60 solved GATE EC questions on Engineering Mathematics, drawn from 6 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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State the domain, convergence, or smoothness condition a formula requires before substituting. These selected foundations connect linear algebra, calculus, differential equations, complex analysis, and probability as they appear in the GATE EC syllabus. Each area needs its own deeper study.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
Eigenvalues satisfy det(A − λI) = 0. Their sum equals the trace and their product equals the determinant. For Ax = b, a unique solution exists when det(A) ≠ 0. The rank-nullity theorem connects the solution space dimension to the number of columns minus the rank.
Check yourself: Can you verify the eigenvalue by checking Av = λv directly?
Partial derivatives hold other variables constant. The gradient points in the direction of steepest ascent. Stokes' and divergence theorems connect surface/volume integrals to boundary integrals under smoothness assumptions. Verify that the vector field satisfies the required continuity conditions.
Check yourself: Is the region simply connected, and is the field continuously differentiable?
Classify the ODE by order, linearity, and coefficient type before choosing a method. For a second-order linear ODE with constant coefficients, the characteristic equation determines the homogeneous solution form. Particular solutions depend on the forcing function; resonance occurs when the forcing frequency matches a natural frequency.
Check yourself: Does your solution satisfy both the equation and the initial/boundary conditions?
An analytic function satisfies the Cauchy-Riemann equations. The residue theorem evaluates contour integrals using residues at enclosed singularities. For a simple pole at z₀, the residue is lim(z→z₀)(z − z₀)f(z). Laurent series converge in annular regions.
Check yourself: Are all singularities inside the contour identified and classified?
For independent events, P(A ∩ B) = P(A)P(B). For a continuous random variable, probability at a single point is zero; integrate the density over an interval. The central limit theorem applies to the sample mean of independent identically distributed random variables with finite variance.
Check yourself: Does the stated independence justify multiplying probabilities?
Original teaching example · not a PYQ
Original mini-example: find the eigenvalues of A = [[3, 1], [0, 2]] and verify using the trace and determinant.
Eigenvalues: 3 and 2.
Evaluate the residue of f(z) = (z + 1)/((z − 1)(z − 3)) at z = 1.
Residue = −1.
z = 1 is a simple pole. Residue = lim(z→1)(z − 1)f(z) = (1 + 1)/(1 − 3) = 2/(−2) = −1.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental lectures, problem sets, and solutions covering ODEs, Laplace transforms, and systems of equations.
Free supplemental lectures by Gilbert Strang covering systems, vector spaces, eigenvalues, and positive-definite matrices.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE EC papers. Questions can carry more than one subject tag; counts are not marks weightage.
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