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 EC Syllabus for the Subject Engineering Mathematics

**Linear Algebra:** Vector space, basis, linear dependence and independence, matrix algebra, Eigen values and eigen vectors, rank, solution of linear equations- existence and uniqueness.

**Calculus:** Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.

**Differential Equations**: First order equations (linear and nonlinear), higher order linear differential equations, Cauchy’s and Euler’s equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.

**Vector Analysis: **Vectors in plane and space, vector operations, gradient, divergence and curl,

Gauss’s, Green’s and Stokes’ theorems.

**Complex Analysis: **Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, sequences, series, convergence tests, Taylor and Laurent series, residue theorem.

**Probability and Statistics:** Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability.

## Analysis of Previous GATE Papers for Engineering Mathematics

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

2023 | 13% |

2022 | 14 % |

2021 | 13 % |

2020 | 13 % |

2019 | 13 % |

2018 | 14 % |

2017 | 14% |

2016 | 12% |

2015 | 13 % |

2014 | 11 % |

2013 | 10 % |

## Recent GATE Paper Questions of Engineering Mathematics

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

Q. Let v_{1}=\begin{bmatrix}1\\2\\0\end{bmatrix} and v_{2}=\begin{bmatrix}2\\1\\3\end{bmatrix} be two vectors. The value of the coefficient α in the expression v_{1} = α v_{2}+ e, which minimizes the length of the error vector e, is

a) 7/2

b) -2/7

c) 2/7

d) -7/2

Q. The value of the contour integral, \oint _{c}\left ( \frac{z+2}{z^{2}+2z+2} \right ) , where the contour C is {z:|z+1-\frac{3}{2}j}|=1 , taken in the R counter clockwise direction, is

a) -π(1+j)

b) π(1+j)

c) π(1-j)

d) -π(1-j)

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