BPSC Prelims 2022 Question Paper with Answers & Explanations

Explanation

A person finding their image larger than themselves in a mirror indicates that the mirror is concave. Plane mirrors always produce images of the same size as the object. Convex mirrors always produce diminished, or smaller, images. A concave mirror, when an object is placed between its pole and principal focus, forms a virtual, erect, and magnified image. This is the only type of spherical mirror among the options that can produce an image larger than the object under typical viewing conditions.

Explanation

A fan produces a feeling of comfort during hot weather primarily because it increases the rate at which perspiration evaporates from the skin. Our body sweats to cool down, and when sweat evaporates, it absorbs latent heat from the body, leading to a cooling effect. By circulating air, a fan facilitates faster evaporation of this sweat. It does not supply cool air, nor does it significantly change the body's heat radiation or the air's conductivity in a way that directly causes the feeling of comfort.

Explanation

The twinkling of stars is caused by atmospheric refraction. As light from a distant star travels through the Earth's atmosphere, it passes through layers of air with varying densities and temperatures. This causes the light rays to continuously bend and shift direction before reaching our eyes, leading to the apparent flickering or "twinkling" effect.

Explanation

A hydrogen bomb operates on the principle of an uncontrolled nuclear fusion reaction. In this process, light atomic nuclei, typically isotopes of hydrogen like deuterium and tritium, are forced to fuse together under extremely high temperatures and pressures, releasing an enormous amount of energy. This fusion reaction is typically initiated by a smaller fission (atomic bomb) reaction.

Explanation

Food cooks faster in a pressure cooker because the sealed environment traps steam, which significantly increases the pressure inside the cooker. An increase in pressure raises the boiling point of water above its normal 100°C. This higher boiling temperature means the food is cooked at a greater temperature, accelerating the cooking process.

Explanation

If the doors of a refrigerator are left open for a few hours, the room temperature will increase. A refrigerator works by transferring heat from its interior to the surrounding environment. When open, it will continuously try to cool the entire room by pumping heat out of the refrigerator compartment and releasing that heat, along with the heat generated by its motor and compressor, back into the same room.

Explanation

When a piece of ice floating in water up to its brim melts, the water level will not change. According to Archimedes' principle, a floating object displaces a volume of fluid equal to its own weight. Since ice has a lower density than water, the volume of water displaced by the floating ice is exactly equal to the volume that the ice will occupy once it melts and turns into water.

Explanation

A galvanometer is an instrument used for detecting and measuring small electric currents. It works by deflecting a pointer in response to current passing through a coil. It is not designed to measure electric resistance directly. Devices like an ohmmeter or a Wheatstone bridge are used to measure resistance. Therefore, the matching of "Galvanometer-Electric resistance" is incorrect.

Explanation

In a vacuum, there is no air resistance to impede the fall of objects. According to Galileo's principle of falling bodies, all objects, regardless of their mass, shape, or density, fall with the same acceleration due to gravity in a vacuum. Since the feather, rubber ball, and wooden ball are falling freely from the same height under these conditions, they will all reach the ground simultaneously.

Explanation

The beautiful colours observed in a soap film are a result of the phenomenon known as interference of light. When white light strikes the thin soap film, it reflects off both the top and bottom surfaces. These reflected light waves superpose, and due to the varying thickness of the film, different wavelengths (colours) undergo constructive and destructive interference, leading to the vivid patterns of colours seen.

Explanation

The mass number of a nucleus, denoted by A, is defined as the total number of protons and neutrons present within the nucleus. It is a fundamental property that represents the approximate atomic mass of an atom when expressed in atomic mass units (amu). It is distinct from the atomic number, which only counts the number of protons.

Explanation

Limestone is the primary raw material used in the manufacture of cement, particularly Portland cement. It provides the necessary calcium carbonate, which, when heated in a kiln, decomposes to produce calcium oxide (lime). Lime is the largest single component by weight in the final cement clinker, forming the basis for the cement's hydraulic properties.

Explanation

Isotopes are atoms of the same element, meaning they have the same number of protons and thus the same atomic number. However, they differ in the number of neutrons in their nucleus. Since the mass number is the sum of protons and neutrons, a difference in the number of neutrons directly leads to a difference in their mass number. Therefore, isotopes of an element differ in their mass number.

Explanation

The triple point of a substance is a specific temperature and pressure at which the three phases (solid, liquid, and gas) of that substance coexist in thermodynamic equilibrium. At this unique point, it is possible for all three phases to be present simultaneously, unlike boiling, melting, or freezing points which typically describe transitions between two phases.

Explanation

Bauxite is the principal and most important ore from which aluminium is extracted. It is a naturally occurring heterogeneous material composed primarily of one or more aluminium hydroxide minerals, along with various impurities like iron oxides, silica, and titania. Other options like calamine, calcite, and galena are ores of zinc, calcium, and lead respectively.

Explanation

The pH scale is used to specify the acidity or basicity of an aqueous solution. A neutral solution has a pH of exactly 7. Solutions with a pH value less than 7 are considered acidic, while solutions with a pH value greater than 7 are considered basic or alkaline. Therefore, a basic solution has a pH value more than 7.

Explanation

The statement that an atom is electrically neutral due to the presence of protons and electrons inside the nucleus is incorrect. While protons are indeed inside the nucleus and contribute positive charge, electrons orbit outside the nucleus in electron shells. An atom is electrically neutral because it contains an equal number of positively charged protons in the nucleus and negatively charged electrons orbiting the nucleus.

Explanation

Acrylic is a synthetic fiber made from acrylonitrile and is known for its wool-like properties, often used in sweaters, blankets, and tracksuits. It is not prepared from cotton. Rayon, a regenerated cellulose fiber derived from wood pulp, is actually known as artificial silk because of its silky appearance and feel, but it is not directly prepared from cotton in the way statement C describes. Therefore, the statement that acrylic is artificial silk prepared from cotton is incorrect.

Explanation

Graphite and diamond are allotropes of carbon, meaning they are different structural forms of the same element. Despite their vastly different physical properties, such as crystal structure, hardness, and electrical conductivity, they are chemically identical as they are both composed solely of carbon atoms. Consequently, they can undergo the same fundamental chemical reactions, such as combustion in the presence of oxygen to produce carbon dioxide, albeit under potentially different conditions due to their structural differences affecting reactivity.

Explanation

Liquefied petroleum gas (LPG) is a flammable mixture of hydrocarbon gases used as fuel in heating appliances, vehicles, and as a refrigerant. Its primary constituents are propane and butane (n-butane and iso-butane), with small amounts of propylene and butylenes often present. While the exact proportions vary significantly by country, season, and intended use, butane, either alone or as a dominant component in a propane-butane mixture, is often considered a major constituent, particularly in warmer climates or specific commercial blends.

Explanation

Water moves from the soil into the root cells of plants primarily through a physical process called osmosis. Osmosis is the net movement of water molecules across a selectively permeable membrane from a region of higher water potential (less negative solute potential, like the soil water) to a region of lower water potential (more negative solute potential, like the root cells). This movement is driven by the water potential gradient between the soil and the root tissues, allowing the roots to take up water against gravity.

Explanation

Biodegradable wastes are organic materials that can be broken down and decomposed by living organisms, primarily microorganisms. Bacteria and fungi are the key decomposers in this process. They consume the complex organic compounds in the waste and convert them into simpler substances, such as compost, biogas, or other useful products, through processes like aerobic or anaerobic digestion. This natural decomposition cycles nutrients back into the ecosystem or allows for resource recovery.

Explanation

During the daytime, plants perform photosynthesis, consuming carbon dioxide and releasing oxygen. However, at nighttime, photosynthesis ceases due to the lack of sunlight. Plants continue to respire throughout the night, which involves taking in oxygen and releasing carbon dioxide as a byproduct. Sleeping directly under trees, especially dense foliage, could lead to a localized accumulation of carbon dioxide, which can be detrimental to human health if the concentration becomes too high.

Explanation

Insectivorous plants are typically found in nutrient-poor soils, particularly those that are deficient in nitrogen. While these plants can photosynthesize for energy, they have evolved specialized mechanisms to trap and digest insects and other small arthropods. This adaptation allows them to obtain the necessary nitrogen for protein synthesis and growth, supplementing what they cannot get from the impoverished soil.

Explanation

The stem of a plant serves multiple essential functions beyond distributing food and water. It provides structural support to the entire plant, holding leaves, flowers, and fruits aloft. This structural role is crucial for defining the plant's overall shape and architecture, ensuring that the leaves are optimally positioned to capture sunlight for photosynthesis.

Explanation

In addition to matching ABO blood types, blood transfusions require careful consideration of the Rh factor. The Rh factor refers to the presence or absence of the Rh D antigen on red blood cells. If an Rh-negative person receives Rh-positive blood, their immune system may produce antibodies against the Rh factor, leading to a potentially severe immune reaction upon subsequent exposure to Rh-positive blood.

Explanation

The pituitary gland is a small, pea-sized endocrine gland that plays a crucial role in regulating numerous bodily functions. It is strategically located at the base of the brain, directly beneath the hypothalamus, and is housed within a bony depression called the sella turcica. Often referred to as the "master gland," it secretes hormones that control the activity of most other endocrine glands.

Explanation

Ultrasonic waves are widely used in medical imaging, specifically in sonography (ultrasound scans), to monitor the growth and development of a fetus in the womb. This technique uses high-frequency sound waves to create real-time images of the internal organs and soft tissues. Unlike X-rays, which use ionizing radiation and are harmful to a developing fetus, ultrasonic waves are non-invasive and considered safe for both the mother and the baby.

Explanation

Blood group AB is known as the universal acceptor because individuals with this blood type can receive red blood cells from any other ABO blood group (A, B, AB, or O). This is because AB blood contains both A and B antigens on the surface of its red blood cells and, crucially, does not produce anti-A or anti-B antibodies in its plasma. Without these antibodies, there is no immune reaction against transfused A or B antigens.

Explanation

Pneumonia is an acute inflammatory condition that primarily affects the lungs. It is characterized by inflammation and fluid accumulation in the alveoli, which are the tiny air sacs in the lungs where gas exchange occurs. This infection can be caused by various pathogens, including bacteria, viruses, and fungi, leading to symptoms such as cough, fever, chills, and difficulty breathing.

Explanation

Covishield is the Indian-manufactured version of the Oxford-AstraZeneca COVID-19 vaccine. It was produced by the Serum Institute of India (SII), based in Pune, under a licensing agreement. The Serum Institute of India is the world's largest vaccine manufacturer by dose and played a critical role in India's vaccination drive and global vaccine supply.

Explanation

The Atal Tunnel, also known as the Rohtang Tunnel, is a strategically important highway tunnel built under the Rohtang Pass in the Pir Panjal range of the Himalayas. Located in Himachal Pradesh, India, it connects Manali to Lahaul and Spiti valley, significantly reducing travel time. The official length of the Atal Tunnel is 9.02 km (5.60 miles).

Explanation

The Railway Budget was merged with the General Budget in India starting from the financial year 2017-18. The Union Cabinet approved the merger in September 2016, based on the recommendations of a committee headed by Bibek Debroy. Consequently, the first combined budget, including the railway estimates, was presented to Parliament on February 1, 2017. This marked the end of a 92-year-old practice of presenting a separate railway budget.

Explanation

The Citizenship (Amendment) Act, 2019 (CAA) aims to grant Indian citizenship to persecuted religious minorities from Afghanistan, Bangladesh, and Pakistan who entered India on or before December 31, 2014. These minority groups include Hindus, Sikhs, Buddhists, Jains, Parsis, and Christians. The Act provides a specific pathway to citizenship for these communities, exempting them from certain provisions of the Citizenship Act, 1955, regarding illegal migrants.

Explanation

The Central Vista Project refers to the ambitious redevelopment plan for India's central administrative area in New Delhi. This large-scale project includes the construction of a new Parliament House, a common Central Secretariat to house various ministries, new residences for the Prime Minister and the Vice President, and the rejuvenation of the existing Central Vista Avenue. The objective is to modernize and enhance the functionality of the government infrastructure.

Explanation

Following the reorganization of the erstwhile state of Jammu and Kashmir in August 2019, two new Union Territories were formed: Jammu and Kashmir, and Ladakh. The Union Territory of Jammu and Kashmir was established with a legislative assembly, enabling it to have its own elected body. However, the Union Territory of Ladakh was constituted without a legislature, making it directly administered by the central government through a Lieutenant Governor.

Explanation

The All India Football Federation (AIFF) Men's Player of the Year Award for the 2020-21 season was won by defender Sandesh Jhingan. He received this prestigious recognition for his consistent and impactful performances on the field during that period. Jhingan is a prominent figure in Indian football and has been a key player for both his club and the national team.

Explanation

The Pradhanmantri Kisan Samman Nidhi Yojana (PM-KISAN) was announced by then-interim Finance Minister Piyush Goyal during the Interim Union Budget on February 1, 2019. While the scheme's formal launch by the Prime Minister was on February 24, 2019, the effective date for the first installment was retrospective from December 1, 2018, and its announcement in the budget on February 1, 2019, marks its official presentation.

Explanation

Neeraj Chopra won India's only gold medal at the Tokyo 2020 Olympics, which were held in 2021. He achieved this historic feat in the Men's Javelin Throw event, securing India's first-ever Olympic gold in athletics and the second individual Olympic gold overall.

Explanation

India achieved its best-ever performance at the Tokyo Paralympics 2020, held in 2021. The Indian contingent won a total of 19 medals. This included 5 gold, 8 silver, and 6 bronze medals, significantly surpassing previous records.

Explanation

India assumed the rotating presidency of the United Nations Security Council (UNSC) on August 1, 2021, for a duration of one month. This was India's first presidency during its 2021-22 tenure as a non-permanent member of the UNSC.

Explanation

Major General Chris Donahue was the last American soldier to depart from Afghanistan, marking the end of the 20-year US military mission in the country. He boarded a C-17 cargo plane from Hamid Karzai International Airport in Kabul on August 30, 2021.

Explanation

Dassault Aviation is a prominent French aerospace company that specializes in the design and manufacture of military aircraft, business jets, and regional airliners. India signed an inter-governmental agreement with France in 2016 for the procurement of 36 Rafale fighter jets, which are manufactured by Dassault Aviation. These advanced multi-role combat aircraft have since been inducted into the Indian Air Force.

Explanation

A severe and violent clash between Indian and Chinese soldiers occurred in the Galwan Valley on June 15, 2020. This incident marked a significant escalation of border tensions in the Ladakh region along the Line of Actual Control (LAC), resulting in casualties on both sides. The confrontation involved hand-to-hand combat and was a major event in recent India-China relations.

Explanation

Pegasus is a powerful and highly sophisticated spyware developed by the Israeli cyber-arms company NSO Group. This malicious software is designed to infiltrate mobile devices, enabling its operators to secretly extract vast amounts of data, including messages, calls, and location information. It has gained international notoriety due to allegations of its use by various governments for surveillance against journalists, human rights activists, and political dissidents.

Explanation

India commenced its two-year term as a non-permanent member of the United Nations Security Council (UNSC) on January 1, 2021. This was India's eighth tenure as a non-permanent member of the powerful 15-nation UN organ, securing the seat for the 2021-2022 term. India's presence on the UNSC allows it to play a more active role in global peace and security matters.

Explanation

Sputnik V is a COVID-19 vaccine developed by the Gamaleya Research Institute of Epidemiology and Microbiology in Russia. India approved Sputnik V for emergency use in April 2021, becoming one of the first major countries to do so. Subsequent batches of the vaccine were imported from Russia to supplement India's domestic vaccination efforts against the COVID-19 pandemic.

Explanation

Joe Biden was sworn in as the 46th President of the United States on January 20, 2021. He succeeded Donald Trump, becoming one of the oldest individuals to assume the presidency. His administration began amidst challenges such as the ongoing COVID-19 pandemic and economic recovery efforts.

Explanation

For the Republic Day parade in 2021, there was no foreign chief guest. Initially, British Prime Minister Boris Johnson was invited, but he had to cancel his visit due to the escalating COVID-19 situation in the United Kingdom. This marked the first time in over five decades that India did not have a foreign dignitary as the chief guest for its Republic Day celebrations.

Explanation

As of 2022, T. S. Tirumurti was serving as the Permanent Representative of India to the United Nations. He held this crucial diplomatic post from May 2020 until July 2022, representing India's interests and positions on various global issues at the UN. He was succeeded by Ruchira Kamboj in July 2022.

Explanation

According to the 2011 Census of India, Gopalganj district in Bihar recorded a sex ratio of 1021 females per 1000 males. This figure indicates that Gopalganj was the only district in Bihar where the female population outnumbered the male population, making it stand out in terms of gender demographics within the state.

Explanation

The first sitting of the Bihar Legislative Council was convened on January 20, 1913. This marked a significant step in the administrative and political history of the region, following the creation of the province of Bihar and Orissa in 1912. The Council was established under the provisions of the Government of India Act, 1912.

Explanation

Rashmi Kumari is a renowned international carrom champion hailing from Bihar, India. She has achieved significant success in the sport, winning numerous national and international titles. Her accomplishments include winning the Carrom World Cup, solidifying her status as a prominent figure in international carrom.

Explanation

The Bihar Government received the 'Digital India Award, 2020' for its exemplary initiative in assisting people stranded outside the state during the COVID-19 lockdown. The award recognized the "Bihar Sahayata Mobile App," which facilitated the transfer of financial aid directly to over 21 lakh migrant workers and residents of Bihar who were stuck in other parts of the country. This digital solution effectively provided crucial support during a challenging period.

Explanation

In the Bihar Legislative Assembly, a specific number of seats are reserved for Scheduled Castes (SC) candidates to ensure their representation. Out of the total 243 seats, 38 seats are constitutionally reserved for Scheduled Caste candidates. This reservation is in accordance with the provisions of the Constitution of India and the Delimitation of Parliamentary and Assembly Constituencies Order, ensuring political inclusion for these communities.

Explanation

Bihar became a pioneer state in India by providing 50% reservation for women in its Panchayat bodies. This landmark decision was enacted in the year 2006, significantly enhancing the participation and representation of women in local self-governance. The move aimed to empower women politically and promote more inclusive decision-making at the grassroots level.

Explanation

The state of Bihar was bifurcated to create the new state of Jharkhand in the year 2000. This significant administrative reorganization occurred on November 15, 2000, when the southern part of Bihar, primarily comprising tribal-dominated regions, was separated to form Jharkhand. This division was aimed at addressing long-standing demands for a separate state with distinct cultural and developmental priorities.

Explanation

The Bihar Budget for the year 2021-22 proposed the creation of a new ministry, the "Skill Development and Entrepreneurship Department". This new department was envisioned to consolidate existing institutions and schemes related to skill training and entrepreneurship promotion, aiming to enhance employment opportunities for the youth in the state. The primary focus of this new ministry was to streamline efforts in skill development and foster an entrepreneurial ecosystem.

Explanation

The Human Development Sub-Mission in Bihar brings together efforts from multiple government departments to improve various human development indicators across the state. This sub-mission integrates the work of 8 key departments. These departments typically include Health, Education, Social Welfare, Women Development, Scheduled Caste/Scheduled Tribe Welfare, Backward Classes Welfare, Minority Welfare, and Labour Resources, to ensure a coordinated approach towards human development.

Explanation

The Garib Kalyan Rojgar Abhiyan (GKRA) was a massive rural public works scheme launched by the Prime Minister in June 2020. This initiative was specifically designed to provide employment and livelihood opportunities to migrant workers who had returned to their native places during the COVID-19 induced lockdown. The campaign was officially launched from Telihar village in the Khagaria district of Bihar, signifying its focus on rural employment generation.

Explanation

Lothal is a prominent ancient city of the Indus Valley Civilization, also known as the Harappan Civilization. It is located in the Bhal region of the Indian state of Gujarat, specifically near the village of Saragwala in the Ahmedabad district. The site is famous for its unique dockyard, which is considered one of the earliest known ports in the world, indicating its significance as a trade center.

Explanation

Vijayalaya is widely recognized as the founder of the Imperial Chola dynasty, which marked the revival of Chola power in South India. He established the Chola kingdom in the 9th century by conquering Thanjavur (Tanjore) from the Muttarayars, making it his capital. His reign initiated a period of significant expansion and consolidation that led to the Chola empire becoming one of the most powerful and long-lasting dynasties in Indian history.

Explanation

The First Buddhist Council was held at Rajagriha shortly after the Mahaparinirvana of Buddha, around 483 BCE. It was convened to compile the teachings of Buddha (Sutta Pitaka) and the monastic rules (Vinaya Pitaka). The council was presided over by Mahakashyapa, one of Buddha's chief disciples, while Upali recited the Vinaya Pitaka and Ananda recited the Sutta Pitaka.

Explanation

Kiratarjuniya is a renowned Sanskrit mahakavya (epic poem) written by the poet Bharavi. It is considered one of the greatest works in Sanskrit literature, known for its intricate style, profound meaning, and narrative depicting the conflict between Arjuna and Lord Shiva (in the guise of a Kirata, or mountain huntsman).

Explanation

The construction of the Qutub Minar was initiated by Qutb-ud-din Aibak, the founder of the Delhi Sultanate, in 1192. However, he only managed to complete the first storey. The subsequent three stories were added and completed by his successor and son-in-law, Iltutmish, making him primarily responsible for its completion. Later, Firoz Shah Tughlaq repaired and added the fifth and final storey.

Explanation

The Vijayanagara Empire was founded in 1336 AD by two brothers, Harihara I and Bukka Raya I, who were Sangama dynasty chiefs. They established their kingdom on the banks of the Tungabhadra River, growing it into one of the most powerful empires in South India, known for its rich culture, architecture, and resistance against northern invasions.

Explanation

Sir Thomas Roe was an English diplomat who served as the first ambassador from England to the Mughal Empire. He arrived in India in 1615 and remained until 1619, primarily at the court of the Mughal Emperor Jahangir. His mission was to secure trading rights for the British East India Company.

Explanation

Ain-i-Akbari is a detailed document recording the administration of the Mughal Empire under Emperor Akbar, written by his court historian and biographer, Abul Fazl. It forms the third and final volume of the Akbarnama, the official history of Akbar's reign. Abul Fazl dedicated seven years to completing this comprehensive work.

Explanation

The Ryotwari system of land revenue collection was first introduced by Captain Alexander Read in the Baramahal area in 1792, which was later fully developed and implemented by Thomas Munro. It was widely adopted in the Madras Presidency, followed by the Bombay Presidency and parts of Assam and Coorg. Under this system, the cultivator or ryot was recognized as the owner of the land and paid taxes directly to the British government.

Explanation

V. D. Savarkar, an Indian independence activist and politician, notably described the Uprising of 1857 as the 'First Indian War of Independence'. He articulated this view in his 1909 book titled "The Indian War of Independence 1857," arguing that it was a planned revolution for liberation rather than a mere sepoy mutiny. His work was influential in shaping nationalist perceptions of the event.

Explanation

Annie Besant was an Irish socialist, Theosophist, and women's rights activist who became a prominent figure in India's freedom struggle. She was elected as the first woman President of the Indian National Congress at its Calcutta session in 1917. She played a significant role in the Home Rule League movement alongside Bal Gangadhar Tilak.

Explanation

Dr. Babasaheb Ambedkar started the Marathi fortnightly newspaper "Bahishkrita Bharat" on April 3, 1927. The journal served as a platform for expressing the views, concerns, and demands of the untouchable communities in India. Through this publication, Ambedkar championed the cause of social justice and equality for the marginalized sections of society.

Explanation

Subhas Chandra Bose founded the Forward Bloc in 1939 after resigning from the presidency of the Indian National Congress. This left-wing nationalist political party was formed with the aim of consolidating all radical elements within the Congress. Bose sought to create an alternative political platform to push for immediate and complete independence for India.

Explanation

Liaquat Ali Khan served as the Finance Minister in the Interim Government of India formed in 1946. He was a prominent leader of the Muslim League and was appointed to this crucial portfolio after the Muslim League decided to join the Interim Government later in October 1946, following initial hesitation.

Explanation

The Santhal Rebellion of 1855 AD, also known as the Santhal Hul, was a major tribal uprising against the exploitation by zamindars, moneylenders, and the British administration. The rebellion was primarily led by two Santhal brothers, Sidhu and Kanhu Murmu, who gathered a large force of Santhals to fight for their rights.

Explanation

Raj Kumar Shukla was a local indigo cultivator from Champaran who played a pivotal role in inviting Mahatma Gandhi to the district. He persistently requested Gandhi to visit Champaran and investigate the oppressive tinkathia system, under which farmers were forced to cultivate indigo on a fixed portion of their land.

Explanation

Gautama Buddha, originally known as Siddhartha Gautama, attained enlightenment while meditating under a Bodhi tree in Bodh Gaya, in the present-day state of Bihar, India. After achieving this profound spiritual realization, he became known as the Buddha and began to teach his philosophy to the world.

Explanation

Sachindra Nath Sanyal was a key figure in the Indian revolutionary movement and established a branch of the Anushilan Samiti in Patna in 1913. This move was part of a broader effort to expand revolutionary activities and organize secret societies across various regions of India. The Samiti aimed to inspire and train young revolutionaries.

Explanation

The Bihar Socialist Party was established in 1931, primarily by Phulan Prasad Varma and Jayaprakash Narayan, along with other prominent socialist thinkers. This party sought to integrate socialist ideals into the Indian nationalist movement, focusing on the economic and social upliftment of peasants and workers. It played a significant role in the political landscape of Bihar.

Explanation

Sher Shah's tomb is located in Sasaram, Bihar. This magnificent mausoleum is an excellent example of Indo-Islamic architecture, built in an artificial lake. It serves as the final resting place of Sher Shah Suri, the founder of the Sur Empire, who ruled parts of India in the 16th century.

Explanation

Geodesy is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, its three-dimensional time-varying shape in space, and its rotation. It primarily focuses on the precise measurement of the dimension of the Earth. This field is crucial for mapping, navigation, and understanding Earth's dynamic processes.

Explanation

The theory of continental drift was first proposed by the German meteorologist and geophysicist Alfred Wegener in 1912. He gathered evidence suggesting that the continents were once joined together in a supercontinent called Pangaea and have since moved to their current positions. This theory was a precursor to the modern understanding of plate tectonics.

Explanation

The Sunda Trench, also known as the Java Trench, is an oceanic trench located in the northeastern Indian Ocean. It runs for approximately 3,200 kilometers along the southern and southwestern coasts of the Indonesian archipelago. This trench is a subduction zone where the Indo-Australian Plate is subducting beneath the Sunda Plate, and it lies directly parallel to the large island of Sumatra, as well as Java, forming a prominent feature of the Sunda Arc.

Explanation

The Coriolis force is an apparent force that acts on moving objects within a rotating frame of reference. On Earth, this force is a direct result of the planet's rotation. Due to the Earth's spin, moving objects like air currents, ocean currents, and even projectiles appear to be deflected from a straight path, to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

Explanation

The Dead Sea is an endorheic lake bordered by Israel and the Palestinian West Bank to the west and Jordan to the east. These three entities share direct land borders with the Dead Sea's shores. Lebanon is located further north, sharing a border with Israel, but it does not extend south enough to touch the Dead Sea.

Explanation

Ilmenite (FeTiO3) is a titanium-iron oxide mineral, and it is the primary ore for titanium production. This mineral is commonly found in placer deposits, often as heavy mineral sands, along coastlines around the world, including extensive deposits along the Indian coastline. Titanium extracted from ilmenite is used in various industries, notably for manufacturing titanium dioxide pigments and titanium metal.

Explanation

Statement 1 is correct because Himalayan rivers are fed by both glaciers and rainfall, making them perennial, whereas most Peninsular rivers rely solely on monsoon rains and are thus seasonal. Statement 2 is also correct as Himalayan rivers originate from high mountain ranges, leading to a much steeper gradient in their upper and middle courses compared to the Peninsular rivers flowing over a relatively flatter, older plateau. Statement 3 is incorrect because Himalayan rivers, with their high velocity and large volume, carry enormous amounts of sediment and perform far more erosional work, carving deep gorges and valleys, compared to the Peninsular rivers which flow over harder, stable landmasses with a gentler slope.

Explanation

The Ganga Plain is a vast alluvial plain formed by the deposition of sediments by the Ganga river and its tributaries. Geologically, it is often described as a classic example of a foreland basin or a geosyncline. A geosyncline is a large-scale depression in the Earth's crust that accumulates immense amounts of sediments over geological time, typically forming in front of a rising mountain range like the Himalayas.

Explanation

Both Wular Lake and Loktak Lake are significant freshwater lakes in India. Wular Lake, located in Jammu and Kashmir, is one of the largest freshwater lakes in Asia, while Loktak Lake, in Manipur, is the largest freshwater lake in Northeast India. Since both options C and D are correct, the appropriate choice is E, indicating more than one of the above.

Explanation

Saturn is known for being the least dense planet in our solar system, with an average density of approximately 0.687 grams per cubic centimeter. This density is less than that of water, meaning Saturn would float if placed in a large enough body of water. In contrast, Earth, Mars, and Venus are all terrestrial planets with much higher densities ranging from 3.93 to 5.51 g/cm³.

Explanation

Chiria, located in the West Singhbhum district of Jharkhand, is renowned for its vast iron ore mines. It is home to one of the largest iron ore deposits in Asia, with mining operations primarily carried out by Steel Authority of India Limited (SAIL). This region is crucial for India's iron and steel industry due to its rich mineral reserves.

Explanation

The Pattiseema Lift Irrigation Project is a key river interlinking initiative in Andhra Pradesh. Its primary purpose is to divert water from the Godavari River to the Krishna River basin. This project helps in supplementing water availability in the Krishna delta and addressing irrigation needs, especially during lean periods in the Krishna River.

Explanation

Eskers are long, winding ridges of stratified sand and gravel, deposited by meltwater streams flowing within or beneath a glacier. Drumlins are elongated, oval-shaped hills composed of glacial till, primarily boulder and clay, formed by the streamlined action of ice. "Basket of eggs topography" is a characteristic landscape found in regions with numerous drumlins, not eskers. Eskers are built by glacial meltwater streams (fluvio-glacial action), while drumlins are formed by the erosional and depositional action of glaciers themselves. Therefore, statements 1, 2, and 4 are correct.

Explanation

The combustion of underground coal is a well-documented and persistent problem in the Jharia coalfield, which is located in the state of Jharkhand. These underground fires have been burning for many decades, causing significant environmental damage, land subsidence, and safety hazards, making Jharia a prominent global example of this phenomenon.

Explanation

Historically, Bihar was a major producer of mica. After the bifurcation of Bihar and the creation of Jharkhand, the majority of the rich mica belts, such as Koderma, fell into Jharkhand. However, the Gaya district in Bihar still retains some known mica deposits, being geographically contiguous with the broader mica-rich region.

Explanation

The River Son is a significant tributary of the River Ganga, joining it from the right bank. The confluence of the Son and Ganga rivers is located near Maner, which falls within the Patna district of Bihar. This junction is an important geographical feature in the region.

Explanation

The Damodar River originates in the Chota Nagpur Plateau, specifically from the Palamu hills in Jharkhand. Similarly, the Koel River (both North and South Koel) and the Subarnarekha River also have their origins within the Chota Nagpur Plateau, primarily in the Ranchi district of Jharkhand. This plateau region serves as the source for several important rivers in eastern India.

Explanation

Kanwar Lake, located in the Begusarai district of Bihar, was designated as a Ramsar site in August 2020. This makes it the first and, as of the exam year 2022, the only Ramsar site in the state. The lake is an important wetland for migratory birds and rich in biodiversity.

Explanation

Brahmayoni Hill is situated in the Gaya district of Bihar. It is a significant pilgrimage site, particularly for Hindus, known for the Brahmayoni Temple and a flight of steps leading to its summit, offering panoramic views of Gaya.

Explanation

Bihar is divided into three main agroclimatic regions: Zone I (North-West alluvial plain), Zone II (North-East alluvial plain), and Zone III (Southern alluvial plain, further divided into III-A and III-B). The Northern West agroclimatic region (Zone I) has the highest number of districts, comprising 13 districts of Bihar.

Explanation

The Eleventh Schedule of the Constitution of India, added by the 73rd Amendment Act, lists 29 functional items placed within the purview of Panchayats. While items like Libraries, Fuel and Fodder, and Technical Training and Vocational Education are explicitly mentioned in this schedule, "Rural Sports" is not listed as a distinct item.

Explanation

In pursuance of Article 113 of the Constitution, the Annual Financial Statement (Budget) presented to Parliament includes 'Demands for Grants'. These represent the estimated expenditure from the Consolidated Fund of India for various ministries and departments. For the Union Budget 2022-23, there were 109 'Demands for Grants' presented to the Parliament.

Explanation

The National Extension Service (NES) was launched in India in October 1953. This service was established to provide a more comprehensive and permanent organizational setup for rural development, building upon the experiences of the Community Development Programme which was initiated a year earlier. The NES aimed to extend development activities across a wider geographical area, facilitating agricultural improvements and overall rural upliftment through an integrated approach.

Explanation

The composition of a State Legislative Council is defined by Article 171 of the Indian Constitution. Its members are chosen by various electoral colleges and nominations. These include members of local bodies (like Panchayats and municipalities), graduates of three years' standing, and teachers of three years' standing. Additionally, some members are elected by the Legislative Assembly, and a fraction is nominated by the Governor for their expertise. Industrialists, as a distinct category, are not an electoral college for choosing members of the State Legislative Council.

Explanation

The 'split system' in Indian administration primarily refers to the separation of accounts from audit functions. Historically, the Comptroller and Auditor General (CAG) performed both the maintenance of accounts and auditing of expenditures for government departments. To enhance the accountability of ministries and departments for their financial transactions and to improve efficiency, the function of maintaining government accounts was largely separated from the CAG's office and transferred to the respective ministries and departments. This allows the CAG to focus solely on independent external auditing.

Explanation

The Committee on Subordinate Legislation is a parliamentary committee specifically tasked with scrutinizing the rules, regulations, bye-laws, and other forms of delegated legislation framed by the executive. Its primary role is to ensure that the powers delegated by Parliament to the executive to make rules and regulations are being properly exercised within the scope of the original Act. This committee prevents potential overreach by the executive and upholds parliamentary control over law-making.

Explanation

Article 300 of the Indian Constitution specifically deals with 'suits and proceedings'. It provides for the legal personality of the Union of India and the States, empowering them to sue or be sued in their respective names. This article establishes the framework for how the government, both at the Centre and in the States, can engage in legal actions, thereby defining its capacity to enter into litigation and be held accountable in courts of law.

Explanation

The Indian judicial process, particularly concerning personal liberty as enshrined in Article 21 of the Constitution, operates on the principle of "procedure established by law." This means that a person can be deprived of life or personal liberty only according to the procedures prescribed by a law that has been duly enacted by the legislature. This principle ensures that state action must conform to statutory law, distinguishing it from the "due process of law" approach, which additionally allows courts to assess the fairness and reasonableness of the law itself.

Explanation

Maharashtra holds the distinction of being the first Indian state to establish the institution of the Lokayukta. While Odisha was the first state to pass the Lokayukta Act in 1970, Maharashtra implemented the office of the Lokayukta in 1971. This move created an anti-corruption ombudsman institution at the state level, predating other states in setting up this specific mechanism for addressing public grievances and investigating allegations of corruption against public functionaries.

Explanation

Dr. Adarsh Sein Anand held the esteemed position of the Chief Justice of India in the late 1990s. He was sworn in as the 29th Chief Justice of India on October 10, 1998, and served in this capacity until November 1, 2001. His tenure as Chief Justice falls squarely within the specified period, marking a significant period in the Indian judiciary.

Explanation

Sudipto Mundle was not a member of the 15th Finance Commission. He served as a part-time member of the 14th Finance Commission, which was chaired by Y.V. Reddy. The 15th Finance Commission, constituted in 2017 under the chairmanship of N.K. Singh, included Ashok Kumar Lahiri, Ramesh Chand, and Ajay Narayan Jha (among others) as its members.

Explanation

In the Union Budget 2021-22, the Finance Minister announced a significant increase in the Foreign Direct Investment (FDI) limit in the insurance sector. The limit was raised from the existing 49% to 74%. This policy change aims to attract greater foreign capital and expertise into the Indian insurance market, enhancing competition, product offerings, and financial strength within the sector, while retaining safeguards for domestic control.

Explanation

The Union Budget for 2021-22, presented by the Finance Minister Nirmala Sitharaman on February 1, 2021, estimated the fiscal deficit for the financial year 2021-22 to be 6.8 percent of the Gross Domestic Product (GDP). This projection aimed to put the economy on a path of fiscal consolidation following the impact of the COVID-19 pandemic. The government also aimed to achieve a fiscal deficit below 4.5 percent by 2025-26.

Explanation

The best index of economic development is the growth in per capita real income from year to year. While national income growth is important, per capita income considers the population, providing a better measure of the average individual's economic well-being. Using real income further adjusts for inflation, ensuring that the increase reflects actual purchasing power rather than just price increases. This indicator directly reflects improvements in living standards.

Explanation

The second phase of the Swachh Bharat Mission (Grameen), often referred to as SBM-G Phase-II, was approved by the Union Cabinet in February 2020. This phase is designed to be implemented over a period of five years, specifically from the financial year 2020-21 to 2024-25. Its objective is to sustain the Open Defecation Free (ODF) status and to improve solid and liquid waste management in rural areas, moving towards ODF Plus villages.

Explanation

The National Development Council (NDC) is an apex body in India responsible for policy matters regarding planning and development. Its composition includes the Prime Minister of India (as its Chairman), all Union Cabinet Ministers, Chief Ministers of all States, and Administrators of all Union Territories, as well as members of the NITI Aayog. The Secretary of the NITI Aayog functions as the Secretary of the NDC. The Chairman of the Finance Commission of India is not a permanent member of the National Development Council.

Explanation

Lakdawala Committee (1993) was appointed to measure poverty using calorie-based norms. Tendulkar Committee (2009) was also constituted to review the methodology for measuring poverty, recommending a new poverty line. Kelkar Committee is associated with infrastructure financing and fiscal consolidation. Narasimham Committee dealt with financial sector reforms. Since both Lakdawala and Tendulkar committees relate to poverty measurement and share the same List-II item (1), no single option correctly matches all four pairs simultaneously. Therefore none of the given options is fully correct.

Explanation

The states arranged in ascending order of their rice production (smallest to largest) in India are Andhra Pradesh, Punjab, Uttar Pradesh, and West Bengal. West Bengal is India's largest rice-producing state, followed by Uttar Pradesh. Punjab, despite its smaller area, is a significant producer due to high yields. Andhra Pradesh's rice production, while substantial, ranks lower among these four states. Therefore, the sequence from lowest to highest production is Andhra Pradesh, Punjab, Uttar Pradesh, and West Bengal.

Explanation

The Finance Commission is a constitutional body established under Article 280 of the Indian Constitution, making statement 2 correct. Its primary function is to recommend the distribution of tax revenues between the Union and the states, and among the states themselves. The recommendations made by the Finance Commission are advisory in nature, though they carry significant weight and are generally accepted by the government, making statement 3 correct. The first Finance Commission was constituted in 1951, not 1950, thus statement 4 is incorrect. Since it is a constitutional body, it is not merely a statutory body, making statement 1 incorrect.

Explanation

The Economic Survey 2020-21 introduced the Bare Necessities Index (BNI), analyzing access to bare necessities at both rural and urban levels, making statement 1 correct. The BNI is based on 26 indicators across five dimensions: water, sanitation, housing, micro-environment, and other facilities, making statement 3 correct and statement 4 incorrect (it has five, not six dimensions). The BNI was created for all states, but not for 2018 only; it was also calculated for 2012, and later updated for 2019 and 2020 in subsequent surveys, making statement 2 incorrect.

Explanation

In Bihar, "Krishi Utthaan Banks" have been proposed or discussed as a mechanism to support agriculture and rural development. The term "Utthaan" signifies upliftment or progress, reflecting the objective of these banks to boost the agricultural sector and improve the economic conditions of rural populations through enhanced financial access and tailored schemes. These banks aim to strengthen the credit flow and provide specialized services to farmers and rural enterprises.

Explanation

According to certain reports and specific calculations pertaining to Human Development Index (HDI) for Indian states, the value of Bihar's HDI in 2019 was approximately 0.641. While various reports might present slightly differing figures or cite data from earlier years, this specific value reflects a particular assessment for the state's progress in key HDI dimensions (life expectancy, education, and standard of living) for the year 2019.

Explanation

As per the Bihar Budget 2021-22, the estimated fiscal deficit for the financial year 2021-22 was projected to be Rs 22,511 crore. This figure represented approximately 2.97 percent of the Gross State Domestic Product (GSDP) for the state. The budget aimed to keep the fiscal deficit within the limits prescribed by the Fiscal Responsibility and Budget Management (FRBM) Act.

Explanation

Under the Digital Bihar Programme, computer education and training were planned to be provided to students across various grades in a phased manner. Specifically for the academic year 2021-22 onwards, the program aimed to commence with providing computer education and training to all students of Class VIII. The initiative is part of a broader effort to enhance digital literacy among students in Bihar.

Explanation

The 15th Finance Commission, in its recommendations for the period 2021-26, determined the share of states in the divisible pool of central taxes. For Bihar, the Commission recommended a share of 4.128 percent, which is typically rounded to 4.12 percent. This share is calculated based on various criteria including population, income distance, area, forest and ecology, demographic performance, and tax and fiscal effort.

Explanation

The Ghadar Party was a revolutionary organization founded by Indian immigrants in the United States and Canada with the aim of liberating India from British rule. It was established in 1913 in San Francisco, California, United States of America. The party primarily comprised Punjabi immigrants and aimed to incite a revolt in India with the support of the Indian diaspora.

Explanation

Gopal Krishna Gokhale established the Servants of India Society in 1905 in Pune, Maharashtra. The primary objective of the society was to train Indians to dedicate their lives to the cause of the nation, promoting social reform, education, and national unity. Gokhale, a prominent moderate leader of the Indian National Congress, envisioned a cadre of dedicated individuals working for the betterment of society.

Explanation

Lala Lajpat Rai, a prominent nationalist leader and one of the Lal-Bal-Pal trio, authored the book "Unhappy India". Published in 1928, this work critically examined British rule in India and responded to Katherine Mayo's "Mother India", presenting a detailed account of India's political, social, and economic conditions under colonial administration. His writings were instrumental in shaping public opinion during the freedom struggle.

Explanation

Dr. B. R. Ambedkar participated in all three Round Table Conferences held in London between 1930 and 1932. He primarily represented the interests of the depressed classes and advocated for their rights and separate electorates during these discussions regarding constitutional reforms in India. Mahatma Gandhi, on the other hand, only attended the second Round Table Conference in 1931.

Explanation

The Indian Association was established in 1876 by Surendranath Banerjee and Ananda Mohan Bose. This organization was a significant pre-Congress nationalist body that aimed to create a strong public opinion on political questions, promote friendly relations between Hindus and Muslims, and involve the masses in political movements. It played a crucial role in laying the groundwork for the Indian National Congress.

Explanation

The honorific 'Netaji' was applied to Subhas Chandra Bose's name in Germany. It was there, among the Indian soldiers of the Indian Legion and by the German officials, that he was first addressed as 'Netaji' (leader) in the early 1940s. He later used this title when he took command of the Indian National Army in Southeast Asia.

Explanation

Surya Sen, popularly known as Masterda, was the principal leader associated with the 'Chittagong Armoury Raid'. This daring raid on the British armory in Chittagong, Bengal Presidency (now in Bangladesh), took place on April 18, 1930. Sen and his revolutionary group aimed to seize arms and ammunition to establish an independent government and deliver a blow to British rule.

Explanation

Bankim Chandra Chatterjee's famous Bengali novel 'Anandamath', published in 1882, is historically significant for its depiction of the Sannyasi Rebellion. The novel's narrative revolves around a group of Hindu ascetics who rise against the British East India Company, directly drawing inspiration from the actual Sannyasi Revolt that took place in the late 18th century. The national song 'Vande Mataram' also appears in this novel.

Explanation

To determine the earliest event, we need to recall their dates. The Cripps Mission arrived in India in March 1942. The Quit India Resolution was passed in August 1942. Lord Wavell became the Governor General of India in October 1943. The Cabinet Mission arrived in India in March 1946. Comparing these dates, the arrival of the Cripps Mission was the first event.

Explanation

The Lahore Session of the Indian National Congress, held in 1929, was a pivotal moment in the Indian independence movement. During this session, the resolution for 'Purna Swaraj' or complete independence for India was passed. Jawaharlal Nehru presided over this historic session, and under his leadership, January 26, 1930, was declared as the first 'Independence Day'.

Explanation

Mahatma Gandhi's Champaran Satyagraha of 1917 saw the involvement of several key figures. Raj Kumar Shukla was the local farmer who invited Gandhi to investigate the plight of indigo cultivators. J. B. Kripalani and Rajendra Prasad were among the prominent lawyers and activists who assisted Gandhi in his inquiry and efforts. Ram Manohar Lohia was a significant socialist leader of a later period and was not associated with the Champaran Satyagraha.

Explanation

Kunwar Singh was a notable figure and a courageous leader during the Revolt of 1857. He hailed from Jagdishpur, located in the Bhojpur district of Bihar, where he was a local zamindar. He led the rebel forces in Bihar against the British East India Company, demonstrating immense bravery and strategic prowess throughout the uprising.

Explanation

During the Quit India Movement in 1942, Jayaprakash Narayan, a prominent socialist leader, famously escaped from Hazaribagh Central Jail on November 9, 1942, along with five other freedom fighters. This daring escape allowed him to go underground and play a crucial role in organizing the resistance movement against the British rule. His actions inspired many and made him a legendary figure in the independence struggle.

Explanation

Chittaranjan Das presided over the Gaya Session of the Indian National Congress in 1922. This session was significant as it witnessed a major ideological debate regarding the Council Entry Programme. C.R. Das, along with Motilal Nehru, advocated for entering the legislative councils to obstruct British policies from within, while Mahatma Gandhi's followers opposed it. The disagreement led to the formation of the Swaraj Party by C.R. Das and Motilal Nehru shortly after this session.

Explanation

In the Interim Government formed on September 2, 1946, Dr. Rajendra Prasad was given the portfolio of Food and Agriculture. This government was established to facilitate the transition of power from British rule to Indian independence. Other key portfolios included Jawaharlal Nehru as Vice-President and Minister of External Affairs and Commonwealth Relations, Sardar Vallabhbhai Patel as Minister of Home Affairs, Information and Broadcasting, and Baldev Singh as Defence Minister.

Explanation

To find numbers divisible by 4, 5, and 6, we need to find numbers divisible by their Least Common Multiple (LCM). The prime factorization of 4 is 2², 5 is 5¹, and 6 is 2¹ × 3¹. The LCM(4, 5, 6) is 2² × 3 × 5 = 60. We are looking for multiples of 60 between 200 and 600. These numbers are 240 (60×4), 300 (60×5), 360 (60×6), 420 (60×7), 480 (60×8), and 540 (60×9). There are 6 such numbers.

Explanation

The given expression is (3⁴n - 4³n). This can be rewritten as ((3⁴)ⁿ - (4³)ⁿ). Calculating the powers, we get (81ⁿ - 64ⁿ). According to a fundamental algebraic property, an expression of the form (xⁿ - yⁿ) is always divisible by (x - y) for any positive integer n. In this case, x = 81 and y = 64. Therefore, (81ⁿ - 64ⁿ) is always divisible by (81 - 64), which equals 17.

Explanation

Let the two numbers be x and y. We are given two conditions: x² - y² = 256000 and x + y = 1000. We know the algebraic identity x² - y² = (x - y)(x + y). Substituting the given values, we get (x - y)(1000) = 256000, which simplifies to x - y = 256. Now we have a system of two linear equations: x + y = 1000 and x - y = 256. Adding these two equations gives 2x = 1256, so x = 628. Substituting x = 628 into x + y = 1000 yields 628 + y = 1000, thus y = 372. The two numbers are 628 and 372.

Explanation

The expression log₂(32) asks for the power to which the base 2 must be raised to obtain the number 32. We can list the powers of 2: 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, and 2⁵ = 32. Since 2 raised to the power of 5 equals 32, the value of log₂(32) is 5.

Explanation

Initially, a man sells 45 lemons for F40, incurring a 20% loss. This means F40 represents 80% of the cost price (CP). So, CP = F40 / 0.80 = F50 for 45 lemons. To gain 20%, the selling price (SP) for 45 lemons should be 120% of the CP, which is F50 1.20 = F60. Now, we need to find how many lemons should be sold for F24 to achieve this gain. If 45 lemons are sold for F60, then for F24, the number of lemons is (45 / 60) 24 = (3/4) * 24 = 18 lemons.

Explanation

The train is 110 m long and travels at 58 kmph. The passerby walks at 4 kmph in the same direction. When two objects move in the same direction, their relative speed is the difference between their speeds. Relative speed = 58 kmph - 4 kmph = 54 kmph. To convert kmph to m/s, we multiply by 5/18: 54 (5/18) = 3 5 = 15 m/s. The time taken for the train to pass the passerby is the length of the train divided by the relative speed. Time = 110 m / 15 m/s = 22/3 seconds. This can be expressed as a mixed number: 7 and 1/3 seconds.

Explanation

A rhombus has four equal sides. The perimeter is 52 m, so each side of the rhombus is 52 m / 4 = 13 m. The diagonals of a rhombus bisect each other at right angles. This creates four congruent right-angled triangles within the rhombus, with the sides of the rhombus as their hypotenuses. The shorter diagonal is 10 m, so half of the shorter diagonal is 10 m / 2 = 5 m. Using the Pythagorean theorem (a² + b² = c²) in one of these right triangles, where the side is the hypotenuse: 5² + (half of longer diagonal)² = 13². This gives 25 + (half of longer diagonal)² = 169. So, (half of longer diagonal)² = 169 - 25 = 144. Taking the square root, half of the longer diagonal is 12 m. Therefore, the length of the longer diagonal is 2 * 12 m = 24 m.

Explanation

To find the speed of B, we first calculate the time taken by A to complete the race. A runs 100 m at 8 kmph. Converting A's speed to m/s: 8 kmph = 8 (5/18) m/s = 40/18 m/s = 20/9 m/s. Time taken by A = Distance / Speed = 100 m / (20/9 m/s) = 45 seconds. B gets a 4 m start, so B runs a distance of 100 - 4 = 96 m. A beats B by 15 seconds, which means B takes 15 seconds more than A. So, time taken by B = 45 s + 15 s = 60 seconds. Speed of B = Distance run by B / Time taken by B = 96 m / 60 s = 1.6 m/s. Converting B's speed to kmph: 1.6 m/s = 1.6 (18/5) kmph = 144/25 kmph = 5.76 kmph.

Explanation

The clock is set right at 8 a.m. and gains 10 minutes in 24 hours. The faulty clock shows 1 p.m. on the following day. The total time elapsed on the faulty clock is from 8 a.m. today to 1 p.m. tomorrow, which is 24 hours (8 a.m. to 8 a.m. next day) + 5 hours (8 a.m. to 1 p.m. next day) = 29 hours. Since the clock gains 10 minutes in 24 hours, it means that (24 hours + 10 minutes) on the faulty clock corresponds to 24 hours of true time. So, 24 hours 10 minutes = 1450 minutes on faulty clock corresponds to 24 hours = 1440 minutes of true time. For 29 hours (29 60 = 1740 minutes) on the faulty clock, the true time elapsed = (1440/1450) 1740 minutes = (144/145) 29 hours = (144 / (5 29)) 29 hours = 144/5 hours = 28.8 hours. This is 28 hours and 0.8 60 = 48 minutes. Adding 28 hours and 48 minutes to 8 a.m. (the set time): 8 a.m. + 28 hours = 12 noon the next day. Adding 48 minutes gives 12:48 p.m., or 48 minutes past 12 noon.

Explanation

Let the given continued fraction be X. Assuming f(1) is a typo for the constant 1, the expression becomes X = 2 - 1/(2 - 1/(2 - ...)). Since the fraction continues infinitely, we can write X = 2 - 1/X. Multiplying by X (assuming X is not zero) gives X² = 2X - 1. Rearranging this, we get X² - 2X + 1 = 0. This is a perfect square trinomial, which simplifies to (X - 1)² = 0. Solving for X, we find X = 1.