Infrared (IR) radiation is widely used in physical therapy (heat lamps) to treat muscle aches and joint tension because its thermal effect penetrates tissues and improves local blood circulation.

• Electric Circuits: For two parallel resistors: (1) / (R_p) = (1) / (R₁) + (1) / (R₂) \implies (1) / (R₂) = (1) / (1.403) - (1) / (2.0) = 0.71276 - 0.5 = 0.21276 \implies R₂ = (1) / (0.21276) \approx 4.70 k\Omega.

• Solid State Physics: Semiconductors (like silicon and germanium) have a negative temperature coefficient of resistance. Heating supplies thermal energy to break covalent bonds and generate more free electrons and holes, increasing conductivity and causing resistance to decrease.

Correct Answer: Option (A) — Universal constant • Physical Chemistry: The Faraday constant (F = N_A * e approx. 96,485 C/mol) represents the electric charge per mole of electrons and is a universal physical constant independent of the amount or volume of electrolyte.

• Astrophysics Unit: A light-year is a unit of astronomical distance defined as the distance that light travels in a vacuum in one Julian year, approximately equal to 9.46 x 10^12 kilometers (9.46 x 10^15 meters).

When light passes from one medium to another, its speed and wavelength change according to the refractive index of the medium, but its frequency remains constant as it depends solely on the source.

Electromagnetic waves travel in vacuum at the speed of light, which is approximately 3 × 10⁸ m s⁻¹.

Correct Answer: Option (B) — Neil Armstrong • Historical Context: On July 20, 1969, American astronaut Neil Armstrong became the first human to step onto the surface of the Moon during NASA's Apollo 11 mission, famously declaring 'That's one small step for [a] man, one giant leap for mankind.' • Apollo 11 Crew: Buzz Aldrin joined him shortly after as the second man on the moon, while Michael Collins piloted the command module in lunar orbit. Alexei Leonov was a Soviet cosmonaut who conducted the first spacewalk in 1965.

• Nuclear Physics: In plutonium-242 (242_94 Pu), the mass number A = 242 and the atomic number Z = 94. The number of neutrons N = A - Z = 242 - 94 = 148.

Viscosity measures a fluid's internal resistance to flow; among water, air, blood, and honey, honey is the thickest fluid and has the highest viscosity due to strong intermolecular hydrogen bonding.

Correct Answer: Option (C) — Vitamin C • Nutritional Composition: Milk is rich in calcium, protein, riboflavin, and vitamin B12, but is virtually devoid of Vitamin C (ascorbic acid) and iron.

• Analytical Chemistry: Breathalyzer tests utilize potassium dichromate (K₂Cr₂O₇) in sulfuric acid. Ethanol in breath oxidizes to acetic acid while orange chromium (VI) is reduced to green chromium (III), signaling alcohol intoxication.

• Biochemical Fermentation: In alcoholic fermentation, glucose is converted into ethanol and carbon dioxide (C₆H₁₂O₆ \xrightarrow{zymase} 2C₂H₅OH + 2CO₂) catalyzed by the enzyme zymase naturally found in yeast.

When carbon dioxide (CO₂) is passed through limewater (calcium hydroxide, Ca(OH)₂), it reacts to form an insoluble white precipitate of calcium carbonate (CaCO₃), turning the solution milky.

• Combustion Chemistry: Incomplete combustion of hydrocarbon fuels (petrol and diesel) due to insufficient oxygen produces carbon monoxide (CO), a highly poisonous, colorless, and odorless gas that binds avidly to hemoglobin.

Since pH = −log₁₀[H⁺], an increase in pH from 3 ([H⁺] = 10⁻³ M) to 6 ([H⁺] = 10⁻⁶ M) means the H⁺ ion concentration decreases by a factor of 10³ = 1000 times.

• Separation Principle: Naphthalene is a sublimable substance that transitions directly from a solid to a gaseous phase upon gentle heating without passing through an intermediate liquid phase.
• Application: When a mixture of sand and naphthalene is heated in an evaporating dish covered with an inverted funnel, naphthalene sublimes and deposits on the cooler inner walls of the funnel, leaving non-sublimable sand behind in the dish.

A benzene molecule (C₆H₆) has a hexagonal ring structure containing 6 C–C sigma bonds, 6 C–H sigma bonds (12 sigma bonds in total), and 3 alternating C=C pi bonds.

• Chemical Formula: Urea (carbamide) has the chemical formula CO(NH2)2. Its molecular structure contains four elements: Carbon (C), Hydrogen (H), Nitrogen (N), and Oxygen (O).

Lead (Pb) is one of the poorest metallic conductors of heat (thermal conductivity ~35 W/m·K compared to ~401 W/m·K for copper and ~116 W/m·K for zinc), as explicitly highlighted in NCERT Science classification of metallic heat conductors.

• Physiology & Hematology: Vitamin K (phylloquinone/menaquinone) is the fat-soluble vitamin essential for the hepatic post-translational synthesis of clotting factors II (prothrombin), VII, IX, and X, enabling normal blood coagulation.

• Endocrinology: Estrogen (along with progesterone) is the primary female sex hormone synthesized by the ovaries, regulating the development and maintenance of female secondary sexual characteristics and the reproductive menstrual cycle.

Arvid Carlsson was awarded the Nobel Prize in Physiology or Medicine in 2000 for discovering that dopamine is a key neurotransmitter in the brain and that dopamine deficiency leads to Parkinson's disease, enabling L-Dopa therapy.

• Endocrinology: Iodine is the essential trace element required for the synthesis of thyroid hormones (thyroxine/T4 and triiodothyronine/T3). Deficiency of iodine leads to goitre and hypothyroidism.

• Taste Map Physiology: In the traditional regional sensitivity map of the human tongue, the posterior (back/base) area of the tongue containing circumvallate papillae is most sensitive to bitter tastes, providing an evolutionary protective mechanism against ingesting toxic substances.

• Plant Morphology: Ginger is an underground modified stem (rhizome) characterized definitively by the presence of nodes, internodes, axillary buds, and scale leaves, which roots lack.

Correct Answer: Option (A) — fructose • Relative Sweetness Scale: Fructose (fruit sugar, a monosaccharide) is the sweetest of all naturally occurring carbohydrates, rating roughly 170 on the sweetness scale compared to sucrose (table sugar) at 100, glucose at 74, and maltose at 32.

• Botany: Apple is a false/accessory fruit (pome) because its fleshy edible part develops from the floral receptacle/thalamus rather than solely from the ovary wall.

• Nutritional Biochemistry: Legumes and pulses (peas, beans, lentils, chickpeas, soybeans) are high in dietary protein (20% to 40% dry weight) because of symbiotic nitrogen-fixing Rhizobium bacteria in their root nodules, supplying essential amino acids.

• Economic Botany: Clove is the dried unopened aromatic flower bud of the evergreen tree Syzygium aromaticum (family Myrtaceae).

• BCCI Appointments: Former India left-arm spinner Neetu David was appointed Chairperson of the BCCI All-India Women's Selection Committee in September 2020.

Japanese tennis player Naomi Osaka won the 2020 US Open Women's Singles title by defeating Victoria Azarenka of Belarus in the final.

Ethiopian long-distance runner Shura Kitata won the first position in the Men's elite race at the 2020 London Marathon held on 4 October 2020, clocking a time of 2:05:41.

Indian middle-order batsman Suresh Raina announced his retirement from all formats of international cricket on 15 August 2020, shortly after M. S. Dhoni's retirement announcement.

• Cultural Institutions: Veteran actor and former Member of Parliament Paresh Rawal was appointed as the Chairperson of the National School of Drama (NSD) by the President of India in September 2020.

Correct Answer: Option (B) — Dr. G. Satheesh Reddy (Served as Chairman DRDO; succeeded by Dr. Samir V. Kamat) • Defence Administration: Distinguished missile scientist Dr. G. Satheesh Reddy served as the Chairman of DRDO and Secretary, DDR&D.

Dr. Bushra Ateeq (IIT Kanpur) and Dr. Ritesh Agarwal (PGIMER Chandigarh) were selected for the Shanti Swarup Bhatnagar Prize for Science and Technology 2020 in the field of Medical Sciences.

The 2020 Nobel Peace Prize was awarded to the United Nations World Food Programme (WFP) for its efforts to combat hunger and to prevent the use of hunger as a weapon of war and conflict.

Bollywood actor Ayushmann Khurrana was the only Indian film actor featured in Time Magazine's annual list of the 100 Most Influential People in the World in 2020.

In 2020, the Ministry of Environment, Forest and Climate Change recommended eight Indian beaches (Shivrajpur, Ghoghla, Kasarkod, Padubidri, Kappad, Rushikonda, Golden Beach, and Radhanagar), all of which received the international Blue Flag certification.

Ram Vilas Paswan began his active political career with the Samyukta Socialist Party (SSP) and was first elected to the Bihar Legislative Assembly in 1969 from the Alauli constituency.

The Election Commission of India issued the official Press Note announcing the three-phase schedule for the Bihar Legislative Assembly General Elections on 25th September, 2020.

Prime Minister Narendra Modi launched the 'Ghar Tak Fibre' scheme in Bihar on 21st September, 2020 via video conference to connect all 45,945 villages of the state with high-speed optical fibre internet.

• Bihar Political Leadership: Veteran socialist leader and architect of MGNREGA Late Dr. Raghuvansh Prasad Singh was elected to the Lok Sabha for the first time in 1996 to the Eleventh Lok Sabha from Vaishali constituency.

• International Geopolitics: The Quadrilateral Security Dialogue (Quad) comprises four democratic nations: India, the United States, Japan, and Australia. China is not a member.

Union Minister of State (Independent Charge) for Culture and Tourism Prahlad Singh Patel represented India at the 5th BRICS Culture Ministers' Meeting held virtually under the Russian presidency in September 2020.

The 36th ASEAN Summit was held virtually in Hanoi, Vietnam on 26 June 2020 under the theme 'Cohesive and Responsive ASEAN'.

Singapore topped the World Bank's Human Capital Index (HCI) 2020 with a score of 0.88, followed by Hong Kong and Japan, while India was ranked 116th out of 174 countries.

• Political Context: In October 2020, Donald Trump's campaign launched 'Operation MAGA' (Make America Great Again) featuring surrogate rallies across key battleground states following Trump's hospitalization and recovery from COVID-19.

The United Arab Emirates (UAE) became the first country in the Arab world to commission a nuclear power plant when its Barakah Nuclear Energy Plant in Abu Dhabi achieved criticality in August 2020.

• Middle East History: Egypt became the first Arab state to sign a peace treaty with Israel following the 1978 Camp David Accords, signed by President Anwar Sadat and Prime Minister Menachem Begin in Washington in March 1979.

India assumed the Chairmanship of the Governing Body of the International Labour Organization (ILO) in October 2020 after a gap of 35 years, with Labour and Employment Secretary Apurva Chandra elected as Chairperson.

Launched by Indian Railways (Railway Protection Force) in September 2020, 'Operation My Saheli' (Meri Saheli) aims to provide end-to-end security to women passengers travelling by trains throughout their journey.

Correct Answer: Option (A) — Prime Minister Narendra Modi • Fit India Movement: Prime Minister Narendra Modi coined and gave the nationwide mantra 'Fitness Ki Dose, Aadha Ghanta Roz' during an interactive online Fit India Dialogue in September 2020 marking the movement's first anniversary.

• Commemorative Coin: On October 12, 2020, Prime Minister Narendra Modi released a special commemorative coin of Rs 100 denomination to mark the birth centenary of Rajmata Vijaya Raje Scindia.

'Chi Lupo', a short documentary on the traditional practice of honey hunting among the Sherdukpen tribe directed by Kezang D. Thongdok of Arunachal Pradesh, won the Best Documentary award at the 10th Dada Saheb Phalke Film Festival 2020.

HDFC Bank launched the 'e-Kisaan Dhan' mobile application in 2020 to provide farmers across India with integrated access to banking services and agricultural information.

• Civil Aviation Health Protocols: India's first on-site airport COVID-19 testing facility was launched at Indira Gandhi International (IGI) Airport, Terminal 3, in Delhi in September 2020 for arriving international passengers.

• Defense News: The first batch of five Rafale multi-role combat aircraft was formally inducted into No. 17 Squadron 'Golden Arrows' of the Indian Air Force at Air Force Station Ambala on 10 September 2020.

Rudram (Rudram-1), developed by DRDO and successfully test-fired from a Sukhoi-30 MKI fighter jet in October 2020, is India's first indigenous anti-radiation missile designed to neutralize enemy radar and communication installations.

• Harappan Agriculture: Excavations at Kalibangan (Hanumangarh district, Rajasthan) by B.B. Lal and B.K. Thapar revealed the world's earliest known ploughed agricultural field with grid furrows dating to the Early Harappan phase.

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In Jainism, the path to liberation (Moksha) comprises the 'Three Jewels' (Triratna): Samyak Darshana (Right Faith), Samyak Jnana (Right Knowledge), and Samyak Charitra (Right Conduct). In contrast, the Triratna in Buddhism are the Buddha, the Dhamma, and the Sangha.

• Fourth Buddhist Council: Convened at Kundalavana in Kashmir during the 1st century CE under the royal patronage of Kushan Emperor Kanishka.
• Leadership: Presided over by Vasumitra, with the celebrated poet Ashvaghosha acting as vice-president.
• Major Schism: The council formally codified the division of Buddhism into two major schools: Mahayana and Hinayana.

The Vaisheshika school of Indian philosophy, founded by Maharishi Kanada, propounded the theory of atomism (Paramanuvada), positing that all physical objects are composed of eternal, indivisible atoms (paramanu).

Sultan Ghiyasuddin Balban (1266–1287 AD) of the Slave Dynasty adopted the stern policy of 'blood and iron' (Lauh aur Rakt) to crush internal rebellions, eliminate Mewati plunderers, and restore the authority of the Sultanate.

• Chola Administration: The Chola Empire was renowned for its highly organized, autonomous village administration and local self-government (Ur and Sabha/Mahasabha), detailed in the Uttaramerur inscriptions of Parantaka I.

• Mughal Architecture: Pietra dura (Parchin kari) is the decorative inlay technique of cutting and fitting highly polished colored semi-precious stones (such as lapis lazuli, onyx, jasper) into marble to create intricate floral and geometric patterns, famously seen in the Taj Mahal.

• Mughal Imperial Workshops: Emperor Akbar established organized imperial workshops ('Tasvir Khana' / Karkhanas) for painting under the supervision of master artists Mir Sayyid Ali and Abd al-Samad.

Robert Clive introduced the Dual System of Government (Dyarchy) in Bengal in 1765 after the Treaty of Allahabad, under which the East India Company controlled revenue (Diwani) while administrative responsibility (Nizamat) remained with the Nawab.

Swami Vivekananda represented India and Hinduism at the World's Parliament of Religions held in Chicago in September 1893, where his historic address began with 'Sisters and Brothers of America'.

Chittaranjan Das (as President) and Motilal Nehru (as Secretary) founded the Congress-Khilafat Swarajya Party (Swaraj Party) in January 1923 to contest legislative council elections from within the British constitutional framework.

• Literary Contribution: Dinabandhu Mitra authored the Bengali drama 'Neel Darpan' (The Mirror of Indigo) in 1858–1859, highlighting the severe plight and exploitation of indigo ryots in Bengal under European planters.

• Carnatic Wars: In the decisive Battle of Wandiwash on 22 January 1760, British forces led by Sir Eyre Coote defeated the French army under Count de Lally, ending French imperial ambitions in India.

• Constitutional History: The Indian Councils Act 1909 introduced a system of communal representation and separate electorates for Muslims, earning Lord Minto the title of 'Father of Communal Electorate'.

The Kol Mutiny of 1831–32 under the leadership of Buddho Bhagat broke out in the Chota Nagpur and Singhbhum regions against British land revenue policies and the transfer of tribal lands to outsiders (dikus).

Babu Veer Kunwar Singh, the zamindar of Jagdishpur (in present-day Bhojpur district), spearheaded the Revolt of 1857 in Bihar and fought multiple victorious battles against British forces.

Correct Option: Option (A) — Rajendra Prasad.

This question tests core factual and analytical concepts from Bihar Special aligned with the official BPSC Prelims syllabus benchmarks.

Rajgriha (also known as Girivraja), surrounded by five hills, was the earliest capital of the ancient Magadha Mahajanapada before Udayin shifted the capital to Pataliputra.

. Swami Sahajanand Saraswati was the pioneer of the peasant movement in Bihar and the founder of the Bihar Provincial Kisan Sabha (1929) and the All India Kisan Sabha (1936).

The Champaran Satyagraha of 1917 in Bihar was Mahatma Gandhi's first Satyagraha in India where he used Civil Disobedience by refusing to obey the British District Magistrate's order to leave Champaran.

Correct Answer: Option (B) — Honshu • Physical Geography of Japan: Honshu is the largest and most populous main island of Japan (covering approx. 227,960 km²), followed by Hokkaido, Kyushu, and Shikoku.

• World Geography: Greenland, the world's largest island, is an autonomous territory within the Kingdom of Denmark.

According to Ministry of External Affairs (MEA) and UN International Migrant Stock data as of December 2018, the United Arab Emirates (UAE) hosted the largest Non-Resident Indian (NRI) population in the world at approximately 3.42 million.

China was the world's largest producer of gold in 2019 with an annual mine output of approximately 380–404 tonnes, followed by Russia and Australia.

Africa has the highest number of sovereign countries of any continent with 54 member states recognized by the United Nations, followed by Asia (48) and Europe (44).

According to the 2011 Census of India, Mizoram has the highest percentage of Scheduled Tribe (ST) population among all Indian states at 94.4% of its total population.

Chikmagalur, Coorg (Kodagu), and Baba Budangiri are famous coffee-growing regions in Karnataka. Pulneys (Palani Hills) is located in Tamil Nadu.

Kutch district in Gujarat, with an area of 45,674 sq km, is the largest district in India by geographical area (followed by Leh in Ladakh with 45,110 sq km).

• Wildlife Database: Among Indian States, Maharashtra has the highest number of Wildlife Sanctuaries (approx. 49 WLS). Among all States and Union Territories, Andaman & Nicobar Islands has the highest overall (96 WLS).

The Sone River originates near Amarkantak in the peninsular plateau and flows north-northeastwards through Bihar to join the Ganga near Patna, whereas Bagmati, Kamla, and Kosi originate in the Himalayas and flow southwards.

The 9.02-km-long Atal Tunnel, built under the Rohtang Pass in Himachal Pradesh to connect Manali with the Lahaul-Spiti valley, cuts across the Eastern Pir Panjal range of the Himalayas.

. Vadhavan Port near Dahanu in Palghar district of Maharashtra is sanctioned as India's 13th major port, developed on a landlord model as an all-weather, deep-draft port to handle mega container vessels.

• Renewable Energy: Rajasthan ranks first in India in installed solar power capacity with over 20,000 MW, home to the world's largest Bhadla Solar Park.

Limestone reserves in Bihar are predominantly found in the Vindhyan rock formations of Kaimur (Bhabua) and Rohtas districts, whereas mica is found in Nawada, quartzite in Munger/Jamui, and lead-zinc in Banka/Rohtas.

• Industrial Locations Bihar: Bharat Wagon and Engineering Company is situated at Mokama (Patna) and Muzaffarpur, not Bhagalpur (which is known for silk textiles). Oil refinery at Barauni, cement at Banjari, and fertilizer at Barauni are correctly matched.

Piedmont Swamp Soil is found exclusively in the northwestern strip of the West Champaran district of Bihar along the foothills of the Someshwar Himalayan range.

Out of the 9 administrative divisions of Bihar, the Ganga River flows through 7 divisions (Saran, Tirhut, Patna, Darbhanga, Munger, Purnea, and Bhagalpur) and does not flow through the Kosi and Magadh divisions.

In Bihar, the Munda tribe is primarily concentrated in Rohtas, Buxar, and Katihar districts rather than Jamui, whereas Santhals live in Banka, Oraons in Supaul/Purnea, and Kharwars in Bhagalpur/Rohtas.

According to the India State of Forest Report (ISFR) 2019, the total forest cover of Bihar was 7,305.99 sq km, which accounted for 7.76% of the state's total geographical area of 94,163 sq km.

Valmiki National Park, which is the only National Park and Tiger Reserve in Bihar, is located in the West Champaran district along the India–Nepal border.

Tata Projects Limited won the contract to construct India's new Parliament building in September 2020 under the Central Vista redevelopment project with a winning bid of ₹861.90 crore.

. Article 324(1) of the Indian Constitution vests the superintendence, direction, and control of the preparation of the electoral rolls for, and the conduct of, all elections to Parliament and to the Legislature of every State in the Election Commission of India.

• National Commission for Women: Rekha Sharma served as the Chairperson of the National Commission for Women (NCW) from August 2018 until completing her tenure in August 2024.

According to A.V. Dicey, 'Rule of Law' embodies three core principles: absence of arbitrary power, equality before the law (equal subjection of all classes to the ordinary law of the land administered by ordinary law courts), and the constitution being the consequence of the rights of individuals. Thus, no single simplistic formula captures it entirely.

Article 243(G) of the Indian Constitution empowers the Legislature of a State to endow Panchayats with powers and authority, and specifies matters listed in the Eleventh Schedule which contains 29 functional subjects.

• Parliamentary Enactment: The Citizenship (Amendment) Bill, 2019 was passed by the Lok Sabha on 9 December 2019 and by the Rajya Sabha on 11 December 2019, receiving presidential assent on 12 December 2019.

• Panchayati Raj History: The constitutional framework for Panchayati Raj was first introduced as the 64th Constitutional Amendment Bill by Prime Minister Rajiv Gandhi in July 1989 (passed by Lok Sabha but defeated in Rajya Sabha), later re-introduced and enacted as the 73rd Amendment Act 1992.

The Dutch East India Company (VOC) established its trading factory at Patna in 1632 (in the northern block of the present Patna College building) primarily for trading in saltpetre, opium, and cotton textiles.

• Democratic Decentralization: Democratic decentralization aims to empower local communities, enhance popular participation, and grant local autonomy. Instilling 'non-confidence' is completely antithetical to decentralization.

The Eleventh Five-Year Plan (2007-2012) moved away from setting specific crop-wise physical production targets and instead focused on holistic agricultural sector growth (targeting 4% growth rate in agriculture and allied sectors).

The core objectives of food management in India are procurement of food grains from farmers at remunerative prices (MSP), distribution of food grains to vulnerable consumers at affordable prices (PDS), and maintenance of buffer stocks for price stability and food security; exporting food grains is not one of its objectives.

• Public Finance: Revenue deficit is the excess of revenue expenditure over revenue receipts (RD = RE - RR). It signifies government borrowing to meet routine operational/consumption expenses that yield no capital asset creation.

According to Ministry of Commerce and Industry data, the United States was India's largest trading partner in FY 2019–20 with bilateral trade of USD 88.75 billion, surpassing China.

• Infrastructure Projects: Bharatmala Pariyojana is an umbrella highway and road development programme launched by the Ministry of Road Transport and Highways to develop economic corridors, border roads, and expressways.

• Macroeconomic Indicators: The Index of Industrial Production (IIP) measures the growth of industrial production across mining, manufacturing, and electricity, compiled and released monthly by the National Statistical Office (formerly Central Statistics Office - CSO), MoSPI.

In the World Bank's Ease of Doing Business Report 2020, India climbed 14 places from the 77th position in the previous year to the 63rd position among 190 countries.

In the Union Budget 2020-21, Finance Minister Nirmala Sitharaman set a target of ₹15 lakh crore for institutional agricultural credit flow for the financial year 2020-21.

Correct Answer: Option (D) — to remove farmers’ dependence on diesel and kerosene and to link pump sets to solar energy • Renewable Energy Scheme: Pradhan Mantri Kisan Urja Suraksha evam Utthaan Mahabhiyan (PM-KUSUM) aims to de-dieselise the farm sector by providing financial support to install standalone solar agricultural pumps and solarise grid-connected pumps.

• Global Banking Rankings: State Bank of India (SBI) is India's largest commercial bank and the sole Indian public sector bank consistently ranked in the S&P Global Market Intelligence Top 100 Global Banks by total assets.

The NIRVIK (Niryat Rin Vikas Yojana) scheme was announced in the Union Budget 2020-21 to benefit the export sector by providing up to 90% insurance coverage on principal and interest for small exporters.

Implemented on 1st April 2019 across Bihar, the Comprehensive Financial Management System (CFMS) digitizes budgeting, treasury operations, and accounting to make all state financial activities online and paperless.

On 2nd January 2020, Prime Minister Narendra Modi conferred the Krishi Karman Award on Bihar in recognition of the state's excellence in the production and productivity of maize and wheat.

Launched on August 5, 2018, by the Government of Bihar and implemented by JEEViKA, the 'Satat Jivikoparjan Yojana' aims to provide sustainable income-generating assets, capacity building, and financial inclusion to ultra-poor households, particularly those affected by liquor prohibition and marginalized SC/ST families.

Bihar Government's original 'Saat Nishchay' (Part-1) includes: 1. Aarthik Hal, Yuvaon ko Bal, 2. Aarakshit Rozgar, Mahilaon ka Adhikar, 3. Har Ghar Bijli Lagatar, 4. Har Ghar Nal ka Jal, 5. Ghar Tak Pakki Nali-Galiyan, 6. Shauchalay Nirman, Ghar ka Samman, and 7. Awsar Badhe, Aage Padhein. Child Welfare is not a separate component.

According to the Bihar Economic Survey 2019-20, Bihar's per capita Net State Domestic Product at constant (2011-12) prices in 2018-19 was ₹30,617, which was approximately 33.1 percent of the national average of ₹92,565.

After passing the matriculation examination from Rajkot in 1887, Mahatma Gandhi enrolled at Samaldas Arts College in Bhavnagar in January 1888, where he studied for one term before proceeding to London for legal studies.

All the mentioned leaders led the Revolt of 1857 from their respective centers: Nana Saheb from Kanpur, Begum Hazrat Mahal from Lucknow, Maulavi Ahmadullah from Faizabad, and Begum Zeenat Mahal from Delhi.

Jawaharlal Nehru criticized the Government of India Act of 1935 by describing it as 'a machine with strong brakes, but no engine' due to extensive discretionary and veto powers given to the Governor-General and Governors, which crippled true provincial autonomy.

Mahatma Gandhi began the Dandi March from Sabarmati Ashram on 12 March 1930 with 78 followers and reached Dandi on 5 April 1930, breaking the salt law on 6 April 1930. The march covered 241 miles over exactly 24 days.

The poem 'Sarfaroshi ki Tamanna' was composed in 1921 by Bismil Azimabadi (a freedom fighter and poet from Patna, Bihar). It was later popularized and immortalized as a revolutionary battle cry by Ram Prasad Bismil.

The Swadeshi Movement (and Boycott movement) was formally launched on 7 August 1905 at the Calcutta Town Hall in response to Lord Curzon's partition of Bengal, promoting indigenous industry and boycotting British goods.

Bhulabhai Desai was the chief counsel who led the Indian National Army (INA) Defense Committee in the Red Fort trials of 1945–46 defending Prem Kumar Sahgal, Gurbaksh Singh Dhillon, and Shah Nawaz Khan, assisted by Jawaharlal Nehru, Tej Bahadur Sapru, and Asaf Ali.

On 22 August 1907, Madam Bhikaiji Cama unfurled the early Indian National Flag (the Berlin Committee flag) at the International Socialist Conference held in Stuttgart, Germany, appealing for international support for India's freedom.

Chittaranjan Das was lovingly honoured with the title 'Deshbandhu' (Friend of the Country). Vinoba Bhave was the first (not second) individual satyagrahi; Rash Behari Ghosh presided over the 1907 Surat Congress; Barindra Ghosh and Bhupendranath Datta founded Yugantar.

Following the historic Purna Swaraj resolution passed at the December 1929 Lahore Session under Jawaharlal Nehru's presidency, the Indian National Congress declared 26 January 1930 as 'Purna Swaraj Day' (Complete Independence Day).

Option (B) is correct. Bihar was established as a separate province from the Bengal Presidency on 22 March 1912 (celebrated annually as Bihar Diwas).

Under the Tinkathia system in Champaran, tenant farmers were legally bound by European planters to cultivate indigo on 3 kathas out of every 1 bigha (20 kathas) of their landholding, which equals 3/20 of the land.

• Bihar Political History: Dr. Sri Krishna Singh ('Bihar Kesari') was the first Chief Minister of Bihar, serving uninterruptedly from 1946 until his death in 1961.

The 27th session of the Indian National Congress was held in Bankipore (Patna), Bihar in December 1912. It was presided over by R.N. Mudholkar, and Sachchidananda Sinha served as the General Secretary.

Freedom fighter and socialist leader Jayaprakash Narayan was popularly revered by the title 'Lok Nayak' (Leader of the People) for his leadership during the 1942 Quit India Movement and the 1974 Total Revolution (Sampoorna Kranti).

Correct Answer: Option (C) — 180 • Mathematical Formula: The nth term is given by n^2 (n + 1) or n^3 + n^2: - n=1: 1^2 4 = 4 (or 2^3 - 4 = 4; standard: n^3 - n^2 -> for n=2: 8 - 4 = 4; n=3: 27 - 9 = 18; n=4: 64 - 16 = 48; n=5: 125 - 25 = 100; n=6: 216 - 36 = 180; n=7: 343 - 49 = 294; n=8: 512 - 64 = 448). Hence, the missing term is 180.

Expanding the ratio gives [2n(2n − 1)(2n − 2) / 6] ÷ [n(n − 1) / 2] = 4(2n − 1) / 3 = 44 / 3, which simplifies to 2n − 1 = 11, yielding n = 6.

The sum of m numbers is mn² and the sum of n numbers is nm², so the combined average of (m + n) numbers is (mn² + nm²) / (m + n) = mn(m + n) / (m + n) = mn.

Option (A) is correct. Applying the principle of inclusion-exclusion for three sets to determine the number of members participating across athletic teams gives 10.

In 5 days working together, Mohan and Sohan complete 5 × (1/25 + 1/20) = 5 × (9/100) = 9/20 of the work. Sohan completes the remaining 11/20 of the work at his rate of 1/20 per day in (11/20) ÷ (1/20) = 11 days.

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• Time elapsed from 12:00 to 5:10 = 5 hours 10 minutes = 5 + 10/60 hours = 31/6 hours.
• The hour hand rotates 360° in 12 hours, i.e., 30° per hour.
• Angle rotated = (31/6) × 30° = 31 × 5° = 155°.

The perfect square of any natural number can never end in the unit digits 2, 3, 7, or 8; since 143642 ends in 2, it cannot be the square of a natural number (whereas 163² = 26569, 176² = 30976, and 169² = 28561).

Adding the two equations gives 348(x + y) = 1740 ⇒ x + y = 5, and subtracting them gives 86(x − y) = 86 ⇒ x − y = 1; solving these two linear equations yields x = 3 and y = 2.

Using the algebraic identity (a + b)² - (a - b)² = 4ab, letting a = 598 and b = 479 gives {(a + b)² - (a - b)²} / (ab) = (4ab) / (ab) = 4.

Correct Answer: Option (A) — 194481 • Compound Growth Arithmetic: Population after 2 years = P × (1 + (r) / (100))² = 176400 × (1.05)² = 176400 × 1.1025 = 194,481.