GATE 2021 syllabus for Engineering Mathematics gives you details of the latest GATE syllabus for the subject release by the official gate organizing institute. We also created an easy to use ad-free mobile app for GATE syllabus, previous year papers with keys, gate calculator, virtual calculator, and more. **Download iStudy for all GATE preparation needs.**

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### GATE Engineering Mathematics (XE-A)

#### General Aptitude (Common To All Papers)

**Verbal Ability:** English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.

**Numerical Ability:** Numerical computation, numerical estimation, numerical reasoning and data interpretation.

#### General Aptitude Sample Questions

**Verbal Ability**

Choose the appropriate answer to complete the following sentence:

To those of us who had always thought him timid, his _________________came as a surprise.

(A) intrepidity

(B) inevitability

(C) inability

(D) inertness

Choose the appropriate answer to complete the following sentence:

Medicine is to illness as law is to____

(A) discipline

(B) anarchy

(C) treason

(D) etiquette

Read the following paragraph:

The ordinary form of mercury thermometer is used for temperature ranging from -40 degree fahrenheit to 500 degree fahrenheit. For measuring temperature below -40 degree fahrenheit, thermometers filled with alcohol are used. These are, however, not satisfactory for use in high temperatures. When a mercury thermometer is used for temperature above 500 degree fahrenheit, the space above the mercury is filled with some inert gas, usually nitrogen or carbon dioxide, placed in the thermometer under pressure. As the mercury rises, the gas pressures is increased, so that it is possible to use these thermometers for temperatures as high as 1000 degree fahrenheit.

With what, besides mercury, would a thermometer be filled if it was designed to be used for measuring temperature of about 500 degree fahrenheit?

(A) Pyrometer

(B) Inert gas

(C) Iron and brass

(D) Gas

The cost of manufacturing tractors in Korea is twenty percent less than the cost of manufacturing tractors in Germany. Even after transportation fees and import taxes are added, it is still cheaper to import tractors from Korea to Germany than to produce tractors in Germany.

Which of the following assertions is best supported by the above information?

(A) Labour costs in Korea are twenty percent below those in Germany.

(B) Importing tractors into Germany will eliminate twenty percent of the manufacturing jobs in Germany.

(C) The costs of transporting a tractor from Korea to Germany is more than twenty percent of the cost of manufacturing the tractor in Korea.

(D) The import taxes on a tractor imported from Korea to Germany is less than twenty percent of the cost of manufacturing the tractor in Germany.

**Numerical Ability**

In a survey, 3/16 of the people surveyed told that they preferred to use public transport while commuting daily to office. 5/8 of the people surveyed told that they preferred to use their own vehicles. The remaining 75 respondents said that they had no clear preference. How many people preferred to use public transport?

(A) 75

(B) 100

(C) 125

(D) 133

#### Section 1: Linear Algebra

Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors; Diagonalisation of matrices; Cayley-Hamilton Theorem.

#### Section 2: Calculus

*Functions of single variable:* Limit, continuity and differentiability; Mean value theorems; Indeterminate forms and L’Hospital’s rule; Maxima and minima; Taylor’s theorem; Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.

*Functions of two variables:* Limit, continuity and partial derivatives; Directional derivative; Total derivative; Tangent plane and normal line; Maxima, minima and saddle points; Method of Lagrange multipliers; Double and triple integrals, and their applications.

*Sequence and series:* Convergence of sequence and series; Tests for convergence; Power series; Taylor’s series; Fourier Series; Half range sine and cosine series.

#### Section 3: Vector Calculus

Gradient, divergence and curl; Line and surface integrals; Green’s theorem, Stokes theorem and Gauss divergence theorem (without proofs).

#### Section 3: Complex variables

Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy’s integral theorem and integral formula (without proof); Taylor’s series and Laurent series; Residue theorem (without proof) and its applications.

#### Section 4: Ordinary Differential Equations

First order equations (linear and nonlinear); Higher order linear differential equations with constant coefficients; Second order linear differential equations with variable coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind and their properties.

#### Section 5: Partial Differential Equations

Classification of second order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one dimensional heat and wave equations.

#### Section 6: Probability and Statistics

Axioms of probability; Conditional probability; Bayes’ Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.

#### Section 7: Numerical Methods

Solution of systems of linear equations using LU decomposition, Gauss elimination and Gauss-Seidel methods; Lagrange and Newton’s interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson’s rule and Gaussian quadrature rule; Numerical solutions of first order differential equations by Euler’s method and 4th order Runge-Kutta method.

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