Algebra

Matrix algebra, Systems of linear equations, Eigenvalues, and EigenVectors

Calculus

Functions of a single variable; Mean value theorems, local maxima, and minima, Taylor and Maclaurin series; Limit, continuity, and differentiability; Evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume; Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface, and Volume integrals, Stokes, Gauss, and Green’s theorems; Partial derivatives; Total derivative;

Ordinary Differential Equation (ODE)

First order (linear and nonlinear) equations; higher order linear equations with constant coefficients; Laplace transform and its application in solving linear ODEs; Euler-Cauchy equations and boundary value problems.

Partial Differential Equation (PDE)

Fourier series; solutions of one-dimensional diffusion equation; separation of variables; first and second-order one-dimensional wave equation and two-dimensional Laplace equation.

Probability and Statistics

Definitions of probability and sampling theorems; Conditional probability; Descriptive statistics – Mean, median, mode, and standard deviation; Continuous random variables: normal and exponential distributions; Hypothesis testing; Continuous random variables, Discrete Random variables: Poisson and Binomial distributions: normal and exponential distributions.

Numerical Methods

Accuracy and precision; error analysis. Numerical solutions of algebraic equations; Integration by trapezoidal and Simpson’s rule, single and multi-step methods for first-order differential equations; Least square approximation, Newton’s and Lagrange polynomials, numerical differentiation.

Quantitative Aptitude

Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing the data), 2- and 3-dimensional plots, maps, and tables Numerical computation and estimation: ratios, percentages, powers, exponents, and logarithms, permutations, and combinations, and series Mensuration and geometry Elementary statistics and probability.

Analytical Aptitude

Logic: deduction and induction, Analogy, Numerical relations, and reasoning

Verbal Aptitude

Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech Basic vocabulary: words, idioms, and phrases in context Reading and comprehension Narrative sequencing

Spatial Aptitude

Transformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping Paper folding, cutting, and patterns in 2 and 3 dimensions

Engineering Mechanics

Internal forces in structures; Friction and its applications; Kinematics of point mass and rigid body; System of forces, free-body diagrams, equilibrium equations; Centre of mass; Euler’s equations of motion; Energy methods; Impulse Momentum; Principles of virtual work.

Solid Mechanics

Bending moment and shear force in statically determinate beams; Simple bending theory, flexural and shear stresses, shear centre; Uniform torsion, buckling of column, combined and direct bending stresses; Simple stress and strain relationships; Theories of failures.

Structural Analysis

Statically determinate and indeterminate structures by force/ energy methods; Method of superposition; arches, beams, cables, Analysis of trusses, 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; Timber; Bitumen, Bricks and mortar. Construction Management: Types of construction projects; Tendering and construction contracts; Rate analysis and standard specifications; Cost estimation; Project planning and network analysis – CPM and PERT.

Concrete Structures

Working stress, Limit state, and Ultimate load design concepts; Design of columns, slabs, and beams; Bond and development length; Prestressed concrete; Analysis of beam sections at transfer and service loads.

Steel Structures

Working stress and Limit state design concepts; Connections – simple and eccentric, beam-column connections, plate girders and trusses; Design of tension and compression members, beams and beam-columns, column bases; Plastic Analysis of frames and beams

Soil Mechanics

Origin of soils, soil structure, and fabric; Unified and Indian standard soil classification system; Three-phase system and phase relationships, index properties; Permeability – one-dimensional flow, Darcy’s law; Seepage through soils – two-dimensional flow, flow nets, uplift pressure, piping; Mohr’s circle, stress paths, practical and total shear strength parameters, characteristics of clays and sand of effective stress, capillarity, seepage force, and quicksand condition; One-dimensional consolidation, time rate of consolidation; Mohr’s circle, stress paths, practical and total shear strength parameters, characteristics of clays and sand; Compaction in laboratory and field conditions.

Foundation Engineering

Subsurface investigations – boreholes, drilling, scopes sampling, plate load test, standard penetration, and cone penetration tests; Earth pressure theories – Coulomb and Rankine; Stability of slopes finite and infinite slopes, method of slices and Bishop’s method; Contact pressure; Settlement analysis in sands and clays; Deep foundations – types of piles, static and dynamic formulae, load capacity of piles in sands and clays, pile load test, negative skin friction; Earth pressure theories – Rankine and Coulomb; Stability of slopes finite and infinite slopes, Bishop’s method of slices and Bishop’s method; Stress distribution in soils – Westergaards and Boussinesq’s theories, pressure bulbs; Shallow foundations – Terzaghi’s and Meyerhoff’s bearing capacity theories, the effect of the water table; Combined footing and raft foundation.

Fluid Mechanics

Properties of fluids, fluid statics; Energy, momentum and continuity and corresponding equations; Potential flow, applications of momentum and energy equations; Turbulent and Laminar flow; Flow in pipes, pipe networks; Concept of boundary layer and its growth.

Hydraulics

Flow measurement in channels and pipes; Dimensional analysis and hydraulic similitude; Forces on Immersed bodies; Kinematics of flow, velocity triangles; Basics of hydraulic machines, specific speed of pumps and turbines; Channel Hydraulics – Energy-depth relationships, specific energy, slope profile, critical flow, hydraulic jump, uniform flow, and gradually varied flow.

Hydrology

Hydrologic cycle, precipitation, evaporation, evapotranspiration, watershed, infiltration, unit hydrographs, hydrograph analysis, flood estimation and routing, reservoir capacity, reservoir, channel routing, surface run-off models, groundwater hydrology – steady state well hydraulics and aquifers; Application of Darcy’s laws.

Irrigation

Duty, delta, estimation of evapotranspiration; Crop water requirements; Design of lined and unlined canals, spillways, headworks, gravity dams and; Design of weirs on the permeable foundation; Types of irrigation systems, irrigation methods; Drainage and Water logging; Canal regulation works, cross-drainage structures, outlets, and escapes.

Water and Wastewater

Quality standards, basic unit processes, and operations for water treatment. Drinking water standards, water requirements, basic unit operations, and unit processes for surface water treatment, and distribution of water. Sewage and sewerage treatment, quantity, and characteristics of wastewater. Effluent discharge standards. Domestic wastewater treatment, primary, secondary, and tertiary treatment of wastewater, the number of characteristics of domestic wastewater, and primary and secondary treatment. Unit operations and unit processes of sludge disposal and domestic wastewater.

Air Pollution

Types of pollutants, their sources and impacts, air pollution meteorology, air quality standards, and limits, and air pollution control.

Municipal Solid Wastes

Characteristics, generation, collection, and transportation of solid wastes, engineered systems for solid waste management (energy recovery, reuse/ recycle, treatment, and disposal).

Noise Pollution

Impacts of noise, permissible limits of noise pollution, measurement of noise, and control of noise pollution.

Transportation Infrastructure

Highway alignment and engineering surveys; Geometric design of highways – cross-sectional elements, sight distances, horizontal and vertical alignments; Geometric design of railway track; Airport runway length, taxiway, and exit taxiway design.

Highway Pavements

Highway materials – desirable properties and quality control tests; Design of bituminous paving mixes; Design factors for flexible and rigid pavements; Design of flexible pavement using IRC: 37-2012; Design of rigid pavements using IRC: 58-2011; Distresses in concrete pavements.

Traffic Engineering

Traffic studies on flow, speed, travel time – delay and O-D study, PCU, peak hour factor, parking study, accident study, and Analysis, Statistical Analysis of traffic data; Microscopic and macroscopic parameters of traffic flow, fundamental relationships; Control devices, signal design by Webster’s method; Types of intersections and channelization; Highway capacity and level of service of rural highways and urban roads.

Principles of surveying

Errors and their adjustment; Maps – scale, coordinate system; Distance and angle measurement – Leveling and trigonometric leveling; Traversing and triangulation survey; Total station; Horizontal and vertical curves.

Photogrammetry – scale, flying height; Remote sensing – basics, platform and sensors, visual image interpretation; Basics of Geographical information system (GIS).