GATE PE flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Euler buckling load

Critical axial load for a slender column: P_cr = π²EI/(KL)², where K depends on end conditions and EI is the flexural rigidity.

Mohr's circle radius

For plane stress, radius R = √[((σx − σy)/2)² + τxy²]; principal stresses are the circle centre plus or minus R.

Carnot efficiency

Maximum efficiency of a heat engine between reservoirs at absolute temperatures T_H and T_L: η = 1 − T_L/T_H.

Reynolds number

Ratio of inertial to viscous forces, Re = ρVD/μ; circular pipe flow is laminar near Re < 2000 and turbulent above about 4000.

Castigliano's theorem

The partial derivative of total strain energy with respect to an applied load equals the displacement at that load in the load's direction.

Simply supported midspan deflection

For a central point load W on span L with flexural rigidity EI, maximum deflection is WL³/(48EI), occurring at midspan.

Arrhenius equation

Rate constant k = A·exp(−E_a/RT); plotting ln k against 1/T gives a straight line of slope −E_a/R.

Gibbs free energy criterion

ΔG = ΔH − TΔS; at constant temperature and pressure a process is spontaneous when ΔG is negative.

Beer–Lambert law

Absorbance A = εcl, where ε is molar absorptivity, c concentration and l path length; valid for dilute solutions at a given wavelength.

Particle in a box energy

For a particle confined to a one-dimensional box of length L, E_n = n²h²/(8mL²); level spacing increases as L decreases.

Henderson–Hasselbalch equation

pH = pK_a + log([A⁻]/[HA]); a buffer resists pH change best when the acid and conjugate base concentrations are equal.

Hardy–Weinberg equilibrium

In a large random-mating population without selection or mutation, genotype frequencies are p², 2pq and q² for two alleles.

Net present value rule

NPV = Σ C_t/(1+r)^t − C_0; a positive NPV at the required discount rate means the project adds value.

Capital asset pricing model

Expected return E(R) = R_f + β(E(R_m) − R_f); beta captures only systematic risk relative to the market portfolio.

Weighted average cost of capital

WACC = (E/V)R_e + (D/V)R_d(1 − t), weighting equity and after-tax debt cost by market values.

Break-even quantity

Units needed to cover fixed costs: Q = Fixed cost/(Price − Variable cost per unit), the denominator being contribution margin per unit.

DuPont identity

Return on equity decomposes as net profit margin × total asset turnover × equity multiplier, linking profitability, efficiency and leverage.

Economic order quantity

Order size minimising total ordering and holding cost: EOQ = √(2DS/H), with D annual demand, S order cost, H holding cost per unit-year.

Categorical imperative

Kant's test of moral maxims: act only on principles you could will as universal law, treating persons as ends, not merely means.

Rasa theory

Indian aesthetic theory holding that a performance evokes a relish, rasa, in the spectator; the Natyashastra lists eight, with shanta added later.

Langue versus parole

Saussure's distinction between the shared language system (langue) and the individual act of speech (parole) that realises it.

Modus tollens

A valid inference form: from P → Q and not-Q, conclude not-P; distinct from the fallacy of denying the antecedent.

One-point perspective

A drawing system in which parallel receding lines converge on a single vanishing point on the horizon, fixing relative scale.

Successive percentage change

Two successive changes of a% and b% give a net change of a + b + ab/100 percent; the formula handles signs for increases and decreases.

Combined work rate

If A alone finishes in x days and B in y days, working together they take xy/(x + y) days, the harmonic combination of rates.

Harmonic mean speed

For equal distances travelled at speeds u and v, average speed is 2uv/(u + v), not the arithmetic mean of the speeds.

Compound interest formula

Amount A = P(1 + r/n)^(nt) for principal P, nominal rate r, n compounding periods per year and t years.

Inclusion–exclusion principle

For two sets |A ∪ B| = |A| + |B| − |A ∩ B|; for three sets subtract pairwise intersections and add the triple intersection.

Contrapositive equivalence

The contrapositive ¬Q → ¬P is logically equivalent to P → Q, whereas the converse Q → P need not hold.

Pie chart sector angle

A sector's central angle equals (component/total) × 360°, so the same fraction gives both the angle and the percentage share.

Weighted average

Σ(w_i x_i)/Σw_i; the result always lies between the smallest and largest contributing values, unlike a simple mean.

Grouped data median class

The class interval in which cumulative frequency first reaches half the total N/2; interpolation within it estimates the median.

Circular seating symmetry

For arrangements around a circular table, fix one person's position first, reducing n distinct arrangements to (n − 1)! up to rotation.