GATE 2027 Preparation

Solve systems of linear equations using Gaussian elimination and rank conditions.

Compute eigenvalues and eigenvectors and use them to diagonalize a matrix.

Evaluate limits and determine the continuity and differentiability of single-variable functions.

Construct Taylor and Maclaurin approximations of elementary functions.

Locate and classify extrema of single-variable and multivariable functions.

Evaluate definite and improper integrals using standard integration techniques.

Evaluate double and triple integrals after an appropriate change of coordinates.

Apply gradient, divergence, curl, Gauss's theorem, and Stokes's theorem to vector fields.

Solve first-order ordinary differential equations using standard analytical methods.

Solve linear higher-order ordinary differential equations with constant coefficients.

Test whether a complex function is analytic using the Cauchy–Riemann equations.

Evaluate contour integrals using Cauchy's integral formula and the residue theorem.

Compute conditional probabilities using the law of total probability and Bayes' theorem.

Calculate expectations, variances, and distribution probabilities for standard random variables.

Derive marginal distributions, covariance, and correlation from a joint distribution.

Apply standard numerical methods to root-finding, interpolation, integration, and ordinary differential equations.

Formulate and solve node-voltage and mesh-current equations for linear circuits.

Simplify circuit analysis using Thevenin, Norton, superposition, reciprocity, and maximum-power-transfer theorems.

Determine the complete transient response of first-order RC and RL circuits.

Determine the underdamped, critically damped, and overdamped responses of second-order RLC circuits.

Calculate sinusoidal steady-state voltages, currents, complex power, and power factor.

Determine resonance, bandwidth, and quality factor in series and parallel RLC circuits.

Obtain circuit responses in the Laplace domain using initial conditions and network functions.

Compute transmission, impedance, admittance, and hybrid parameters of two-port networks.

Represent and manipulate standard continuous-time and discrete-time signals.

Determine whether a system is linear, time-invariant, causal, memoryless, and stable.

Compute the output of an LTI system using continuous-time or discrete-time convolution.

Represent periodic signals using trigonometric and exponential Fourier series.

Compute continuous-time Fourier transforms and apply their properties to spectra and LTI systems.

Compute DTFT and DFT representations and interpret discrete-time spectra.

Use Laplace transforms and regions of convergence to analyze continuous-time systems.

Use z-transforms and sampling theory to analyze discrete-time systems and signal reconstruction.

Calculate carrier concentrations, conductivity, and Fermi-level position in intrinsic and doped semiconductors.

Determine semiconductor current from drift, diffusion, generation, recombination, and continuity relations.

Analyze PN-junction electrostatics and derive its current–voltage behavior.

Determine operating voltages and currents in rectifier, clipper, clamper, and Zener-regulator circuits.

Relate BJT terminal currents to operating regions and device parameters.

Analyze MOS-capacitor energy bands, threshold voltage, and operating regimes.

Calculate MOSFET drain current and small-signal parameters in cutoff, triode, and saturation regions.

Determine the operating principles and characteristics of photodiodes, LEDs, and solar cells.

Determine the DC operating point and bias stability of BJT amplifiers.

Determine the DC operating point and bias stability of MOSFET amplifiers.

Calculate gain and input and output resistance of single-stage BJT amplifiers using small-signal models.

Calculate gain and input and output resistance of single-stage MOSFET amplifiers using small-signal models.

Analyze differential amplifiers, current mirrors, and multistage amplifier connections.

Determine the low-frequency and high-frequency response of transistor amplifiers.

Analyze linear and nonlinear circuits built with ideal and nonideal operational amplifiers.

Determine loop gain, stability, and oscillation conditions in feedback amplifiers and oscillators.

Convert among number systems and perform signed and unsigned binary arithmetic.

Minimize Boolean functions using algebraic methods and Karnaugh maps.

Design combinational circuits using gates, multiplexers, decoders, encoders, and comparators.

Analyze arithmetic circuits including adders, subtractors, and arithmetic logic units.

Determine the behavior of latches and edge-triggered flip-flops from timing inputs.

Design synchronous counters, registers, and finite-state machines.

Check setup time, hold time, propagation delay, and maximum clock frequency in sequential circuits.

Determine resolution, accuracy, and conversion behavior of ADCs and DACs.

Derive transfer functions from differential equations, block diagrams, and signal-flow graphs.

Extract transient-response specifications from first-order and second-order system models.

Calculate steady-state error and static error constants for standard test inputs.

Determine closed-loop stability and parameter ranges using the Routh–Hurwitz criterion.

Construct a root locus and use it to predict closed-loop pole movement.

Construct Bode plots and determine gain margin, phase margin, and closed-loop bandwidth.

Apply the Nyquist criterion to determine closed-loop stability.

Analyze controllability, observability, poles, and responses using state-space models.

Compute autocorrelation, cross-correlation, and power spectral density for wide-sense stationary random processes.

Analyze generation, detection, spectra, power, and noise performance of AM, DSB-SC, and SSB systems.

Analyze generation, detection, bandwidth, and noise performance of FM and PM systems.

Calculate sampling, quantization, coding, and signal-to-quantization-noise properties of PCM systems.

Determine line-code spectra and apply the Nyquist criterion for zero intersymbol interference.

Derive the matched-filter receiver and calculate detection error probability in additive white Gaussian noise.

Compare ASK, FSK, PSK, QPSK, and QAM using signal-space representations and error probabilities.

Compute entropy, mutual information, and channel capacity for discrete communication models.

Express electromagnetic vectors and differential operators in Cartesian, cylindrical, and spherical coordinates.

Solve electrostatic field and potential problems using Gauss's law and boundary conditions.

Solve magnetostatic field problems using Ampère's law and magnetic boundary conditions.

Use Maxwell's equations and electromagnetic boundary conditions for time-varying fields.

Calculate propagation, polarization, power flow, reflection, and transmission of uniform plane waves.

Determine voltage, current, impedance, reflection coefficient, and standing-wave ratio on transmission lines.

Analyze propagation, cutoff, and dominant modes in rectangular waveguides and optical fibers.

Calculate radiation pattern, directivity, gain, polarization, and link quantities for basic antennas.

Correct sentence-level errors involving grammar, vocabulary, and usage.

Infer main ideas, logical relationships, and conclusions from short passages.

Solve numerical problems involving ratios, percentages, averages, mixtures, and growth rates.

Solve aptitude problems involving equations, inequalities, exponents, and logarithms.

Interpret tables, charts, graphs, and elementary statistical summaries.

Solve counting, arrangement, probability, and set-relation aptitude problems.

Solve deductive, inductive, and spatial-reasoning problems.

Complete a timed mixed General Aptitude set and classify errors by cause.

Translate a mixed GATE EC problem into the governing model before beginning calculations.

Select an efficient solution method for linked questions spanning mathematics, circuits, signals, and electronics.

Use dimensional analysis, limiting cases, and estimation to reject implausible answer choices.

Use the GATE virtual calculator efficiently for complex arithmetic, logarithms, and numerical evaluation.

Solve numerical-answer-type questions with appropriate precision, units, and rounding.

Apply a time-and-risk strategy to MCQ, MSQ, and numerical-answer-type questions.

Build and maintain an error log that distinguishes conceptual, algebraic, interpretation, and time-management errors.

Complete a timed mixed-subject mock section and convert its analysis into a targeted revision plan.