Hello Aspirant.
Analysis and Expected Questions of Engineering Mathematics in GATE
1-Linear Algebra
(for All GATE streams)
.Important topics
.Eigenvalues and vectors
.Finding rank and determinant of matrices
.Systems of Linear Equations
.Model questions
.Find the Matrix for the given Eigen values and Eigenvectors.
.Properties of Eigenvalues for symmetrical matrices.
.Find the rank or determinant for given matrix.
.Properties of Matrices based on determinant, rank, etc.
.Find the solution for given system of linear equations
2-Calculus
(for all streams, some of the below topics are not there in all streams)
.Limit
.Maxima and Minima
.Gradient, Divergence, and Curl (Vector Analysis in GATE EC)
.Find the maximum and minimum values for the given functions.
.Simple questions on limit and continuity
.Find the Divergence of Given vector field.
3-Differential Equations
.First order equations (linear and nonlinear)
.Cauchy's and Euler's equations
.Find the solution of given differential equation
4-Complex Analysis
(except GATE CS)
Important topics: -
.Analytic Functions
.Cauchy-Riemann equations
.Taylor’s Series
.Numerical Methods
.Newton-Raphson method
.Integration by trapezoidal and Simpson’s rules
Find the iteration value of equation using the Newton-Raphson method.
Find the value of the given integral using Trapezoidal and Simpson’s rules.
5-Probability and Statistics
.Joint and Conditional Probability
.Uniform, Normal, Exponential Distributions
Finding the probability for coin-based problems, dice-based problems, etc.
Finding the probability using distributions
6-Transform Theory
(for GATE EE and ME)
Important topics:-
.Laplace transform
.Model questions:
.Find the Laplace Transform and Inverse Laplace transform of the given function.
7-Discrete Mathematics
(only for GATE CS)
.Mathematical Logic (Propositions, and Predicate logic)
.Relations and Functions
8-Graph Connectivity, and coloring
Model questions
Find the first order logic sentence for the given English statement and with predicates.
Finding tautology, satisfiability, equivalences of given propositional statements.
Find the given relation is reflexive, symmetric, transitive, equivalence, etc.
Finding the number of edges, vertices, or components for the given connected or disconnected graph.
Checking isomorphism, Euler circuit, Hamiltonian cycle for given graphs.
Simple properties of various graphs such as complete graph, bipartite graph, regular graph, cycle graph and line graph.
i hope my answer will help you. All the best.
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