RSMSSB JE Exam cheat sheet

Rajasthan borders Pakistan to the west and five Indian states: Punjab, Haryana, Uttar Pradesh, Madhya Pradesh and Gujarat; it is India's largest state by area (342,239 sq km).

Thar Desert covers about 61% of the state; the Aravalli range runs southwest to northeast and separates the arid west from the relatively fertile east.

Major rivers: Chambal (perennial, from Madhya Pradesh), Luni (the only river of the Thar basin, ends in the Rann of Kutch), Banas (Aravalli-origin, joins Chambal), Mahi and Sabarmati.

Administrative divisions: 7 divisions (Jaipur, Jodhpur, Ajmer, Kota, Udaipur, Bikaner, Bharatpur) grouping the state's districts; district counts change with notifications, so verify current numbers.

Key festivals/fairs: Pushkar Camel Fair (Kartik Purnima, Ajmer), Teej (Jaipur), Gangaur, Desert Festival (Jaisalmer), Urs of Khwaja Moinuddin Chishti (Ajmer).

Protected areas include Ranthambore and Sariska Tiger Reserves, Keoladeo Ghana National Park (Bharatpur, Ramsar/UNESCO site), Desert National Park (Jaisalmer), Mukundra Hills and Ramgarh Vishdhari tiger reserves.

Minerals: Rajasthan leads in zinc-lead (Zawar, Rampura-Agucha), marble (Makrana), and is a major producer of sandstone, gypsum and rock phosphate; Sambhar Lake is a historic salt source.

Current affairs: track state budget, new districts/divisions, Rajasthan Renewable Energy Policy targets for solar parks (Bhadla, Jodhpur) and state government welfare schemes, which change frequently and require a current source.

Indian Constitution: adopted 26 November 1949, enforced 26 January 1950; Fundamental Rights in Part III (Articles 12-35), Directive Principles in Part IV (Articles 36-51).

Constitutional bodies vs statutory: Election Commission and UPSC are constitutional; NITI Aayog, NHRC and CBI are statutory/executive creations.

Indian geography superlatives: longest river Ganga, largest delta Sundarbans, highest peak Kangchenjunga (in India), largest freshwater lake Wular.

World organisations: UN founded 1945 (HQ New York), WTO 1995 (Geneva), IMF and World Bank 1944 Bretton Woods (Washington DC), WHO (Geneva).

Indian economy indicators: GDP, CPI (base year 2012), WPI (base year 2011-12), repo rate set by RBI's Monetary Policy Committee.

Space and defence milestones: ISRO Chandrayaan-3 landed near lunar south pole in 2023; Aditya-L1 solar mission; Gaganyaan human spaceflight programme.

Current affairs method: anchor on static facts (who holds which office, which country hosts which summit) because officeholders and host cities rotate annually.

Newton's laws: F = ma; action-reaction pairs act on different bodies, so they never cancel on one body.

SI units: force newton (kg·m/s²), pressure pascal (N/m²), work/energy joule, power watt, electric charge coulomb.

Ohm's law V = IR; resistors in series add, in parallel reciprocals add; electrical power P = VI = I²R = V²/R.

pH scale 0-14: acids pH<7, bases pH>7; strong acid + strong base gives salt and water (neutralisation).

Human body: largest organ skin, largest gland liver, oxygen-carrying pigment haemoglobin (iron), insulin from pancreas, vitamin C deficiency causes scurvy.

Cell: mitochondria are the powerhouse, ribosomes synthesise protein, chloroplasts carry out photosynthesis; plant cells have a cellulose cell wall.

Light: reflection angle of incidence equals angle of reflection; refraction bends light toward the normal when entering a denser medium; sound cannot travel in vacuum.

Quadratic roots: for ax²+bx+c=0, sum = -b/a, product = c/a; discriminant D = b²-4ac; real distinct roots when D>0.

Arithmetic progression: nth term a+(n-1)d, sum = n/2[2a+(n-1)d]; geometric progression nth term ar^(n-1), sum = a(rⁿ-1)/(r-1) for r≠1.

Percentage and profit: profit% = (SP-CP)/CP × 100; successive discounts of a% and b% equal a+b-ab/100 percent.

Time-speed-distance: distance = speed × time; for equal distances at speeds x and y, average speed = 2xy/(x+y).

Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h, curved surface 2πrh; sphere volume (4/3)πr³, surface 4πr².

Trigonometry: sin²θ+cos²θ=1; values sin30=1/2, sin45=1/√2, sin60=√3/2; tanθ = sinθ/cosθ.

Simple and compound interest: SI = PRT/100; CI amount = P(1+R/100)^T; for 2 years CI exceeds SI by P(R/100)².

Number series: check differences first, then ratios, then squares/cubes or alternating two-series patterns before assuming a rule.

Coding-decoding: map letter positions A=1 to Z=26 and check both forward and reverse (A=26) shifts; reversal of the alphabet is a common rule.

Blood relations: draw a family tree with gender marks; 'mother's brother' = maternal uncle, 'father's sister's son' = cousin.

Direction sense: fix north up; a right turn from north is east; net displacement uses Pythagoras on the north-south and east-west totals.

Seating arrangement: for a circle, facing centre means left is clockwise; facing outward reverses left and right.

Syllogism: apply Venn diagrams; a conclusion is valid only if true in every possible diagram of the premises.

Clock and calendar: hands coincide 11 times in 12 hours; angle = |30H - 5.5M| degrees; a normal year shifts the weekday by 1, a leap year by 2.

Memory hierarchy by speed: registers > cache > RAM > secondary storage; RAM is volatile, ROM and flash are non-volatile.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB.

OSI model has 7 layers; TCP/IP has 4; IPv4 addresses are 32-bit, IPv6 addresses are 128-bit.

Shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+S save, Alt+Tab switch windows, Ctrl+Shift+Esc opens Task Manager in Windows.

File extensions: .docx Word, .xlsx Excel, .pptx PowerPoint, .pdf portable document, .exe executable, .html web page.

Malware types: virus attaches to files, worm self-replicates over networks, trojan disguises as legitimate software, ransomware encrypts data for payment.

Internet basics: HTTP/HTTPS for web, SMTP for sending mail, POP3/IMAP for receiving; URL identifies a resource, DNS resolves names to IP addresses.

Hindi संधि: स्वर संधि (अ+इ=ए), व्यंजन संधि, विसर्ग संधि; संधि-विच्छेद करते समय मूल वर्ण पहचानें।

Hindi समास: तत्पुरुष (अंतिम पद प्रधान), द्वंद्व (दोनों पद प्रधान, 'और' लोप), बहुव्रीहि (अन्य पद प्रधान), द्विगु (संख्यावाची पूर्वपद)।

Hindi पर्यायवाची/विलोम और मुहावरे अर्थ सहित याद करें; 'अंधे की लाठी' का अर्थ है एकमात्र सहारा।

English parts of speech: identify the word's function in the sentence, not its meaning; 'fast' can be adjective, adverb or verb.

English tenses: present perfect (has/have + past participle) for past action with present relevance; past perfect for the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; only transitive verbs take passive.

Spotting errors: check subject-verb agreement, article use, preposition collocation (depend on, consist of) and parallelism in lists.

Civil: stress = force/area; strain = change in length/original length; Young's modulus E = stress/strain in the elastic range.

Civil: for a simply supported beam with central point load W and span L, maximum bending moment = WL/4; with uniform load w per unit length, M = wL²/8.

Civil concrete: nominal mixes M15 (1:2:4), M20 (1:1.5:3), M25 (1:1:2); water-cement ratio controls strength and workability.

Electrical: in a series circuit current is common, voltage divides; in parallel voltage is common, current divides; total resistance of two parallel resistors = R1R2/(R1+R2).

Electrical: three-phase power P = √3 V_L I_L cosφ; transformer EMF per turn is constant, so V1/V2 = N1/N2.

Mechanical: Carnot efficiency = 1 - T_cold/T_hot (absolute temperatures); Otto cycle efficiency = 1 - 1/r^(γ-1) with compression ratio r.

Mechanical: first law of thermodynamics Q = ΔU + W; for an adiabatic process Q = 0, so W = -ΔU.

Agriculture: NPK ratio denotes nitrogen, phosphorus and potassium; legumes fix atmospheric nitrogen via Rhizobium in root nodules; seed rate and spacing determine plant population per hectare.

Rajasthan borders Pakistan to the west and five Indian states: Punjab, Haryana, Uttar Pradesh, Madhya Pradesh and Gujarat; it is India's largest state by area (342,239 sq km).

Thar Desert covers about 61% of the state; the Aravalli range runs southwest to northeast and separates the arid west from the relatively fertile east.

Major rivers: Chambal (perennial, from Madhya Pradesh), Luni (the only river of the Thar basin, ends in the Rann of Kutch), Banas (Aravalli-origin, joins Chambal), Mahi and Sabarmati.

Administrative divisions: 7 divisions (Jaipur, Jodhpur, Ajmer, Kota, Udaipur, Bikaner, Bharatpur) grouping the state's districts; district counts change with notifications, so verify current numbers.

Key festivals/fairs: Pushkar Camel Fair (Kartik Purnima, Ajmer), Teej (Jaipur), Gangaur, Desert Festival (Jaisalmer), Urs of Khwaja Moinuddin Chishti (Ajmer).

Protected areas include Ranthambore and Sariska Tiger Reserves, Keoladeo Ghana National Park (Bharatpur, Ramsar/UNESCO site), Desert National Park (Jaisalmer), Mukundra Hills and Ramgarh Vishdhari tiger reserves.

Minerals: Rajasthan leads in zinc-lead (Zawar, Rampura-Agucha), marble (Makrana), and is a major producer of sandstone, gypsum and rock phosphate; Sambhar Lake is a historic salt source.

Current affairs: track state budget, new districts/divisions, Rajasthan Renewable Energy Policy targets for solar parks (Bhadla, Jodhpur) and state government welfare schemes, which change frequently and require a current source.

Indian Constitution: adopted 26 November 1949, enforced 26 January 1950; Fundamental Rights in Part III (Articles 12-35), Directive Principles in Part IV (Articles 36-51).

Constitutional bodies vs statutory: Election Commission and UPSC are constitutional; NITI Aayog, NHRC and CBI are statutory/executive creations.

Indian geography superlatives: longest river Ganga, largest delta Sundarbans, highest peak Kangchenjunga (in India), largest freshwater lake Wular.

World organisations: UN founded 1945 (HQ New York), WTO 1995 (Geneva), IMF and World Bank 1944 Bretton Woods (Washington DC), WHO (Geneva).

Indian economy indicators: GDP, CPI (base year 2012), WPI (base year 2011-12), repo rate set by RBI's Monetary Policy Committee.

Space and defence milestones: ISRO Chandrayaan-3 landed near lunar south pole in 2023; Aditya-L1 solar mission; Gaganyaan human spaceflight programme.

Current affairs method: anchor on static facts (who holds which office, which country hosts which summit) because officeholders and host cities rotate annually.

Newton's laws: F = ma; action-reaction pairs act on different bodies, so they never cancel on one body.

SI units: force newton (kg·m/s²), pressure pascal (N/m²), work/energy joule, power watt, electric charge coulomb.

Ohm's law V = IR; resistors in series add, in parallel reciprocals add; electrical power P = VI = I²R = V²/R.

pH scale 0-14: acids pH<7, bases pH>7; strong acid + strong base gives salt and water (neutralisation).

Human body: largest organ skin, largest gland liver, oxygen-carrying pigment haemoglobin (iron), insulin from pancreas, vitamin C deficiency causes scurvy.

Cell: mitochondria are the powerhouse, ribosomes synthesise protein, chloroplasts carry out photosynthesis; plant cells have a cellulose cell wall.

Light: reflection angle of incidence equals angle of reflection; refraction bends light toward the normal when entering a denser medium; sound cannot travel in vacuum.

Quadratic roots: for ax²+bx+c=0, sum = -b/a, product = c/a; discriminant D = b²-4ac; real distinct roots when D>0.

Arithmetic progression: nth term a+(n-1)d, sum = n/2[2a+(n-1)d]; geometric progression nth term ar^(n-1), sum = a(rⁿ-1)/(r-1) for r≠1.

Percentage and profit: profit% = (SP-CP)/CP × 100; successive discounts of a% and b% equal a+b-ab/100 percent.

Time-speed-distance: distance = speed × time; for equal distances at speeds x and y, average speed = 2xy/(x+y).

Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h, curved surface 2πrh; sphere volume (4/3)πr³, surface 4πr².

Trigonometry: sin²θ+cos²θ=1; values sin30=1/2, sin45=1/√2, sin60=√3/2; tanθ = sinθ/cosθ.

Simple and compound interest: SI = PRT/100; CI amount = P(1+R/100)^T; for 2 years CI exceeds SI by P(R/100)².

Number series: check differences first, then ratios, then squares/cubes or alternating two-series patterns before assuming a rule.

Coding-decoding: map letter positions A=1 to Z=26 and check both forward and reverse (A=26) shifts; reversal of the alphabet is a common rule.

Blood relations: draw a family tree with gender marks; 'mother's brother' = maternal uncle, 'father's sister's son' = cousin.

Direction sense: fix north up; a right turn from north is east; net displacement uses Pythagoras on the north-south and east-west totals.

Seating arrangement: for a circle, facing centre means left is clockwise; facing outward reverses left and right.

Syllogism: apply Venn diagrams; a conclusion is valid only if true in every possible diagram of the premises.

Clock and calendar: hands coincide 11 times in 12 hours; angle = |30H - 5.5M| degrees; a normal year shifts the weekday by 1, a leap year by 2.

Memory hierarchy by speed: registers > cache > RAM > secondary storage; RAM is volatile, ROM and flash are non-volatile.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB.

OSI model has 7 layers; TCP/IP has 4; IPv4 addresses are 32-bit, IPv6 addresses are 128-bit.

Shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+S save, Alt+Tab switch windows, Ctrl+Shift+Esc opens Task Manager in Windows.

File extensions: .docx Word, .xlsx Excel, .pptx PowerPoint, .pdf portable document, .exe executable, .html web page.

Malware types: virus attaches to files, worm self-replicates over networks, trojan disguises as legitimate software, ransomware encrypts data for payment.

Internet basics: HTTP/HTTPS for web, SMTP for sending mail, POP3/IMAP for receiving; URL identifies a resource, DNS resolves names to IP addresses.

Hindi संधि: स्वर संधि (अ+इ=ए), व्यंजन संधि, विसर्ग संधि; संधि-विच्छेद करते समय मूल वर्ण पहचानें।

Hindi समास: तत्पुरुष (अंतिम पद प्रधान), द्वंद्व (दोनों पद प्रधान, 'और' लोप), बहुव्रीहि (अन्य पद प्रधान), द्विगु (संख्यावाची पूर्वपद)।

Hindi पर्यायवाची/विलोम और मुहावरे अर्थ सहित याद करें; 'अंधे की लाठी' का अर्थ है एकमात्र सहारा।

English parts of speech: identify the word's function in the sentence, not its meaning; 'fast' can be adjective, adverb or verb.

English tenses: present perfect (has/have + past participle) for past action with present relevance; past perfect for the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; only transitive verbs take passive.

Spotting errors: check subject-verb agreement, article use, preposition collocation (depend on, consist of) and parallelism in lists.

Civil: stress = force/area; strain = change in length/original length; Young's modulus E = stress/strain in the elastic range.

Civil: for a simply supported beam with central point load W and span L, maximum bending moment = WL/4; with uniform load w per unit length, M = wL²/8.

Civil concrete: nominal mixes M15 (1:2:4), M20 (1:1.5:3), M25 (1:1:2); water-cement ratio controls strength and workability.

Electrical: in a series circuit current is common, voltage divides; in parallel voltage is common, current divides; total resistance of two parallel resistors = R1R2/(R1+R2).

Electrical: three-phase power P = √3 V_L I_L cosφ; transformer EMF per turn is constant, so V1/V2 = N1/N2.

Mechanical: Carnot efficiency = 1 - T_cold/T_hot (absolute temperatures); Otto cycle efficiency = 1 - 1/r^(γ-1) with compression ratio r.

Mechanical: first law of thermodynamics Q = ΔU + W; for an adiabatic process Q = 0, so W = -ΔU.

Agriculture: NPK ratio denotes nitrogen, phosphorus and potassium; legumes fix atmospheric nitrogen via Rhizobium in root nodules; seed rate and spacing determine plant population per hectare.

Rajasthan borders Pakistan to the west and five Indian states: Punjab, Haryana, Uttar Pradesh, Madhya Pradesh and Gujarat; it is India's largest state by area (342,239 sq km).

Thar Desert covers about 61% of the state; the Aravalli range runs southwest to northeast and separates the arid west from the relatively fertile east.

Major rivers: Chambal (perennial, from Madhya Pradesh), Luni (the only river of the Thar basin, ends in the Rann of Kutch), Banas (Aravalli-origin, joins Chambal), Mahi and Sabarmati.

Administrative divisions: 7 divisions (Jaipur, Jodhpur, Ajmer, Kota, Udaipur, Bikaner, Bharatpur) grouping the state's districts; district counts change with notifications, so verify current numbers.

Key festivals/fairs: Pushkar Camel Fair (Kartik Purnima, Ajmer), Teej (Jaipur), Gangaur, Desert Festival (Jaisalmer), Urs of Khwaja Moinuddin Chishti (Ajmer).

Protected areas include Ranthambore and Sariska Tiger Reserves, Keoladeo Ghana National Park (Bharatpur, Ramsar/UNESCO site), Desert National Park (Jaisalmer), Mukundra Hills and Ramgarh Vishdhari tiger reserves.

Minerals: Rajasthan leads in zinc-lead (Zawar, Rampura-Agucha), marble (Makrana), and is a major producer of sandstone, gypsum and rock phosphate; Sambhar Lake is a historic salt source.

Current affairs: track state budget, new districts/divisions, Rajasthan Renewable Energy Policy targets for solar parks (Bhadla, Jodhpur) and state government welfare schemes, which change frequently and require a current source.

Indian Constitution: adopted 26 November 1949, enforced 26 January 1950; Fundamental Rights in Part III (Articles 12-35), Directive Principles in Part IV (Articles 36-51).

Constitutional bodies vs statutory: Election Commission and UPSC are constitutional; NITI Aayog, NHRC and CBI are statutory/executive creations.

Indian geography superlatives: longest river Ganga, largest delta Sundarbans, highest peak Kangchenjunga (in India), largest freshwater lake Wular.

World organisations: UN founded 1945 (HQ New York), WTO 1995 (Geneva), IMF and World Bank 1944 Bretton Woods (Washington DC), WHO (Geneva).

Indian economy indicators: GDP, CPI (base year 2012), WPI (base year 2011-12), repo rate set by RBI's Monetary Policy Committee.

Space and defence milestones: ISRO Chandrayaan-3 landed near lunar south pole in 2023; Aditya-L1 solar mission; Gaganyaan human spaceflight programme.

Current affairs method: anchor on static facts (who holds which office, which country hosts which summit) because officeholders and host cities rotate annually.

Newton's laws: F = ma; action-reaction pairs act on different bodies, so they never cancel on one body.

SI units: force newton (kg·m/s²), pressure pascal (N/m²), work/energy joule, power watt, electric charge coulomb.

Ohm's law V = IR; resistors in series add, in parallel reciprocals add; electrical power P = VI = I²R = V²/R.

pH scale 0-14: acids pH<7, bases pH>7; strong acid + strong base gives salt and water (neutralisation).

Human body: largest organ skin, largest gland liver, oxygen-carrying pigment haemoglobin (iron), insulin from pancreas, vitamin C deficiency causes scurvy.

Cell: mitochondria are the powerhouse, ribosomes synthesise protein, chloroplasts carry out photosynthesis; plant cells have a cellulose cell wall.

Light: reflection angle of incidence equals angle of reflection; refraction bends light toward the normal when entering a denser medium; sound cannot travel in vacuum.

Quadratic roots: for ax²+bx+c=0, sum = -b/a, product = c/a; discriminant D = b²-4ac; real distinct roots when D>0.

Arithmetic progression: nth term a+(n-1)d, sum = n/2[2a+(n-1)d]; geometric progression nth term ar^(n-1), sum = a(rⁿ-1)/(r-1) for r≠1.

Percentage and profit: profit% = (SP-CP)/CP × 100; successive discounts of a% and b% equal a+b-ab/100 percent.

Time-speed-distance: distance = speed × time; for equal distances at speeds x and y, average speed = 2xy/(x+y).

Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h, curved surface 2πrh; sphere volume (4/3)πr³, surface 4πr².

Trigonometry: sin²θ+cos²θ=1; values sin30=1/2, sin45=1/√2, sin60=√3/2; tanθ = sinθ/cosθ.

Simple and compound interest: SI = PRT/100; CI amount = P(1+R/100)^T; for 2 years CI exceeds SI by P(R/100)².

Number series: check differences first, then ratios, then squares/cubes or alternating two-series patterns before assuming a rule.

Coding-decoding: map letter positions A=1 to Z=26 and check both forward and reverse (A=26) shifts; reversal of the alphabet is a common rule.

Blood relations: draw a family tree with gender marks; 'mother's brother' = maternal uncle, 'father's sister's son' = cousin.

Direction sense: fix north up; a right turn from north is east; net displacement uses Pythagoras on the north-south and east-west totals.

Seating arrangement: for a circle, facing centre means left is clockwise; facing outward reverses left and right.

Syllogism: apply Venn diagrams; a conclusion is valid only if true in every possible diagram of the premises.

Clock and calendar: hands coincide 11 times in 12 hours; angle = |30H - 5.5M| degrees; a normal year shifts the weekday by 1, a leap year by 2.

Memory hierarchy by speed: registers > cache > RAM > secondary storage; RAM is volatile, ROM and flash are non-volatile.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB.

OSI model has 7 layers; TCP/IP has 4; IPv4 addresses are 32-bit, IPv6 addresses are 128-bit.

Shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+S save, Alt+Tab switch windows, Ctrl+Shift+Esc opens Task Manager in Windows.

File extensions: .docx Word, .xlsx Excel, .pptx PowerPoint, .pdf portable document, .exe executable, .html web page.

Malware types: virus attaches to files, worm self-replicates over networks, trojan disguises as legitimate software, ransomware encrypts data for payment.

Internet basics: HTTP/HTTPS for web, SMTP for sending mail, POP3/IMAP for receiving; URL identifies a resource, DNS resolves names to IP addresses.

Hindi संधि: स्वर संधि (अ+इ=ए), व्यंजन संधि, विसर्ग संधि; संधि-विच्छेद करते समय मूल वर्ण पहचानें।

Hindi समास: तत्पुरुष (अंतिम पद प्रधान), द्वंद्व (दोनों पद प्रधान, 'और' लोप), बहुव्रीहि (अन्य पद प्रधान), द्विगु (संख्यावाची पूर्वपद)।

Hindi पर्यायवाची/विलोम और मुहावरे अर्थ सहित याद करें; 'अंधे की लाठी' का अर्थ है एकमात्र सहारा।

English parts of speech: identify the word's function in the sentence, not its meaning; 'fast' can be adjective, adverb or verb.

English tenses: present perfect (has/have + past participle) for past action with present relevance; past perfect for the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; only transitive verbs take passive.

Spotting errors: check subject-verb agreement, article use, preposition collocation (depend on, consist of) and parallelism in lists.

Civil: stress = force/area; strain = change in length/original length; Young's modulus E = stress/strain in the elastic range.

Civil: for a simply supported beam with central point load W and span L, maximum bending moment = WL/4; with uniform load w per unit length, M = wL²/8.

Civil concrete: nominal mixes M15 (1:2:4), M20 (1:1.5:3), M25 (1:1:2); water-cement ratio controls strength and workability.

Electrical: in a series circuit current is common, voltage divides; in parallel voltage is common, current divides; total resistance of two parallel resistors = R1R2/(R1+R2).

Electrical: three-phase power P = √3 V_L I_L cosφ; transformer EMF per turn is constant, so V1/V2 = N1/N2.

Mechanical: Carnot efficiency = 1 - T_cold/T_hot (absolute temperatures); Otto cycle efficiency = 1 - 1/r^(γ-1) with compression ratio r.

Mechanical: first law of thermodynamics Q = ΔU + W; for an adiabatic process Q = 0, so W = -ΔU.

Agriculture: NPK ratio denotes nitrogen, phosphorus and potassium; legumes fix atmospheric nitrogen via Rhizobium in root nodules; seed rate and spacing determine plant population per hectare.

Rajasthan borders Pakistan to the west and five Indian states: Punjab, Haryana, Uttar Pradesh, Madhya Pradesh and Gujarat; it is India's largest state by area (342,239 sq km).

Thar Desert covers about 61% of the state; the Aravalli range runs southwest to northeast and separates the arid west from the relatively fertile east.

Major rivers: Chambal (perennial, from Madhya Pradesh), Luni (the only river of the Thar basin, ends in the Rann of Kutch), Banas (Aravalli-origin, joins Chambal), Mahi and Sabarmati.

Administrative divisions: 7 divisions (Jaipur, Jodhpur, Ajmer, Kota, Udaipur, Bikaner, Bharatpur) grouping the state's districts; district counts change with notifications, so verify current numbers.

Key festivals/fairs: Pushkar Camel Fair (Kartik Purnima, Ajmer), Teej (Jaipur), Gangaur, Desert Festival (Jaisalmer), Urs of Khwaja Moinuddin Chishti (Ajmer).

Protected areas include Ranthambore and Sariska Tiger Reserves, Keoladeo Ghana National Park (Bharatpur, Ramsar/UNESCO site), Desert National Park (Jaisalmer), Mukundra Hills and Ramgarh Vishdhari tiger reserves.

Minerals: Rajasthan leads in zinc-lead (Zawar, Rampura-Agucha), marble (Makrana), and is a major producer of sandstone, gypsum and rock phosphate; Sambhar Lake is a historic salt source.

Current affairs: track state budget, new districts/divisions, Rajasthan Renewable Energy Policy targets for solar parks (Bhadla, Jodhpur) and state government welfare schemes, which change frequently and require a current source.

Indian Constitution: adopted 26 November 1949, enforced 26 January 1950; Fundamental Rights in Part III (Articles 12-35), Directive Principles in Part IV (Articles 36-51).

Constitutional bodies vs statutory: Election Commission and UPSC are constitutional; NITI Aayog, NHRC and CBI are statutory/executive creations.

Indian geography superlatives: longest river Ganga, largest delta Sundarbans, highest peak Kangchenjunga (in India), largest freshwater lake Wular.

World organisations: UN founded 1945 (HQ New York), WTO 1995 (Geneva), IMF and World Bank 1944 Bretton Woods (Washington DC), WHO (Geneva).

Indian economy indicators: GDP, CPI (base year 2012), WPI (base year 2011-12), repo rate set by RBI's Monetary Policy Committee.

Space and defence milestones: ISRO Chandrayaan-3 landed near lunar south pole in 2023; Aditya-L1 solar mission; Gaganyaan human spaceflight programme.

Current affairs method: anchor on static facts (who holds which office, which country hosts which summit) because officeholders and host cities rotate annually.

Newton's laws: F = ma; action-reaction pairs act on different bodies, so they never cancel on one body.

SI units: force newton (kg·m/s²), pressure pascal (N/m²), work/energy joule, power watt, electric charge coulomb.

Ohm's law V = IR; resistors in series add, in parallel reciprocals add; electrical power P = VI = I²R = V²/R.

pH scale 0-14: acids pH<7, bases pH>7; strong acid + strong base gives salt and water (neutralisation).

Human body: largest organ skin, largest gland liver, oxygen-carrying pigment haemoglobin (iron), insulin from pancreas, vitamin C deficiency causes scurvy.

Cell: mitochondria are the powerhouse, ribosomes synthesise protein, chloroplasts carry out photosynthesis; plant cells have a cellulose cell wall.

Light: reflection angle of incidence equals angle of reflection; refraction bends light toward the normal when entering a denser medium; sound cannot travel in vacuum.

Quadratic roots: for ax²+bx+c=0, sum = -b/a, product = c/a; discriminant D = b²-4ac; real distinct roots when D>0.

Arithmetic progression: nth term a+(n-1)d, sum = n/2[2a+(n-1)d]; geometric progression nth term ar^(n-1), sum = a(rⁿ-1)/(r-1) for r≠1.

Percentage and profit: profit% = (SP-CP)/CP × 100; successive discounts of a% and b% equal a+b-ab/100 percent.

Time-speed-distance: distance = speed × time; for equal distances at speeds x and y, average speed = 2xy/(x+y).

Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h, curved surface 2πrh; sphere volume (4/3)πr³, surface 4πr².

Trigonometry: sin²θ+cos²θ=1; values sin30=1/2, sin45=1/√2, sin60=√3/2; tanθ = sinθ/cosθ.

Simple and compound interest: SI = PRT/100; CI amount = P(1+R/100)^T; for 2 years CI exceeds SI by P(R/100)².

Number series: check differences first, then ratios, then squares/cubes or alternating two-series patterns before assuming a rule.

Coding-decoding: map letter positions A=1 to Z=26 and check both forward and reverse (A=26) shifts; reversal of the alphabet is a common rule.

Blood relations: draw a family tree with gender marks; 'mother's brother' = maternal uncle, 'father's sister's son' = cousin.

Direction sense: fix north up; a right turn from north is east; net displacement uses Pythagoras on the north-south and east-west totals.

Seating arrangement: for a circle, facing centre means left is clockwise; facing outward reverses left and right.

Syllogism: apply Venn diagrams; a conclusion is valid only if true in every possible diagram of the premises.

Clock and calendar: hands coincide 11 times in 12 hours; angle = |30H - 5.5M| degrees; a normal year shifts the weekday by 1, a leap year by 2.

Memory hierarchy by speed: registers > cache > RAM > secondary storage; RAM is volatile, ROM and flash are non-volatile.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB.

OSI model has 7 layers; TCP/IP has 4; IPv4 addresses are 32-bit, IPv6 addresses are 128-bit.

Shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+S save, Alt+Tab switch windows, Ctrl+Shift+Esc opens Task Manager in Windows.

File extensions: .docx Word, .xlsx Excel, .pptx PowerPoint, .pdf portable document, .exe executable, .html web page.

Malware types: virus attaches to files, worm self-replicates over networks, trojan disguises as legitimate software, ransomware encrypts data for payment.

Internet basics: HTTP/HTTPS for web, SMTP for sending mail, POP3/IMAP for receiving; URL identifies a resource, DNS resolves names to IP addresses.

Hindi संधि: स्वर संधि (अ+इ=ए), व्यंजन संधि, विसर्ग संधि; संधि-विच्छेद करते समय मूल वर्ण पहचानें।

Hindi समास: तत्पुरुष (अंतिम पद प्रधान), द्वंद्व (दोनों पद प्रधान, 'और' लोप), बहुव्रीहि (अन्य पद प्रधान), द्विगु (संख्यावाची पूर्वपद)।

Hindi पर्यायवाची/विलोम और मुहावरे अर्थ सहित याद करें; 'अंधे की लाठी' का अर्थ है एकमात्र सहारा।

English parts of speech: identify the word's function in the sentence, not its meaning; 'fast' can be adjective, adverb or verb.

English tenses: present perfect (has/have + past participle) for past action with present relevance; past perfect for the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; only transitive verbs take passive.

Spotting errors: check subject-verb agreement, article use, preposition collocation (depend on, consist of) and parallelism in lists.

Civil: stress = force/area; strain = change in length/original length; Young's modulus E = stress/strain in the elastic range.

Civil: for a simply supported beam with central point load W and span L, maximum bending moment = WL/4; with uniform load w per unit length, M = wL²/8.

Civil concrete: nominal mixes M15 (1:2:4), M20 (1:1.5:3), M25 (1:1:2); water-cement ratio controls strength and workability.

Electrical: in a series circuit current is common, voltage divides; in parallel voltage is common, current divides; total resistance of two parallel resistors = R1R2/(R1+R2).

Electrical: three-phase power P = √3 V_L I_L cosφ; transformer EMF per turn is constant, so V1/V2 = N1/N2.

Mechanical: Carnot efficiency = 1 - T_cold/T_hot (absolute temperatures); Otto cycle efficiency = 1 - 1/r^(γ-1) with compression ratio r.

Mechanical: first law of thermodynamics Q = ΔU + W; for an adiabatic process Q = 0, so W = -ΔU.

Agriculture: NPK ratio denotes nitrogen, phosphorus and potassium; legumes fix atmospheric nitrogen via Rhizobium in root nodules; seed rate and spacing determine plant population per hectare.

Rajasthan borders Pakistan to the west and five Indian states: Punjab, Haryana, Uttar Pradesh, Madhya Pradesh and Gujarat; it is India's largest state by area (342,239 sq km).

Thar Desert covers about 61% of the state; the Aravalli range runs southwest to northeast and separates the arid west from the relatively fertile east.

Major rivers: Chambal (perennial, from Madhya Pradesh), Luni (the only river of the Thar basin, ends in the Rann of Kutch), Banas (Aravalli-origin, joins Chambal), Mahi and Sabarmati.

Administrative divisions: 7 divisions (Jaipur, Jodhpur, Ajmer, Kota, Udaipur, Bikaner, Bharatpur) grouping the state's districts; district counts change with notifications, so verify current numbers.

Key festivals/fairs: Pushkar Camel Fair (Kartik Purnima, Ajmer), Teej (Jaipur), Gangaur, Desert Festival (Jaisalmer), Urs of Khwaja Moinuddin Chishti (Ajmer).

Protected areas include Ranthambore and Sariska Tiger Reserves, Keoladeo Ghana National Park (Bharatpur, Ramsar/UNESCO site), Desert National Park (Jaisalmer), Mukundra Hills and Ramgarh Vishdhari tiger reserves.

Minerals: Rajasthan leads in zinc-lead (Zawar, Rampura-Agucha), marble (Makrana), and is a major producer of sandstone, gypsum and rock phosphate; Sambhar Lake is a historic salt source.

Current affairs: track state budget, new districts/divisions, Rajasthan Renewable Energy Policy targets for solar parks (Bhadla, Jodhpur) and state government welfare schemes, which change frequently and require a current source.

Indian Constitution: adopted 26 November 1949, enforced 26 January 1950; Fundamental Rights in Part III (Articles 12-35), Directive Principles in Part IV (Articles 36-51).

Constitutional bodies vs statutory: Election Commission and UPSC are constitutional; NITI Aayog, NHRC and CBI are statutory/executive creations.

Indian geography superlatives: longest river Ganga, largest delta Sundarbans, highest peak Kangchenjunga (in India), largest freshwater lake Wular.

World organisations: UN founded 1945 (HQ New York), WTO 1995 (Geneva), IMF and World Bank 1944 Bretton Woods (Washington DC), WHO (Geneva).

Indian economy indicators: GDP, CPI (base year 2012), WPI (base year 2011-12), repo rate set by RBI's Monetary Policy Committee.

Space and defence milestones: ISRO Chandrayaan-3 landed near lunar south pole in 2023; Aditya-L1 solar mission; Gaganyaan human spaceflight programme.

Current affairs method: anchor on static facts (who holds which office, which country hosts which summit) because officeholders and host cities rotate annually.

Newton's laws: F = ma; action-reaction pairs act on different bodies, so they never cancel on one body.

SI units: force newton (kg·m/s²), pressure pascal (N/m²), work/energy joule, power watt, electric charge coulomb.

Ohm's law V = IR; resistors in series add, in parallel reciprocals add; electrical power P = VI = I²R = V²/R.

pH scale 0-14: acids pH<7, bases pH>7; strong acid + strong base gives salt and water (neutralisation).

Human body: largest organ skin, largest gland liver, oxygen-carrying pigment haemoglobin (iron), insulin from pancreas, vitamin C deficiency causes scurvy.

Cell: mitochondria are the powerhouse, ribosomes synthesise protein, chloroplasts carry out photosynthesis; plant cells have a cellulose cell wall.

Light: reflection angle of incidence equals angle of reflection; refraction bends light toward the normal when entering a denser medium; sound cannot travel in vacuum.

Quadratic roots: for ax²+bx+c=0, sum = -b/a, product = c/a; discriminant D = b²-4ac; real distinct roots when D>0.

Arithmetic progression: nth term a+(n-1)d, sum = n/2[2a+(n-1)d]; geometric progression nth term ar^(n-1), sum = a(rⁿ-1)/(r-1) for r≠1.

Percentage and profit: profit% = (SP-CP)/CP × 100; successive discounts of a% and b% equal a+b-ab/100 percent.

Time-speed-distance: distance = speed × time; for equal distances at speeds x and y, average speed = 2xy/(x+y).

Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h, curved surface 2πrh; sphere volume (4/3)πr³, surface 4πr².

Trigonometry: sin²θ+cos²θ=1; values sin30=1/2, sin45=1/√2, sin60=√3/2; tanθ = sinθ/cosθ.

Simple and compound interest: SI = PRT/100; CI amount = P(1+R/100)^T; for 2 years CI exceeds SI by P(R/100)².

Number series: check differences first, then ratios, then squares/cubes or alternating two-series patterns before assuming a rule.

Coding-decoding: map letter positions A=1 to Z=26 and check both forward and reverse (A=26) shifts; reversal of the alphabet is a common rule.

Blood relations: draw a family tree with gender marks; 'mother's brother' = maternal uncle, 'father's sister's son' = cousin.

Direction sense: fix north up; a right turn from north is east; net displacement uses Pythagoras on the north-south and east-west totals.

Seating arrangement: for a circle, facing centre means left is clockwise; facing outward reverses left and right.

Syllogism: apply Venn diagrams; a conclusion is valid only if true in every possible diagram of the premises.

Clock and calendar: hands coincide 11 times in 12 hours; angle = |30H - 5.5M| degrees; a normal year shifts the weekday by 1, a leap year by 2.

Memory hierarchy by speed: registers > cache > RAM > secondary storage; RAM is volatile, ROM and flash are non-volatile.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB.

OSI model has 7 layers; TCP/IP has 4; IPv4 addresses are 32-bit, IPv6 addresses are 128-bit.

Shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+S save, Alt+Tab switch windows, Ctrl+Shift+Esc opens Task Manager in Windows.

File extensions: .docx Word, .xlsx Excel, .pptx PowerPoint, .pdf portable document, .exe executable, .html web page.

Malware types: virus attaches to files, worm self-replicates over networks, trojan disguises as legitimate software, ransomware encrypts data for payment.

Internet basics: HTTP/HTTPS for web, SMTP for sending mail, POP3/IMAP for receiving; URL identifies a resource, DNS resolves names to IP addresses.

Hindi संधि: स्वर संधि (अ+इ=ए), व्यंजन संधि, विसर्ग संधि; संधि-विच्छेद करते समय मूल वर्ण पहचानें।

Hindi समास: तत्पुरुष (अंतिम पद प्रधान), द्वंद्व (दोनों पद प्रधान, 'और' लोप), बहुव्रीहि (अन्य पद प्रधान), द्विगु (संख्यावाची पूर्वपद)।

Hindi पर्यायवाची/विलोम और मुहावरे अर्थ सहित याद करें; 'अंधे की लाठी' का अर्थ है एकमात्र सहारा।

English parts of speech: identify the word's function in the sentence, not its meaning; 'fast' can be adjective, adverb or verb.

English tenses: present perfect (has/have + past participle) for past action with present relevance; past perfect for the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; only transitive verbs take passive.

Spotting errors: check subject-verb agreement, article use, preposition collocation (depend on, consist of) and parallelism in lists.

Civil: stress = force/area; strain = change in length/original length; Young's modulus E = stress/strain in the elastic range.

Civil: for a simply supported beam with central point load W and span L, maximum bending moment = WL/4; with uniform load w per unit length, M = wL²/8.

Civil concrete: nominal mixes M15 (1:2:4), M20 (1:1.5:3), M25 (1:1:2); water-cement ratio controls strength and workability.

Electrical: in a series circuit current is common, voltage divides; in parallel voltage is common, current divides; total resistance of two parallel resistors = R1R2/(R1+R2).

Electrical: three-phase power P = √3 V_L I_L cosφ; transformer EMF per turn is constant, so V1/V2 = N1/N2.

Mechanical: Carnot efficiency = 1 - T_cold/T_hot (absolute temperatures); Otto cycle efficiency = 1 - 1/r^(γ-1) with compression ratio r.

Mechanical: first law of thermodynamics Q = ΔU + W; for an adiabatic process Q = 0, so W = -ΔU.

Agriculture: NPK ratio denotes nitrogen, phosphorus and potassium; legumes fix atmospheric nitrogen via Rhizobium in root nodules; seed rate and spacing determine plant population per hectare.

Rajasthan borders Pakistan to the west and five Indian states: Punjab, Haryana, Uttar Pradesh, Madhya Pradesh and Gujarat; it is India's largest state by area (342,239 sq km).

Thar Desert covers about 61% of the state; the Aravalli range runs southwest to northeast and separates the arid west from the relatively fertile east.

Major rivers: Chambal (perennial, from Madhya Pradesh), Luni (the only river of the Thar basin, ends in the Rann of Kutch), Banas (Aravalli-origin, joins Chambal), Mahi and Sabarmati.

Administrative divisions: 7 divisions (Jaipur, Jodhpur, Ajmer, Kota, Udaipur, Bikaner, Bharatpur) grouping the state's districts; district counts change with notifications, so verify current numbers.

Key festivals/fairs: Pushkar Camel Fair (Kartik Purnima, Ajmer), Teej (Jaipur), Gangaur, Desert Festival (Jaisalmer), Urs of Khwaja Moinuddin Chishti (Ajmer).

Protected areas include Ranthambore and Sariska Tiger Reserves, Keoladeo Ghana National Park (Bharatpur, Ramsar/UNESCO site), Desert National Park (Jaisalmer), Mukundra Hills and Ramgarh Vishdhari tiger reserves.

Minerals: Rajasthan leads in zinc-lead (Zawar, Rampura-Agucha), marble (Makrana), and is a major producer of sandstone, gypsum and rock phosphate; Sambhar Lake is a historic salt source.

Current affairs: track state budget, new districts/divisions, Rajasthan Renewable Energy Policy targets for solar parks (Bhadla, Jodhpur) and state government welfare schemes, which change frequently and require a current source.

Indian Constitution: adopted 26 November 1949, enforced 26 January 1950; Fundamental Rights in Part III (Articles 12-35), Directive Principles in Part IV (Articles 36-51).

Constitutional bodies vs statutory: Election Commission and UPSC are constitutional; NITI Aayog, NHRC and CBI are statutory/executive creations.

Indian geography superlatives: longest river Ganga, largest delta Sundarbans, highest peak Kangchenjunga (in India), largest freshwater lake Wular.

World organisations: UN founded 1945 (HQ New York), WTO 1995 (Geneva), IMF and World Bank 1944 Bretton Woods (Washington DC), WHO (Geneva).

Indian economy indicators: GDP, CPI (base year 2012), WPI (base year 2011-12), repo rate set by RBI's Monetary Policy Committee.

Space and defence milestones: ISRO Chandrayaan-3 landed near lunar south pole in 2023; Aditya-L1 solar mission; Gaganyaan human spaceflight programme.

Current affairs method: anchor on static facts (who holds which office, which country hosts which summit) because officeholders and host cities rotate annually.

Newton's laws: F = ma; action-reaction pairs act on different bodies, so they never cancel on one body.

SI units: force newton (kg·m/s²), pressure pascal (N/m²), work/energy joule, power watt, electric charge coulomb.

Ohm's law V = IR; resistors in series add, in parallel reciprocals add; electrical power P = VI = I²R = V²/R.

pH scale 0-14: acids pH<7, bases pH>7; strong acid + strong base gives salt and water (neutralisation).

Human body: largest organ skin, largest gland liver, oxygen-carrying pigment haemoglobin (iron), insulin from pancreas, vitamin C deficiency causes scurvy.

Cell: mitochondria are the powerhouse, ribosomes synthesise protein, chloroplasts carry out photosynthesis; plant cells have a cellulose cell wall.

Light: reflection angle of incidence equals angle of reflection; refraction bends light toward the normal when entering a denser medium; sound cannot travel in vacuum.

Quadratic roots: for ax²+bx+c=0, sum = -b/a, product = c/a; discriminant D = b²-4ac; real distinct roots when D>0.

Arithmetic progression: nth term a+(n-1)d, sum = n/2[2a+(n-1)d]; geometric progression nth term ar^(n-1), sum = a(rⁿ-1)/(r-1) for r≠1.

Percentage and profit: profit% = (SP-CP)/CP × 100; successive discounts of a% and b% equal a+b-ab/100 percent.

Time-speed-distance: distance = speed × time; for equal distances at speeds x and y, average speed = 2xy/(x+y).

Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h, curved surface 2πrh; sphere volume (4/3)πr³, surface 4πr².

Trigonometry: sin²θ+cos²θ=1; values sin30=1/2, sin45=1/√2, sin60=√3/2; tanθ = sinθ/cosθ.

Simple and compound interest: SI = PRT/100; CI amount = P(1+R/100)^T; for 2 years CI exceeds SI by P(R/100)².

Number series: check differences first, then ratios, then squares/cubes or alternating two-series patterns before assuming a rule.

Coding-decoding: map letter positions A=1 to Z=26 and check both forward and reverse (A=26) shifts; reversal of the alphabet is a common rule.

Blood relations: draw a family tree with gender marks; 'mother's brother' = maternal uncle, 'father's sister's son' = cousin.

Direction sense: fix north up; a right turn from north is east; net displacement uses Pythagoras on the north-south and east-west totals.

Seating arrangement: for a circle, facing centre means left is clockwise; facing outward reverses left and right.

Syllogism: apply Venn diagrams; a conclusion is valid only if true in every possible diagram of the premises.

Clock and calendar: hands coincide 11 times in 12 hours; angle = |30H - 5.5M| degrees; a normal year shifts the weekday by 1, a leap year by 2.

Memory hierarchy by speed: registers > cache > RAM > secondary storage; RAM is volatile, ROM and flash are non-volatile.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB.

OSI model has 7 layers; TCP/IP has 4; IPv4 addresses are 32-bit, IPv6 addresses are 128-bit.

Shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+S save, Alt+Tab switch windows, Ctrl+Shift+Esc opens Task Manager in Windows.

File extensions: .docx Word, .xlsx Excel, .pptx PowerPoint, .pdf portable document, .exe executable, .html web page.

Malware types: virus attaches to files, worm self-replicates over networks, trojan disguises as legitimate software, ransomware encrypts data for payment.

Internet basics: HTTP/HTTPS for web, SMTP for sending mail, POP3/IMAP for receiving; URL identifies a resource, DNS resolves names to IP addresses.

Hindi संधि: स्वर संधि (अ+इ=ए), व्यंजन संधि, विसर्ग संधि; संधि-विच्छेद करते समय मूल वर्ण पहचानें।

Hindi समास: तत्पुरुष (अंतिम पद प्रधान), द्वंद्व (दोनों पद प्रधान, 'और' लोप), बहुव्रीहि (अन्य पद प्रधान), द्विगु (संख्यावाची पूर्वपद)।

Hindi पर्यायवाची/विलोम और मुहावरे अर्थ सहित याद करें; 'अंधे की लाठी' का अर्थ है एकमात्र सहारा।

English parts of speech: identify the word's function in the sentence, not its meaning; 'fast' can be adjective, adverb or verb.

English tenses: present perfect (has/have + past participle) for past action with present relevance; past perfect for the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; only transitive verbs take passive.

Spotting errors: check subject-verb agreement, article use, preposition collocation (depend on, consist of) and parallelism in lists.

Civil: stress = force/area; strain = change in length/original length; Young's modulus E = stress/strain in the elastic range.

Civil: for a simply supported beam with central point load W and span L, maximum bending moment = WL/4; with uniform load w per unit length, M = wL²/8.

Civil concrete: nominal mixes M15 (1:2:4), M20 (1:1.5:3), M25 (1:1:2); water-cement ratio controls strength and workability.

Electrical: in a series circuit current is common, voltage divides; in parallel voltage is common, current divides; total resistance of two parallel resistors = R1R2/(R1+R2).

Electrical: three-phase power P = √3 V_L I_L cosφ; transformer EMF per turn is constant, so V1/V2 = N1/N2.

Mechanical: Carnot efficiency = 1 - T_cold/T_hot (absolute temperatures); Otto cycle efficiency = 1 - 1/r^(γ-1) with compression ratio r.

Mechanical: first law of thermodynamics Q = ΔU + W; for an adiabatic process Q = 0, so W = -ΔU.

Agriculture: NPK ratio denotes nitrogen, phosphorus and potassium; legumes fix atmospheric nitrogen via Rhizobium in root nodules; seed rate and spacing determine plant population per hectare.