• Geometrical Optics: A concave mirror is the only type of spherical mirror capable of producing an upright, magnified (larger than object) virtual image when the object is placed between the focal point and the pole.

Moving air from a fan accelerates the evaporation of sweat (perspiration) from the skin surface. Because evaporation is an endothermic process that absorbs latent heat of vaporization from the body, it produces a cooling sensation.

• Optics & Atmospheric Physics: Star twinkling (astronomical scintillation) occurs due to atmospheric refraction. Starlight passes through multiple turbulent layers of Earth's atmosphere with varying air densities and refractive indices, continually bending the light path and fluctuating its apparent brightness.

A hydrogen bomb (thermonuclear weapon) operates on the principle of an uncontrolled nuclear fusion reaction, in which isotopes of hydrogen (deuterium and tritium) fuse under extreme temperature and pressure to form helium and release massive energy.

• Thermodynamics: In a sealed pressure cooker, steam accumulation increases internal pressure above 1 atmosphere, elevating the boiling point of water from 100 °C to approximately 120 °C, enabling food to cook much faster.

A refrigerator is a heat pump that extracts heat from its interior and exhausts both that heat and the electrical work energy consumed by its compressor into the room. Leaving its door open causes continuous compressor operation, increasing the net room temperature.

• Fluid Physics: According to Archimedes' principle, the weight of the water displaced by the floating ice equals the weight of the ice. When the ice melts into water, it occupies exactly the same volume as the displaced water; thus no water overflows and the level remains unchanged.

Constitutional provisions and their respective Schedules:

• (A) Public Health and Sanitation: Correctly placed in the State List (Seventh Schedule, List II, Entry 6).
• (B) Census: Correctly placed in the Union List (Seventh Schedule, List I, Entry 69).
• (C) Allocation of seats in the Council of States (Rajya Sabha): Matched with 'Second Schedule' is INCORRECT. Allocation of seats in the Rajya Sabha to States and Union Territories is contained in the Fourth Schedule (Articles 4(1) and 80(2)). The Second Schedule deals with provisions as to the salaries, allowances, and emoluments of constitutional functionaries (President, Governors, Judges, CAG, etc.).
• (D) Anti-Defection Law: Correctly placed in the Tenth Schedule (inserted by the 52nd Constitutional Amendment Act, 1985; Articles 102(2) and 191(2)).

Therefore, (C) is NOT correctly matched.

In the Fourth Schedule, Uttar Pradesh has the highest allocation of seats in the Rajya Sabha (31 seats), as well as the highest in the Lok Sabha (80 seats).

Do not confuse Second Schedule (Salaries and Emoluments) with Third Schedule (Forms of Oaths/Affirmations) and Fourth Schedule (Allocation of Rajya Sabha seats).

• 1st Schedule: Names of States and UTs.
• 2nd Schedule: Salaries and Allowances.
• 3rd Schedule: Oaths and Affirmations.
• 4th Schedule: Rajya Sabha Seat Allocation.

Allocation of Rajya Sabha seats is universally known to be in the Fourth Schedule, making its matching with the Second Schedule factually erroneous (Option C).

• Physics Principle: In a vacuum, there is no air resistance. Acceleration due to gravity (g) is independent of the mass or shape of falling objects (g = GM/R²), so all objects fall with identical acceleration and reach the ground at the exact same time.

A thin soap film on water displays vibrant colours in daylight due to thin-film interference of light waves reflected from the upper and lower surfaces of the film.

The mass number (A) of an atomic nucleus is defined as the total number of nucleons, which is the sum of the number of protons (Z) and neutrons (N) present in the nucleus.

Limestone (calcium carbonate, which yields calcium oxide/lime upon heating) is the primary raw material and main ingredient of Portland cement, accounting for about 60–65% of its composition.

• Nuclear Chemistry: Isotopes of a given chemical element possess the same atomic number Z (number of protons and electrons) but differ in the number of neutrons in their nucleus, and therefore differ in mass number A (protons + neutrons).

In thermodynamics, the triple point of a substance is the unique temperature and pressure at which its solid, liquid, and gaseous phases coexist in thermodynamic equilibrium (for water, 273.16 K or 0.01 °C at 611.657 Pa).

Bauxite (Al₂O₃·2H₂O), a hydrated aluminium oxide mineral, is the principal commercial ore of aluminium. Calamine is an ore of zinc, calcite is a calcium mineral, and galena is the primary ore of lead.

• Acid-Base Scale: On the pH scale from 0 to 14, acidic solutions have pH < 7, neutral solutions have pH = 7, and basic/alkaline solutions have pH > 7.

• Atomic Structure: Protons and neutrons reside inside the atomic nucleus, whereas electrons orbit in shells outside the nucleus. Therefore, stating that electrons are inside the nucleus is factually incorrect.

Rayon (regenerated cellulose fiber), not acrylic, is called artificial silk. Acrylic is a synthetic polymer fiber (polyacrylonitrile) that resembles wool and is used as an artificial wool substitute.

Graphite and diamond are allotropes of the identical chemical element carbon (C). Because their chemical composition is strictly elemental carbon, both undergo identical chemical reactions; for example, combustion of both diamond and graphite in excess oxygen yields solely carbon dioxide gas (C + O₂ → CO₂).

Butane (including n-butane and isobutane, along with propane) is the primary hydrocarbon constituent of domestic Liquefied Petroleum Gas (LPG), whereas methane is the main constituent of Compressed Natural Gas (CNG).

• Plant Physiology: Water moves from the dilute soil solution into the concentrated cell sap of root hair cells across the semipermeable plasma membrane down a water potential gradient by Osmosis.

• Decomposition & Composting: Biodegradable organic wastes are decomposed by aerobic and anaerobic bacteria and fungi into humus-rich compost, biogas, and useful soil nutrients.

• Plant Physiology: During nighttime in the absence of sunlight, photosynthesis ceases but cellular respiration continues, causing plants to absorb oxygen and release carbon dioxide (CO₂), which can cause suffocation if sleeping directly underneath.

Correct Answer: Option (C) — Nitrogen • Plant Nutrition: Insectivorous plants (such as Pitcher plant, Sundew, Venus flytrap, Utricularia) grow in acidic, waterlogged bogs deficient in nitrogen, trapping and digesting insects to meet their nitrogen nutritional requirements.

• Plant Morphology: The plant stem conducts water and nutrients, supports leaves/branches, stores surplus food/water (e.g., in modified stems like potato, ginger, sugarcane), and shapes the vegetative structure.

Correct Answer: Option (C) — Rh factor • Transfusion Medicine: In blood transfusion, compatibility requires matching not only the ABO blood group antigens but crucially also the Rh (Rhesus) factor (Rh-positive or Rh-negative D antigen) to avoid severe hemolytic transfusion reactions.

• Human Anatomy: The pituitary gland (hypophysis cerebri), known as the 'master gland' of the endocrine system, is situated at the base of the brain in a bony depression of the sphenoid bone called the sella turcica.

Ultrasonic waves (high-frequency sound waves above 20 kHz) are used in obstetric ultrasonography (ultrasound scans) to safely monitor fetal growth and development inside the womb without ionizing radiation.

Blood group AB (specifically AB positive) is the universal acceptor/recipient because its red blood cells have both A and B antigens and its plasma lacks both anti-A and anti-B antibodies.

• Medical Pathology: Pneumonia is an acute inflammatory infection of the lung parenchyma, primarily affecting the microscopic air sacs (alveoli). It causes alveoli to fill with fluid or pus, resulting in cough, fever, chills, and difficulty breathing.

• Pharmaceuticals in India: Covishield was produced and manufactured by the Serum Institute of India (SII) in Pune under license from AstraZeneca and the University of Oxford.

Atal Tunnel, built under the Rohtang Pass in the Eastern Pir Panjal range of the Himalayas on the Leh-Manali Highway in Himachal Pradesh, has a length of 9.02 km.

• Budgetary Reforms: On the recommendations of the Bibek Debroy Committee, the 92-year-old practice of a separate Railway Budget was scrapped, and the first unified Union Budget was presented on February 1, 2017.

Correct Option: Option (C) — To remove Bangladeshi illegal immigrants.

This question tests core factual, empirical, and analytical knowledge from Indian Polity (Constitution Making, Preamble, Fundamental Rights, DPSP & Local Governance) directly aligned with the official BPSC Prelims syllabus and historical question patterns.

• Project Overview: The Central Vista Redevelopment Project revamps India's central administrative area along Kartavya Path in New Delhi, including the new triangular Parliament building inaugurated in 2023, common Central Secretariat buildings, and executive enclaves.

• Jammu and Kashmir Reorganisation Act 2019: Under the 2019 Act, the state of J&K was divided into two UTs: Jammu & Kashmir (with a Legislative Assembly modeled after Puducherry) and Ladakh (a UT without a legislature, directly governed by a Lieutenant Governor).

Senior Indian national team defender Sandesh Jhingan won the AIFF Men's Footballer of the Year Award for the 2020–21 season, while Suresh Singh Wangjam was named the Emerging Player of the Year.

• Government Schemes: PM-KISAN was officially announced by Finance Minister Piyush Goyal in the Union Interim Budget on 1 February 2019 (providing ₹6,000 per year in three equal instalments of ₹2,000).

Neeraj Chopra won India's sole Gold Medal at the Tokyo 2020 Olympics (held in August 2021) in Men's Javelin Throw with a best throw of 87.58 metres.

India won a total of 19 medals (5 Gold, 8 Silver, and 6 Bronze) at the Tokyo 2020 Summer Paralympics held in August–September 2021, finishing 24th in the medal tally.

During its 2021–22 tenure as a non-permanent member, India assumed the rotating monthly Presidency (Chairmanship) of the United Nations Security Council on 1 August 2021.

Major General Chris Donahue, commander of the U.S. Army's 82nd Airborne Division, was the last American soldier to board the final C-17 transport aircraft out of Hamid Karzai International Airport in Kabul on 30 August 2021.

• Defense Procurement: The 36 twin-engine multi-role Rafale combat aircraft inducted into the Indian Air Force were manufactured and supplied by French aerospace major Dassault Aviation.

• Cybersecurity: Pegasus is a zero-click surveillance spyware developed and marketed by the Israeli cyber-arms company NSO Group.

India began its eighth two-year term (2021–2022) as an elected non-permanent member of the United Nations Security Council on 1 January 2021.

Sputnik V is an adenoviral vector COVID-19 vaccine developed by the Gamaleya National Center of Epidemiology and Microbiology in Moscow and exported to India by Russia.

• US Presidential Succession: Joseph R. Biden Jr. was inaugurated on January 20, 2021 as the 46th President of the United States of America.

British Prime Minister Boris Johnson was invited as the Chief Guest for India's 72nd Republic Day Parade on 26 January 2021, though he subsequently had to cancel his visit due to a surge in COVID-19 cases in the UK.

Senior diplomat T. S. Tirumurti served as the Permanent Representative of India to the United Nations in New York from May 2020 to June 2022.

• Census 2011 Bihar: Gopalganj is the only district in Bihar with a sex ratio favorable to women, recording 1,021 females per 1,000 males (followed by Siwan at 988 and Saran at 954).

Following the creation of the Bihar and Orissa province in 1912, the first sitting of the Bihar Legislative Council was convened on 20 January 1913 at Patna College, Bankipore.

• Sports Achievement: Rashmi Kumari is a prominent Indian international carrom player hailing from Patna, Bihar. She is a multiple-time World Carrom Champion, having won the World Carrom Championship title in 2012, 2014, 2016, and 2024.

The Bihar Government won the Digital India Award 2020 (in the Pandemic Category) for transferring financial assistance directly to over 21 lakh stranded workers outside Bihar during the COVID-19 lockdown via the 'Bihar Corona Sahayata' mobile app.

• Bihar Assembly Seats: Out of the 243 total constituencies in the Bihar Legislative Assembly, 38 seats are reserved for Scheduled Castes (SC) and 2 seats (Manihaari and Katoria) are reserved for Scheduled Tribes (ST).

Through the Bihar Panchayati Raj Act, 2006, Bihar became the first state in India to grant 50% reservation to women in all three tiers of Panchayati Raj Institutions.

• State Reorganization: The southern 18 districts of Bihar were separated to form the new state of Jharkhand on 15 November 2000 under the Bihar Reorganisation Act, 2000.

In the Bihar Budget 2021–22 under Saat Nishchay-2 ('Yuva Shakti – Bihar Ki Pragati'), the state government proposed creating a separate Department of Skill and Entrepreneurship Development to promote technical education and youth self-employment.

• Bihar Governance: The Human Development Sub-Mission (Manav Vikas Up-Mission) in Bihar coordinates and covers 7 key social-sector departments (Health, Education, Social Welfare, SC/ST Welfare, Minority Welfare, Rural Development, and Labour Resources).

Prime Minister Narendra Modi launched the Garib Kalyan Rojgar Abhiyan on 20 June 2020 from Telihar village in Beldaur block of Khagaria district, Bihar, to provide livelihood opportunities to returning migrant workers.

• Harappan Ports: Lothal, famous for its ancient tidal dockyard, bead-making factory, and rice husk remains, is located on the Bhogava river in the Gulf of Khambhat in Gujarat.

• South Indian Dynasties: Vijayalaya Chola (c. 850–871 CE), a feudatory of the Pallavas, captured Thanjavur (Tanjore) from the Muttarayars and established the Imperial Chola dynasty.

• Ancient History: The First Buddhist Council was convened in 483 BCE at the Saptaparni cave in Rajagriha under the patronage of King Ajatashatru and was presided over by the venerable elder Mahakassapa (Mahakashyapa).

• Classical Sanskrit Literature: The epic poem (Mahakavya) 'Kiratarjuniya'—narrating the combat between Arjuna and Lord Shiva disguised as a Kirata mountain hunter—was composed by the 6th-century poet Bharavi.

• Delhi Sultanate Architecture: The foundation and basement storey of Qutb Minar were started by Qutb-ud-din Aibak around 1199 CE, but the minaret was structurally completed by adding three more storeys by his successor, Sultan Shamsuddin Iltutmish (c. 1220 CE).

. The Vijayanagara Empire was founded on the southern banks of the Tungabhadra river in 1336 CE by two brothers, Harihara I and Bukka Raya I of the Sangama dynasty, with the spiritual blessings of saint Vidyaranya.

• Mughal Diplomatic History: Sir Thomas Roe was sent by King James I of England as the official ambassador to the court of Mughal Emperor Jahangir, residing at his court in Ajmer/Agra from 1615 to 1619 to secure trade privileges for the English East India Company.

Ain-i-Akbari, a detailed 16th-century Persian document recording the administration, revenue, and culture of Emperor Akbar's empire, was written by his court historian Abul Fazl as the third volume of the Akbarnama.

The Ryotwari land revenue system was first introduced in 1792 by Captain Alexander Read and Thomas Munro in the Baramahal district of the Madras Presidency, and later extended across Madras when Munro became Governor in 1820.

Vinayak Damodar (V. D.) Savarkar described the Revolt of 1857 as the 'First War of Indian Independence' in his famous 1909 book 'The Indian War of Independence of 1857'.

• Historical Precedent: Annie Besant was the first woman ever to preside over the Indian National Congress, chairing the 1917 Calcutta session. Sarojini Naidu was the first Indian woman President, presiding over the 1925 Kanpur session.

• Dalit Empowerment & Journalism: Dr. Bhimrao Ramji Ambedkar launched the Marathi fortnightly journal 'Bahishkrit Bharat' (Excluded India) on 3 April 1927 to articulate the grievances and rights of the depressed classes.

Correct Answer: Option (A) — Subhas Chandra Bose • Historical Background: Netaji Subhas Chandra Bose resigned from the presidency of the Indian National Congress in April 1939 due to ideological rifts with Gandhi and the Congress Working Committee, and founded the All India Forward Bloc on May 3, 1939 in Unnao/Makur (UP) to unite radical leftist and anti-imperialist forces.

• Interim Government 1946: When the Muslim League joined the Interim Government in October 1946, Liaquat Ali Khan was appointed as the Finance Member (Minister), presenting the controversial 'Poor Man's Budget'.

The Santhal Rebellion (Santhal Hul) of 1855–56 in the Damin-i-Koh region (Rajmahal Hills) against British colonial rule and zamindari exploitation was led by the Murmu brothers Sidhu and Kanhu, along with Chand and Bhairav.

• Champaran Satyagraha: Raj Kumar Shukla, a local indigo farmer from Champaran, met Mahatma Gandhi at the 1916 Lucknow session of the Indian National Congress and persuaded him to visit Champaran.

• Enlightenment at Bodh Gaya: Siddhartha Gautama attained supreme enlightenment (Samyak Sambodhi) at the age of 35 at Uruvela (modern Bodh Gaya) on the banks of the Niranjana (Phalgu) River under the Bodhi tree.
• Contrasted with Mahavira: Vardhamana Mahavira attained Kaivalya under a Sal tree on the bank of the Rijupalika River near Jimbhikagrama.

• Revolutionary Activities in Bihar: In 1913, revolutionary leader Sachindra Nath Sanyal established a branch of the Anushilan Samiti in Patna to recruit youth and spread revolutionary ideas in Bihar.

The Bihar Socialist Party was established in July 1931 in Patna by Phulan Prasad Varma and Jayaprakash Narayan, along with Ganga Sharan Sinha, Rambriksh Benipuri, and Ramanand Mishra.

The octagonal red sandstone tomb of Sur Empire founder Sher Shah Suri is located in the middle of an artificial lake at Sasaram in Rohtas district of Bihar.

• Earth Science: Geodesy is the branch of applied mathematics and earth science concerned with measuring and representing the Earth's geometric shape, orientation in space, gravitational field, and dimensions.

German meteorologist and geophysicist Alfred Wegener formally published his comprehensive 'Continental Drift Theory' (Kontinentalverschiebung) in 1912, hypothesizing that all continents were once joined in a supercontinent called Pangaea surrounded by the universal ocean Panthalassa.

• Oceanographic Feature: The Sunda Trench (Java Trench), located in the northeastern Indian Ocean, extends parallel to the southern coast of the Indonesian island of Java and Sumatra, forming the deepest oceanic trench in the Indian Ocean (approx. 7,290 m).

The Coriolis force is an apparent inertial force resulting from the rotation of the Earth on its axis, which deflects moving winds and ocean currents to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

The Dead Sea is a landlocked salt lake bordered by Jordan to the east and Israel and the Palestinian West Bank to the west; Lebanon lies further north along the Mediterranean coast and does not share a border with the Dead Sea.

• Mineralogy: Ilmenite (FeTiO3) is an iron-black, titanium-iron oxide mineral and the primary economic ore of titanium metal and titanium dioxide (TiO2) pigment, found abundantly in beach placer sands of Kerala, Tamil Nadu, and Odisha.

Himalayan rivers are perennial (fed by glaciers and rainfall) and flow down steeper gradients across young fold mountains, causing much greater erosion than the seasonal, rain-fed Peninsular rivers flowing over mature, graded plateaus (Statements 1 and 2 are correct, while Statement 3 is incorrect).

Geologists (notably Eduard Suess) have described the Ganga Plain as a foredeep or geosyncline—a linear tectonic depression between the Himalayas and the Peninsular plateau that was gradually filled with alluvial sediments.

• Hydrology: Wular Lake in Jammu and Kashmir (fed by the Jhelum river) is one of the largest freshwater lakes in India and Asia. Chilika Lake (brackish lagoon), Sambhar Lake (salt lake), and Pangong Tso (saline endorheic lake) are saline/brackish.

Saturn is a gas giant with the lowest mean density of any planet in the Solar System at approximately 0.687 g/cm³ (less than the density of liquid water, 1.0 g/cm³), whereas Earth has the highest density (5.51 g/cm³).

Correct Answer: Option (A) — Iron Ore Mining • Mineral Geography: Chiria in West Singhbhum district of Jharkhand contains India's largest single iron ore reserve, estimated at over 2 billion tonnes, leased to SAIL.

The Pattiseema Lift Irrigation Project in Andhra Pradesh links the Godavari and Krishna rivers by diverting surplus water from the Godavari river into the Polavaram Right Main Canal to feed the Krishna river basin.

Eskers are sinuous ridges of sand and gravel deposited by subglacial meltwater streams, whereas drumlins are oval hills of boulder clay (glacial till) formed directly by glacial ice action that produce a characteristic 'basket of eggs' topography (making Statement 3 incorrect and Statements 1, 2, and 4 correct).

• Mining Hazard: The most prominent and long-standing underground coalfield fires in India occur in the Jharia and Bokaro coalfields located in the Dhanbad district of Jharkhand, raging continuously since 1916.

Mica deposits in Bihar are concentrated along the southern belt bordering Jharkhand, primarily in Nawada, Gaya, Jamui, and Banka districts.

The Son River originates near Amarkantak in Madhya Pradesh and merges with the Ganga River near Maner (Danapur) in Patna district of Bihar.

• Drainage System: The Damodar (near Tori, Latehar), South Koel, and Subarnarekha (near Nagri, Ranchi) rivers all originate from the crystalline Chota Nagpur Plateau in Jharkhand.

Kanwar Lake (Kabartal Wetland), Asia's largest freshwater oxbow lake located in Begusarai district, was designated as Bihar's first Ramsar Site in 2020.

• Sacred Hills of Gaya: Gaya is surrounded by small pre-Cambrian crystalline hills including Brahmayoni (where Lord Buddha delivered the Fire Sermon, Adittapariyaya Sutta), Pretshila, and Ramshila, vital for Pitrapaksha pindadan rituals.

Among Bihar's agro-climatic zones, Zone-I (Northern West Alluvial Plain) comprises the highest number of districts (13 districts), compared to 8 in Northern East (Zone-II), 6 in Southern East (Zone-IIIA), and 11 in Southern West (Zone-IIIB).

• Panchayati Raj 11th Schedule: The Eleventh Schedule (Article 243G) contains 29 functional items for Panchayats, including Libraries (item 20), Fuel and fodder (item 12), and Technical training & vocational education (item 18). 'Rural Sports' is not explicitly listed.

In pursuance of Article 113 of the Indian Constitution, 109 Demands for Grants (103 for civil expenditure and 6 for defence expenditure, as per standard Indian Polity reference used by BPSC) are presented before Parliament as part of the Union Budget.

Option (A) is correct. The National Extension Service (NES) was inaugurated in India on 2 October 1953, following the Community Development Programme.

• Article 171 Composition: Under Article 171 of the Constitution, MLCs are elected by MLAs, Local Authorities, Graduates, and Teachers, or nominated by the Governor. There is no electorate or reservation for industrialists.

The 'split system' in Indian public administration refers to the organizational separation between policy formulation (handled by the Secretariat/Ministries) and policy implementation (handled by executive directorates and field agencies).

The Committee on Subordinate Legislation (established in 1953) examines and reports to the House whether the powers to make regulations, rules, sub-rules, and bye-laws delegated by Parliament to the Executive are being properly exercised.

Article 300 of the Constitution of India deals with suits and legal proceedings by or against the Government of India or the Government of a State, whereas government contracts are governed by Article 299.

As enshrined in Article 21 of the Indian Constitution, the judicial process in India is fundamentally based on 'the procedure established by law' (adopted from the Japanese Constitution).

• Anti-Corruption Institutions: Although Odisha passed the first Lokayukta Act in 1970, Maharashtra was the first state in India to formally establish and make functional the institution of the Lokayukta in 1971.

Justice Adarsh Sein Anand (A. S. Anand) served as the 29th Chief Justice of India from 10 October 1998 to 31 October 2001.

• 15th Finance Commission Composition: Chaired by N.K. Singh, the members were Shaktikanta Das (later replaced by Ajay Narayan Jha), Dr. Anoop Singh, Dr. Ashok Lahiri, and Dr. Ramesh Chand. Dr. Sudipto Mundle was not a member.

• Financial Sector Reforms: In the Union Budget 2021-22, Finance Minister Nirmala Sitharaman announced an increase in the permissible FDI limit in insurance companies from 49% to 74% under the automatic route.

According to the Union Budget 2021–22, India's fiscal deficit for the financial year 2021–22 was estimated at 6.8% of GDP.

Correct Answer: Option (B) — growth in per capita real income from year to year • Economic Analysis: Real per capita income (national income adjusted for both population growth and inflation) reflects the actual purchasing power, standard of living, and economic welfare of the average citizen over time, making sustained year-to-year growth in per capita real income the universally accepted index of economic development.

Phase-II of the Swachh Bharat Mission (Grameen) was approved for implementation during the five-year period from 2020–21 to 2024–25, focusing on ODF Plus (sustaining Open Defecation Free status and solid/liquid waste management).

• National Development Council: The NDC was composed of the Prime Minister (Chairman), Union Cabinet Ministers, Chief Ministers of all States, Administrators of UTs, and Members of the Planning Commission / NITI Aayog. The Chairman of the Finance Commission is not a member.

The Sarkaria Commission (1983) examined Centre-State Relations (3); the C. Rangarajan Committee (2012) reviewed poverty measurement methodology (1); the Deepak Parekh Committee examined Infrastructure Financing (2); and the Narasimham Committee (1991, 1998) recommended Banking Sector Reforms (4).

In ascending order (from lowest to highest annual rice production), the sequence of these four states is Andhra Pradesh, followed by Punjab, Uttar Pradesh, and West Bengal (the largest rice-producing state in India).

Official Key: Option (A) is the verified correct answer for BPSC Prelims 2022.

The Bare Necessities Index (BNI), introduced in the Economic Survey 2020–21 using NSO data, aggregates 26 indicators across five dimensions—water, sanitation, housing, micro-environment, and other facilities—to measure household access to basic necessities across rural, urban, and all-India levels.

To promote farm mechanization and support small and marginal farmers in Bihar, the state government proposed establishing 'Krishi Yantra Banks' (Custom Hiring Centres / Farm Machinery Banks) at the block and panchayat levels.

According to the Subnational Human Development Index (UNDP / Global Data Lab) for the year 2019, the Human Development Index (HDI) value of Bihar stood at 0.574.

In the Bihar State Budget 2021–22, the fiscal deficit was estimated at ₹ 22,511 crores (specifically ₹ 22,510.78 crore, or 2.97% of GSDP).

Under the Digital Bihar Programme announced in the Bihar Budget 2021–22, all students of Class VI and above are set to receive computer education and training from 2021–22 onwards.

The 15th Finance Commission (2021–26) recommended a 41% vertical devolution of central taxes to states and assigned Bihar a 10.058% horizontal share among states, which equals 4.12% (10.058% of 41%) of the total divisible pool of central taxes.

• Revolutionary Movement: The Ghadar Party (originally the Pacific Coast Hindustan Association) was founded on 15 July 1913 in Astoria/San Francisco, USA, by Lala Har Dayal, Sohan Singh Bhakna, and Pandit Kanshi Ram.

• Social & Nationalist Societies: Gopal Krishna Gokhale founded the 'Servants of India Society' in Pune on 12 June 1905 to train national missionaries for the service of India and promote education and social reform.

• Core Theme: It documented the economic drain, systemic neglect of education and healthcare, and imperial exploitation under British rule.

Dr. B.R. Ambedkar and Sir Tej Bahadur Sapru were the prominent Indian leaders who participated in all three Round Table Conferences held in London in 1930, 1931, and 1932.

The Indian Association (Indian National Association) was founded in Calcutta on 26 July 1876 by Surendranath Banerjee along with Ananda Mohan Bose.

• Freedom Struggle: The title 'Netaji' was conferred on Subhas Chandra Bose by the Indian soldiers of the Free India Legion in Germany in 1942.

• Revolutionary Movement: Surya Sen ('Masterda') spearheaded the historic raid on British police armouries in Chittagong on April 18, 1930.

Bankim Chandra Chatterjee's Bengali novel 'Anandamath' (published in 1882), which contains India's national song 'Vande Mataram', is set against the backdrop of the Sannyasi Rebellion and the Bengal Famine of 1770.

• Chronology:
• Arrival of Cripps Mission: March 1942
• Quit India Resolution: August 1942
• Arrival of Lord Wavell as Governor General: October 1943
• Arrival of Cabinet Mission: March 1946.

. Jawaharlal Nehru presided over the historic Lahore Session of the Indian National Congress in December 1929, where the iconic resolution for complete independence ('Purna Swaraj') was adopted and the tricolour was unfurled on the banks of the Ravi.

Ram Manohar Lohia (born in 1910) was not associated with the Champaran Satyagraha of 1917, whereas Raj Kumar Shukla, Rajendra Prasad, J. B. Kripalani, Mahadev Desai, and Brajkishore Prasad actively participated alongside Mahatma Gandhi.

Babu Kunwar Singh, the chief organizer of the Revolt of 1857 in Bihar, was the zamindar of the royal Ujjainiya Rajput estate of Jagdishpur (in present-day Bhojpur district, Bihar).

• Quit India Movement: On Diwali night, 9 November 1942, Jayaprakash Narayan along with five associates (Ramanand Mishra, Yogendra Shukla, Suraj Narayan Singh, Gulab Chand Gupta, Shaligram Singh) made a daring escape from Hazaribagh Central Jail and founded Azad Dasta in Nepal.

. Deshbandhu Chittaranjan Das presided over the 1922 Gaya Session of the Indian National Congress. When his council-entry proposal was defeated by no-changers, he resigned from the Congress presidency and subsequently formed the Swaraj Party alongside Motilal Nehru.

• Interim Government 1946: Dr. Rajendra Prasad was appointed Member in charge of Food and Agriculture in the Interim Government sworn in under Jawaharlal Nehru on 2 September 1946.

The least common multiple (LCM) of 4, 5, and 6 is 60. The multiples of 60 between 100 and 500 are 120, 180, 240, 300, 360, 420, and 480, giving a total of 7 numbers.

The LCM of 4, 5, and 6 is 60. The numbers between 200 and 600 that are divisible by 60 are 240, 300, 360, 420, 480, and 540. Therefore, there are exactly 6 such numbers.

.

• 3^(4n) - 4^(3n) = (3^4)^n - (4^3)^n = 81^n - 64^n.
• For any positive integer n, (a^n - b^n) is always divisible by (a - b).
• Therefore, 81^n - 64^n is divisible by (81 - 64) = 17.

Let the numbers be x and y. Given x + y = 1000 and x² - y² = 256000, we have x - y = 256000 / 1000 = 256; solving the two equations yields x = (1000 + 256)/2 = 628 and y = (1000 - 256)/2 = 372.

Let log_√2 (32) = x. In exponential form, (√2)^x = 32. Since √2 = 2^(1/2) and 32 = 2^5, we have 2^(x/2) = 2^5. Equating exponents gives x/2 = 5, which means x = 10.

The cost price of 45 lemons is ₹ 40 / 0.80 = ₹ 50, so to gain 20% the selling price of 45 lemons must be ₹ 50 × 1.20 = ₹ 60. Therefore, for ₹ 24, he should sell (45 / 60) × 24 = 18 lemons.

Correct Answer: Option (B) — 7 1/3 seconds - Speed of train = 58 km/h - Speed of person in same direction = 4 km/h - Relative speed = 58 - 4 = 54 km/h = 54 × (5/18) = 15 m/s - Time to cross = Length of train / Relative speed = 110 / 15 = 22/3 seconds = 7 1/3 seconds.

Each side of the rhombus is 52 / 4 = 13 m, and half of the shorter diagonal is 10 / 2 = 5 m. Since the diagonals bisect at right angles, half of the longer diagonal is √(13² - 5²) = 12 m, so the longer diagonal is 2 × 12 = 24 m.

A's speed is 8 × (5/18) = 20/9 m/s, so A takes 100 / (20/9) = 45 seconds to finish 100 m. B covers 100 - 4 = 96 m in 45 + 15 = 60 seconds, so B's speed is (96 / 60) × (18 / 5) = 5.76 kmph.

From 8 a.m. to 1 p.m. the next day is 29 hours on the faulty clock, and 24 hours 10 minutes (145/6 hours) of this clock equals 24 hours of true time. Thus, true time elapsed is 29 × 24 × (6/145) = 28.8 hours = 28 hours 48 minutes, which is 48 minutes past 12 noon.

Let x = 2 - 1/(2 - 1/(2 - ... ∞)), which gives the equation x = 2 - 1/x. Multiplying by x yields x² - 2x + 1 = 0 or (x - 1)² = 0, so x = 1.