MPSC Prep मराठी

Last-week revision

Revision sheet

One line of analogy and the key formulas for every topic. Read it the night before; if a line doesn't trigger the full idea, open that topic again.

Speed maths: know these cold

Every value below is a tool you should not have to compute in the hall. The numbers are generated by the build, not typed, so they are exact.

Squares

nn²nn²nn²
1²12²43²9
4²165²256²36
7²498²649²81
10²10011²12112²144
13²16914²19615²225
16²25617²28918²324
19²36120²40021²441
22²48423²52924²576
25²62526²67627²729
28²78429²84130²900

Cubes

nn³nn³nn³
1³12³83³27
4³645³1256³216
7³3438³5129³729
10³100011³133112³1728
13³219714³274415³3375

Powers of 2

2ⁿ2ⁿ2ⁿ
201212224
23824162532
26642712828256
2951221010242112048
2124096213819221416384
2153276821665536

Fraction ↔ percent

%%
1/250%1/333.33%
1/425%1/520%
1/616.67%1/714.29%
1/812.5%1/911.11%
1/1010%1/119.09%
1/128.33%1/166.25%
1/205%1/254%

Divisibility rules

ByRule
2last digit even
3digit sum divisible by 3
4last two digits divisible by 4
5ends in 0 or 5
6divisible by both 2 and 3
8last three digits divisible by 8
9digit sum divisible by 9
11(sum of odd-place digits) − (sum of even-place digits) is 0 or a multiple of 11

Constants and logs

√21.414
√31.732
√52.236
π3.1416 ≈ 22/7
e2.718
log10 20.3010
log10 30.4771
log10 70.8451
ln 102.3026

Trig values

0°30°45°60°90°
sin01/21/√2√3/21
cos1√3/21/√21/20
tan01/√31√3—

History

Indus Valley, Vedic Age, Buddhism and Jainism

A village tired of costly pujas: When the village priest’s yajnas grew costly and the bullocks needed for ploughing were sacrificed, two local teachers offered a simple path of right conduct in the people’s own language: that is the rise of Buddhism and Jainism.

  • Harappa 1921 (Daya Ram Sahni, on the Ravi); Mohenjo-daro 1922 (R.D. Banerji, on the Indus)
  • Signature sites: Lothal — dockyard; Kalibangan — ploughed field, fire altars; Dholavira — reservoirs; Rakhigarhi (Haryana) — largest Indian site; Daimabad (Maharashtra) — bronze chariot
  • Rigveda: 10 mandalas, 1028 hymns; Gayatri mantra in mandala 3; Purusha Sukta (four varnas) in mandala 10
  • Battle of Ten Kings (Dasharajna) on the Parushni (Ravi): Sudas of the Bharata tribe won
  • Later Vedic: iron (krishna ayas), Painted Grey Ware, Ganga plain, rigid varna, big sacrifices
  • Buddha: Lumbini (birth), Bodh Gaya (enlightenment), Sarnath (first sermon), Kushinagar (mahaparinirvana)
  • Buddhist councils: 1st Rajagriha (Ajatashatru), 2nd Vaishali (Kalashoka), 3rd Pataliputra (Ashoka, Moggaliputta Tissa), 4th Kundalvana, Kashmir (Kanishka, Vasumitra; Mahayana split)
  • Tripitaka (Pali): Sutta, Vinaya, Abhidhamma Pitaka
  • Jainism: Rishabhadeva 1st, Parshvanatha 23rd, Mahavira 24th tirthankara; Mahavira added brahmacharya as the 5th vow
  • Jain councils: 1st Pataliputra (Sthulabhadra); 2nd Vallabhi (Devardhi Kshamashramana) — canon compiled

Maharashtra’s Dynasties and the Varkari Saints (Satavahanas to Yadavas; Dnyaneshwar to Tukaram)

A village temple built over generations: Each ruling family left its own monument on Maharashtra’s land, and the saints built a temple of devotion on it: Dnyaneshwar laid the foundation, Namdev spread it, Eknath raised the pillar and Tukaram became the pinnacle.

  • Satavahana capital: Pratishthan (Paithan); founder Simuka; greatest Gautamiputra Satakarni (Nashik inscription of Gautami Balashri)
  • Hala — Gathasaptashati in Maharashtri Prakrit; Satavahanas gave the earliest land grants
  • Vakatakas: Prabhavatigupta (daughter of Chandragupta II) as regent; Pravarasena II — Setubandha; Harishena — later Ajanta caves
  • Rashtrakutas: founder Dantidurga; Krishna I — Kailasa temple, Ellora; Amoghavarsha I — Kavirajamarga, capital Manyakheta
  • Yadavas of Devagiri: Bhillama V (founder), Singhana, Ramachandra (defeated by Alauddin Khalji, 1296); minister Hemadri
  • Dnyaneshwari: 1290, Nevasa; Dnyaneshwar’s samadhi at Alandi, 1296
  • Namdev: 61 hymns in the Guru Granth Sahib; Eknath: Paithan, Eknathi Bhagwat, Bhavarth Ramayan
  • Tukaram: Dehu, the Gatha; Ramdas: Dasbodh, Manache Shlok (Samarth, not Varkari)
  • Mahanubhav sect: Chakradhar Swami; Lilacharitra by Mhaimbhat (first Marathi prose biography)

Shivaji Maharaj and Swarajya: Administration and Ashtapradhan

A cooperative sugar factory with salaried department heads: Like a well-run cooperative sugar factory that pays its department heads salaries instead of handing them cane land, Shivaji Maharaj ran Swarajya through eight appointed, transferable ministers paid in cash, not hereditary jagirdars.

  • Born 19 February 1630, Shivneri; parents Shahaji and Jijabai
  • Afzal Khan killed at Pratapgad, 10 November 1659; Shaista Khan attacked at Lal Mahal, Pune, 1663
  • Treaty of Purandar, 1665, with Mirza Raja Jai Singh: 23 forts surrendered, 12 retained
  • Coronation at Raigad, 6 June 1674, by Gaga Bhatt; Rajyabhishek Shaka begun; died 3 April 1680, Raigad
  • Ashtapradhan: Peshwa — general administration; Amatya — finance; Sachiv — correspondence; Mantri — king’s records, intelligence; Senapati — army; Sumant — foreign affairs; Nyayadhish — justice; Panditrao — religion and charity
  • All Ashtapradhan except Nyayadhish and Panditrao could be sent on military expeditions
  • Chauth = 25% (one-fourth); Sardeshmukhi = 10% (one-tenth), additional
  • Fort officers: Havaldar, Sabnis, Sarnobat (and Karkhanis), drawn from different castes as a check
  • Cavalry: bargir (state horse) vs shiledar (own horse); navy forts: Sindhudurg, Vijaydurg, Kolaba

The Peshwas and the Maratha Confederacy (to 1818)

The joint-family business run by the munim: Like a joint-family business where the munim (manager) takes over the running while the owner’s name stays on the signboard and the cousins’ branch shops drift apart, the Peshwas ran the Maratha state for the Chhatrapati until the quarrelling branches let the British buy them out in 1818.

  • Balaji Vishwanath — Peshwa 1713; Mughal sanads 1719 (chauth and sardeshmukhi of six Deccan subahs)
  • Bajirao I: Palkhed 1728 (Nizam); Delhi raid 1737; Chimaji Appa takes Vasai from the Portuguese 1739
  • Nanasaheb Peshwa: Sangola agreement 1750; Third Battle of Panipat, 14 January 1761 (Ahmad Shah Abdali)
  • Madhavrao I: Rakshasbhuvan 1763; died at Theur 1772
  • First Anglo-Maratha War 1775–82: Treaty of Surat 1775, Purandar 1776, Convention of Wadgaon 1779, Treaty of Salbai 1782
  • Treaty of Bassein, 31 December 1802: Bajirao II accepts the subsidiary alliance
  • Second war 1803–05: Assaye, Laswari; Treaties of Deogaon (Bhonsle) and Surji-Anjangaon (Shinde), 1803
  • Third war 1817–18: Khadki, Koregaon (1 January 1818), Ashti; Bajirao II pensioned to Bithur
  • Confederacy houses: Shinde — Gwalior; Holkar — Indore; Gaikwad — Baroda; Bhonsle — Nagpur

British Expansion: Subsidiary Alliance, Doctrine of Lapse, Land Revenue Systems

The society that hired a security agency: Subsidiary Alliance was a “protection” contract: the agency’s guards live on your premises at your cost, its supervisor sits in your office, you may deal with no one else, and if you cannot pay you hand over land, until the agency effectively owns you.

  • Subsidiary Alliance: Lord Wellesley, 1798; first accepted by the Nizam of Hyderabad (1798)
  • Others: Mysore 1799, Tanjore 1799, Awadh 1801, Peshwa 1802 (Bassein), Bhonsle and Shinde 1803
  • Terms: British troops at the state’s cost, a British Resident, no other Europeans, no independent foreign policy
  • Doctrine of Lapse: Lord Dalhousie; first annexation Satara 1848; also Jaitpur, Sambalpur, Baghat, Udaipur, Jhansi, Nagpur (1854)
  • Awadh annexed 1856 on grounds of misgovernance, not lapse
  • Permanent Settlement: Cornwallis, 1793, Bengal–Bihar–Orissa; zamindar as owner; revenue fixed in perpetuity
  • Ryotwari: Thomas Munro and Alexander Read; Madras and Bombay presidencies; direct settlement with the cultivator
  • Mahalwari: Holt Mackenzie, Regulation VII of 1822; village (mahal) as the unit; North-Western Provinces, Punjab
  • Deccan Riots, 1875 (Supa, Pune) → Deccan Agriculturists’ Relief Act, 1879

The Revolt of 1857 (with Maharashtra’s role)

The strike at the sugar factory: 1857 was like a factory strike that began with the workers over one insult, was joined by angry farmers and dispossessed former owners each with their own grievance, was crushed with loyal workers from other units, and ended with the board being dissolved and the government taking over.

  • Mangal Pandey (34th BNI), Barrackpore, 29 March 1857; outbreak at Meerut, 10 May 1857; Delhi taken 11 May
  • Immediate cause: greased cartridges of the Enfield rifle; Governor-General: Lord Canning
  • Kanpur — Nana Saheb, Tatya Tope; Lucknow — Begum Hazrat Mahal; Jhansi — Rani Lakshmibai; Jagdishpur — Kunwar Singh; Bareilly — Khan Bahadur Khan
  • British commanders: Nicholson, Hodson (Delhi); Colin Campbell (Lucknow, Kanpur); Hugh Rose (Jhansi)
  • Tatya Tope: born Yeola (Nashik); hanged at Shivpuri, 18 April 1859
  • Maharashtra: 27th NI at Kolhapur, 31 July 1857; Rango Bapuji (Satara); Bhagoji Naik (Bhils, Ahmednagar–Nashik)
  • Government of India Act, 1858: Crown rule, Secretary of State + Council of India (15 members), Viceroy
  • Queen’s Proclamation, 1 November 1858, Allahabad: Doctrine of Lapse given up
  • Interpretations: Savarkar — The Indian War of Independence of 1857 (1909); S.N. Sen — Eighteen Fifty-Seven; R.C. Majumdar — “neither first, nor national, nor war of independence”

Social Reformers of Maharashtra (Phule, Ranade, Agarkar, Shahu, Ambedkar, Karve…)

Opening the village water tank: Faced with a water tank that some castes were forbidden to touch, Phule opened his own tank to all, Ranade persuaded the panchayat slowly, Agarkar said clean the tank before building the new temple, Shahu used the ruler’s authority, Karve built a separate home for the excluded, and Ambedkar marched to the public tank to claim it as a right.

  • Darpan — Bal Shastri Jambhekar, 6 January 1832, first Marathi newspaper; Digdarshan (1840), first Marathi monthly
  • Shatapatre — Lokhitwadi (Gopal Hari Deshmukh); Nibandhamala — Vishnushastri Chiplunkar
  • Prarthana Samaj, 1867, Bombay — founded by Atmaram Pandurang; Ranade and R.G. Bhandarkar prominent
  • Phule: girls’ school 1848; Satyashodhak Samaj 24 September 1873; Gulamgiri (1873), Shetkaryacha Asud (1883); “Mahatma” 1888
  • Agarkar: first editor of Kesari (1881); Sudharak (1888); Tilak edited Mahratta
  • Shahu Maharaj: 50% reservation in Kolhapur state, 26 July 1902; free compulsory primary education, 1917
  • Karve: home for widows (1896, Hingne, Pune); women’s university 1916 (SNDT); Bharat Ratna 1958
  • Pandita Ramabai: Arya Mahila Samaj (1882), Sharada Sadan (1889); Tarabai Shinde: Stri Purush Tulana (1882)
  • V.R. Shinde: Depressed Classes Mission (1906); Gokhale: Servants of India Society (1905); Bhaurao Patil: Rayat Shikshan Sanstha (1919)
  • Ambedkar: Mooknayak 1920; Bahishkrit Hitakarini Sabha 1924; Mahad 20 March 1927; Kalaram temple 1930; Poona Pact 1932; ILP 1936; Deekshabhoomi, Nagpur, 14 October 1956

INC, Moderates and Extremists, Tilak, Partition of Bengal and Swadeshi

Cane growers versus the sugar factory: Moderates were the cane growers who wrote polite petitions to the factory chairman trusting his fairness; Extremists were those who said stop supplying cane, make our own jaggery and run our own schools: same grievance, different method, and the 1907 Surat meeting is where the growers’ union split.

  • INC: 28 December 1885, Gokuldas Tejpal Sanskrit College, Bombay; 72 delegates; president W.C. Bonnerjee; founder A.O. Hume; Viceroy Dufferin
  • First Muslim president Badruddin Tyabji (1887, Madras); first European George Yule (1888); first woman Annie Besant (1917)
  • 1896 Calcutta — Vande Mataram first sung; 1911 Calcutta — Jana Gana Mana first sung
  • 1906 Calcutta (Dadabhai Naoroji): Swaraj, Swadeshi, Boycott, National Education resolutions
  • 1907 Surat (Rash Behari Ghosh): split; 1916 Lucknow (A.C. Mazumdar): reunion and Lucknow Pact
  • Tilak: Kesari (Marathi) and Mahratta (English), 1881; public Ganeshotsav 1893; Mandalay — Gita Rahasya; Home Rule League, Belgaum, April 1916
  • Partition of Bengal: Curzon; effective 16 October 1905; annulled 1911 (Delhi Durbar); capital moved to Delhi
  • Muslim League: Dhaka, December 1906; Morley–Minto reforms, 1909: separate electorates
  • Maharashtra revolutionaries: Vasudev Balwant Phadke; Chapekar brothers (Rand, 1897); Abhinav Bharat (Savarkar, Nashik); Anant Kanhere (Jackson, 1909)

The Gandhian Era to Independence (NCM, CDM, Quit India, 1942 in Maharashtra)

The wari to Pandharpur: Gandhi turned the freedom struggle into something like the wari: lakhs of ordinary people of every caste walking together under strict discipline, each village’s dindi under its own leader, the march halting if the discipline breaks, and the walk itself (Dandi) becoming the message.

  • Gandhi returns 9 January 1915; Champaran 1917; Ahmedabad and Kheda 1918
  • GoI Act 1919: dyarchy in provinces — reserved (police, finance, land revenue) vs transferred (education, health, local government) subjects
  • NCM: Calcutta special session (September 1920), Nagpur (December 1920); withdrawn after Chauri Chaura, 5 February 1922
  • Lahore 1929 (Jawaharlal Nehru): Purna Swaraj; 26 January 1930 first Independence Day
  • Dandi March: 12 March – 6 April 1930; Gandhi–Irwin Pact: 5 March 1931; Second RTC 1931 (Gandhi attended)
  • Poona Pact: 24 September 1932, Gandhi–Ambedkar, reserved seats in place of separate electorates
  • GoI Act 1935: provincial autonomy; 1937 Bombay ministry under B.G. Kher; first individual satyagrahi Vinoba Bhave (1940)
  • Quit India: 8 August 1942, Gowalia Tank Maidan, Bombay; “Do or Die”
  • Maharashtra: Chimur and Ashti (16 August 1942); Satara Prati Sarkar — Nana Patil (1943–46); Solapur martial law 1930; Babu Genu, 12 December 1930
  • RIN mutiny, Bombay, February 1946; Mountbatten Plan 3 June 1947

The Samyukta Maharashtra Movement and the State’s Formation (1960)

Dividing the joint-family house: Like Marathi-speaking brothers scattered across three different households who demand one home of their own, including the big city flat both they and their Gujarati cousins claim, the Samyukta Maharashtra movement united Marathi areas from Bombay State, Madhya Pradesh and Hyderabad into Maharashtra on 1 May 1960, with Mumbai as its capital.

  • Congress accepted linguistic provinces at the Nagpur session, 1920
  • Before 1956: Vidarbha in Madhya Pradesh; Marathwada in Hyderabad State (liberated September 1948; 17 September)
  • Belgaum Marathi Sahitya Sammelan, 1946 — Samyukta Maharashtra resolution; Parishad under Shankarrao Deo
  • Dar Commission (1948) and JVP Committee (1949) — against immediate linguistic states
  • Nagpur Pact, 28 September 1953 — guarantees for Vidarbha; annual session at Nagpur
  • SRC: Fazl Ali, K.M. Panikkar, H.N. Kunzru; report 1955 recommended bilingual Bombay State and separate Vidarbha
  • Flora Fountain firing, 21 November 1955; about 106 martyrs → Hutatma Chowk; C.D. Deshmukh resigned (1956)
  • Samyukta Maharashtra Samiti: formed 6 February 1956, Pune; S.M. Joshi general secretary; Acharya Atre, Dange, Prabodhankar Thackeray, Senapati Bapat
  • Bilingual Bombay State: 1 November 1956 (CM Y.B. Chavan); Bombay Reorganisation Act, 1960 → Maharashtra, 1 May 1960
  • First CM Yashwantrao Chavan; first Governor Sri Prakasa; Article 371(2) — development boards

Geography

Earth's Interior, Plate Tectonics, Earthquakes and Volcanoes

Malai on a pot of boiling milk: The lithosphere is the malai skin on a pot of hot milk: the milk below churns, and the skin cracks into pieces that drift apart, push together and slide past each other.

  • Layers: crust → mantle (to ~2,900 km) → outer core (liquid) → inner core (solid); Earth's radius ~6,371 km
  • Discontinuities: Conrad (within crust), Moho (crust/mantle), Gutenberg (mantle/core), Lehmann (outer/inner core)
  • P-waves: fastest, longitudinal, pass through solids and liquids; S-waves: transverse, solids only; surface waves: last, most destructive
  • Focus (hypocentre) = point inside the Earth where the quake starts; epicentre = point on the surface directly above it
  • Richter scale is logarithmic: one unit up = 10 times the wave amplitude and about 32 times the energy
  • Boundaries: divergent (Mid-Atlantic Ridge), convergent (Himalaya, Andes, Japan), transform (San Andreas)
  • Wegener: continental drift, 1912; Holmes: mantle convection; Hess: sea-floor spreading; plate tectonics: 1967 onwards
  • Deccan Traps: basalt from fissure eruptions, ~66 million years ago
  • Koyna 1967: reservoir-induced earthquake; Killari (Latur) 30 September 1993
  • Only active volcano in India: Barren Island (Andaman); Lonar crater lake: meteorite impact, Ramsar site (2020)

Latitude, Longitude and Time (IST, time-zone calculations)

Every village's own noon versus the railway station clock: Each village's shortest-shadow noon is its local time; the station clock that the whole country follows is standard time (IST, set by 82°30′E).

  • 360° in 24 h → 15° per hour, 1° per 4 minutes, 1′ of longitude per 4 seconds
  • East of a place = ahead in time (add); west = behind (subtract)
  • Opposite sides of Greenwich: add the longitudes to get the difference
  • IST meridian 82°30′E, through Mirzapur (UP); IST = GMT + 5:30
  • Standard meridian crosses 5 states: UP, MP, Chhattisgarh, Odisha, Andhra Pradesh
  • India: about 68°7′E–97°25′E and 8°4′N–37°6′N (mainland); east–west time gap almost 2 hours
  • Tropic of Cancer crosses 8 states: Gujarat, Rajasthan, MP, Chhattisgarh, Jharkhand, West Bengal, Tripura, Mizoram
  • 1° of latitude ≈ 111 km everywhere; 1° of longitude ≈ 111 km at the Equator, 0 at the poles
  • International Date Line ≈ 180°: crossing westward add a day, eastward subtract a day

Atmosphere, Pressure Belts, Coriolis Force and Planetary Winds

Bhandara cooking at the jatra ground and the merry-go-round: Air rises over the hottest spot like steam over the bhandara chulha, sinks far away, and flows back along the ground; on a spinning Earth that flow bends like a ball thrown on a merry-go-round.

  • Composition: N₂ ~78%, O₂ ~21%, Ar ~0.93%, CO₂ ~0.04%
  • Troposphere: weather layer, thickest at the equator (~18 km), thinnest at the poles (~8 km); normal lapse rate ~6.5 °C per km
  • Ozone layer: stratosphere; ionosphere (radio waves): thermosphere; coldest layer: mesosphere
  • Pressure belts: equatorial low, subtropical highs (~30°), subpolar lows (~60°), polar highs
  • Thermal belts: equatorial low and polar highs; dynamic belts: subtropical highs and subpolar lows
  • Coriolis force ∝ sin(latitude): zero at the equator, maximum at the poles; right in NH, left in SH (Ferrel's law)
  • NH cyclone: anticlockwise inflow; NH anticyclone: clockwise outflow (reversed in SH)
  • Doldrums = equatorial calm; horse latitudes = subtropical high calm
  • Trades → equator; westerlies → subpolar lows (Roaring Forties in SH); polar easterlies
  • Winds are named by the direction they blow from

How the Indian Monsoon Works (ITCZ, jet streams, El Niño, IOD)

The hot summer kitchen and the cool courtyard tank: In summer the land is the hot kitchen pulling in moist air from the cool courtyard tank (the Indian Ocean); in winter the flow reverses — that seasonal reversal is the monsoon.

  • ITCZ / monsoon trough over the Ganga plain (~20°–25°N) in July; SE trades cross the equator, deflect right, become the SW monsoon
  • Subtropical westerly jet shifts north of the Himalaya before the monsoon; tropical easterly jet (~15°N) sets in over the peninsula
  • Normal onset over Kerala ~1 June; whole country ~8 July; withdrawal from west Rajasthan begins ~17 September
  • Two branches: Arabian Sea (Western Ghats, orographic rain) and Bay of Bengal (north-east India, Ganga plain)
  • Rain-shadow: leeward (east) side of the Western Ghats — Madhya Maharashtra, Marathwada
  • El Niño: warm central/eastern Pacific, usually weak monsoon; La Niña: usually good monsoon; ENSO = El Niño + Southern Oscillation
  • Positive IOD: western Indian Ocean warmer than eastern, favourable for the monsoon
  • Western disturbances (from the Mediterranean, via the westerly jet): winter rain in north-west India, helps rabi wheat
  • NE (retreating) monsoon: main rainy season of the Tamil Nadu coast (October–December)
  • IMD "normal" monsoon: 96–104% of LPA; LPA = 87 cm (1971–2020)

Ocean Currents and Tides

The dabbawala loop: Ocean currents run in closed loops like the dabbawala relay: warm "full tiffins" travel from the tropics towards the poles, cold "empty tiffins" come back towards the equator, and where the two streams cross, the station gets crowded and busy.

  • Drivers: planetary winds, Coriolis force, coastline shape, temperature/salinity (thermohaline) differences
  • Gyres: clockwise in the NH, anticlockwise in the SH
  • Warm currents: east coasts of continents (Gulf Stream, Kuroshio, Brazil, Agulhas, East Australian)
  • Cold currents: west coasts of continents (Canary, Benguela, Humboldt/Peru, California, West Australian); also Labrador, Oyashio
  • Cold current + desert: Atacama–Humboldt, Namib–Benguela, Sahara–Canary, Sonoran–California
  • Fishing grounds where warm meets cold: Grand Banks (Gulf Stream + Labrador), off Japan (Kuroshio + Oyashio)
  • North Indian Ocean currents reverse with the monsoon
  • Spring tide: new moon and full moon (Sun, Earth, Moon aligned); neap tide: first and last quarter (at right angles)
  • Tidal day ≈ 24 h 50 min; successive high tides ≈ 12 h 25 min apart
  • Highest tidal range in India: Gulf of Khambhat; world: Bay of Fundy

India's Physiographic Divisions and Drainage

Rainwater on a village house roof: India drains like a house roof: a high snow-capped back wall (Himalaya) feeds rivers all year, while the Deccan is a roof whose ridge (the Western Ghats) sits near the west edge, so most water runs a long way east.

  • Six divisions (NCERT): Himalaya, Northern plains, Peninsular plateau, Indian desert, Coastal plains, Islands
  • Himalayan ranges north to south: Himadri (Greater) → Himachal (Lesser) → Shiwaliks; duns lie between Himachal and Shiwaliks
  • Plains belts: bhabar (pebbles) → terai (marshy) → bhangar (old alluvium, kankar) and khadar (new alluvium)
  • Western Ghats: continuous, higher; Eastern Ghats: discontinuous, lower
  • Anamudi (2,695 m, Anaimalai): highest peak of peninsular India
  • Western coastal plain: narrow, estuaries; eastern coastal plain: broad, deltas
  • Narmada and Tapi: west-flowing through rift valleys, form estuaries
  • Ganga: longest river of India (~2,525 km); Godavari: longest peninsular river (~1,465 km), "Dakshin Ganga"
  • Himalayan rivers: perennial, antecedent, deltas; peninsular rivers: seasonal, older, graded valleys

Population and Census (density, sex ratio, literacy, urbanisation; Census 2011 data, with the census exercise status stated carefully)

The headmaster's ten-yearly school survey: A census is a once-in-ten-years full count of every person, like a headmaster counting every pupil; density, sex ratio, literacy and urbanisation are just ratios worked out from that count.

  • Census 2011: 15th census, 7th after independence; last completed census (as of November 2026)
  • Census 2027 (16th, first digital, with caste enumeration): houselisting April–September 2026; population enumeration 25 January–28 February 2027 in most states; reference date 1 March 2027 (1 October 2026 for snow-bound areas)
  • India 2011: ~121.09 crore; growth ~17.7%; density 382; sex ratio 943; literacy 74.04% (provisional) / 72.98% (final); urban ~31%
  • Maharashtra 2011: 11.24 crore (2nd after UP); density 365; sex ratio 929; literacy 82.34%; urban ~45.2%
  • Highest sex ratio: Kerala 1,084; lowest: Haryana 879
  • Highest density: Bihar 1,106; lowest: Arunachal Pradesh 17
  • Literate = age 7+ who can read and write with understanding
  • Census town: population ≥ 5,000, density ≥ 400/km², ≥ 75% of male main workers non-agricultural
  • Sex ratio = females per 1,000 males; decadal growth = (P₂ − P₁) ÷ P₁ × 100
  • First census 1872; first synchronous census 1881; Census Act 1948

Maharashtra: Konkan, Sahyadri and the Deccan Plateau

A hill-side wada: front yard, steep stairs, big terrace: Maharashtra is built like a hill-side wada: a narrow front yard by the sea (Konkan), a steep stone staircase (the Sahyadri escarpment) and a huge terrace of poured layers sloping gently back to the east (the Deccan plateau).

  • Area 3,07,713 km² (3rd largest state); coastline ~720 km
  • 36 districts (as of November 2026; Palghar, 2014, the newest); 6 revenue divisions
  • Renamed: Aurangabad → Chhatrapati Sambhajinagar; Osmanabad → Dharashiv; Ahmednagar → Ahilyanagar
  • Kalsubai 1,646 m (Ahilyanagar): highest peak of Maharashtra; Salher 1,567 m (Nashik): second
  • Ghats: Thal/Kasara (Mumbai–Nashik), Bor (Mumbai–Pune), Kumbharli (Karad–Chiplun), Amba (Kolhapur–Ratnagiri)
  • Water-divide ranges: Satmala–Ajanta (Tapi/Godavari), Harishchandra–Balaghat (Godavari/Bhima), Shambhu Mahadev (Bhima/Krishna)
  • Deccan plateau: horizontal basalt flows, tilts east; weathers into black soil
  • Satpura on the northern border: Toranmal (Nandurbar), Chikhaldara (Amravati, Gawilgarh hills)
  • Gondwana coal rocks in eastern Vidarbha (Chandrapur)

Rivers and Dams of Maharashtra (Godavari, Krishna, Tapi, Bhima…; west- vs east-flowing)

ST buses leaving a Sahyadri depot: From the Sahyadri crest, rivers leave like ST buses from a hill-top depot: a few take the short steep ghat road down to the Konkan, most take the long highway east across the Deccan, picking up feeder routes (tributaries) and halting at big stations (dams).

  • Godavari: Trimbakeshwar (Nashik), ~1,465 km, "Dakshin Ganga"; Jayakwadi dam at Paithan (Nath Sagar)
  • Wardha + Wainganga → Pranhita → joins Godavari near Sironcha (Gadchiroli); Gosikhurd dam on Wainganga
  • Krishna: Mahabaleshwar (Satara); Krishna–Koyna confluence at Karad (Preeti Sangam)
  • Koyna dam (Shivsagar reservoir), Satara: major hydroelectric project; Koyna earthquake 1967
  • Bhima: Bhimashankar (Pune); called Chandrabhaga at Pandharpur; Ujani dam (Solapur); joins Krishna in Karnataka
  • Tapi: Multai (Betul, MP); flows west through Jalgaon, Dhule, Nandurbar; tributaries Purna, Girna, Panzara
  • West-flowing: Tapi, Narmada (border), Konkan rivers (Vaitarna, Ulhas, Savitri, Vashishti…)
  • East-flowing: Godavari, Krishna, Bhima and their tributaries (to the Bay of Bengal)
  • Towns: Nashik and Nanded (Godavari), Pandharpur (Bhima), Karad and Sangli (Krishna), Kolhapur (Panchganga), Alandi (Indrayani)

Soils, Climate Regions and Crops of Maharashtra

The potter's yard in the monsoon: Black soil behaves like the potter's clay that holds water and cracks when dry, laterite is what is left after rain washes a yard again and again, and each kind of earth suits its own "pot" — its own crop.

  • Black (regur) soil: from basalt; high moisture retention; swells and cracks (self-ploughing); rich in lime, iron, magnesia, potash; poor in N, P and organic matter
  • Laterite: high rainfall and leaching (Konkan, Ghats); rich in iron oxide; poor in N, P, Ca, organic matter; used as jambha building stone
  • Red and yellow soils: eastern Vidarbha (Bhandara, Gondia, Chandrapur, Gadchiroli)
  • Rainfall: heavy in Konkan and Ghats → rain-shadow (500–750 mm) east of the Ghats → higher again in eastern Vidarbha
  • Nine agro-climatic zones, including the Scarcity zone (rain-shadow) and the Eastern Vidarbha zone
  • Kharif: rice, jowar, bajra, soybean, cotton, tur; rabi: rabi jowar, wheat, gram
  • Konkan: rice, Alphonso mango (GI), cashew, coconut, kokum
  • Nashik: grapes and onion (Lasalgaon market); Solapur: pomegranate; Sangli: turmeric; Nagpur: oranges
  • Sugarcane seasons: adsali (July–August, ~18 months), pre-seasonal (October–November), suru (January–February)

Polity

Making of the Constitution (Acts of 1773–1935, Constituent Assembly, sources)

A housing society writing its own bye-laws: For 175 years the builder (the British) wrote the society’s rules and handed residents a little more say each time; in 1946 the residents’ general body (Constituent Assembly) finally drafted its own bye-laws, borrowing the best clauses from other societies’ model bye-laws.

  • Regulating Act 1773: first Governor-General of Bengal (Warren Hastings); Supreme Court at Calcutta (1774)
  • Charter Act 1833: first Governor-General of India (William Bentinck); Charter Act 1853: open competition for civil services
  • GoI Act 1858: Crown rule, Secretary of State, Viceroy; Indian Councils Act 1861: portfolio system
  • 1909 Morley–Minto: separate electorate for Muslims; 1919 Montagu–Chelmsford: provincial dyarchy, bicameral Centre
  • GoI Act 1935: provincial autonomy, three lists, Federal Court (1937), proposed All-India Federation (never formed)
  • Constituent Assembly: 389 seats under the Cabinet Mission Plan, 299 after Partition; indirectly elected
  • First sitting 9 Dec 1946 (Sachchidananda Sinha, temporary); Rajendra Prasad president from 11 Dec 1946
  • Objectives Resolution: moved by Nehru 13 Dec 1946, adopted 22 Jan 1947
  • Drafting Committee: 29 Aug 1947, seven members, chairman B.R. Ambedkar; adviser B.N. Rau
  • Adopted 26 Nov 1949; in force 26 Jan 1950; original 395 articles, 22 parts, 8 schedules
  • Dr Ambedkar entered the Assembly from Bengal in 1946; when the Partition plan put that seat in East Pakistan, he was elected from Bombay on 14 July 1947 in the seat vacated by M.R. Jayakar

Preamble, Salient Features and Amending the Constitution (Art. 368, basic structure)

Renovating the ancestral wada: You may renovate the ancestral wada room by room, but you cannot pull out the central pillars that hold up the roof: Parliament may amend any part of the Constitution, but not its basic structure.

  • Preamble ideals: Liberty, Equality, Fraternity from France; social, economic and political justice from the Russian Revolution
  • Preamble amended once: 42nd Amendment 1976 added Socialist, Secular, Integrity
  • Berubari (1960): Preamble not a part; Kesavananda (1973) and LIC of India (1995): it is a part
  • Art. 368 is in Part XX; amendment bill in either House, no President’s prior recommendation, no joint sitting
  • Special majority = majority of total membership + two-thirds of members present and voting, in each House separately
  • State ratification: half the states, simple majority, no time limit; needed for federal provisions and Art. 368 itself
  • 24th Amendment (1971): President’s assent to an amendment bill is obligatory
  • Case chain: Shankari Prasad 1951 → Sajjan Singh 1965 → Golaknath 1967 → Kesavananda 1973 → Minerva Mills 1980 → Waman Rao 1981
  • Art. 1: India, that is Bharat, shall be a Union of States
  • 61st Amendment (1988): voting age 21 → 18

Fundamental Rights and Writs (Art. 12–35)

The headmaster’s five orders: Fundamental Rights are the promises in the school rulebook that even the management cannot break, and the writs are the five kinds of orders the headmaster (Supreme Court or High Court) issues to enforce them.

  • Equality 14–18; Freedom 19–22; Exploitation 23–24; Religion 25–28; Cultural & Educational 29–30; Remedies 32
  • Art. 12 defines “State”; Art. 13 makes inconsistent laws void (judicial review)
  • Right to property removed by 44th Amendment (1978); now Art. 300A, a legal right
  • Citizens only: Art. 15, 16, 19, 29, 30
  • Art. 21A (86th, 2002): education 6–14 years; Art. 15(6) and 16(6) (103rd, 2019): EWS up to 10%
  • Art. 19(1)(c) “co-operative societies” added by 97th Amendment (2011)
  • Art. 20 and 21 cannot be suspended even in a National Emergency (44th Amendment)
  • Art. 358 suspends Art. 19 only in a war / external aggression emergency; Art. 359 suspends enforcement of others
  • Writs: habeas corpus, mandamus, prohibition, certiorari, quo warranto; SC under Art. 32, HC under Art. 226 (wider)
  • Art. 32 “heart and soul of the Constitution” (Ambedkar)

Directive Principles and Fundamental Duties

The sugar cooperative’s goals and its members’ duties: Directive Principles are the sugar cooperative’s long-term goals that members cannot sue the board over but judge it by at the next election; Fundamental Duties are what each member owes the cooperative.

  • DPSP: Part IV, Art. 36–51; source Ireland; Art. 37 non-justiciable but fundamental in governance
  • Gandhian: Art. 40, 43, 43B, 46, 47, 48 (cow slaughter); Art. 44 Uniform Civil Code is liberal-intellectual
  • 42nd Amendment added DPSP: 39A, 43A, 48A (and recast 39(f))
  • 44th added 38(2); 86th substituted 45; 97th added 43B
  • Art. 50: separation of judiciary from executive; Art. 51: international peace and security
  • Art. 31C (25th Amendment, 1971) protects laws under Art. 39(b) and (c)
  • Minerva Mills (1980): harmony between FRs and DPSP is a basic feature
  • Fundamental Duties: Part IVA, Art. 51A; 42nd Amendment 1976; Swaran Singh Committee; USSR source
  • Originally 10 duties; 11th (51A(k), education of child 6–14) by 86th Amendment 2002
  • Duties apply only to citizens; the National Song is not mentioned in Art. 51A

President, Vice-President, Prime Minister and Council of Ministers

The temple trust chairman and the managing committee: Like the chairman of a big temple trust in whose name every order is issued while the managing committee actually decides, the President is the nominal head and the Prime Minister with the Council of Ministers is the real executive.

  • Art. 52 President; Art. 53 executive power; Art. 54 electoral college; Art. 55 STV method
  • Electoral college: elected MPs + elected MLAs of states and of Delhi and Puducherry (70th Amendment)
  • Minimum age: President 35, Vice-President 35; term 5 years for both
  • Impeachment (Art. 61): only ground “violation of the Constitution”; two-thirds of total membership of each House
  • Art. 72 pardon (includes death sentence and court-martial); Art. 123 ordinance
  • Vetoes: absolute, suspensive, pocket; no qualified veto; no veto on constitutional amendment bills
  • Art. 74: advice binding (42nd); can be returned once (44th)
  • Art. 75(3): collective responsibility to Lok Sabha; 75(1A): ministers ≤ 15% of Lok Sabha strength (91st, 2003)
  • Vice-President: ex officio RS Chairman (Art. 64); elected by all MPs incl. nominated; removed by RS majority of all members, agreed by LS
  • President resigns to Vice-President; Vice-President resigns to President

Parliament: Lok Sabha, Rajya Sabha and How a Bill Becomes Law (money bill, joint sitting)

The wedding committee and the elders’ council: In a big Maharashtrian wedding the purse-holding committee decides money matters while the elders’ council can only advise for a few days, just as the Lok Sabha controls money bills and the Rajya Sabha gets only 14 days to recommend.

  • Art. 79: Parliament = President + Rajya Sabha + Lok Sabha
  • Rajya Sabha max 250 (238 + 12 nominated); permanent; 6-year term; one-third retire every 2 years
  • Lok Sabha max 550 elected; present 543; Anglo-Indian nomination ended by 104th Amendment
  • Maharashtra: 48 Lok Sabha seats, 19 Rajya Sabha seats
  • Joint sitting Art. 108, presided by Speaker; held thrice: 1961, 1978, 2002
  • Money bill Art. 110; special procedure Art. 109; RS must return in 14 days; Speaker’s decision final
  • Financial bills Art. 117(1) and 117(3); Annual Financial Statement Art. 112; Appropriation Bill Art. 114
  • RS exclusive powers: Art. 249 (State List in national interest), Art. 312 (All-India Services)
  • Tenth Schedule (anti-defection): 52nd Amendment 1985; 91st Amendment 2003 removed split clause
  • 106th Amendment 2023: one-third seats for women in LS and assemblies (Art. 330A, 332A), not RS or councils

Supreme Court, High Courts and Judicial Review

Umpires, the third umpire and the rulebook: As the third umpire can overturn any on-field decision that breaks the Laws of Cricket, courts can strike down any law or order that breaks the Constitution, and the top body’s rulings bind every umpire below.

  • Supreme Court: Art. 124; sanctioned strength 38 including the CJI (2026 Act; it was 34 from 2019)
  • Retirement: Supreme Court 65, High Court 62
  • Removal: proved misbehaviour or incapacity; special majority of each House in the same session; Judges (Inquiry) Act 1968
  • Collegium: Second Judges case 1993, Third Judges case 1998; NJAC (99th Amendment) struck down 2015
  • Art. 129 court of record; 131 original; 136 special leave; 137 review; 141 binding law; 142 complete justice; 143 advisory
  • Constitution bench: at least five judges (Art. 145(3))
  • Art. 231: common High Court for two or more states
  • Bombay High Court: Maharashtra, Goa, DNH & DD; benches at Nagpur, Aurangabad, Panaji; Kolhapur circuit bench from August 2025
  • Judicial review is a basic feature (Minerva Mills 1980; L. Chandra Kumar 1997)

Governor, Chief Minister and the State Legislature (Maharashtra’s bicameral legislature)

The hostel mess committee and its rector: A hostel mess is run by its elected committee while the rector appointed by the university signs every order on the committee’s advice; the large general body decides, and a smaller seniors’ panel can only delay — that is Governor, Chief Minister, Vidhan Sabha and Vidhan Parishad.

  • Governor: Art. 153; appointed by President (Art. 155); holds office during President’s pleasure (Art. 156); age 35
  • 7th Amendment 1956: one Governor for two or more states
  • Art. 161 pardon: only offences against laws on matters within the state’s executive power; no power over court-martial sentences; Art. 213 ordinance; Art. 200 assent
  • Art. 164(1A): ministers ≤ 15% of assembly, minimum 12 (91st Amendment)
  • Bicameral states (6): Andhra Pradesh, Bihar, Karnataka, Maharashtra, Telangana, Uttar Pradesh
  • Art. 169: council created/abolished by Parliament after assembly’s special-majority resolution
  • Art. 171: council ≤ one-third of assembly, minimum 40
  • Maharashtra: Vidhan Sabha 288; Vidhan Parishad 78 = 30 (MLAs) + 22 (local bodies) + 7 (graduates) + 7 (teachers) + 12 (nominated)
  • Council can delay an ordinary bill 3 months + 1 month; money bill 14 days; no joint sitting in states
  • Nagpur Pact 1953: winter session of the Maharashtra legislature at Nagpur

Panchayati Raj and Urban Local Bodies (73rd/74th Amendments; Maharashtra’s three tiers)

Water flowing from the dam to the field channel: Power and money flow from the state like canal water from a dam, through the main canal (Zilla Parishad) and distributary (Panchayat Samiti) to the field channel (Gram Panchayat), where all the farmers together (Gram Sabha) decide their turns.

  • Balwantrai Mehta 1957 (three tiers); Ashok Mehta 1977 (two tiers); G.V.K. Rao 1985; L.M. Singhvi 1986
  • Rajasthan first: Nagaur, 2 October 1959
  • Maharashtra: Vasantrao Naik Committee (1960) → ZP and PS Act 1961 → ZPs from 1 May 1962
  • 73rd: Part IX, Art. 243–243-O, Eleventh Schedule (29 subjects), in force 24 April 1993
  • 74th: Part IXA, Art. 243P–243ZG, Twelfth Schedule (18 subjects), in force 1 June 1993
  • Art. 243A Gram Sabha; 243D reservation (≥ one-third women); 243E 5-year term; 243I State Finance Commission; 243K State Election Commission
  • Art. 243Q three urban bodies; 243S ward committees (3 lakh+); 243ZD DPC; 243ZE MPC (10 lakh+)
  • Maharashtra: 34 ZPs; 50–75 councillors + PS chairpersons ex officio; President’s term 2½ years; CEO is administrative head
  • Panchayat Samiti: Sabhapati + BDO; Gram Panchayat: Sarpanch + Upa-Sarpanch
  • Maharashtra Gram Sabha: at least 4 meetings per financial year; women’s meeting before each regular Gram Sabha; 50% seats for women in local bodies

Centre–State Relations and Emergency Provisions (Art. 352, 356, 360)

A joint family with separate chulhas: Like a joint family where each brother runs his own kitchen but the karta controls the farm, the purse and takes over every kitchen in a flood, India is federal in normal times and becomes unitary in an emergency.

  • Art. 1 “Union of States”; federalism is a basic feature (S.R. Bommai, 1994)
  • Seventh Schedule: Union, State, Concurrent lists (originally 97, 66, 47 entries); residuary powers with Parliament (Art. 248)
  • 42nd Amendment moved education, forests, weights and measures, wildlife protection, administration of justice to Concurrent List
  • Art. 249 (RS resolution), 250 (emergency), 252 (states’ request), 253 (treaties): Parliament on State subjects
  • Art. 263 Inter-State Council (1990); Sarkaria 1983, Punchhi 2007
  • 101st Amendment 2016: Art. 246A, 269A, 279A (GST Council); GST from 1 July 2017
  • Art. 352: war, external aggression, armed rebellion; approval in 1 month by special majority; 6-month extensions; proclaimed 1962, 1971, 1975
  • Art. 356: approval in 2 months by simple majority; max 3 years; beyond 1 year only with emergency + EC certificate
  • Art. 360: approval in 2 months; continues until revoked; never used
  • Maharashtra under President’s Rule: 1980, 2014, 2019

Constitutional Bodies: Election Commission, CAG, Finance Commission, UPSC and State PSCs

The neutral referees of a village jatra: A village jatra stays honest only if the person running the trustee election, the auditor, the elder dividing the collection and the panel hiring staff are all independent of the committee they watch — just as the Election Commission, CAG, Finance Commission and PSCs are protected from the government.

  • Election Commission: Art. 324; set up 25 January 1950; multi-member (CEC + 2 ECs) since 1993
  • CEC Act 2023: selection by PM, Leader of Opposition (LS), a Cabinet Minister; term 6 years or 65
  • CEC removed like an SC judge; other ECs only on CEC’s recommendation
  • Panchayat and municipal elections: State Election Commission (Art. 243K, 243ZA), not ECI
  • CAG: Art. 148–151; 6 years or 65; no further office; Union reports to President, state reports to Governor
  • Finance Commission: Art. 280; every 5 years; chairman + 4 members; advisory; 1st K.C. Neogy; 16th Arvind Panagariya (2026–31)
  • UPSC/SPSC: Art. 315–323; UPSC 6 years or 65, SPSC 6 years or 62 (41st Amendment)
  • Removal of PSC members only by President; misbehaviour needs a Supreme Court inquiry (Art. 317)
  • NCSC Art. 338; NCST Art. 338A (89th); NCBC Art. 338B (102nd)
  • Non-constitutional: NITI Aayog (executive, 2015), NHRC and CVC (statutory)

Economy

National Income: GDP, GNP, NNP, Factor Cost vs Market Prices, Real vs Nominal

A Satara farm family’s year-end account: GDP is everything grown on the family’s own land whoever worked it; GNP is what the family members earned wherever they worked; NNP subtracts the tractor’s wear; factor cost strips out the mandi cess and adds back the fertiliser subsidy.

  • GDP = C + I + G + (X − M); counts only final goods and services produced within the domestic territory in a year
  • GNP = GDP + NFIA; NNP = GNP − depreciation; National Income = NNP at factor cost
  • Factor cost = Market price − indirect taxes + subsidies (market price − net indirect taxes)
  • GDP = GVA at basic prices + product taxes − product subsidies
  • GDP deflator = (Nominal GDP ÷ Real GDP) × 100; real growth ≈ nominal growth − inflation
  • Excluded: transfer payments, second-hand sales, purely financial transactions, unpaid household work. Included: imputed rent, farm produce kept for self-consumption
  • First estimate of India’s national income: Dadabhai Naoroji (1867-68, in Poverty and Un-British Rule in India); first scientific estimate: V.K.R.V. Rao (1931-32)
  • National Income Committee (1949) chaired by P.C. Mahalanobis; the CSO and NSSO were merged into the National Statistics Office (NSO) under MoSPI in 2019
  • Current GDP base year: 2022-23 (new series released 27 February 2026; previous base 2011-12)
  • Per capita income = National income ÷ population

Inflation: CPI, WPI, Demand-pull vs Cost-push, Stagflation, Deflation

The onion price at the Lasalgaon market: Onions get dearer either because buyers arrive with more money (demand-pull) or because growing and moving them costs more (cost-push); prices rising while farm work vanishes is stagflation, and a glut where prices fall is deflation.

  • Inflation rate = (Indexnow − Indexearlier) ÷ Indexearlier × 100
  • CPI (Rural/Urban/Combined): NSO, MoSPI; base year 2024 (series released 12 February 2026); includes services
  • WPI: Office of the Economic Adviser, DPIIT; base year 2022-23 (released 15 June 2026); goods only, no services
  • CPI-IW, CPI-AL, CPI-RL: Labour Bureau (Ministry of Labour and Employment)
  • RBI’s target variable is CPI (Combined) headline inflation (Urjit Patel Committee, 2014)
  • GDP deflator = Nominal GDP ÷ Real GDP × 100; widest coverage of all price measures
  • Demand-pull: excess demand; cost-push: rising input costs or supply shocks
  • Disinflation = falling rate of inflation; deflation = falling price level; stagflation = inflation + stagnation + unemployment
  • Core inflation excludes food and fuel; headline includes everything
  • Inflation helps debtors and hurts creditors and fixed-income earners

Money and Banking: Functions of Money, Money Supply (M0, M1, M3), Credit Creation, Types of Banks

The village patpedhi that lends the same rupees again and again: A village credit society keeps only a fraction of each deposit in its safe and lends the rest, which comes back as fresh deposits, so ₹1,000 of cash can support ₹10,000 of deposits when the safe-keeping share is 10%.

  • Functions: medium of exchange, unit of account, store of value, standard of deferred payment
  • M0 = currency in circulation + bankers’ deposits with RBI + other deposits with RBI (high-powered money)
  • M1 = currency with public + demand deposits + other deposits with RBI (narrow money)
  • M3 = M1 + net time deposits of banks (broad money); M2 and M4 add post office deposits
  • Money multiplier (simple) = 1 ÷ CRR; total deposits = initial deposit ÷ CRR
  • RBI: established 1 April 1935; nationalised 1 January 1949; headquarters Mumbai
  • Bank nationalisation: 14 banks on 19 July 1969, 6 banks on 15 April 1980
  • RRBs: from 2 October 1975 (RRB Act 1976); shareholding Centre 50 : sponsor bank 35 : State 15
  • Payments banks: deposits up to ₹2 lakh per customer, no lending, can issue debit (not credit) cards
  • ₹1 notes and all coins are issued by the Government of India; other notes by the RBI

RBI and Monetary Policy: Repo, Reverse Repo, CRR, SLR, MPC and Inflation Targeting

The irrigation dam and its canal committee: The RBI runs liquidity like a dam: the repo rate is the price of canal water released to banks, CRR is water that must stay locked in the dam, SLR is water each farmer must keep in his own tank, and the MPC is the six-member committee that sets the water price to keep the reservoir level near 4%.

  • Repo: RBI lends to banks against securities; SDF (floor) = repo − 0.25%; MSF (ceiling) = repo + 0.25%
  • Bank rate (RBI Act s. 49) is aligned with the MSF rate
  • CRR: cash with RBI, RBI Act s. 42, earns no interest; SLR: with the bank itself, Banking Regulation Act s. 24, ceiling 40%
  • Inflation control: raise repo/CRR/SLR, sell securities (OMO). Growth support: the reverse
  • Inflation target: CPI (Combined) 4% ± 2%; notified on 25 March 2026 for 1 April 2026 – 31 March 2031 (RBI Act s. 45ZA)
  • Failure: inflation outside 2–6% for three consecutive quarters; RBI reports to the Government
  • MPC (s. 45ZB): 6 members, 3 from RBI (Governor, Deputy Governor, one officer) + 3 external appointed by Centre for 4 years
  • MPC meets at least 4 times a year; quorum 4; Governor has a casting vote
  • Framework introduced by amending the RBI Act through the Finance Act 2016; Urjit Patel Committee (2014)
  • Qualitative tools: margin requirement, credit rationing, moral suasion, direct action

Union Budget and Fiscal Policy: Revenue vs Capital, Fiscal, Revenue and Primary Deficits, FRBM

A farm family’s yearly hisab: Borrowing to buy groceries is a revenue deficit, all new borrowing is the fiscal deficit, and borrowing beyond the interest on old loans is the primary deficit; FRBM is the family rule that caps the debt.

  • Revenue deficit = revenue expenditure − revenue receipts
  • Fiscal deficit = total expenditure − revenue receipts − non-debt capital receipts = total borrowing
  • Primary deficit = fiscal deficit − interest payments
  • Effective revenue deficit = revenue deficit − grants for creation of capital assets
  • Interest received and PSU dividends are revenue receipts; recovery of loans and disinvestment are non-debt capital receipts
  • Art. 112 Annual Financial Statement; Art. 266 Consolidated Fund; Art. 267 Contingency Fund; Art. 116 vote on account; Art. 265 no tax without law
  • FRBM Act 2003; 2018 amendment: FD 3% by March 2021, central debt 40% of GDP by 2024-25, revenue-deficit target dropped, escape clause
  • From 2026-27: debt-to-GDP is the anchor, central debt about 50 ± 1% of GDP by 31 March 2031
  • Budget 2026-27 fiscal deficit target: 4.3% of GDP (2025-26 revised estimate: 4.4%)
  • Budget date 1 February and Railway Budget merged: both from 2017

Taxation and GST: Direct vs Indirect, Progressive vs Regressive, GST Structure and Council

Sugarcane to jaggery to pedha: tax only on what each stage adds: Under GST each person in the cane → jaggery → sweet-shop chain pays tax only on the value they add, getting credit for tax already paid; the GST Council is a joint table where the Centre holds one-third of the votes, the states two-thirds, and nothing passes without three-quarters.

  • Direct: impact and incidence on the same person (income tax, corporation tax). Indirect: burden shifted (GST, customs)
  • Progressive: rate rises with income; proportional: same rate; regressive: share of income falls as income rises
  • GST: 101st Amendment Act 2016; in force from 1 July 2017; Art. 246A, 269A (IGST), 279A (Council), 366(12A)
  • Intra-state supply: CGST + SGST; inter-state supply and imports: IGST
  • Outside GST by the Constitution: alcoholic liquor for human consumption. Five petroleum products: in scope, rate not yet notified
  • GST Council chair: Union Finance Minister; Vice-Chairperson: chosen from state ministers
  • Council voting: Centre 1/3 weight, states 2/3; decision needs ≥ 3/4 of weighted votes present and voting; quorum one-half
  • Rates after the 56th Council meeting (in force from 22 Sept 2025): 5% and 18% main slabs, 40% on sin/luxury goods
  • Mohit Minerals (2022): Council recommendations are not binding on Parliament and states
  • Income-tax Act, 2025 in force from 1 April 2026; introduces a single “tax year”

Planning in India: Five-Year Plans to NITI Aayog

The joint family’s karta and the family adviser: The Planning Commission was like a karta who drew up the five-year family plan and controlled each son’s share of money from the top; NITI Aayog is like a trusted adviser who brings all the brothers to one table but holds no purse.

  • Planning Commission: 15 March 1950, Cabinet resolution, extra-constitutional and non-statutory; chairman PM
  • National Development Council: 1952; approved Five-Year Plans
  • 1st Plan 1951–56: agriculture, Harrod–Domar model
  • 2nd Plan 1956–61: heavy industry, Mahalanobis model
  • Plan holiday: 1966–69 (three annual plans); Rolling Plan: 1978–80
  • 4th Plan (1969–74): growth with stability; D.R. Gadgil, Gadgil formula (1969) for central assistance to states
  • 5th Plan: “Garibi Hatao”; 8th Plan (1992–97): first after LPG reforms, indicative planning
  • 11th Plan: faster and more inclusive growth; 12th Plan (2012–17): faster, more inclusive and sustainable growth; last plan
  • NITI Aayog: 1 January 2015; think tank, cooperative federalism; no power to allocate funds
  • NITI Governing Council: PM + CMs of all states and UTs with legislature + LGs of other UTs

Poverty and Unemployment: Measurement, Types, Schemes (MGNREGA etc.)

Who has work in a Beed village?: Five brothers on a two-acre farm (disguised), cane-cutters idle after the crushing season (seasonal), powerloom weavers replaced by new machines (structural), a graduate between two jobs (frictional): each is a different kind of unemployment needing a different cure.

  • Alagh (1979): 2,400 kcal rural, 2,100 kcal urban; Lakdawala (1993); Tendulkar (2009): 21.9% in 2011-12; Rangarajan (2014): 29.5% in 2011-12
  • National MPI (NITI Aayog): 3 dimensions, 12 indicators; 29.17% (2013-14) → 11.28% (2022-23); 24.82 crore escaped
  • Unemployment rate = unemployed ÷ labour force × 100 (not ÷ population)
  • LFPR = labour force ÷ population; WPR = employed ÷ population
  • PLFS (NSO) since 2017-18; usual status = 365 days, current weekly status = 7 days
  • Disguised unemployment: marginal productivity of labour is zero; typical of agriculture
  • Maharashtra EGS: V.S. Page; began 1972-73; Maharashtra Employment Guarantee Act 1977; model for MGNREGA
  • MGNREGA 2005: from 2 February 2006; 100 days; repealed from 1 July 2026
  • VB-G RAM G Act 2025: in force 1 July 2026; 125 days; Centre : State 60 : 40 (90 : 10 NE and Himalayan); up to 60-day pause in peak farm season
  • DAY-NRLM 2011; PMKVY 2015; PM-KISAN 2019; NFSA 2013

Agricultural Economics: MSP, Green Revolution, APMC, Cooperatives (Maharashtra’s sugar and dairy co-ops)

A milk can’s journey from a Kolhapur village: The village dairy society’s assured rate is like MSP, the crossbred cow with feed and vet care is the Green Revolution package, the licensed vegetable yard is the APMC, and the farmer-owned society, union and factory are the cooperative model.

  • MSP: announced by the Centre on CACP’s recommendation for 22 mandated crops; not statutory; at least 1.5 × A2 + FL since 2018-19
  • CACP: 1965 (as Agricultural Prices Commission; renamed 1985); attached office of the Ministry of Agriculture
  • Sugarcane: FRP fixed by the Centre under the Sugarcane (Control) Order 1966; replaced SMP from 2009-10
  • Green Revolution: mid-1960s; Norman Borlaug, M.S. Swaminathan, C. Subramaniam; mainly wheat; Punjab, Haryana, western UP
  • Agricultural markets: State List Entry 28; Maharashtra APMC Act 1963; Lasalgaon = Asia’s largest onion market
  • e-NAM launched 14 April 2016; three farm laws of 2020 repealed in 2021
  • Pravara (Pravaranagar, Ahilyanagar district): Asia’s first cooperative sugar factory; organised 1948, commissioned 1950; Vithalrao Vikhe Patil and D.R. Gadgil
  • Operation Flood from 1970; NDDB 1965; Verghese Kurien; Amul 1946
  • 97th Amendment 2011: Art. 19(1)(c), Art. 43B, Part IXB; Ministry of Cooperation July 2021
  • Maharashtra Co-operative Societies Act 1960

External Sector: Balance of Payments, Exchange Rates, FDI vs FPI, WTO

A Nashik grape village’s dealings with the outside world: The village’s grape sales minus what it buys from outside, plus money its sons send home, is its current account; a city firm building a cold storage that stays is FDI, a city investor buying shares for quick gains is FPI.

  • Current account = merchandise trade + invisibles (services, primary income, transfers)
  • Capital account: FDI, FPI, ECBs, external assistance, banking capital, NRI deposits
  • CA + KA + errors and omissions = change in forex reserves
  • Rupee depreciation: exports cheaper, imports dearer; may narrow trade deficit but raises imported inflation
  • Rupee depreciation % = (1 − old rate ÷ new rate) × 100 when the rate is ₹ per $
  • FDI ≥ 10% of equity of a listed company; FPI < 10% (Arvind Mayaram Committee, 2014)
  • Current account convertibility: August 1994; capital account partially convertible
  • LERMS 1992; market-determined rate 1993; FEMA 1999 replaced FERA 1973
  • WTO: 1 January 1995; Marrakesh Agreement; Uruguay Round; HQ Geneva; India a founder member
  • WTO agreements: AoA (amber/blue/green box), TRIPS, TRIMS, GATS

Science and Environment

Light: Reflection, Refraction, Lenses and Defects of Vision

A wari dindi stepping from the road onto the riverbank sand at Pandharpur: Light bends at a boundary for the same reason a row of warkaris swings when one end reaches soft sand first: the side that slows down first turns the whole line.

  • Refractive index n = c / v; light in glass (n = 1.5) travels at 2 × 10⁸ m/s
  • Power P = 1/f (f in metres); unit dioptre (D); convex +, concave −; P = P₁ + P₂ for lenses in contact
  • Mirror formula 1/v + 1/u = 1/f; lens formula 1/v − 1/u = 1/f; f = R/2 for mirrors
  • Convex mirror: rear-view mirror (wide field, erect diminished image). Concave mirror: headlights, shaving, dentist
  • Total internal reflection: optical fibre, diamond sparkle, mirage (denser → rarer, angle > critical angle)
  • Dispersion: violet deviates most, red least. Scattering: blue sky; red sunset and red danger signals
  • Atmospheric refraction: twinkling stars, Sun visible about 2 minutes before sunrise and after sunset
  • Near point of normal eye 25 cm, far point infinity; accommodation by ciliary muscles
  • Myopia → concave lens; hypermetropia → convex lens; presbyopia → bifocal; astigmatism → cylindrical
  • Cataract: opaque eye lens, corrected by surgery; rods = dim light, cones = colour

Electricity and Magnetism: Ohm’s Law, Series/Parallel, Household Wiring, Electromagnetic Induction

Canal water from a dam reaching the fields of a village: Voltage is the height of water in the dam, current is the flow in the canal, resistance is a narrow channel, and each house on its own branch is a parallel connection.

  • Ohm’s law V = IR; R = ρL/A; SI unit of resistivity ohm-metre (Ω m)
  • Series: R = R₁ + R₂ + …; parallel: 1/R = 1/R₁ + 1/R₂ + … (total less than the smallest)
  • P = VI = I²R = V²/R; heat H = I²Rt (Joule’s law)
  • 1 kWh = 3.6 × 10⁶ J = 1 unit; units = (watts × hours) ÷ 1000
  • Indian mains: AC, 50 Hz; appliances in parallel; fuse/MCB in series with the live wire
  • NCERT wire colours: live red, neutral black, earth green
  • Nichrome: heating elements; tungsten: bulb filament; copper: wiring
  • Oersted (1820): current produces magnetic field; Faraday (1831): electromagnetic induction
  • Motor: Fleming’s left-hand rule; generator: Fleming’s right-hand rule; transformer works only on AC
  • High-voltage transmission reduces current and hence I²R losses

Atomic Structure, Isotopes and the Periodic Table

Allotting flats in a Mumbai cooperative housing society: The periodic table is a housing society where flats are numbered by atomic number, each floor is a period, and flats stacked in the same column share the same layout and so the same habits.

  • Thomson: electron (1897); Rutherford: nucleus (1911); Bohr: energy levels (1913); Chadwick: neutron (1932)
  • Neutrons = A − Z; maximum electrons in a shell = 2n²
  • Isotopes: same Z, different A; isobars: same A, different Z; isotones: same neutrons
  • Isotope uses: U-235 fuel, C-14 dating, Co-60 cancer therapy, I-131 thyroid, D₂O moderator
  • Mendeleev (1869): by atomic mass, left gaps (gallium, germanium, scandium predicted)
  • Moseley (1913): modern periodic law based on atomic number
  • Modern table: 18 groups, 7 periods, 118 elements
  • Across a period: radius ↓, metallic character ↓, electronegativity ↑; down a group: radius ↑
  • Most electronegative: fluorine; liquid metal: mercury; liquid non-metal: bromine
  • Most abundant in Earth’s crust: oxygen (element), aluminium (metal)

Acids, Bases, Salts and pH (everyday chemicals)

The soil health card at the Krishi Vigyan Kendra: An acidic Konkan field gets lime and a sodic Deccan field gets gypsum, just as an acid is neutralised by a base; the pH number on the soil card climbs one step for every tenfold drop in acidity.

  • pH = −log[H⁺]; 7 neutral at 25 °C; one pH unit = tenfold change in H⁺
  • Approximate pH: gastric juice 1.5–2, lemon 2, milk 6.5, blood 7.4; acid rain below 5.6; enamel corrodes below 5.5
  • Tamarind – tartaric; tomato – oxalic; curd – lactic; vinegar – acetic; ant sting – methanoic (formic)
  • Phenolphthalein: colourless in acid, pink in base; methyl orange: red in acid, yellow in base
  • Baking soda NaHCO₃; washing soda Na₂CO₃·10H₂O; bleaching powder CaOCl₂
  • Plaster of Paris CaSO₄·½H₂O; gypsum CaSO₄·2H₂O
  • Chlor-alkali process (brine electrolysis) → NaOH + Cl₂ + H₂
  • Antacid: milk of magnesia Mg(OH)₂; acidic soil corrected with lime, sodic soil with gypsum
  • Aqua regia = conc. HCl : conc. HNO₃ = 3 : 1, dissolves gold

Cell, DNA and Heredity (Mendel, sex determination, genetic disorders)

A cooperative sugar factory and its master register: A cell runs like a sugar factory: the nucleus is the head office holding the master register (DNA), and a child inherits one copy of each register page from each parent.

  • Hooke 1665 (cork cells); cell theory Schleiden and Schwann 1838–39; Virchow 1855 (cells from cells)
  • Prokaryote: no nuclear membrane (bacteria); plant cell: cell wall, chloroplast, large vacuole
  • Mitochondria: ATP, own DNA; ribosome: protein synthesis; lysosome: suicide bag; Golgi: packaging
  • DNA double helix: Watson and Crick, 1953; A–T, G–C; RNA has uracil instead of thymine
  • Humans: 46 chromosomes = 22 pairs autosomes + XX or XY; gametes have 23
  • Mendel: garden pea, 7 traits; laws of dominance, segregation, independent assortment
  • Monohybrid F₂: 3 : 1 phenotype, 1 : 2 : 1 genotype; dihybrid F₂: 9 : 3 : 3 : 1
  • Father’s sperm (X or Y) decides the child’s sex
  • Down = trisomy 21; Turner = XO; Klinefelter = XXY; haemophilia and colour blindness X-linked recessive
  • Sickle-cell anaemia: autosomal recessive; Elimination Mission launched 1 July 2023, target 2047

Human Body Systems: Digestion, Circulation, Respiration, Nervous and Endocrine

Mumbai’s dabbawalas, local trains and control room: Blood is Mumbai’s dabbawala network delivering tiffins (oxygen and food) and collecting empties (carbon dioxide), nerves are the phone line for instant orders, and hormones are the slow posted circulars.

  • Starch digestion begins in the mouth (salivary amylase); protein digestion begins in the stomach (pepsin)
  • Bile (from liver, stored in gall bladder) emulsifies fats; it contains no enzymes
  • Villi of the small intestine absorb digested food; large intestine absorbs water
  • Pulmonary artery: deoxygenated blood; pulmonary vein: oxygenated blood
  • SA node = pacemaker; normal BP about 120/80 mm Hg; RBC lifespan about 120 days
  • O = universal donor, AB = universal recipient (ABO system, Landsteiner)
  • Anaerobic respiration in muscles → lactic acid; in yeast → ethanol + CO₂
  • Cerebrum: thinking; cerebellum: balance; medulla: heartbeat and breathing
  • Pituitary = master gland; thyroxine needs iodine; insulin (β-cells) lowers blood sugar
  • Adrenaline: emergency (fight or flight) hormone from the adrenal gland

Nutrition, Vitamins, Diseases and Immunity (vaccines, pathogens)

Defending a Sahyadri hill fort: The body defends itself like a Maratha hill fort: walls and gates stop most raiders, guards attack any intruder, and a mock drill with a dummy enemy (a vaccine) trains the garrison to recognise the real one fast.

  • Fat-soluble: A, D, E, K; water-soluble: B-complex, C
  • A – night blindness; B1 – beriberi; B3 – pellagra; B12 – pernicious anaemia; C – scurvy; D – rickets; K – clotting failure
  • Iron – anaemia; iodine – goitre; kwashiorkor = protein deficiency; marasmus = protein + calorie deficiency
  • Bacterial: TB, cholera, typhoid, tetanus, leprosy; viral: polio, measles, dengue, rabies, AIDS; protozoan: malaria, kala-azar
  • Aedes: dengue, chikungunya (day-biting); female Anopheles: malaria; Culex: filariasis, Japanese encephalitis
  • B-cells: antibodies; T-cells: cell-mediated immunity; HIV attacks helper T-cells
  • Active immunity: infection or vaccine (long-lasting); passive: ready-made antibodies (short-lived)
  • Antibiotics act on bacteria, not viruses; penicillin – Alexander Fleming, 1928
  • Jenner – smallpox vaccine 1796; smallpox declared eradicated 1980; India certified polio-free 27 March 2014
  • Universal Immunisation Programme 1985; Mission Indradhanush December 2014

Ecology: Food Chains, Energy Flow (10% law), Biogeochemical Cycles

A cooperative sugar factory’s crushing season: Like cane passing through a sugar factory, only about a tenth of the energy at each step reaches the next, and the rest leaves as heat; but the press mud goes back to the fields, just as nutrients cycle.

  • Trophic levels: producers → primary consumers → secondary → tertiary; decomposers recycle
  • 10% law: Raymond Lindeman, 1942; only about 10% of energy passes to the next level
  • Energy flow is unidirectional; nutrients cycle
  • Pyramid of energy always upright; number (tree) and biomass (ocean) can be inverted
  • Plants capture only 2–10% of photosynthetically active radiation (NCERT)
  • N₂ fixation: Rhizobium (legume nodules), Azotobacter (free-living), Anabaena and Nostoc (cyanobacteria)
  • Nitrification: Nitrosomonas (NH₃ → NO₂⁻), Nitrobacter (NO₂⁻ → NO₃⁻); denitrification: Pseudomonas
  • Phosphorus cycle: sedimentary, no significant atmospheric phase
  • Pioneer species on bare rock: lichens; ecotone shows edge effect
  • Biomagnification: concentration of DDT or mercury rises up the food chain

Biodiversity and Conservation (hotspots, IUCN categories, Maharashtra’s national parks and tiger reserves)

A tribal community seed bank in the Sahyadri hills: Biodiversity is like a village’s collection of traditional seed varieties: keep growing them in the fields (in-situ) or store them in the seed bank (ex-situ), and grade each variety by how close it is to being lost.

  • Three levels of biodiversity: genetic, species, ecosystem
  • Hotspot criteria: at least 1,500 endemic vascular plants and at least 70% habitat lost; 36 worldwide; India has parts of 4
  • India’s hotspots: Himalaya, Indo-Burma, Western Ghats and Sri Lanka, Sundaland (Nicobar)
  • IUCN threatened categories: Vulnerable, Endangered, Critically Endangered; Near Threatened is not “threatened”
  • Great Indian Bustard: Critically Endangered; Forest Owlet (Melghat): Endangered
  • In-situ: national parks, sanctuaries, tiger reserves, sacred groves; ex-situ: zoos, botanical gardens, seed banks
  • Wildlife (Protection) Act 1972; Project Tiger 1 April 1973; Biological Diversity Act 2002
  • Maharashtra has 6 tiger reserves: Melghat, Tadoba-Andhari, Pench, Sahyadri, Nawegaon-Nagzira, Bor
  • Melghat – Amravati; Tadoba-Andhari – Chandrapur; Pench – Nagpur; Nawegaon-Nagzira – Gondia/Bhandara; Bor – Wardha; Sahyadri – Satara/Sangli/Kolhapur/Ratnagiri
  • Tadoba (1955): oldest national park in Maharashtra; Bor (2014): newest tiger reserve; Nandur Madhameshwar: first Ramsar site of Maharashtra

Climate Change, Ozone Depletion and Pollution (greenhouse effect, Kyoto, Paris, Montreal Protocol)

A polyhouse and its shade net on a Nashik flower farm: Greenhouse gases act like a polyhouse film that lets sunlight in but traps the heat, while the ozone layer is the shade net above it that blocks harsh ultraviolet; thickening the film warms the Earth, tearing the net lets UV through.

  • Natural greenhouse effect keeps Earth near 15 °C (would be about −18 °C without it)
  • Major GHGs: water vapour, CO₂, CH₄, N₂O, HFCs, PFCs, SF₆; CO₂ is the largest human-caused contributor
  • Ozone layer: stratosphere; absorbs UV; destroyed by chlorine from CFCs and bromine from halons
  • Vienna Convention 1985; Montreal Protocol 1987 (World Ozone Day 16 September); Kigali Amendment 2016 (HFCs)
  • UNFCCC 1992 (Rio); Kyoto 1997 (in force 2005), binding cuts only for developed countries
  • Paris Agreement 2015 (COP21): well below 2 °C, pursue 1.5 °C; NDCs from all countries
  • India: net-zero target 2070, announced at COP26 Glasgow (2021)
  • Acid rain: pH below 5.6 (SO₂, NOₓ); higher BOD = more polluted water
  • Eutrophication: excess N and P → algal bloom → oxygen depletion
  • Bhopal 1984 (methyl isocyanate) → Environment (Protection) Act 1986; NGT 2010

CSAT (Paper II)

Reading Comprehension: Main Idea, Inference and Assumption

Listening to a gram sabha speech: Like a villager at the gram sabha, answer only from what the sarpanch actually said, not from what you already believe about the village.

  • Main idea = covers the whole passage; too narrow (one detail) and too broad (beyond the text) are the two classic wrong options
  • Inference = must be true from the passage alone; “could be true” is not enough
  • Assumption = unstated premise; negate it, and if the argument collapses it was assumed
  • Extreme words (always, never, only, all, completely) usually signal a wrong option
  • Signal words: however, but, yet mark a turn; therefore, thus, hence mark the conclusion
  • Outside knowledge, even if true, is not a valid basis for an answer
  • Tone words to know: critical, cautionary, optimistic, neutral, sarcastic, analytical
  • Order: read the question stem first, then the passage, then eliminate options

Decision Making and Problem Solving (administrative situations)

The talathi’s four-question sieve: Pass every option through four sieves, legal, honest, humane and effective, and the one that passes all four is the answer.

  • Four tests: legality, integrity, empathy, effectiveness; the best option passes all four
  • Life and safety come first in any disaster or emergency situation
  • Dialogue before force; force (if ever) only as a last resort and within law
  • Conflict of interest (relative, friend, own interest): disclose and recuse, do not decide yourself
  • Bribe or gift offer: refuse, record and report as per rules, then decide the file on merits
  • Passive options (wait and watch, pass it on, ignore) are almost never the best
  • Harsh options (suspend, punish first, use force first) are rarely the best for a first or honest lapse
  • Fix the individual case, then fix the process so it does not recur
  • Negative marking for decision-making is commonly said to be nil in MPSC CSAT: check the current notification

Number System: Divisibility, HCF and LCM, Remainders, Unit Digits

Packing mangoes into crates at the Ratnagiri orchard: HCF is the biggest crate that empties every heap exactly; LCM is the first day all the trucks are back at the orchard together.

  • Divisible by 8: last three digits divisible by 8; by 11: (odd-place sum − even-place sum) is 0 or a multiple of 11
  • HCF × LCM = product of the two numbers (only for two numbers)
  • HCF of fractions = HCF of numerators ÷ LCM of denominators; LCM of fractions = LCM of numerators ÷ HCF of denominators
  • Largest number dividing a, b, c leaving remainders p, q, r = HCF(a−p, b−q, c−r)
  • Least number leaving the same remainder r with x, y, z = LCM(x, y, z) + r
  • Unit digit cycles: 2 → 2,4,8,6; 3 → 3,9,7,1; 7 → 7,9,3,1; 8 → 8,4,2,6 (period 4); 4 and 9 period 2; 0,1,5,6 fixed
  • Exponent remainder 0 (when divided by 4) means take the 4th term of the cycle
  • Dividend = divisor × quotient + remainder; remainder is always less than the divisor

Percentages, Profit and Loss, Simple and Compound Interest

The kirana shop’s base price: A percentage is always “of something”: find which price the kirana owner is talking about before you calculate.

  • Successive change of a% and b%: net = a + b + ab/100
  • Price up r%: cut consumption by r/(100 + r) × 100% to keep expenditure unchanged (25% up → 20% cut)
  • Profit or loss % is on CP; discount % is on MP
  • SP = CP × (100 + profit%)/100 = MP × (100 − discount%)/100
  • False weight: gain % = (error ÷ true value given) × 100, e.g. 900 g for 1 kg → 11.11%
  • SI = PRT/100; A = P(1 + R/100)T for compound interest
  • CI − SI for 2 years = P(R/100)²
  • Two successive discounts of a% and b% = single discount of a + b − ab/100

Ratio, Proportion, Averages and Mixtures

Sharing the sugar cooperative’s bonus: A ratio is a share of the cooperative’s pot; an average is levelling every member’s cane to one height; a mixture is two grades of cane crushed into one.

  • Share in ratio a : b : c = total × part ÷ (a + b + c)
  • Fraction ratios: multiply all terms by the LCM of denominators (1/2 : 1/3 : 1/4 = 6 : 4 : 3)
  • Proportion a : b = c : d ⇔ ad = bc; mean proportional of a and b = √(ab)
  • Average = sum ÷ number; removed item = old total − new total
  • Corrected average = old average − (wrong value − right value) ÷ n
  • Alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper)
  • In “add water” problems, the quantity of milk does not change
  • Average speed over equal distances = 2xy ÷ (x + y)

Time and Work, Pipes and Cisterns

Tankers filling the village water tank: Think of every worker as a tanker pouring a fixed share of the village tank each hour: add the shares of those pouring in, subtract the leaks.

  • A does a job in a days ⇒ A’s rate = 1/a per day
  • A and B together: ab/(a + b) days
  • LCM method: total work = LCM of the days; rate = LCM ÷ days
  • Chain rule: M₁D₁H₁/W₁ = M₂D₂H₂/W₂
  • If A is k times as efficient as B, A takes 1/k of B’s time
  • Pipe fills in x h, with leak in y h ⇒ leak empties in xy/(y − x) h
  • Outlet or leak = negative rate; net rate = sum of inlets − sum of outlets
  • Wages are shared in the ratio of work done

Time, Speed and Distance (trains, boats, relative speed)

Two ST buses on the Pune–Nashik highway: Two ST buses approaching each other close the gap at the sum of their speeds; one chasing the other closes it at the difference.

  • Distance = speed × time; 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h
  • Average speed (equal distances at x and y) = 2xy ÷ (x + y)
  • Opposite directions: relative speed = sum; same direction: difference
  • Train passing a pole or person: distance = train length
  • Train passing a platform or another train: distance = sum of lengths
  • Downstream = b + s; upstream = b − s
  • b = (down + up) ÷ 2; s = (down − up) ÷ 2
  • Meeting time of two bodies starting together towards each other = gap ÷ (sum of speeds)

Number and Letter Series, Coding–Decoding

The dabbawala’s tiffin code: Like a dabbawala reading the painted marks on a tiffin, find the one rule that turns each mark into the next, then apply it.

  • Check differences first, then second differences, then ratios
  • Common forms: n² ± 1, n(n + 1), n³ ± 1, × 2 + 1, primes
  • Alternating series: split odd- and even-position terms and solve each
  • Letter positions: E = 5, J = 10, O = 15, T = 20, Y = 25 (EJOTY)
  • Reverse position = 27 − position (A ↔ Z, M ↔ N)
  • Shift past Z wraps around to A
  • Coding: verify the rule on every letter before applying it

Blood Relations and Direction Sense

Drawing the family tree at a village wedding: At a wedding, an aunt places everyone by drawing the family tree; in direction questions, a farmer places himself by drawing his walk across the fields.

  • Draw a family tree: one generation per row, spouses joined, gender marked
  • Read long relation chains from the inner end outwards
  • If gender is not given, the answer may be “cannot be determined”
  • Right turn = clockwise 90°; left turn = anticlockwise 90°
  • Facing north: right is east; facing south: right is west
  • Net displacement: add N–S moves and E–W moves separately, then √(x² + y²)
  • Morning shadow falls west; evening shadow falls east
  • Clockwise order of directions: N, NE, E, SE, S, SW, W, NW (45° apart)

Syllogisms and Statement–Conclusion

Venn circles of a village’s farmers and voters: Draw the village’s groups as circles on the gram panchayat register; a conclusion follows only if it is true in every way the circles can be drawn.

  • All A are B ⇒ Some A are B and Some B are A (but not All B are A)
  • Some A are B ⇒ Some B are A; No A is B ⇒ No B is A
  • All A are B + All B are C ⇒ All A are C
  • All A are B + No B is C ⇒ No A is C
  • Some + Some ⇒ no definite conclusion between the end terms
  • Either–or: same terms, neither follows alone, one is “some” and the other “no” (or “all” and “some not”)
  • A conclusion must hold in every possible Venn diagram; one counter-diagram kills it
  • Statements are taken as true even if they contradict common knowledge

Data Interpretation: Tables, Bar and Pie Charts

Reading the APMC market’s daily arrivals board: Read a DI table like the APMC arrivals board: know the units, compare like with like, and only then calculate.

  • Percentage change = (new − old) ÷ old × 100, always on the base (old) value
  • Percentage share = part ÷ total × 100
  • Pie chart: 100% = 360°, so 1% = 3.6°; angle = share % × 3.6
  • Amount in a pie sector = share % × total
  • Highest absolute increase is not necessarily the highest percentage increase
  • Average = total ÷ number of items; check units (thousand tonnes, ₹ lakh)
  • Approximate first; calculate exactly only when options are close