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 Equations: First order (linear and nonlinear) equations; higher order linear equations with constant coefficients; EulerCauchy equations; Laplace transform and its application in solving linear ODEs; initialand boundary value problems
Partial Differential Equation:(PDE: Fourier series; separation of variables; solutions of onedimensional diffusion equation; first and second order onedimensional wave equation and twodimensional 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 nonlinear algebraic equations; Least square approximation, Newton’s and Lagrange polynomials, numerical differentiation, Integration by trapezoidal and Simpson’s rule, single and multistep methods for first order differential equations

Section3: Geotechincal Engineering: 
Soil Mechanics: Origin of soils, soil structure and fabric; Threephase system and phase relationships, index properties; Unified and Indian standard soil classification system; Permeability one dimensional flow, Darcy’s law; Seepage through soils twodimensional flow, flow nets, uplift pressure, piping; Principle of effective stress, capillarity, seepage force and quicksand condition; Compaction in laboratory and field conditions; Onedimensional consolidation, time rate of consolidation; Mohr’s circle, stress paths, effective and total shear strength parameters, characteristics of clays and sand.
Foundation Engineering: Subsurface investigations scope, drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests; Earth pressure theoriesRankine 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. 

Section4: Water Resources Engineering: 
Fluid Mechanics and Hydraulics: 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; Dimensional analysis and hydraulic similitude; Kinematics of flow, velocity triangles; Basics of hydraulic machines, specific speed of pumps and turbines; Channel Hydraulics Energydepth relationships, specific energy, critical flow, slope profile, 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 and channel routing, surface runoff models, ground water hydrology steady state well hydraulics and aquifers; Application of Darcy’s law.
Irrigation: Duty, delta, estimation of evapotranspiration; Crop water requirements; Design of lined and unlined canals, head works, gravity dams and spillways; Design of weirs on permeable foundation; Types of irrigation systems, irrigation methods; Water logging and drainage; Canal regulatory works, crossdrainage structures, outlets and escapes 

Section5: Environmental Engineering: 
Water and Waste Water: 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, distribution of water. Sewage and sewerage treatment, quantity and characteristics of wastewater. Primary, secondary and tertiary treatment of wastewater, effluent discharge standards. Domestic wastewater treatment, quantity of characteristics of domestic wastewater, primary and secondary treatment. Unit operations and unit processes of domestic wastewater, sludge disposal
Air Pollution: Types of pollutants, their sources and impacts, air pollution meteorology, air pollution control, air quality standards and limits.
Municipal Solid Wastes: Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment and disposal).
Noise Pollution: Impacts of noise, permissible limits of noise pollution, measurement of noise and control of noise pollution. 

Section6: Transportation Engineering: 
Transportation Infrastructure: Highway alignment and engineering surveys; Geometric design of highways crosssectional elements, sight distances, horizontal and vertical alignments; Geometric design of railway track; Airport runway length, taxiway and exit taxiway design.
Highway Payments: 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: 372012; Design of rigid pavements using IRC: 582011; Distresses in concrete pavements
Traffic Engineering: Traffic studies on flow, speed, travel time delay and OD 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. 

Section7: Geomatics Engineering 
Principles of surveying; Errors and their adjustment; Maps scale, coordinate system; Distance and angle measurement Levelling and trigonometric levelling; 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) and Geographical Positioning system (GPS). 
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