RVUNL JE cheat sheet

Power in DC circuits: P = VI = I²R = V²/R; in single-phase AC, P = VI cos φ, Q = VI sin φ, S = VI (VA). Three-phase: P = √3 V_L I_L cos φ.

Transformer EMF equation: E = 4.44 f N Φ_max; turns ratio a = N1/N2 = V1/V2, and for an ideal transformer I1/I2 = 1/a. Efficiency peaks when copper loss equals iron loss.

Induction motor: synchronous speed N_s = 120f/P; slip s = (N_s − N_r)/N_s; rotor frequency = sf. Starting torque is maximum when rotor resistance equals standoff reactance.

DC machines: back EMF E_b = (PφNZ)/(60A); for a shunt generator V = E_b − I_aR_a. Commutator converts AC in armature to DC at terminals.

Thermodynamics: first law Q = ΔU + W; for a closed system W = ∫P dV. Carnot efficiency η = 1 − T_c/T_h (absolute temperatures). Otto cycle η = 1 − 1/r^(γ−1).

Strength of materials: axial stress σ = P/A; Hooke's law σ = Eε; bending stress σ = My/I; torsion τ = Tr/J; Euler buckling load P_cr = π²EI/(L_eff)².

Surveying and concrete: 1 bag cement = 50 kg = 0.0347 m³; nominal concrete mix M20 ≈ 1:1.5:3; bulking of sand increases volume with moisture up to about 4–6%.

Instrumentation: strain gauge gauge factor GF = (ΔR/R)/(ΔL/L); thermocouple works on Seebeck effect; RTD uses positive temperature coefficient of platinum.

Electronics/IT: op-amp closed-loop gain inverting = −R_f/R_in, non-inverting = 1 + R_f/R_in; binary-to-decimal place values 2^n; half-adder sum = A⊕B, carry = AB.

Unit-conversion anchors: 1 hp = 746 W; 1 kWh = 3.6 × 10⁶ J; 1 kgf = 9.81 N; 1 bar = 10⁵ Pa; 1 inch = 25.4 mm.

Gear/pulley reasoning: velocity ratio = product of driven teeth / product of driver teeth; for belts, N1D1 = N2D2 (same belt speed).

Ohm's-law chains: series resistances add; parallel conductance adds. Two parallel resistors: R = R1R2/(R1 + R2).

Efficiency chain rule: overall efficiency = product of stage efficiencies; never add efficiencies directly.

Shaft power: P = 2πNT/60 with N in rpm and T in N·m; doubling speed at constant torque doubles power.

Material selection logic: higher strength-to-weight ratio favours aluminium alloys; cast iron chosen for damping and compressive duty.

Error reasoning: percentage error in a product or quotient equals the sum of percentage errors of the individual quantities.

Beam sign convention: sagging moment positive, hogging negative; shear force changes sign where a concentrated load acts.

Rajasthan formed 30 March 1949 (Greater Rajasthan); Jaipur became capital; Rajasthan Day is celebrated 30 March.

State symbols: animal - chinkara (and camel as state animal-livestock); bird - godawan (Great Indian Bustard); tree - khejri; flower - rohida.

Geographic extremes: westernmost district Jaisalmer; largest district by area Jaisalmer; smallest Dholpur; district with highest population density Jaipur.

Rivers: Chambal (perennial, from Janapav hills), Banas (only river wholly within Rajasthan, Aravalli origin), Luni (saline, ends in Rann of Kutch).

Administrative structure: 7 divisions and 33 districts; divisional commissioners head divisions, district collectors head districts.

Major institutions: Rajasthan Atomic Power Station at Rawatbhata (Chittorgarh); Rajasthan's only oil refinery at Barmer (HPCL); Vedanta zinc smelter at Chanderiya.

Current-affairs discipline: track state budget, new districts/divisions, major irrigation projects (ERCP/Parbati–Kalisindha–Chambal link) and state schemes from official state portals.

Constitution adopted 26 November 1949, came into force 26 January 1950; Constituent Assembly formed under Cabinet Mission Plan, 1946.

Fundamental Rights: Articles 12–35; Right to Constitutional Remedies (Art. 32) called the heart and soul of the Constitution by Dr. Ambedkar.

Directive Principles: Articles 36–51, non-justiciable; Art. 40 panchayats, Art. 44 uniform civil code, Art. 48A environment.

President: elected indirectly by electoral college; impeachment under Art. 61 for violation of Constitution. Money Bill defined in Art. 110, introduced only in Lok Sabha with President's recommendation.

Emergency: national (Art. 352), state (Art. 356), financial (Art. 360). 44th Amendment (1978) replaced 'internal disturbance' with 'armed rebellion'.

Amendments: Art. 368; Kesavananda Bharati (1973) established the basic structure doctrine; 42nd Amendment (1976) added 'socialist, secular, integrity'.

Panchayati Raj: 73rd Amendment (1992) gave constitutional status; three-tier structure; Gram Sabha as base; elections every five years.

Rajasthan's ancient names: Maru, Marusthali, Rajputana; the term 'Rajasthan' popularised by James Tod and George Thomas.

Major dynasties: Guhilas/Sisodias of Mewar, Rathores of Marwar, Kachwahas of Amber, Chauhans of Ajmer, Bhatis of Jaisalmer.

Battles: Haldighati (1576) between Maharana Pratap and Mughal forces; Khanwa (1527) Babur defeated Rana Sanga.

Forts of Rajasthan inscribed by UNESCO: Chittorgarh, Kumbhalgarh, Ranthambore, Amber, Jaisalmer and Gagron.

Folk deities: Pabuji (camel, Phad painting), Tejaji (snakebite), Gogaji (snakes), Ramdevji (Kamad), Devnarayan (Phad).

Painting schools: Kishangarh (Bani-Thani), Bundi, Kota, Mewar, Marwar; Phad and Pichhwai are textile/scroll traditions.

Indian history anchors: Indus Valley (Harappa, Mohenjo-daro), Mauryas (321 BCE), Gupta 'Golden Age', 1857 revolt, 1947 independence.

Rajasthan area 3,42,239 km² - largest Indian state; Thar Desert covers roughly 60% of the state.

Aravalli range: oldest fold mountains; highest peak Guru Shikhar (1,722 m) on Mount Abu; separates arid west from semi-humid east.

Climate: tropical arid west (less than 25 cm rainfall), semi-arid east; southwest monsoon July–September; Mawar receives most rain.

Soils: sandy (west), loamy (east), saline-sodic (Indira Gandhi Canal command), black soil in Hadoti.

Lakes: Sambhar (largest saline, salt production), Pushkar, Pichola, Jaisamand (largest artificial lake in Rajasthan).

India: Tropic of Cancer passes through 8 states; Western Ghats and Eastern Ghats meet at Nilgiri Hills; highest peak Kanchenjunga (8,586 m).

Rivers of India: Ganga (longest within India), Brahmaputra (longest course in India), Godavari (longest peninsular river, 'Dakshin Ganga').

Physics: Newton's three laws; F = ma; work = F·d cos θ; kinetic energy = ½mv²; momentum conserved in collisions.

Optics: mirror formula 1/f = 1/v + 1/u; lens maker's equation; myopia corrected by concave lens, hypermetropia by convex.

Electricity: V = IR; series current constant, parallel voltage constant; power P = V²/R; 1 unit = 1 kWh.

Chemistry: pH scale 0–14, acids below 7; Avogadro number 6.022 × 10²³; mole = mass/molar mass.

Periodic trends: atomic radius decreases across a period, increases down a group; electronegativity highest for fluorine.

Biology: cell is the structural unit; mitochondria - powerhouse; chloroplast - photosynthesis; human chromosomes 46 (23 pairs).

Human body: blood groups A, B, AB, O with Rh factor; universal donor O-negative; largest organ skin; vitamin C deficiency causes scurvy.

Percentage: x% of y = xy/100; successive change a% then b% gives net (a + b + ab/100)%.

Profit and loss: profit% = (SP − CP)/CP × 100; when SP is same and gains/losses equal, net loss = (x/10)²%.

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

Time-speed-distance: distance = speed × time; conversion 1 km/h = 5/18 m/s; average speed of equal distances = 2v1v2/(v1 + v2).

Time and work: if A does work in x days and B in y days, together = xy/(x + y) days; use LCM of days as total work units.

Ratio and mixture: alligation rule (cheaper/more expensive) gives ratio = (d − m):(m − c); repeated dilution leaves P(1 − x/V)^n.

Mensuration: circle area πr², sphere 4πr², cylinder volume πr²h, cone ⅓πr²h, triangle area ½ × base × height.

Series: check differences, then ratios, then alternating patterns; squares 1–30 and cubes 1–15 should be memorised.

Coding-decoding: alphabet positions A=1 … Z=26; reverse positions A=26 … Z=1; shift patterns often constant or +1, +2, +3.

Blood relations: draw a family tree; 'maternal' refers to mother's side, 'paternal' to father's side; never assume gender.

Direction sense: net displacement uses Pythagoras; if a person turns right after facing north, they face east.

Number series and syllogism: in syllogism, a conclusion is valid only if true in every possible Venn diagram of the premises.

Clocks: minute hand gains 5.5° per minute over hour hand; hands coincide 11 times in 12 hours.

Calendar: odd days - ordinary year 1, leap year 2; century years divisible by 400 are leap years.

Hindi sandhi: स्वर संधि (दो स्वर), व्यंजन संधि, विसर्ग संधि; उदाहरण: विद्या + आलय = विद्यालय (दीर्घ संधि).

समास भेद: तत्पुरुष (अंतिम पद प्रधान), द्वंद्व (दोनों प्रधान), बहुव्रीहि (अन्य पद प्रधान), कर्मधारय (विशेषण-विशेष्य).

अलंकार: अनुप्रास (वर्ण की आवृत्ति), उपमा (समानता), रूपक (अभेद आरोप), उत्प्रेक्षा (संभावना).

English grammar: subject-verb agreement, articles (a/an/the), prepositions of time (in/on/at), active-passive voice transformation.

Tenses: present perfect uses 'has/have + past participle'; past perfect uses 'had + past participle' for the earlier of two past actions.

Idioms: 'once in a blue moon' (rarely), 'bite the bullet' (face pain bravely), 'at the drop of a hat' (immediately).

Vocabulary: synonym/antonym and one-word substitution are common; e.g., 'philanthropist' - one who loves mankind.