GATE 2026 Syllabus

Common for all branches: Gate General Aptitude Syllabus

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.

Quantitative Aptitude

Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing 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.

Spatial Aptitude

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

 

GATE Exam 2026 Syllabus for Computer science, Civil, Electrical, Instrumentation, Electronic and Mechanical

1. Computer Science and Engineering

 

Section 1: Engineering Mathematics

Discrete Mathematics: Propositional and first order logic. Sets, relations, functions, partial orders and lattices. Monoids, Groups. Graphs: connectivity, matching, colouring. Combinatorics: counting, recurrence relations, generating functions.

Linear Algebra: Matrices, determinants, system of linear equations, eigenvalues and eigenvectors, LU decomposition.

 

Calculus: Limits, continuity and differentiability, Maxima and minima, Mean value theorem, Integration.

 

Probability and Statistics: Random variables, Uniform, normal, exponential, Poisson and binomial

distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem.

 

 

Section 2: Digital Logic

 

Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and

computer arithmetic (fixed and floating point).

 

Section 3: Computer Organization and Architecture

 

Machine instructions and addressing modes. ALU, data‐path and control unit. Instruction pipelining,

pipeline hazards. Memory hierarchy: cache, main memory and secondary storage; I/O interface (interrupt

and DMA mode).

 

Section 4: Programming and Data Structures

 

Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.

 

Section 5: Algorithms

 

Searching, sorting, hashing. Asymptotic worst case time and space complexity. Algorithm design

techniques: greedy, dynamic programming and divide‐and‐conquer. Graph traversals, minimum spanning trees, shortest paths.

 

Section 6: Theory of Computation

 

Regular expressions and finite automata. Context-free grammars and push-down automata. Regular and context-free languages, pumping lemma. Turing machines and undecidability.

 

Section 7: Compiler Design

 

Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code

generation. Local optimisation, Data flow analyses: constant propagation, liveness analysis, common sub expression elimination.

 

Section 8: Operating System

 

System calls, processes, threads, inter‐process communication, concurrency and synchronization.

Deadlock. CPU and I/O scheduling. Memory management and virtual memory. File systems.

 

Section 9: Databases

 

ER‐model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints, normal forms.

File organization, indexing (e.g., B and B+ trees). Transactions and concurrency control.

Section 10: Computer Networks

 

Concept of layering: OSI and TCP/IP Protocol Stacks; Basics of packet, circuit and virtual circuitswitching; Data link layer: framing, error detection, Medium Access Control, Ethernet bridging; Routing protocols: shortest path, flooding, distance vector and link state routing; Fragmentation and IP addressing,

IPv4, CIDR notation, Basics of IP support protocols (ARP, DHCP, ICMP), Network Address Translation

(NAT); Transport layer: flow control and congestion control, UDP, TCP, sockets; Application layer

protocols: DNS, SMTP, HTTP, FTP, Email.

 

2. Civil Engineering

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 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.

Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher order

Linear equations with constant coefficients; Euler-Cauchy equations; 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: Sampling theorems; Conditional probability; Descriptive statistics –

Mean, median, mode and standard deviation; Random Variables – Discrete and Continuous,

Poisson and Normal Distribution; Linear regression.

Numerical Methods: Error analysis. Numerical solutions of linear and non-linear algebraic

Equations; Newton’s and Lagrange 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; Frictions and its applications; Centre of mass; Free Vibrations of undammed

SDOF system.

Solid Mechanics: Bending moment and shear force in statically determinate beams; Simple stress

And strain relationships; simple bending theory, flexural and shear stresses, shear center; Uniform

Torsion, Transformation of stress; 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. Construction Management: Types of construction projects; Project planning and

network analysis - PERT and CPM; Cost estimation.

Concrete Structures: Working stress and Limit state design concepts; Design of beams, slabs,

columns; Bond and development length; Prestressed concrete beams.

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; Concept of plastic analysis -beams

and frames.

Section 3: Geotechnical Engineering

Soil Mechanics: Three-phase system and phase relationships, index properties; Unified and Indian

standard soil classification system; Permeability - one dimensional flow, Seepage through soils –

two - dimensional flow, flow nets, uplift pressure, piping, capillarity, seepage force; Principle of

effective stress and quicksand condition; Compaction of soils; One- dimensional consolidation,

time rate of consolidation; Shear Strength, Mohr’s circle, effective and total shear strength

parameters, Stress-Strain characteristics of clays and sand; Stress paths.

Foundation Engineering: Sub-surface investigations - 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, Bishop’s method; Stress distribution in

soils – Boussinesq’s theory; 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 – dynamic and static formulae,

Axial load capacity of piles in sands and clays, pile load test, pile under lateral loading, pile group

efficiency, negative skin friction.

 

Section 4: Water Resources Engineering

Fluid Mechanics: Properties of fluids, fluid statics; Continuity, momentum and energy equations

and their applications; Potential flow, Laminar and turbulent flow; Flow in pipes, pipe networks;

Concept of boundary layer and its growth; Concept of lift and drag.

Hydraulics: Forces on immersed bodies; Flow measurement in channels and pipes; Dimensional

analysis and hydraulic similitude; Channel Hydraulics - Energy-depth relationships, specific

energy, critical flow, hydraulic jump, uniform flow, gradually varied flow and water surface

profiles.

Hydrology: Hydrologic cycle, precipitation, evaporation, evapo-transpiration, watershed,

infiltration, unit hydrographs, hydrograph analysis, reservoir capacity, flood estimation and

routing, surface run-off models, ground water hydrology - steady state well hydraulics and

aquifers; Application of Darcy’s Law.

Irrigation: Types of irrigation systems and methods; Crop water requirements - Duty, delta,

evapotranspiration; Gravity Dams and Spillways; Lined and unlined canals, Design of weirs on

permeable foundation; cross drainage structures.

 

Section 5: Environmental Engineering

Water and Waste Water Quality and Treatment: Basics of water quality standards – Physical,

chemical and biological parameters; Water quality index; Unit processes and operations; Water

requirement; Water distribution system; Drinking water treatment.

Sewerage system design, quantity of domestic wastewater, primary and secondary treatment.

Effluent discharge standards; Sludge disposal; Reuse of treated sewage for different applications.

Air Pollution: Types of pollutants, their sources and impacts, air pollution control, air quality

standards, Air quality Index 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).

Section 6: Transportation Engineering

Transportation Infrastructure: Geometric design of highways - cross-sectional elements, sight

Distances, horizontal and vertical alignments.

Geometric design of railway Track – Speed and Cant.

Concept of airport runway length, calculations and corrections; taxiway and exit taxiway design.

Highway Pavements: Highway materials - desirable properties and tests; Desirable properties of

Bituminous paving mixes; Design factors for flexible and rigid pavements; Design of flexible and

Rigid pavement using IRC codes.

Traffic Engineering: Traffic studies on flow and speed, peak hour factor, accident study, statistical

analysis of traffic data; Microscopic and macroscopic parameters of traffic flow, fundamental

relationships; Traffic signs; Signal design by Webster’s method; Types of intersections; Highway

Capacity.

Section 7: 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 and Remote Sensing - Scale, flying height; Basics of remote sensing and GIS.

 

1.  Electrical Engineering

 

Section 1: Engineering Mathematics

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values, Eigen vectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and

improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series,

Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral,

Stokes’s theorem, Gauss’s theorem, Divergence theorem, Green’s theorem.

Differential Equations: First order equations (linear and nonlinear), Higher order linear differential

Equations with constant coefficients, Method of variation of parameters, Cauchy’s equation,

Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of

separation of variables.

Complex Variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula,

Taylor series, Laurent series, Residue theorem, Solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode,

Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson

distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.

 

Section 2: Electric circuits

Network Elements: Ideal voltage and current sources, dependent sources, R, L, C, M elements;

Network solution methods: KCL, KVL, Node and Mesh analysis; Network Theorems: Thevenin’s,

Norton’s, Superposition and Maximum Power Transfer theorem; Transient response of DC and

AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase

circuits, star-delta transformation, complex power and power factor in AC circuits.

 

Section 3: Electromagnetic Fields

Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence, Electric

field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric

medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s

law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and

Mutual inductance of simple configurations.

 

Section 4: Signals and Systems

Representation of continuous and discrete time signals, shifting and scaling properties, linear time

invariant and causal systems, Fourier series representation of continuous and discrete time periodic

signals, sampling theorem, Applications of Fourier Transform for continuous and discrete time

signals, Laplace Transform and Z transform. R.M.S. value, average value calculation for any

general periodic waveform.

 

Section 5: Electrical Machines

Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests,

regulation and efficiency; Three-phase transformers: connections, vector groups, parallel

operation; Auto-transformer, Electromechanical energy conversion principles; DC machines:

separately excited, series and shunt, motoring and generating mode of operation and their

characteristics, speed control of dc motors; Three-phase induction machines: principle of

operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests,

equivalent circuit, starting and speed control; Operating principle of single-phase induction

motors; Synchronous machines: cylindrical and salient pole machines, performance and

characteristics, regulation and parallel operation of generators, starting of synchronous motors;

Types of losses and efficiency calculations of electric machines.

 

Section 6: Power Systems

Basic concepts of electrical power generation, AC and DC transmission concepts, Models and

performance of transmission lines and cables, Economic Load Dispatch (with and without

considering transmission losses), Series and shunt compensation, Electric field distribution and

insulators, Distribution systems, Per‐unit quantities, Bus admittance matrix, Gauss- Seidel and

Newton-Raphson load flow methods, Voltage and Frequency control, Power factor correction,

Symmetrical components, Symmetrical and unsymmetrical fault analysis, Principles of over‐

current, differential, directional and distance protection; Circuit breakers, System stability

concepts, Equal area criterion.

 

Section 7: Control Systems

Mathematical modelling and representation of systems, Feedback principle, transfer function,

Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of linear time

invariant systems, Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root

loci, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State space model, Solution

of state equations of LTI systems.

 

 

Section 8: Electrical and Electronic Measurements

Bridges and Potentiometers, Measurement of voltage, current, power, energy and power factor;

Instrument transformers, Digital voltmeters and multi-meters, Phase, Time and Frequency

measurement; Oscilloscopes, Error analysis.

 

Section 9: Analog and Digital Electronics

Simple diode circuits: clipping, clamping, rectifiers; Amplifiers: biasing, equivalent circuit and

frequency response; oscillators and feedback amplifiers; operational amplifiers: characteristics and

applications; single stage active filters, Active Filters: Sallen Key, Butterwoth, VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers, Schmitt triggers, sample

and hold circuits, A/D and D/A converters.

 

Section 10: Power Electronics

Static V-I characteristics and firing/gating circuits for Thyristor, MOSFET, IGBT; DC to DC

conversion: Buck, Boost and Buck-Boost Converters; Single and three-phase configuration of

uncontrolled rectifiers; Voltage and Current commutated Thyristor based converters; Bidirectional

ac to dc voltage source converters; Magnitude and Phase of line current harmonics for uncontrolled

and thyristor based converters; Power factor and Distortion Factor of AC to DC converters; Single phase and three-
phase voltage and current source inverters, sinusoidal pulse width modulation.

 

2. Electronics engineering

 

Section 1: Engineering Mathematics

 

Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigen

values and eigen vectors, rank, solution of linear equations - existence and uniqueness.

 

Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper

integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume

integrals, Taylor series.

 

Differential Equations: First order equations (linear and nonlinear), higher order linear differential

equations, Cauchy's and Euler's equations, methods of solution using variation of parameters,

complementary function and particular integral, partial differential equations, variable separable

method, initial and boundary value problems.

 

Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl,

Gauss's, Green's and Stokes’ theorems.

Complex Analysis: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula,

sequences, series, convergence tests, Taylor and Laurent series, residue theorem.

 

Probability and Statistics: Mean, median, mode, standard deviation, combinatorial probability,

probability distributions, binomial distribution, Poisson distribution, exponential distribution,

normal distribution, joint and conditional probability.

 

 

Section 2: Networks, Signals and Systems

 

Circuit Analysis: Node and mesh analysis, superposition, Thevenin's theorem, Norton’s theorem,

reciprocity. Sinusoidal steady state analysis: phasors, complex power, maximum power transfer.

Time and frequency domain analysis of linear circuits: RL, RC and RLC circuits, solution of

network equations using Laplace transform.

 

Linear 2-port network parameters, wye-delta transformation.

 

Continuous-time Signals: Fourier series and Fourier transform, sampling theorem and

•  

 

Discrete-time Signals: DTFT, DFT, z-transform, discrete-time processing of continuous-time

signals. LTI systems: definition and properties, causality, stability, impulse response, convolution,

poles and zeroes, frequency response, group delay, phase delay.

 

Section 3: Electronic Devices

 

Energy bands in intrinsic and extrinsic semiconductors, equilibrium carrier concentration, direct

and indirect band-gap semiconductors.

 

Carrier Transport: Diffusion current, drift current, mobility and resistivity, generation and

recombination of carriers, Poisson and continuity equations.

P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photo diode and solar cell.

 

Section 4: Analog Circuits

 

Diode Circuits: Clipping, clamping and rectifiers.

 

BJT and MOSFET Amplifiers: Biasing, AC coupling, small signal analysis, frequency response.

Current mirrors and differential amplifiers.

 

Op-amp Circuits: Amplifiers, summers, differentiators, integrators, active filters, Schmitt triggers

and oscillators.

 

Section 5: Digital Circuits

Number Representations: Binary, integer and floating-point- numbers. Combinatorial circuits:

Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic

gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers,

•  

 

Sequential Circuits: Latches and flip-flops, counters, shift-registers, finite state machines,

propagation delay, setup and hold time, critical path delay.

 

Data Converters: Sample and hold circuits, ADCs and DACs.

 

Semiconductor Memories: ROM, SRAM, DRAM.

 

Computer Organization: Machine instructions and addressing modes, ALU, data-path and control

unit, instruction pipelining.

 

Section 6: Control Systems

 

Basic control system components; Feedback principle; Transfer function; Block diagram

representation; Signal flow graph; Transient and steady-state analysis of LTI systems; Frequency

response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; Lag, lead and

lag-lead compensation; State variable model and solution of state equation of LTI systems.

 

Section 7: Communications

 

Random Processes: Auto correlation and power spectral density, properties of white noise, filtering

of random signals through LTI systems.

Analog Communications: Amplitude modulation and demodulation, angle modulation and

demodulation, spectra of AM and FM, super heterodyne receivers.

Information Theory: Entropy, mutual information and channel capacity theorem.

Digital Communications: PCM, DPCM, digital modulation schemes (ASK, PSK, FSK, QAM),

bandwidth, inter-symbol interference, MAP, ML detection, matched filter receiver, SNR and BER.

Fundamentals of error correction, Hamming codes, CRC.

 

Section 8: Electromagnetics

 

Maxwell's Equations: Differential and integral forms and their interpretation, boundary conditions,

wave equation, Poynting vector.

Plane Waves and Properties: Reflection and refraction, polarization, phase and group velocity,

propagation through various media, skin depth.

Transmission Lines: Equations, characteristic impedance, impedance matching, impedance

transformation, S-parameters, Smith chart. Rectangular and circular waveguides, light propagation

in optical fibers, dipole and monopole antennas, linear antenna arrays.

 

3. Mechanical Engineering

 

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,

indeterminate forms; evaluation of definite and improper integrals; double and triple integrals;

partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima,

Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface

and volume integrals, applications of Gauss, Stokes and Green’s theorems.

 

Differential Equations: First order equations (linear and nonlinear); higher order linear differential

equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems;

Laplace transforms; solutions of heat, wave and Laplace's equations.

 

Complex Variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem

and integral formula; Taylor and Laurent series.

 

Probability and Statistics: Definitions of probability, sampling theorems, conditional probability;

mean, median, mode and standard deviation; random variables, binomial, Poisson and normal

•  

 

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration

by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.

 

 

Section 2: Applied Mechanics and Design

 

Engineering Mechanics: Free-body diagrams and equilibrium; friction and its applications

including rolling friction, belt-pulley, brakes, clutches, screw jack, wedge, vehicles, etc.; trusses

and frames; virtual work; kinematics and dynamics of rigid bodies in plane motion; impulse and

momentum (linear and angular) and energy formulations; Lagrange’s equation.

 

Mechanics of Materials: Stress and strain, elastic constants, Poisson's ratio; Mohr’s circle for plane

stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and

shear stresses; concept of shear centre; deflection of beams; torsion of circular shafts; Euler’s

theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of

materials with universal testing machine; testing of hardness and impact strength.

 

Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms;

dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of

reciprocating and rotating masses; gyroscope.

Vibrations: Free and forced vibration of single degree of freedom systems, effect of damping;

vibration isolation; resonance; critical speeds of shafts.

 

Machine Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs.

 

 

 

Section 3: Fluid Mechanics and Thermal Sciences

 

Fluid Mechanics: Fluid properties; fluid statics, forces on submerged bodies, stability of floating

bodies; control-volume analysis of mass, momentum and energy; fluid acceleration; differential

equations of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous flow

of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head

losses in pipes, bends and fittings; basics of compressible fluid flow.

 

Heat Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept and

electrical analogy, heat transfer through fins; unsteady heat conduction, lumped parameter system, Heisler's charts; thermal boundary layer, dimensionless parameters in free and forced convective heat transfer, heat transfer correlations for flow over flat plates and through pipes, effect of turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, StefanBoltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis

 

Thermodynamics: Thermodynamic systems and processes; properties of pure substances, behavior

of ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat in

various processes; second law of thermodynamics; thermodynamic property charts and tables,

availability and irreversibility; thermodynamic relations.

 

Applications: Power Engineering: Air and gas compressors; vapour and gas power cycles,

concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel and dual cycles.

Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; properties

of moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse and

reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines; steam and gas

•  

 

Section 4: Materials, Manufacturing and Industrial Engineering

 

Engineering Materials: Structure and properties of engineering materials, phase diagrams, heat

treatment, stress-strain diagrams for engineering materials.

 

Casting, Forming and Joining Processes: Different types of castings, design of patterns, moulds

and cores; solidification and cooling; riser and gating design. Plastic deformation and yield criteria;

fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling,

extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes;

principles of powder metallurgy. Principles of welding, brazing, soldering and adhesive bonding.

 

Machining and Machine Tool Operations: Mechanics of machining; basic machine tools; single

and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of

machining; principles of non-traditional machining processes; principles of work holding, jigs and

fixtures; abrasive machining processes; NC/CNC machines and CNC programming.

 

 

Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements;

comparators; interferometry; form and finish measurement; alignment and testing methods;

tolerance analysis in manufacturing and assembly; concepts of coordinate-measuring machine

1.  

 

Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools;

additive manufacturing.

 

Production Planning and Control: Forecasting models, aggregate production planning, scheduling,

materials requirement planning; lean manufacturing.

 

Inventory Control: Deterministic models; safety stock inventory control systems.

 

Operations Research: Linear programming, simplex method, transportation, assignment, network

flow models, simple queuing models, PERT and CPM.

 

4. Instrumentation Engineering

 

Section 1: Engineering Mathematics

Linear Algebra: Matrix algebra, systems of linear equations, consistency and rank, Eigenvalue and

•  

 

Calculus: Mean value theorems, theorems of integral calculus, partial derivatives, maxima and

minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals,

Stokes, Gauss and Green’s theorems.

 

Differential Equations: First order equation (linear and nonlinear), second order linear differential

equations with constant coefficients, method of variation of parameters, Cauchy’s and Euler’s

equations, initial and boundary value problems, solution of partial differential equations: variable

separable method.

 

Analysis of Complex Variables: Analytic functions, Cauchy’s integral theorem and integral

formula, Taylor’s and Laurent’s series, residue theorem, solution of integrals.

Probability and Statistics: Sampling theorems, conditional probability, mean, median, mode,

standard deviation and variance; random variables: discrete and continuous distributions: normal,

Poisson and binomial distributions.

 

Numerical Methods: Matrix inversion, solutions of non-linear algebraic equations, iterative

methods for solving differential equations, numerical integration, regression and correlation

•  

 

 

Section 2: Electricity and Magnetism

 

Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence,

Electric field and potential due to point, line, plane and spherical charge distributions,

Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law,

Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force,

Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.

 

Section 3: Electrical Circuits and Machines

 

Voltage and Current Sources: Independent, dependent, ideal and practical; v-i relationships of

resistor, inductor, mutual inductance and capacitor; transient analysis of RLC circuits with dc

•  

Kirchoff’s laws, mesh and nodal analysis, superposition, Thevenin, Norton, maximum power

transfer and reciprocity theorems.

Peak-, average- and rms values of AC quantities; apparent-, active- and reactive powers; phasor

analysis, impedance and admittance; series and parallel resonance, locus diagrams, realization of

basic filters with R, L and C elements. transient analysis of RLC circuits with ac excitation.

One-port and two-port networks, driving point impedance and admittance, open-, and short circuit

81579240699157.  

Single Phase Transformer: Equivalent circuit, phasor diagram, open circuit and short circuit tests,

regulation and efficiency; Three phase induction motors: principle of operation, types,

performance, torque-speed characteristics, no-load and blocked rotor tests, equivalent circuit,

starting and speed control; Types of losses and efficiency calculations of electric machines.

 

Section 4: Signals and Systems

 

Periodic, aperiodic and impulse signals; Laplace, Fourier and z-transforms; transfer function,

frequency response of first and second order linear time invariant systems, impulse response of

systems; convolution, correlation. Discrete time system: impulse response, frequency response,

pulse transfer function; DFT and FFT; basics of IIR and FIR filters.

 

Section 5: Control Systems

 

Feedback principles, signal flow graphs, transient response, steady-state-errors, Bode plot, phase

and gain margins, Routh and Nyquist criteria, root loci, design of lead, lag and lead-lag

compensators, state-space representation of systems; time-delay systems; mechanical, hydraulic

and pneumatic system components, synchro pair, servo and stepper motors, servo valves; on-off,

P, PI, PID, cascade, feed forward, and ratio controllers, tuning of PID controllers and sizing of

control valves.

 

Section 6: Analog Electronics

 

Characteristics and applications of diode, Zener diode, BJT and MOSFET; small signal analysis

of transistor circuits, feedback amplifiers. Characteristics of ideal and practical operational

amplifiers; applications of opamps: adder, subtractor, integrator, differentiator, difference

amplifier, instrumentation amplifier, precision rectifier, active filters, oscillators, signal

generators, voltage controlled oscillators and phase locked loop, sources and effects of noise and

interference in electronic circuits.

 

Section 7: Digital Electronics

 

Combinational logic circuits, minimization of Boolean functions. IC families: TTL and CMOS.

Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flip-flops,

shift registers, timers and counters; sample-and-hold circuit, multiplexer, analog-to-digital

(successive approximation, integrating, flash and sigma-delta) and digital-to-analog converters

(weighted R, R-2R ladder and current steering logic). Characteristics of ADC and DAC

(resolution, quantization, significant bits, conversion/settling time); basics of number systems,

Embedded Systems: Microprocessor and microcontroller applications, memory and input-output

interfacing; basics of data acquisition systems, basics of distributed control systems (DCS) and

programmable logic controllers (PLC).

 

Section 8: Measurements

 

SI units, standards (R, L, C, voltage, current and frequency), systematic and random errors in

measurement, expression of uncertainty - accuracy and precision, propagation of errors, linear and

weighted regression. Bridges: Wheatstone, Kelvin, Megohm, Maxwell, Anderson, Schering and

Wien for measurement of R, L, C and frequency, Q-meter. Measurement of voltage, current and

power in single and three phase circuits; ac and dc current probes; true rms meters, voltage and

current scaling, instrument transformers, timer/counter, time, phase and frequency measurements,

digital voltmeter, digital multimeter; oscilloscope, shielding and grounding.

 

Section 9: Sensors and Industrial Instrumentation

 

Resistive-, capacitive-, inductive-, piezoelectric-, Hall effect sensors and associated signal

conditioning circuits; transducers for industrial instrumentation: displacement (linear and angular),

velocity, acceleration, force, torque, vibration, shock, pressure (including low pressure), flow

(Variable head, variable area, electromagnetic, ultrasonic, turbine and open channel flow meters)

temperature (thermocouple, bolometer, RTD (3/4 wire), thermistor, pyrometer and

semiconductor); liquid level, pH, conductivity and viscosity measurement. 4-20 mA two-wire

•  

 

Section 10: Communication and Optical Instrumentation

 

Amplitude- and frequency modulation and demodulation; Shannon's sampling theorem, pulse code

modulation; frequency and time division multiplexing, amplitude-, phase-, frequency-, quadrature

amplitude, pulse shift keying for digital modulation; optical sources and detectors: LED, laser,

photo-diode, light dependent resistor, square law detectors and their characteristics;

interferometer: applications in metrology; basics of fiber optic sensing. UV-VIS Spectrophotometers, Mass spectrometer.