SSC JE Mechanical cheat sheet

Series rule check: compute first differences, then second differences; a constant second difference signals a quadratic (square/n-square) pattern.

Alphabet position: A=1 to Z=26; reverse position = 27 − forward position. Opposite pairs sum to 27 (A–Z, B–Y, M–N).

Coding-decoding: test shift (+k/−k), reversal, and position-product rules in that order before assuming letter substitution.

Blood relations: draw a tree, not prose. Vertical line = generation, horizontal line = siblings/spouse; verify gender symbols before answering.

Direction sense: use Pythagoras for displacement; net displacement = √(x² + y²) after summing north-south and east-west components separately.

Syllogism: a conclusion is valid only if it holds in every Venn diagram consistent with the premises; "some A are B" does not imply "some B are A" for all-relations but does for the given some-relation.

Clock: angle between hands = |30H − 5.5M| degrees; hands coincide 11 times in 12 hours, i.e. every 65 5/11 minutes.

Calendar: in a non-leap year, 1 Jan and 31 Dec fall on the same weekday; a leap year shifts the next year's day by 2.

Mirror/water image: mirror reverses left-right (vertical axis), water reverses top-bottom (horizontal axis); digits 0,1,8 and letters like A,H,I,M,O,T,U,V,W,X,Y are symmetric in a vertical mirror.

Indian Constitution: adopted 26 November 1949, came into force 26 January 1950; Fundamental Rights in Part III (Articles 12–35), DPSP in Part IV (Articles 36–51).

Fundamental Duties were added by the 42nd Amendment (1976) on the Swaran Singh Committee recommendation; the 44th Amendment (1978) removed the right to property from Fundamental Rights.

Basic SI and physical constants: g ≈ 9.81 m/s², speed of light 3×10⁸ m/s, 1 hp = 746 W, 1 kWh = 3.6×10⁶ J.

SI base units: length metre, mass kilogram, time second, current ampere, temperature kelvin, amount mole, luminous intensity candela.

Indian geography: Tropic of Cancer passes through 8 states; Deccan Plateau is bounded by the Satpura range to the north and the Western/Eastern Ghats on the flanks.

National firsts commonly asked: first Indian Nobel laureate Rabindranath Tagore (1913, Literature); first Indian to win a science Nobel C. V. Raman (1930, Physics).

Static GK dates: Indian Railways first train 1853 (Bombay–Thane); Reserve Bank of India established 1935, nationalised 1949.

Economics basics: repo rate is the rate at which RBI lends to banks; CRR is the share of deposits kept with RBI; inflation erodes purchasing power and is measured in India by CPI and WPI.

Stress = Force/Area (N/m² = Pa); strain is dimensionless; Young's modulus E = stress/strain in the linear-elastic region.

Simply supported beam with central point load W and span L: max bending moment = WL/4 at midspan; max deflection = WL³/(48EI).

Cantilever with end load W: max BM = WL at the fixed end; max deflection = WL³/(3EI).

Thermodynamics: first law Q − W = ΔU; for a closed system at constant pressure W = pΔV, so Q = ΔU + pΔV = ΔH.

Carnot efficiency η = 1 − T_cold/T_hot with absolute temperatures in kelvin; no real engine between the same reservoirs can exceed it.

Ohm's law V = IR; power P = VI = I²R = V²/R. In series, current is common and resistances add; in parallel, voltage is common and conductances add.

Three-phase: line voltage = √3 × phase voltage in star, line current = √3 × phase current in delta; total power P = √3 V_L I_L cos φ.

Concrete: nominal mixes 1:1:2 (M25), 1:1.5:3 (M20), 1:2:4 (M15), 1:3:6 (M10); water-cement ratio controls strength and workability inversely.

Bernoulli's equation p/ρg + v²/2g + z = constant along a streamline for steady, incompressible, frictionless flow; continuity A₁V₁ = A₂V₂.

Slope and deflection standard results: cantilever with uniformly distributed load w gives max deflection wL⁴/(8EI) and max slope wL³/(6EI) at the free end.

Bending equation M/I = σ/y = E/R relates moment, second moment of area, bending stress, and radius of curvature.

Torsion: τ/r = T/J = Gθ/L; for a solid circular shaft J = πd⁴/32, so τ_max = 16T/(πd³).

Mechanical power: P = 2πNT/60 with N in rpm and T in N·m; brake thermal efficiency = brake power / heat supplied by fuel.

Otto cycle efficiency = 1 − 1/r^(γ−1); Diesel cycle efficiency depends additionally on the cut-off ratio and is lower than Otto for the same compression ratio.

Transformer EMF equation E = 4.44 f N Φ_max; for an ideal transformer V₁/V₂ = N₁/N₂ = I₂/I₁.

DC machine EMF: E = (ΦZN P)/(60A) for a generator; back EMF in a motor is E_b = V − I_a R_a.

Induction motor slip s = (N_s − N)/N_s with synchronous speed N_s = 120f/P; rotor frequency = sf.

Surveying and structures: leveling uses the height of instrument method (HI = RL + backsight); for a simply supported beam under UDL w over span L, max BM = wL²/8 and max shear = wL/2.