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Engineering Mathematics PYQs (previous year questions) for GATE EE: Engineering Mathematics (Engineering Mathematics) had 102 questions across the 11 official GATE EE papers we tagged (2016–2026), and appeared in 11 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Calculus, Complex Analysis, Vector Calculus.
Year-wise question count
Asked in 11 of 11 years.
| Year | Questions |
|---|---|
| GATE EE 2026 | 11 |
| GATE EE 2025 | 10 |
| GATE EE 2024 | 9 |
| GATE EE 2023 | 9 |
| GATE EE 2022 | 8 |
| GATE EE 2021 | 8 |
| GATE EE 2020 | 8 |
| GATE EE 2019 | 12 |
| GATE EE 2018 | 11 |
| GATE EE 2017 | 7 |
| GATE EE 2016 | 9 |
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| Calculus | 16 | 9 | 2026, 2024, 2023, 2022, 2021, 2020, 2018, 2017, 2016 |
| Complex Analysis | 13 | 9 | 2026, 2025, 2024, 2021, 2020, 2019, 2018, 2017, 2016 |
| Vector Calculus | 15 | 8 | 2026, 2025, 2024, 2023, 2022, 2020, 2019, 2018 |
| Probability | 10 | 8 | 2026, 2025, 2024, 2023, 2022, 2021, 2019, 2016 |
| Differential Equations | 9 | 8 | 2026, 2025, 2024, 2020, 2019, 2018, 2017, 2016 |
| Eigenvalues | 8 | 7 | 2026, 2024, 2022, 2021, 2019, 2017, 2016 |
| Matrix Properties | 4 | 4 | 2026, 2022, 2021, 2018 |
| Numerical Methods | 3 | 3 | 2023, 2018, 2017 |
| Linear Algebra | 3 | 2 | 2026, 2023 |
| Cayley-Hamilton Theorem | 2 | 2 | 2022, 2018 |
| Laplace Transform | 2 | 2 | 2019, 2016 |
| Linear Equations | 2 | 2 | 2026, 2025 |
| Matrix Inverse | 2 | 2 | 2024, 2019 |
| Matrix Rank | 2 | 2 | 2019, 2016 |
| Algebra | 1 | 1 | 2020 |
| Eigenvectors | 1 | 1 | 2025 |
| Fourier Series | 1 | 1 | 2019 |
| Least Squares | 1 | 1 | 2023 |
| Matrix Algebra | 1 | 1 | 2025 |
| Matrix Decomposition | 1 | 1 | 2020 |
| Optimization | 1 | 1 | 2025 |
| Orthogonal Matrices | 1 | 1 | 2026 |
| Series | 1 | 1 | 2016 |
| Statistics | 1 | 1 | 2023 |
| Taylor Series | 1 | 1 | 2024 |
How to practise Engineering Mathematics PYQs
- Start with the concepts at the top of the table. They have come back the most.
- Solve one year’s Engineering Mathematics questions from the official PDF against the clock, then check the answer listed below.
- Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
- Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.
Questions by year
Each line gives the question number, type, concept, our one-line summary and the official answer, with a link to the official PDF.
GATE EE2026
- Q.14 · MCQ · Differential Equations: Classify a second-order variable-coefficient ODE (official answer: A) PDF
- Q.30 · MSQ · Eigenvalues: Consequences of two matrices sharing an eigenvalue and eigenvector (official answer: A, B, D) PDF
- Q.32 · NAT · Vector Calculus: Flux of a vector field over a unit sphere (official answer: 0) PDF
- Q.35 · NAT · Matrix Properties: Quadratic form of a skew-symmetric matrix (official answer: 0) PDF
- Q.49 · MCQ · Linear Algebra: Linear dependence of a set of column vectors (official answer: A) PDF
- Q.50 · MCQ · Differential Equations: Solution of a constant-coefficient second-order ODE (official answer: A) PDF
- Q.55 · MSQ · Orthogonal Matrices: Properties of a real orthogonal matrix (official answer: A, B, D) PDF
- Q.56 · MSQ · Linear Equations: Statements about a linear system with a unique solution (official answer: A, B, C) PDF
- Q.62 · NAT · Complex Analysis: Contour integral using residues inside a circle (official answer: 25.00–25.60) PDF
- Q.64 · NAT · Probability: Value of a coefficient minimising a mean-square error (official answer: 0.1) PDF
- Q.65 · NAT · Calculus: Value of a definite integral with a high power term (official answer: 0.25) PDF
GATE EE2025
- Q.11 · MCQ · Optimization: Nature of the set of minimisers of a two-variable function (official answer: B) PDF
- Q.12 · MCQ · Eigenvectors: Property of eigenvectors of a real symmetric matrix (official answer: B) PDF
- Q.13 · MCQ · Linear Equations: Nature of solutions of a 3x3 linear system (official answer: B) PDF
- Q.14 · MCQ · Matrix Algebra: Express the square of a given matrix in terms of the matrix (official answer: A) PDF
- Q.15 · MCQ · Probability: Property of two discrete random variables from a joint distribution (official answer: B) PDF
- Q.36 · MCQ · Probability: Density of the square of a uniform random variable (official answer: A) PDF
- Q.51 · MSQ · Vector Calculus: Exponents making the divergence of a radial field constant (official answer: B, D) PDF
- Q.53 · NAT · Vector Calculus: Directional derivative of a scalar function at the origin (official answer: 0–1) PDF
- Q.54 · NAT · Differential Equations: Value of a state at t = 1 for a pair of simple ODEs (official answer: 2) PDF
- Q.55 · NAT · Complex Analysis: Contour integral of a complex function around the unit circle (official answer: 0) PDF
GATE EE2024
- Q.11 · MCQ · Matrix Inverse: Which of the given matrices is invertible (official answer: C) PDF
- Q.29 · MSQ · Probability: Which functions of a uniform discrete variable stay uniform (official answer: B, D) PDF
- Q.30 · MSQ · Complex Analysis: Which complex functions are analytic everywhere (official answer: D) PDF
- Q.31 · NAT · Taylor Series: Coefficient of z^5 in the Taylor series of a complex function (official answer: 0.0) PDF
- Q.32 · NAT · Eigenvalues: Sum of eigenvalues of a 2x2 matrix (official answer: 29) PDF
- Q.36 · MCQ · Vector Calculus: Directional derivative of a log function at a point (official answer: C) PDF
- Q.43 · MSQ · Calculus: Statements about extrema of a function with positive second derivative (official answer: B) PDF
- Q.44 · MSQ · Calculus: Differentiability of the square of the ramp function (official answer: B) PDF
- Q.45 · MSQ · Differential Equations: Identify the nonlinear differential equations (official answer: B, D) PDF
GATE EE2023
- Q.11 · MCQ · Linear Algebra: Vector normal to a plane defined by a given vector (official answer: D) PDF
- Q.24 · MCQ · Linear Algebra: Transformation matrix relating two given vectors (official answer: A) PDF
- Q.25 · MCQ · Statistics: Comparing two estimators of standard deviation (official answer: C) PDF
- Q.34 · NAT · Numerical Methods: Numerical value of an ODE solution at t = 1 (official answer: 0.48–0.52) PDF
- Q.35 · NAT · Least Squares: Slope of the least-squares line through three points (official answer: 0.9–1.1) PDF
- Q.42 · MSQ · Calculus: Area enclosed by a superellipse-type curve for various values of p (official answer: A, B, D) PDF
- Q.45 · NAT · Probability: Probability of first head on the second toss of a biased coin (official answer: 0.187–0.188) PDF
- Q.62 · NAT · Vector Calculus: Line integral of a vector field around a cardioid (official answer: 9–10) PDF
- Q.65 · NAT · Vector Calculus: Maximum rate of change of a quadratic function at a point (official answer: 10) PDF
GATE EE2022
- Q.20 · MCQ · Matrix Properties: Type of 3x3 matrix whose elements depend on (i - j) (official answer: B) PDF
- Q.40 · MCQ · Eigenvalues: Eigenvalue and eigenvector properties of a matrix exponential (official answer: C) PDF
- Q.41 · MCQ · Calculus: Interval where an integral-defined function decreases (official answer: A) PDF
- Q.42 · MCQ · Cayley-Hamilton Theorem: Find constants in a matrix polynomial identity (official answer: A) PDF
- Q.50 · MCQ · Vector Calculus: Direction of fastest increase of a scalar function at a point (official answer: B) PDF
- Q.51 · MCQ · Vector Calculus: Expression that does not give the area of a region via line integrals (official answer: C) PDF
- Q.52 · MCQ · Vector Calculus: Volume integral of divergence over a unit cube (official answer: C) PDF
- Q.54 · NAT · Probability: Normalising constant of a Laplacian probability density (official answer: 0.99–1.01) PDF
GATE EE2021
- Q.1 · MCQ · Eigenvalues: Eigenvalues of a 2 x 2 matrix with a constraint (official answer: B) PDF
- Q.2 · MCQ · Complex Analysis: True statement about a complex polynomial (official answer: D) PDF
- Q.3 · MCQ · Calculus: Local minima of a function with positive second derivative (official answer: C) PDF
- Q.13 · NAT · Calculus: Orthogonal intersection point of two circles (official answer: 1) PDF
- Q.26 · MCQ · Calculus: Number of real roots of a polynomial in an interval (official answer: B) PDF
- Q.27 · MCQ · Probability: Expected tosses until the first head (official answer: C) PDF
- Q.28 · MCQ · Complex Analysis: Contour integral around a rectangle (official answer: C) PDF
- Q.38 · NAT · Matrix Properties: Determinant of A + I for a nilpotent matrix (official answer: 1) PDF
GATE EE2020
- Q.1 · MCQ · Algebra: True statement about a cubic polynomial's roots (official answer: A OR D) PDF
- Q.2 · MCQ · Calculus: Orthogonality integrals of sines and cosines (official answer: C) PDF
- Q.5 · MCQ · Complex Analysis: Contour integral over the unit circle (official answer: C) PDF
- Q.16 · NAT · Differential Equations: Value of a first-order ODE solution at ln 2 (official answer: 0.8774–0.8952) PDF
- Q.26 · MCQ · Calculus: Maximum and minimum of a quadratic over an interval (official answer: A) PDF
- Q.27 · MCQ · Vector Calculus: Constants making a vector field conservative (official answer: C) PDF
- Q.42 · MCQ · Matrix Decomposition: Real elements in a Cholesky-type factor (official answer: Marks to all) PDF
- Q.44 · NAT · Vector Calculus: Line integral along a parabola (official answer: -3.05–-2.95) PDF
GATE EE2019
- Q.1 · MCQ · Laplace Transform: Inverse Laplace transform of a rational function (official answer: C) PDF
- Q.2 · MCQ · Eigenvalues: Eigenvalues of the square of a matrix (official answer: D) PDF
- Q.3 · MCQ · Differential Equations: Name of a given partial differential equation (official answer: B) PDF
- Q.4 · MCQ · Complex Analysis: Function analytic inside the unit disc (official answer: B) PDF
- Q.5 · MCQ · Probability: Standard deviation of a thermal noise process (official answer: B) PDF
- Q.18 · NAT · Vector Calculus: Line integral of a gradient along a contour (official answer: 139) PDF
- Q.24 · NAT · Matrix Rank: Rank of a 3 x 3 matrix (official answer: 3) PDF
- Q.26 · MCQ · Matrix Inverse: Statements about a matrix and its inverse (official answer: C) PDF
- Q.27 · MCQ · Complex Analysis: Closed contour integral of a rational function (official answer: A) PDF
- Q.28 · MCQ · Fourier Series: Fourier coefficients of a half-wave sine function (official answer: D) PDF
- Q.39 · NAT · Vector Calculus: Divergence of a scalar times a vector field (official answer: 45) PDF
- Q.40 · NAT · Probability: Probability of two or more defective resistors (official answer: 0.25–0.27) PDF
GATE EE2018
- Q.11 · MCQ · Calculus: Continuity and differentiability of a piecewise function (official answer: D) PDF
- Q.12 · MCQ · Vector Calculus: Directional derivative of a scalar field (official answer: A) PDF
- Q.13 · MCQ · Complex Analysis: Contour integral around a circle centred at -2 (official answer: A) PDF
- Q.17 · NAT · Matrix Properties: Determinant from traces of A and A squared (official answer: 5.5) PDF
- Q.18 · NAT · Calculus: Integral of the fractional-part function (official answer: 0.49–0.51) PDF
- Q.30 · MCQ · Numerical Methods: Newton-Raphson iteration for a power angle (official answer: C) PDF
- Q.33 · MCQ · Differential Equations: Final values of a coupled linear system (official answer: C) PDF
- Q.35 · MCQ · Complex Analysis: Contour integral using residues (official answer: B) PDF
- Q.42 · NAT · Vector Calculus: Line integral along a circular arc (official answer: 0.0) PDF
- Q.43 · NAT · Calculus: Maximum of a cubic over an interval (official answer: 11.5–12.5) PDF
- Q.44 · NAT · Cayley-Hamilton Theorem: Determinant of a matrix polynomial (official answer: 0.9–1.1) PDF
GATE EE2017
- Q.1 · MCQ · Eigenvalues: Another eigenvector of a 3 x 3 symmetric matrix (official answer: C) PDF
- Q.2 · MCQ · Complex Analysis: Limit of a complex rational function at z = i (official answer: D) PDF
- Q.17 · NAT · Calculus: Double integral over a trapezoidal region (official answer: 0.99–1.01) PDF
- Q.26 · MCQ · Calculus: Differentiability of a piecewise function at x = 1 (official answer: B) PDF
- Q.27 · MCQ · Differential Equations: Interval of existence of a unique ODE solution (official answer: A) PDF
- Q.28 · MCQ · Complex Analysis: Complex line integral along a straight path (official answer: B) PDF
- Q.42 · NAT · Numerical Methods: Bisection iterations needed for a given accuracy (official answer: 10) PDF
GATE EE2016
- Q.1 · NAT · Calculus: Maximum of a cubic function over an interval (official answer: 0.0) PDF
- Q.2 · NAT · Eigenvalues: Non-zero eigenvalue of a 3 x 3 matrix of ones (official answer: 3.0) PDF
- Q.3 · MCQ · Laplace Transform: Laplace transform of an exponentially weighted sinusoid (official answer: A) PDF
- Q.4 · MCQ · Differential Equations: Value at t=2 of a solution of a second-order ODE (official answer: B) PDF
- Q.5 · MCQ · Complex Analysis: Contour integral over the unit circle (official answer: B) PDF
- Q.26 · NAT · Probability: Probability that all three pens have the same colour (official answer: 0.2) PDF
- Q.27 · NAT · Series: Value of x for which a power series sum takes a value (official answer: 0.28–0.31) PDF
- Q.28 · MCQ · Eigenvalues: Eigenvalues and eigenvectors of a matrix polynomial (official answer: A) PDF
- Q.29 · MCQ · Matrix Rank: Rank of A-transpose A for a 4 x 3 matrix of rank 2 (official answer: B) PDF
Engineering Mathematics in other exams
The same topic in other official papers we tagged: GATE ME (99 questions).
Other Engineering Mathematics topics
FAQ
How many Engineering Mathematics questions come in GATE EE?
In the official papers we tagged: 11 in 2026, 10 in 2025, 9 in 2024, 9 in 2023, 8 in 2022, 8 in 2021, 8 in 2020, 12 in 2019, 11 in 2018, 7 in 2017 and 9 in 2016. That is 102 questions in all, about 100% of Engineering Mathematics.
Which Engineering Mathematics topics repeat in GATE EE?
Asked in the most papers: Calculus, Complex Analysis, Vector Calculus. The concept table lists every one with its count.
Are these official GATE EE questions?
Yes. Every question is from an official GATE EE paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.