Gate Syllabus 2021

Section 1: Engineering Mathematics

Linear Algebra:

Matrix algebra;

Systems of linear equations;

Eigen values and Eigen vectors.


Calculus:

Functions of single variable;

Limit, continuity and differentiability;

Mean value theorems,

local maxima and minima,

Taylor and Maclaurin series;

Evaluation of definite and indefinite integrals,

application of definite integral to obtain area and volume;

Partial derivatives;

Total derivative;

Gradient,

Divergence and Curl,

Vector identities,

Directional derivatives,

Line, Surface and Volume integrals,

Stokes, Gauss and Green’s theorems.


Ordinary Differential Equation (ODE):

First order (linear and non-linear) equations;

higher order linear equations with constant coefficients;

Euler-Cauchy equations;

Laplace transform and its application in solving linear ODEs;

initial and boundary value problems.

Partial Differential Equation (PDE):

Fourier series;

separation of variables;

solutions of one-dimensional diffusion equation;

first and second order one-dimensional wave equation and two-dimensional Laplace equation.


Probability and Statistics:

Definitions of probability and sampling theorems;

Conditional probability;

Discrete Random variables:

Poisson and Binomial distributions;

Continuous random variables:

normal and exponential distributions;

Descriptive statistics - Mean, median, mode and standard deviation;

Hypothesis testing.


Numerical Methods:

Accuracy and precision,

error analysis,

Numerical solutions of linear and non-linear algebraic equations;

Least square approximation,

Newton’s and Lagrange’s polynomials,

numerical differentiation,

Integration by trapezoidal and Simpson’s rule,

single and multi-step methods for first order differential equations.


Section 2: Structural Engineering

Engineering Mechanics:

System of forces,

free-body diagrams,

equilibrium equations;

Internal forces in structures;

Friction and its applications;

Kinematics of point mass and rigid body;

Centre of mass;

Euler’s equations of motion;

Impulse-momentum;

Energy methods;

Principles of virtual work.

Solid Mechanics:


Bending moment and shear force in statically determinate beams;

Simple stress and strain relationships;

Theories of failures;

Simple bending theory,

flexural and shear stresses,

shear centre; Uniform torsion,

buckling of column,

combined and direct bending stresses.


Structural Analysis:

Statically determinate and indeterminate structures by force/ energy methods;

Method of superposition;

Analysis of trusses, arches, beams, cables and frames;

Displacement methods:

Slope deflection and moment distribution methods;

Influence lines;

Stiffness and flexibility methods of structural analysis.


Construction Materials and Management:

Construction Materials:

Structural steel - composition, material properties and behaviour ;

Concrete - constituents, mix design, short-term and long-term properties;

Bricks and mortar; Timber; Bitumen.

Construction Management:

Types of construction projects;

Tendering and construction contracts;

Rate analysis and standard specifications;

Cost estimation;

Project planning and network analysis - PERT and CPM.


Concrete Structures:

Working stress,

Limit state and Ultimate load design concepts;

Design of beams, slabs, columns;

Bond and development length;

Prestressed concrete;

Analysis of beam sections at transfer and service loads.

Steel Structures:

Working stress and Limit state design concepts;

Design of tension and compression members,

beams and beam- columns, column bases;

Connections - simple and eccentric,

beam-column connections,

plate girders and trusses;

Plastic analysis of beams and frames.

Section 3: Geotechnical Engineering

Soil Mechanics:

Origin of soils,

soil structure and fabric;

Three-phase system and phase relationships,

index properties;

Unified and Indian standard soil classification system;

Permeability - one dimensional flow,

Darcy’s law;

Seepage through soils - two-dimensional flow,

flow nets,

uplift pressure, piping;

Principle of effective stress,

capillarity,

seepage force and quicksand condition;

Compaction in laboratory and field conditions;

One-dimensional consolidation,

time rate of consolidation;

Mohr’s circle, stress paths,

effective and total shear strength parameters,

characteristics of clays and sand.


Foundation Engineering:

Sub-surface investigations - scope,

drilling bore holes, sampling, plate load test,

standard penetration and cone penetration tests;

Earth pressure theories - Rankine and Coulomb;

Stability of slopes - finite and infinite slopes,

method of slices and Bishop’s method;

Stress distribution in soils - Boussinesq’s and Westergaard’s theories,

pressure bulbs;

Shallow foundations - Terzaghi’s and Meyerhoff’s bearing capacity theories,

effect of water table;

Combined footing and raft foundation;

Contact pressure;

Settlement analysis in sands and clays;

Deep foundations - types of piles,

dynamic and static formulae,

load capacity of piles in sands and clays,

pile load test,

negative skin friction.

Section 4: Water Resources Engineering

Fluid Mechanics:

Properties of fluids,

fluid statics;

Continuity, momentum, energy and corresponding equations;

Potential flow,

applications of momentum and energy equations;

Laminar and turbulent flow;

Flow in pipes, pipe networks;

Concept of boundary layer and its growth.


Hydraulics:

Forces on immersed bodies;

Flow measurement in channels and pipes;