COMEDK UGET cheat sheet

Projectile motion: range R = u²sin2θ/g; maximum range at θ = 45°; time of flight T = 2u sinθ/g; max height H = u²sin²θ/(2g).

Work-energy theorem: net work equals change in kinetic energy, W_net = ΔKE = ½mv² − ½mu²; conservative forces admit potential energy U with F = −dU/dx.

Ideal gas: PV = nRT; at STP 1 mol occupies 22.4 L; average translational KE per molecule = (3/2)k_BT independent of gas identity.

Le Chatelier rule: increasing pressure shifts equilibrium toward the side with fewer gas moles; raising temperature shifts toward the endothermic direction (ΔH > 0).

pH and buffers: pH = −log[H⁺]; Henderson–Hasselbalch pH = pKa + log([A⁻]/[HA]); buffer capacity peaks when pH = pKa.

Differentiation and integration essentials: d/dx(sin x) = cos x, d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x; ∫dx/(1+x²) = tan⁻¹x + C; ∫eˣdx = eˣ + C.

Conic sections: circle x² + y² = a²; parabola y² = 4ax with focus (a,0) and directrix x = −a; ellipse x²/a² + y²/b² = 1 with e = √(1 − b²/a²).

Sign conventions and units: use SI base units (kg, m, s, A, K, mol, cd); check dimensional homogeneity before finalizing any numerical answer.

Scale rule: scale = drawing length / actual length; 1:100 means 1 cm on paper equals 1 m in reality; area scales as the square of the linear ratio.

Golden ratio φ ≈ 1.618; a rectangle of sides a and b is golden when (a+b)/a = a/b; used in proportion and facade composition problems.

Standard human dimensions for aptitude items: average adult eye level ≈ 1.5–1.6 m; door height ≈ 2.1 m; stair riser 150–190 mm with tread 250–300 mm.

Orthographic projection: first-angle places the view on the far side of the object (common in Indian practice); third-angle places views on the near side; plan is a horizontal cut ~1.2 m above floor.

Structural basics: a simply supported beam carries maximum bending moment wL²/8 under uniform load; a cantilever carries wL²/2 at the fixed support.

Climate-responsive design: in hot-dry climates use thick walls, small openings and courtyards; in warm-humid climates use cross-ventilation, large openings and shading devices.

Architectural vocabulary: plinth, lintel, chajja, coping, parapet, baluster, soffit, spandrel - each has a distinct location and function to be matched in MCQs.

Drawing-test decision rule: keep line weights consistent (thick for cut walls, thin for furniture), maintain a single-point or two-point perspective with consistent vanishing points.