GIKI Test cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R for a resistive element.

Thevenin equivalent: open-circuit voltage V_th in series with R_th found by deactivating independent sources (voltage sources shorted, current sources opened).

Norton equivalent: short-circuit current I_N in parallel with R_N; R_N = R_th and I_N = V_th/R_th.

Impedance of R, L, C at angular frequency ω: Z_R = R, Z_L = jωL, Z_C = 1/(jωC).

Resonant frequency of a series RLC circuit: f₀ = 1/(2π√(LC)); at resonance Z is purely resistive.

Three-phase balanced load: total power P = √3 V_L I_L cos φ, where V_L is line voltage and I_L line current.

Transformer ideal relation: V₁/V₂ = N₁/N₂ = I₂/I₁; real transformers add core and copper losses.

Boolean identities: A + A'B = A + B; De Morgan: (AB)' = A' + B' and (A+B)' = A'B'.

Binary search requires a sorted array and runs in O(log n) time; linear search is O(n).

Big-O compares growth rates: merge sort O(n log n), quicksort average O(n log n) but worst O(n²).

A hash table with load factor α has average O(1) lookup; collisions are resolved by chaining or open addressing.

TCP is connection-oriented and reliable; UDP is connectionless and does not guarantee delivery or ordering.

Stack is LIFO, queue is FIFO; recursion uses the call stack implicitly.

SQL JOIN types: INNER returns matching rows; LEFT keeps all left-table rows with NULLs where unmatched.

Process vs thread: threads of one process share the address space; processes are isolated.

Two's complement: negate an n-bit integer by inverting bits and adding 1; range is −2^(n−1) to 2^(n−1)−1.

Newton's second law: ΣF = ma; for rotation Στ = Iα.

Conservation of energy: for a conservative system, KE + PE = constant.

Bernoulli equation along a streamline: P + ½ρv² + ρgh = constant for steady, incompressible, inviscid flow.

Reynolds number Re = ρvD/μ; laminar flow typically Re < 2000 in pipes, turbulent Re > 4000.

First law of thermodynamics: ΔU = Q − W, with sign convention W done by the system.

Heat conduction (Fourier): q = −kA dT/dx.

Hooke's law in 1D: σ = Eε; shear stress τ = Gγ.

Dimensional analysis: all terms in a physically meaningful equation must have the same dimensions.

Stress σ = F/A; strain ε = ΔL/L; Young's modulus E = σ/ε in the elastic region.

Bending stress in a beam: σ = My/I, where M is bending moment, y distance from neutral axis, I second moment of area.

Torsion of a circular shaft: τ = Tr/J, with polar second moment J = πd⁴/32 for a solid shaft.

Euler buckling load for a pin-ended column: P_cr = π²EI/L².

Carnot efficiency of a heat engine: η = 1 − T_C/T_H (temperatures in kelvin).

Otto cycle thermal efficiency: η = 1 − 1/r^(γ−1), where r is compression ratio and γ = c_p/c_v.

Continuity equation for steady incompressible flow: A₁v₁ = A₂v₂.

Fatigue failure occurs under cyclic loading below the yield strength; endurance limit applies to steels.

Atomic packing factor: FCC 0.74, HCP 0.74, BCC 0.68; FCC has 4 atoms per unit cell.

Miller indices (hkl) describe planes; [uvw] describe directions; families are {hkl} and ⟨uvw⟩.

Hall–Petch relation: yield strength increases as grain size decreases, σ_y = σ₀ + k/√d.

Fick's first law of diffusion: J = −D(dC/dx).

Phase rule: F = C − P + 2 for a system with C components and P phases.

Tensile test: yield strength is the 0.2% offset stress; ultimate tensile strength is the maximum engineering stress.

Steel phases: ferrite (BCC), austenite (FCC), cementite (Fe₃C); martensite is a supersaturated BCT phase formed by rapid quenching.

Polymers: thermoplastic softens on heating; thermoset cross-links irreversibly.

Ideal gas law: PV = nRT; at STP 1 mol occupies 22.4 L.

Arrhenius equation: k = A e^(−E_a/RT); higher E_a means stronger temperature dependence.

First-order reaction: C = C₀e^(−kt); half-life t₁/₂ = ln2/k.

Le Chatelier's principle: increasing pressure favors the side with fewer gas moles.

Mass balance for a steady-state CSTR: input − output + generation = 0.

Heat exchanger effectiveness: ε = actual heat transfer / maximum possible heat transfer.

Distillation: relative volatility α > 1 enables separation; minimum reflux corresponds to infinite stages.

Reynolds number in a pipe: Re = ρvD/μ; laminar below ~2000, turbulent above ~4000.

Axial deformation: δ = PL/(AE) for a prismatic member under axial load P.

Simply supported beam under uniformly distributed load w: maximum bending moment wL²/8 at midspan.

Cantilever beam under point load P at free end: maximum deflection PL³/(3EI).

Concrete mix design: water–cement ratio controls strength and durability; lower w/c generally increases strength.

Slump test measures workability of fresh concrete.

Soil bearing capacity (Terzaghi): q_u = cN_c + γDN_q + 0.5γBN_γ for a strip footing.

Hydraulic gradient: i = Δh/L; Darcy's law flow velocity v = ki.

Surveying: closed traverse angular error is distributed proportionally to the number of angles.

Break-even quantity: Q = Fixed Costs / (Price − Variable Cost per Unit).

Net present value: NPV = Σ C_t/(1+r)^t − C₀; accept if NPV > 0.

Payback period is the time to recover the initial investment; it ignores cash flows after payback.

Elasticity of demand: E = (%ΔQ)/(%ΔP); |E| > 1 is elastic, |E| < 1 is inelastic.

CAPM: required return = R_f + β(R_m − R_f).

Inventory EOQ = √(2DS/H), where D annual demand, S order cost, H holding cost per unit per year.

Critical path method: project duration equals the longest path through the network.

Double-entry accounting: assets = liabilities + equity.

Kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as for constant acceleration.

Ideal gas law: PV = nRT; combine with Avogadro's law for molar volume.

pH = −log[H⁺]; a pH change of 1 corresponds to a tenfold change in hydrogen-ion concentration.

Le Chatelier's principle: systems at equilibrium shift to oppose imposed changes.

Differentiation rules: d/dx(xⁿ) = nx^(n−1); d/dx(eˣ) = eˣ; d/dx(ln x) = 1/x.

Integration by parts: ∫u dv = uv − ∫v du.

Mole concept: one mole contains 6.022 × 10²³ particles.

Projectile motion: horizontal range R = u² sin2θ/g for level ground.

Supervised learning uses labeled data; unsupervised learning finds structure without labels.

Bias–variance trade-off: high bias underfits, high variance overfits.

Precision = TP/(TP+FP); recall = TP/(TP+FN); F1 = 2·precision·recall/(precision + recall).

Gradient descent update: θ ← θ − α∇J(θ), where α is the learning rate.

Convolution layer parameters: output size = (W − F + 2P)/S + 1 for width W, filter F, padding P, stride S.

A* search uses f(n) = g(n) + h(n); admissible h never overestimates the true cost.

Overfitting is reduced by regularization, dropout, early stopping, and more training data.

Softmax converts logits into a probability distribution: softmax(z_i) = e^{z_i}/Σ e^{z_j}.