GATE GE key terms

The maximum pressure a soil mass can safely carry at the base of a foundation without failing in shear or settling excessively. It governs footing size and type in geotechnical design.

The cohesion and angle of internal friction that describe how much shear stress a soil can resist before failure. They are measured by triaxial or direct shear tests and used in slope and foundation analysis.

The time-dependent compression of saturated clay as water is squeezed out of its voids under an applied load. It is predicted from the compression index and coefficient of consolidation.

The intergranular stress carried by soil particles, equal to total stress minus pore water pressure. It controls soil strength, stiffness, and volume change, and is central to Terzaghi's principle.

Loss of soil strength when saturated loose sand loses effective stress because cyclic loading raises pore pressure until it approaches total stress. It causes foundations to sink or tilt during earthquakes.

A design philosophy that checks a structure against defined performance thresholds: ultimate limit states for collapse and serviceability limit states for deflection or cracking. Partial safety factors are applied to loads and material strengths.

A multiplier applied to loads or material resistance in limit state design to account for uncertainty and variability. Load factors exceed one while strength factors are below one, ensuring adequate reliability.

The stress at which a beam or slab fails in bending, determined by the section modulus and the moment capacity of the cross-section. Reinforcement is proportioned so that steel yields before concrete crushes.

Graphical plots of internal shear and moment along a beam for given loads and supports. They locate maximum moment, points of contraflexure, and critical sections for design.

An independent coordinate needed to fully describe the configuration of a mechanical system. A planar rigid body has three, and the count determines the number of equations of motion.

The frequency at which a system oscillates freely after a disturbance, set by its mass and stiffness. Excitation near this frequency produces resonance and large amplitudes.

A dimensionless measure of how quickly oscillations decay, comparing actual damping to critical damping. Values below one give underdamped vibration, exactly one gives the fastest non-oscillatory return.

A formulation of dynamics using kinetic and potential energy rather than direct force balance. The Lagrangian equals kinetic minus potential energy, and its Euler-Lagrange equations yield the equations of motion.

A function representing total energy in terms of generalized coordinates and momenta, whose equations generate the system's time evolution. It underlies canonical transformations and quantum analogues.

A dimensionless ratio of inertial to viscous forces in a flow, equal to density times velocity times length divided by viscosity. It predicts whether flow is laminar or turbulent.

An energy relation for steady, incompressible, inviscid flow stating that pressure, velocity, and elevation heads sum to a constant along a streamline. It is used for pitot tubes, orifices, and venturis.

The thin region near a solid surface where velocity rises from zero at the wall to the free-stream value. Its growth and separation determine skin friction and pressure drag.

Entropy of an isolated system never decreases, so heat flows spontaneously from hot to cold and no cycle converts all heat input to work. It sets the maximum efficiency of engines and refrigerators.

The maximum possible efficiency of a heat engine operating between two reservoirs, equal to one minus the cold-to-hot absolute temperature ratio. No real cycle between the same reservoirs can exceed it.

A state property measuring the dispersal of energy in a system, defined by the reversible heat transfer divided by absolute temperature. It increases in irreversible processes and quantifies lost work potential.

Any linear two-terminal network can be replaced by an equivalent voltage source in series with a resistance. The source equals the open-circuit voltage and the resistance is found with sources deactivated.

In a linear circuit with multiple independent sources, the response equals the sum of responses computed with each source acting alone and the others deactivated. It fails for nonlinear elements such as diodes.

The dual of Thevenin's theorem: a linear two-terminal network is replaced by a current source in parallel with a resistance. The current equals the short-circuit current.

A stability test for feedback systems that counts encirclements of the minus-one point by the open-loop frequency response. It reveals closed-loop stability from open-loop data, including for systems with delays.

A pair of logarithmic plots showing magnitude in decibels and phase in degrees against frequency for a system's transfer function. Gain margin and phase margin are read directly from it.

The path traced by closed-loop poles in the complex plane as a gain parameter varies from zero to infinity. It shows how controller gain affects transient response and stability.

An asymptotic measure of how an algorithm's running time grows with input size, usually expressed in big-O notation. It allows comparison of algorithms independent of hardware and constants.

The asymptotic measure of extra memory an algorithm needs beyond its input as a function of input size. Recursion and auxiliary arrays are common contributors.

A technique solving problems by combining solutions to overlapping subproblems, storing results to avoid recomputation. It requires optimal substructure and is used for shortest paths, knapsack, and sequence alignment.

A strategy that builds a solution step by step by choosing the locally best option at each stage without backtracking. It is correct only when the problem has the greedy-choice property.

In relational databases, organizing tables to reduce redundancy and update anomalies by decomposing them according to functional dependencies. Higher normal forms like 3NF and BCNF impose stricter conditions.

Atomicity, consistency, isolation, and durability: the four guarantees a database transaction must provide. They ensure that partial failures do not corrupt data and concurrent transactions do not interfere.

A rule for updating the probability of a hypothesis given evidence, expressed as prior times likelihood divided by marginal probability. It underpins classification, diagnostic testing, and Bayesian inference.

The probability that an event occurs given that another event has already occurred, equal to the joint probability divided by the conditioning event's probability. It is the foundation of Bayes' rule and independence tests.

A method of estimating parameters by choosing values that make the observed data most probable under the assumed model. The estimate maximizes the likelihood or, equivalently, its logarithm.

The sampling distribution of the mean of many independent observations tends toward a normal distribution as sample size grows, regardless of the population shape. It justifies normal-based confidence intervals and tests.

A range of values, computed from sample data, that is expected to contain the true parameter in a stated proportion of repeated samples. Width shrinks with larger samples or lower confidence level.

A formal procedure comparing sample evidence against a null hypothesis, producing a p-value or test statistic. A decision to reject depends on the chosen significance level and error trade-offs.

A differential equation together with conditions imposed at more than one point of the domain, such as fixed temperatures at both ends of a rod. Solutions often require eigenfunction expansion rather than simple integration.

A representation of a periodic function as a sum of sines and cosines whose frequencies are integer multiples of a fundamental. Coefficients are found by integrating the function against each basis function.

An integral transform converting a function of time into a function of a complex variable, turning linear differential equations into algebraic ones. It handles initial conditions naturally and is standard in control analysis.

The ratio of the Laplace transform of a system's output to that of its input, assuming zero initial conditions. Its poles and zeros determine stability and dynamic response.