JSSC JE cheat sheet

Harappan sites: Mohenjo-daro (Great Bath, Great Granary), Harappa (granaries), Lothal (dockyard), Kalibangan (ploughed field), Dholavira (water reservoirs, signboard).

Mauryan administration: Arthashastra by Kautilya; Ashoka's dhamma policy recorded in Major Rock Edicts; Chandragupta Maurya founded the dynasty around 322 BCE.

Mughal sequence: Babur (1526 First Battle of Panipat) → Humayun → Akbar (1561-1605 reign, Din-i-Ilahi 1582) → Jahangir → Shah Jahan → Aurangzeb.

Indian National Congress founded 1885 by A.O. Hume; Partition of Bengal 1905; Jallianwala Bagh 1919; Non-Cooperation 1920; Quit India 1942.

Fundamental Rights: Articles 12-35; Right to Constitutional Remedies (Art 32) called the heart and soul of the Constitution by Dr. Ambedkar; Art 21A is Right to Education.

Directive Principles: Articles 36-51; Art 40 panchayats, Art 44 uniform civil code, Art 48A environment; not enforceable in courts.

Indian geography: Tropic of Cancer passes through 8 states; Western Ghats are older than the Himalayas; Deccan Trap soils are black cotton soils.

Economics basics: GDP = C + I + G + (X − M); repo rate is the rate at which RBI lends to banks; CRR is the cash reserve ratio held with RBI.

General science: Newton's three laws; Ohm's law V = IR; photosynthesis converts CO2 + H2O to glucose using chlorophyll and light; SI unit of force is newton.

Average = Sum of observations / Number of observations; if a quantity is added, new average shifts by (added value − old average)/(n+1).

Percentage change = ((New − Old)/Old) × 100; successive percentage changes of a% and b% give net change a + b + ab/100.

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

Speed–time–distance: Distance = Speed × Time; relative speed in same direction = difference, opposite direction = sum.

Work: if A does work in x days and B in y days, together they take xy/(x + y) days; efficiency is inversely proportional to time.

Profit and loss: Profit% = (SP − CP)/CP × 100; when two articles sold at same price with equal % gain and loss, net loss = (x/10)^2 percent.

Permutation and combination: nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!); nC0 = nCn = 1.

Mensuration: area of circle = πr², circumference = 2πr; volume of cylinder = πr²h; volume of sphere = (4/3)πr³; cone = (1/3)πr²h.

Probability: P(E) = favourable outcomes / total outcomes; P(E) + P(not E) = 1; for independent events P(A∩B) = P(A)·P(B).

Number series: check differences, then ratios, then squares/cubes; alternating series often have two interleaved patterns.

Coding–decoding: apply the same letter shift to all letters; A=1, B=2 ... Z=26 for positional-value questions; opposite letter of A is Z (sum 27).

Blood relations: draw a family tree with gender symbols; 'brother of my father's only son' means the speaker himself.

Direction sense: use a compass sketch; net displacement from start = √(east² + north²) when the path turns at right angles.

Syllogism: valid from 'All A are B' and 'All B are C' is 'All A are C'; converse of 'All A are B' is 'Some B are A'.

Seating arrangement: for circular facing centre, left is clockwise; for facing outward, left is anticlockwise.

Clock: angle between hands = |30H − 5.5M| degrees; hands coincide 11 times in 12 hours.

Calendar: odd days in an ordinary year = 1, leap year = 2; a century has 5 odd days if divisible by 400 (e.g., 2000), otherwise 4 or 6.

Analogy and classification: identify the relationship (part–whole, cause–effect, worker–tool) before selecting the answer.

Stress σ = F/A; strain ε = ΔL/L; Young's modulus E = σ/ε; Hooke's law valid within the proportional limit.

Thermodynamics first law: Q = ΔU + W (sign convention: work done by system positive); second law: entropy of isolated system never decreases.

Ideal gas law PV = mRT; universal gas constant R = 8.314 J/(mol·K); standard atmospheric pressure 101.325 kPa.

Bernoulli's equation: P/γ + v²/2g + z = constant along a streamline for steady, incompressible, frictionless flow.

Continuity equation: A₁V₁ = A₂V₂ for incompressible flow; Reynolds number Re = ρVD/μ, laminar below 2000 in pipes.

Basic units: force = newton (kg·m/s²), pressure = pascal (N/m²), power = watt (J/s); 1 bar = 100 kPa; 1 hp = 746 W.

Factor of safety = ultimate (or yield) stress / allowable working stress; it accounts for material, load and fabrication uncertainties.

Mechanical advantage = load/effort; velocity ratio = distance moved by effort / distance moved by load; efficiency = MA/VR × 100.

Building materials: initial and final setting times of ordinary Portland cement are 30 min and 10 h; cement soundness tested by Le Chatelier apparatus.

Surveying: 1 chain = 66 ft = 20.1168 m; included angle between chain lines = 180° − angle measured with tape; true bearing = magnetic bearing + magnetic declination.

Levelling: height of instrument HI = reduced level of BM + backsight; RL of new point = HI − foresight; check ΣBS − ΣFS = last RL − first RL.

Structural analysis: for a simply supported beam with central point load W and span L, maximum BM = WL/4 and maximum deflection = WL³/48EI.

RCC design: nominal mix M20 = 1:1.5:3; minimum grade for reinforced concrete is M20; characteristic strength means 28-day cube strength at 95% acceptance.

Geotechnical: dry unit weight γd = γ/(1 + w); void ratio e = n/(1 − n); coefficient of active earth pressure Ka = (1 − sinφ)/(1 + sinφ).

Hydraulics: discharge over a rectangular weir Q = (2/3)·Cd·√(2g)·L·H^(3/2); Chezy's formula V = C√(RS); Manning's V = (1/n)R^(2/3)S^(1/2).

Transportation: stopping sight distance SSD = 0.278Vt + V²/(254f); superelevation e = V²/(127R) − f; camber provides surface drainage.

Environmental: BOD is oxygen consumed by microbes over 5 days at 20 °C; typical BOD5 of domestic sewage is 200-300 mg/L; chlorination is the final disinfection step.

Carnot efficiency η = 1 − T_cold/T_hot (absolute temperatures); no real engine between the same reservoirs exceeds it.

Otto cycle efficiency = 1 − 1/r^(γ−1); Diesel cycle efficiency = 1 − [1/(γ·r^(γ−1))]·[(ρ^γ − 1)/(ρ − 1)], where r is compression ratio.

Rankine cycle: thermal efficiency = (h1 − h2)/(h1 − hf2); superheating raises efficiency and reduces moisture at turbine exit.

Strength of materials: torsion τ/r = T/J = Gθ/L; maximum shear stress in a solid circular shaft = 16T/(πd³).

Bending: M/I = σ/y = E/R; section modulus Z = I/ymax, so σ = M/Z.

Fluid mechanics: dynamic viscosity unit is Pa·s; kinematic viscosity ν = μ/ρ in m²/s; Bernoulli applies to steady, inviscid, incompressible flow.

Theory of machines: for a four-bar linkage, Grashof condition s + l ≤ p + q gives a crank-rocker or double-crank; gear ratio = N₁/N₂ = T₂/T₁.

Manufacturing: in orthogonal cutting, shear angle tanφ = r·cosα/(1 − r·sinα), where r = chip thickness ratio; tool life follows Taylor's equation VTⁿ = C.

Industrial engineering: EOQ = √(2DS/H); critical path in CPM has zero total float; PERT uses three time estimates (optimistic, most likely, pessimistic).