GATE EY flashcards

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

Hooke's Law

Within the elastic limit, stress is proportional to strain, σ = Eε, where E is Young's modulus, a material property measured in pascals.

Poisson's ratio

The negative ratio of lateral strain to axial strain, ν = −ε_lateral/ε_axial; typical metals have values near 0.3, and it cannot exceed 0.5 for isotropic materials.

Second moment of area

A geometric property of a cross-section about an axis, I = ∫y²dA; for a rectangle it is bd³/12 and it governs bending stiffness.

Carnot efficiency

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

Entropy change, reversible process

For a reversible path, ΔS = ∫δQ_rev/T; entropy is a state function, so the change depends only on the initial and final states.

Thevenin's theorem

Any linear two-terminal network can be replaced by a single voltage source V_th in series with a resistance R_th, simplifying circuit analysis.

Virtual short in op-amps

With negative feedback and ideal op-amp assumptions, the inverting and non-inverting input terminals are at nearly the same potential, though no current flows between them.

Karnaugh map grouping

Adjacent cells differing in one variable are grouped in powers of two to eliminate variables; larger groups yield simpler sum-of-products expressions.

Water-cement ratio

The mass ratio of water to cement in a concrete mix; lower values increase compressive strength and durability but reduce workability.

Height of instrument method

A leveling technique where the elevation of the instrument line of sight is computed from a backsight and used to derive foresight reduced levels.

Effective stress in soil

Terzaghi's principle: σ' = σ − u, where σ is total stress and u is pore water pressure; effective stress controls soil shear strength and consolidation.

Degree of static indeterminacy

For a plane frame, D_s = 3m + r − 3j, where m is members, r reactions, and j joints; it counts redundant reactions and internal forces.

Nyquist sampling criterion

A signal must be sampled at more than twice its highest frequency component to avoid aliasing during analog-to-digital conversion.

PID controller

A feedback controller combining proportional, integral, and derivative actions; integral action removes steady-state error, derivative action improves damping.

Reynolds number

Re = ρVD/μ, the ratio of inertial to viscous forces; flow is typically laminar below about 2100 in pipes and turbulent above 4000.

Time complexity of binary search

Binary search on a sorted array of n elements runs in O(log n) time, halving the search interval at each step.

Commutator [x̂, p̂]

In quantum mechanics, the position and momentum operators satisfy [x̂, p̂] = iħ, which underlies the Heisenberg uncertainty relation.

Particle in a box

An infinite square well of width L has quantized energies E_n = n²π²ħ²/(2mL²), with n = 1, 2, 3, ... and zero-point energy at n = 1.

Partition function

Z = Σ exp(−E_i/k_BT) sums Boltzmann factors over all states; all equilibrium thermodynamic properties can be derived from it.

Gibbs free energy criterion

At constant temperature and pressure, a process is spontaneous if ΔG < 0; equilibrium corresponds to ΔG = 0 and minimum G.

Michaelis-Menten equation

v = V_max[S]/(K_m + [S]) describes enzyme kinetics; K_m is the substrate concentration at which the reaction rate is half of V_max.

SN1 versus SN2

SN1 is a two-step, first-order reaction via a carbocation with racemization; SN2 is a one-step, second-order backside attack with inversion.

Beer-Lambert law

Absorbance A = εcl, where ε is the molar absorptivity, c the concentration, and l the path length; absorbance is linear in concentration.

Hardy-Weinberg equilibrium

Allele and genotype frequencies remain constant in a large, randomly mating population without mutation, migration, selection, or drift; p² + 2pq + q² = 1.

Standard error of the mean

SEM = s/√n, where s is the sample standard deviation and n the sample size; it quantifies uncertainty in the estimated mean.

Central limit theorem

The sampling distribution of the mean approaches normality as sample size increases, regardless of the underlying population distribution, enabling z- and t-tests.

Polymerase chain reaction

PCR amplifies DNA through repeated cycles of denaturation, primer annealing, and extension by a thermostable polymerase, doubling the target each cycle.

IR absorption condition

A vibrational mode is infrared-active only if it produces a change in the molecular dipole moment; symmetric stretches may be IR-inactive.

Enzyme inhibition types

Competitive inhibitors raise apparent K_m at constant V_max; non-competitive inhibitors lower V_max without changing K_m in the simplest case.

First law of thermodynamics

Energy is conserved: ΔU = Q − W for a closed system, where Q is heat added to the system and W is work done by it.

Le Chatelier's principle

A system at equilibrium shifts to counteract a disturbance in concentration, pressure, or temperature, partially opposing the imposed change.

Confidence interval interpretation

A 95% confidence interval, computed repeatedly from many samples, would contain the true parameter about 95% of the time; it does not give a probability for a fixed parameter.