek words "ophthalmos" (eye) and "logia" (study).
• The misspelled options include:
• Option 2: Opthalmolgist - Incorrect due to missing 'h' after 'p'.
• Option 3: Ophthalmolgist - Incorrect due to missing 'o' after 'm'.
• Option 4: Opthalmologist - Incorrect due to missing 'h' after 'p'.

Correct sentence: An Ophthalmologist is a medical professional who diagnoses and treats eye disorders.

Additional Information

• Synonyms: Eye doctor, Eye specialist.
• Examples:
• The Ophthalmologist prescribed new glasses for my poor vision.
• She consulted an Ophthalmologist for her eye infection.

The correct answer is - Horizontal scroll bar

Key Points

• Horizontal scroll bar
• This control is typically located at the bottom of the application window.
• It is used to navigate horizontally (left and right) when the document or webpage content is wider than the visible area of the screen.
• The bar appears automatically in most word processors and browsers when the zoom level is high or the document layout exceeds the window width.
• By clicking and dragging the scroll box (thumb) or clicking the arrows at either end, the user can reveal hidden parts of the document.

Additional Information

• Vertical scroll bar
• Located on the right side of the window.
• It allows the user to move up and down through the pages of a document that is longer than the screen height.
• Navigation pane
• A feature often found in Microsoft Word that appears on the left side.
• It provides a way to search for specific text and browse through headings, pages, or results within the document.
• Status Bar
• Found at the very bottom of the window frame.
• Displays information such as page number, word count, and language, and often houses the zoom slider.
• Zoom Control
• Consists of a slider and buttons to magnify or reduce the view of the document.
• Increasing the zoom percentage often triggers the appearance of the horizontal scroll bar.

The correct answer is - Ctrl + Home

Key Points

• Ctrl + Home
• In MS Word, this shortcut is used to move the insertion point (cursor) immediately to the beginning of the document.
• Regardless of how many pages the document contains, this command bypasses manual scrolling to reach the first page and first line.
• It is a standard navigation shortcut used for efficiency in document editing and reviewing.

Additional Information

• Ctrl + End
• This shortcut moves the insertion point directly to the end of the document.
• It is useful for quickly adding content to the very last page of a file.
• Home Key
• Pressing the Home key alone moves the insertion point to the beginning of the current line.
• It does not change the page unless the cursor is already at the start of the document.
• Ctrl + Up Arrow
• This shortcut moves the cursor to the beginning of the current paragraph or the previous paragraph if the cursor is already at the start.
• Ctrl + Page Up/Down
• Ctrl + Page Up moves the cursor to the beginning of the previous page.
• Ctrl + Page Down moves the cursor to the beginning of the next page.

The correct answer is - Internet Service Provider

Key Points

• Internet Service Provider (ISP)
• An ISP is an organization or company that provides services for accessing, using, or participating in the Internet.
• It acts as the gateway that connects a user's computer or local network to the rest of the global internet.
• ISPs utilize various technologies to provide connectivity over wide areas, such as Fiber Optics, Cable, DSL, and Satellite.
• In addition to internet access, many ISPs provide related services like email accounts, domain registration, and web hosting.

Additional Information

• Modem and Router
• A Modem is a hardware device that connects a computer or router to a broadband network (via the ISP).
• A Router is a device that joins multiple networks together and directs data packets to their destinations.
• Broadband
• Refers to high-speed internet access that is always on and faster than traditional dial-up access.
• Common types include Asymmetric Digital Subscriber Line (ADSL) and Cable Television Lines.
• World Wide Web (WWW)
• An information system where documents and other web resources are identified by URLs and are accessible via the internet.
• It is often confused with the internet itself, but the Internet is the underlying hardware and network infrastructure, while the web is a service built on top of it.
• IP Address
• Every device connected to the internet is assigned a unique Internet Protocol (IP) address for identification and communication.
• ISPs are responsible for assigning these IP addresses to their customers' devices.

The correct answer is - They help narrow results to more relevant items based on selected criteria

Key Points

• Relevance and Precision
• Search filters allow users to refine search engine results by eliminating unnecessary data and focusing on specific criteria.
• This process reduces information overload, making it easier to find the most accurate information quickly.
• Time Range Filtering
• Users can filter results by date (e.g., past hour, past year) to ensure they are viewing the most current information or specific historical records.
• This is particularly useful for news and real-time updates.
• Content Type Filtering
• Filters allow users to categorize results by format, such as images, videos, news articles, or shopping results.
• This ensures that the output format matches the user's intent.

Additional Information

• Boolean Operators
• Words like AND, OR, and NOT are used to further refine searches by connecting or excluding specific keywords.
• Advanced Search Tools
• Many search engines offer advanced search options to filter by language, region, or site/domain (e.g., .gov or .edu).
• File type filters (such as searching specifically for PDF or PPT files) help in finding professional or academic documents.
• SafeSearch Filters
• These are used to block explicit content from appearing in search results, providing a filtered browsing experience suitable for all ages.

The correct answer is - Click File -> Close

Key Points

• File -> Close
• Using the File -> Close command specifically terminates the active workbook while leaving the Microsoft Excel application running.
• This is the standard procedure when a user wants to finish working on one file but intends to open or create another spreadsheet immediately after.
• If changes have been made to the file, Excel will prompt the user to save their work before the workbook is cleared from the workspace.
• The primary keyboard shortcuts to achieve this same result are Ctrl + W or Ctrl + F4.

Additional Information

• File -> Exit (or Close Application)
• The Exit command (or the 'X' button in the top-right corner of the window) closes the entire Excel program along with all open workbooks.
• The keyboard shortcut for closing the entire application is Alt + F4.
• Workbook vs. Worksheet
• A Workbook refers to the entire Excel file (.xlsx or .xls) that is saved on the disk.
• A Worksheet is a single tab or page within that workbook where data is entered into cells.
• Improper Shutdown Methods
• Turning off the computer directly or removing the file from the disk while it is open are unsafe practices.
• These actions can lead to data loss, file corruption, or temporary file fragments remaining in the system memory.

The correct answer is - It indicates a deliberate structure

Key Points

• Deliberate structure
• Naming sheets according to their specific function (e.g., Data, Summary, Charts) is a fundamental practice in worksheet organization.
• It allows users to navigate the workbook efficiently by providing immediate context for the content within each tab.
• This practice differentiates between input data, analytical summaries, and visual representations, which is essential for clear communication.
• A structured naming convention reduces cognitive load and minimizes the risk of errors when multiple people collaborate on the same file.

Additional Information

• Best Practices for Spreadsheet Design
• Separating raw data from analysis and presentation layers helps maintain data integrity and prevents accidental modification of source values.
• Using descriptive names instead of default names like "Sheet1" or "Sheet2" makes cross-sheet formulas much easier to read and audit.
• Consistent organization ensures that the spreadsheet is scalable and can be easily updated as more data or charts are added.
• Efficiency and Navigation
• While not mandatory for the software to run, organization is critical for user experience (UX) within complex financial or statistical models.
• Color-coding tabs in addition to naming provides another layer of visual organization to group related worksheets.

The correct answer is - Total formulas often refer to all rows above them

Key Points

• Automatic Range Expansion
• When a new row is inserted directly above a formula (like SUM), spreadsheet applications automatically expand the range to include the new cells.
• If data is typed below the total row, it falls outside the existing formula's defined range, leading to inaccurate totals.
• This behavior maintains data integrity by ensuring that every new entry is accounted for in the final calculation without manual formula updates.
• It prevents omission errors which are common when users forget to extend the cell references in a grand-total cell.

Additional Information

• The SUM Function
• Commonly used as =SUM(Cell1:CellN) to aggregate values in a column or row.
• The colon (:) operator defines a continuous range; inserting rows within these boundaries shifts the end-point cell reference downward.
• Excel Tables (Ctrl+T)
• Converting a data range into an Official Table provides a "Total Row" feature that is even more robust.
• Tables use structured references, which automatically include any newly added rows at the bottom of the data set into the total.
• Cell Referencing
• Relative References adjust when the structure of the worksheet changes (like inserting rows).
• Absolute References (using the $ sign) remain fixed, but even these will often adjust their row numbers if a row is inserted above the referenced cell.