Aspiring engineers who are preparing for the Graduate Aptitude Test in Engineering (GATE) understand the significance of thorough preparation and comprehensive study resources.

Through a meticulous examination of previous years’ question papers, we aim to provide you with valuable insights, key trends, and effective strategies to excel in Engineering Mathematics for your GATE exam.

## GATE EE Syllabus for the Subject Engineering Mathematics

**Linear Algebra**: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.

**Calculus:** Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral,

Volume integral, Stokes’s theorem, Gauss’s theorem, Divergence theorem, Green’s theorem.

**Differential Equations:** First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.

**Complex Variables:** Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.

**Probability and Statistics: **Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.

## Analysis of Previous GATE Papers for Engineering Mathematics

Year | Percentage of Marks |
---|---|

2023 | 11% |

2022 | 13 % |

2021 | 12 % |

2020 | 12 % |

2019 | 14 % |

2018 | 11 % |

2017 | 12% |

2016 | 12% |

2015 | 11 % |

2014 | 10 % |

2013 | 14 % |

## Recent GATE Paper Questions of Engineering Mathematics

The following questions have been asked from Engineering Mathematics , in GATE-EE 2023 Paper.

Q. A quadratic function of two variables is given as

f(x_{1},x_{2})=x_{1}^{2}+2x_{2}^{2}+3x_{1}+3x_{2}+x_{1}x_{2}+1

The magnitude of the maximum rate of change of the function at the point (1.1) is

(Round off to the nearest integer) _____.

Q. Consider the state-space description ot an LTI system with matrices

A=\begin{bmatrix}0 & 1\\-1 & -2\end{bmatrix},B=\begin{bmatrix}0\\1
\end{bmatrix} C=\left [ 3 \; \; -2 \right ]

For the input. sin( \omega t). \omega> 0. the value of for which the steady-state output of the system will be zero, is _____.(Round off to the nearest integer).

Q. The period of the discrete-time signal x[n] described by the equation below is N=_____. (Round off to the nearest integer).

x[n]=1+3sin\left ( \frac{15\pi }{8}n+\frac{3\pi }{4} \right )-5sin\left ( \frac{\pi }{3}n-\frac{\pi }{4} \right )

## GATE Paper Solutions for Engineering Mathematics

Last 25+ years GATE Papers with Authentic Solutions