### Education

# GATE Exam Syllabus | Branch Wise Syllabus for GATE Exam

GATE Exam Syllabus is entirely based on your** disciplines studied** in the qualifying examination. The **Indian Institute of Technology Guwahati** has specified all the syllabus according to the **23 papers**, with that this examination is conducted for M.Tech programmes. Now, this year syllabus is similar to the previous year. Mostly, the national level **PG engineering** entrance exam will be conducted in February. Once before they start studying for the exam, the candidates have to go through the syllabus of the paper that they appear for. The syllabus that is given for this year has coved all the topics that used to qualify for the entrance exam. Moreover, all the candidates have to appear in the **GATE Exam** appropriate to the discipline of their qualifying degree. There is no common syllabus for all disciplines each, and every discipline has separate Syllabus which are given below.

## GATE Exam Syllabus

- GATE CSE Syllabus
- GATE EEE Syllabus
- GATE ECE Syllabus
- GATE Civil Syllabus
- GATE Mechanical Syllabus
- GATE IE Syllabus

## GATE CSE Syllabus

The GATE Syllabus for CSE disciplines is given below, where it is used here for covering all the topics that require for qualifying the GATE Exam are given here. Once before preparing for your GATE Exam go through the Syllabus of your department.

### Engineering Mathematics

**Discrete Mathematics**

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

**Linear Algebra**

Matrices, determinants, the system of linear equations, eigenvalues and eigenvectors, LU decomposition.

**Calculus**

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

**Probability**

Random variables. Uniform, normal, exponential, Poisson and binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem.

### Computer Science and Information Technology

**Digital Logic**

Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point).

**Computer Organization and Architecture**

Machine instructions and addressing modes. ALU, data?path and control unit. Instruction pipelining. Memory hierarchy: main memory, cache, and secondary storage; I/O interface (Interrupt and DMA mode).

**Programming and Data Structures**

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

**Algorithms**

Searching, sorting, hashing. Asymptotic worst-case time and space complexity. Algorithm design techniques: greedy, dynamic programming and divide?and?conquer. Graph search, minimum spanning trees, shortest paths.

**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.

**Compiler Design**

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

**Operating System**

Processes, threads, inter? Process communication, concurrency and synchronization. Deadlock. CPU scheduling. Memory management and virtual memory. File systems.

**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.

**Computer Networks**

The concept of layering. LAN technologies (Ethernet). Flow and error control techniques,

switching. IPv4/IPv6, routers and routing algorithms (distance vector, link state). TCP/UDP and sockets, congestion control. Application layer protocols (DNS, SMTP, POP, FTP, HTTP). Basics of Wi-Fi. Network security: authentication, basics of a public key and private key cryptography, digital signatures and certificates, firewalls.

## GATE EEE Syllabus

The GATE Syllabus for EEE disciplines is given below, where it is used here for covering all the topics that require for qualifying the GATE Exam are given here. Once before preparing for your GATE Exam go through the Syllabus of your department.

### Engineering Mathematics

**Linear Algebra**

Matrix Algebra, Systems of linear equations, Eigen values and eigenvectors.

**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, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

**Differential equations**

First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables

**Complex variables**

Analytic functions, Taylor’s and Laurent’ series, Cauchy’s integral theorem and integral formula, Residue theorem, solution integrals.

**Probability and Statistics**

Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

**Numerical Methods**

Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

**Transform Theory**

Fourier transform, Laplace transform, Z-transform

### Electrical Engineering

**Electric Circuits**

Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac networks, Sinusoidal steady? State analysis, Resonance, Passive filters, Ideal current and voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem, Two?port networks, Three phase circuits, Power and power factor in ac circuits.

**Electromagnetic Fields**

Coulomb’s Law, Electric Field Intensity, Electric Flux Density, Gauss’s Law, Divergence, Electric field and potential due to the point, line, plane and spherical charge distributions, Effect of the 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.

**Signals and Systems**

Representation of continuous and discrete-time signals; Scaling and shifting operations; Fourier series representation of continuous periodic signals; linear, time-invariant and causal systems; sampling theorem; Fourier, Laplace and Z transforms.

**Electrical Machines**

Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit Tests, regulation and efficiency; Three phase transformers: connections, parallel operation; Auto? Transformer, Electromechanical energy conversion principles, DC machines: separately excited, series and shunt, motoring and generating mode of operation and starting and speed control of dc motors, and their characteristics; Three phase induction motors: principle of operation, types, performance, torque-speed characteristics, no-load and blocked rotor tests, starting, equivalent circuit and speed control; Operating principle of single phase induction motors; Synchronous machines: cylindrical and salient pole machines, regulation, performance and parallel operation of generators, starting of synchronous motor, characteristics; Types of efficiency and Losses calculations of electric machines.

**Power Systems**

Power generation concepts, ac and dc transmission concepts, Models and performance of transmission lines and cables, Series and shunt compensation, Electric field distribution and insulators, Distribution systems, Per?unit quantities, Bus admittance matrix, GaussSeidel 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 and distance protection; Circuit breakers, System stability concepts, Equal area criterion.

**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, Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci, Stability analysis, Lag, Lead and Lead?Lag compensators; P, PI and PID controllers; State space model, State transition matrix.

**Electrical and Electronic Measurements**

Bridges and Potentiometers, Measurement of voltage, current, power, energy and power factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and Frequency measurement; Oscilloscopes, Error analysis.

**Analog and Digital Electronics**

Characteristics of diodes, BJT, MOSFET; Simple diode circuits: clamping, clipping, rectifiers; Amplifiers: Biasing, Equivalent circuit and Frequency response; Oscillators and Feedback, amplifiers; Operational amplifiers: Characteristics and applications; Simple active filters, VCOs and Combinational, Timers, and Sequential logic circuits, Multiplexer, Demultiplexer, Sample, Schmitt trigger and hold circuits, A/D and D/A converters, 8085Microprocessor: Architecture, Interfacing and Programming

**Power Electronics**

Characteristics of semiconductor power devices: Diode, Thyristor, Triac, GTO, MOSFET, IGBT; DC to DC conversion: Buck, Boost and Buck-Boost converters; Single and three phase configuration of uncontrolled rectifiers, Line commutated thyristor-based converters, Bidirectional ac to dc voltage source converters, Issues of line current harmonics, Power factor, Distortion factor of ac to dc converters, Single phase and three phase inverters, Sinusoidal pulse width modulation.

## GATE ECE Syllabus

The GATE Syllabus for ECE disciplines is given below, where it is used here for covering all the topics that require for qualifying the GATE Exam are given here. Once before preparing for your GATE Exam go through the Syllabus of your department.

### Engineering Mathematics

**Linear Algebra**

Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues and eigenvectors, rank, the 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 equation**

First order equations (linear and nonlinear), higher order linear differential equations, Cauchy’s and Euler’s equations, methods of solution using the 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 Stoke’s theorems.

**Complex Analysis**

Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula; Taylor’s and Laurent’s series, residue theorem.

**Numerical Methods**

The solution of nonlinear equations, single and multi-step methods for differential equations, convergence criteria.

**Probability and Statistics**

Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions – binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis.

### Electronics and Communication Engineering

**Networks, Signals and Systems**

Network solution methods: nodal and mesh analysis; Network theorems: superposition, Thevenin and Norton’s, maximum power transfer; Wye?Delta transformation; Steady state sinusoidal analysis using phasors; Time domain analysis of simple linear circuits; Solution of network equations using Laplace transform; Frequency domain analysis of RLC circuits; Linear 2?port network parameters: transfer function and driving point; State equations for the network.

Continuous-time signal: Fourier transform and Fourier series representations, sampling theorem and applications; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform, LTI systems: definition and properties, interpolation of discrete-time signals causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, group delay, phase delay, frequency response, digital filter design technique.

**Electronic Device**

Energy band in intrinsic and extrinsic silicon; Carrier transport: drift, the diffusion current, resistivity and current mobility; Generation and recombination of carriers; Poisson and continuity equations; P-N junction,BJT, MOS capacitor, Zener diode, MOSFET, LED, a photodiode and solar cell; Integrated circuit fabrication process: oxidation, diffusion, ion implantation, photolithography and twin-tub CMOS process.

**Analog Circuits**

Small signal equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits: clipping, clamping and rectifiers; Single-stage BJT and MOSFET amplifiers: biasing, bias stability, mid-frequency small signal analysis and frequency response; BJT and MOSFET amplifiers: multi-stage, differential, feedback, power and operational; Simple op-amp circuits; Active filters; Sinusoidal oscillators: criterion for oscillation, single-transistor and op-amp configurations; Function generators, wave-shaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation.

**Digital circuits**

Number systems; 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, decoders and PLAs; Sequential circuits: latches and flip?flops, counters, shift?registers and finite state machines; Data converters: sample and hold circuits, ADCs and DACs; Semiconductor memories: ROM, SRAM, DRAM; 8-bit microprocessor (8085): architecture, programming, memory and I/O interfacing.

**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.

**Communications**

Random processes: autocorrelation and power spectral density, filtering of random signals through LTI systems, properties of white noise; Analog communications: amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers, circuits for analog communications; Information theory: entropy, mutual information and channel capacity theorem; Digital communications: PCM, DPCM, digital modulation schemes, amplitude, phase and frequency shift keying

(ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; Timing and frequency synchronization, inter-symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA.

**Electromagnetics**

Electrostatics; 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;

Waveguides: modes, boundary conditions, cut-off frequencies, dispersion relations; Antennas: antenna types, radiation pattern, gain and directivity, return loss, antenna arrays; Basics of radar; Light propagation in optical fibres.

## GATE Civil Syllabus

The GATE Syllabus for Civil disciplines is given below, where it is used here for covering all the topics that require for qualifying the GATE Exam are given here. Once before preparing for your GATE Exam go through the Syllabus of your department.

### Engineering Mathematics

**Linear Algebra**

Systems of linear equations, Matrix algebra, Eigenvalues and Eigen Vectors.

**Calculus**

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

**Ordinary Differential Equation **

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 Ordinary Differential Equations; initial and boundary value problems.

**Partial Differential Equation**

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

**Complex variables**

Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series. Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.

**Probability and Statistics**

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

**Numerical Method**

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

### Structural Engineering

**Engineering Mechanics**

The system of forces, free-body diagrams, equilibrium equations; Internal forces in structures; Friction and its applications; Kinematics of a point mass and rigid body; Centre of mass; Euler’s equations of motion; Impulse-momentum; The energy methods; Principle of virtual work.

**Solid Mechanic**

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

**Structural Analysis**

Statically determinate and indeterminate structures by the force or 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 Material and Management**

Construction Materials: Structural steel – composition, properties, material and behaviour; Concrete – Bricks and mortar; Timber; Bitumen and constituents, mix design, short-term and long-term properties. Construction Management: Types of construction projects; Tendering and construction contracts; Cost estimation; Rate analysis and standard specifications; Project planning and network analysis – PERT and CPM.

**Concrete Structures**

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

**Steel Structures**

Working stress and Limit state design concept; 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.

### 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.

### 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 the 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 – Energy-depth 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 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, head works, gravity dams and spillways; Design of weirs on the permeable foundation; Types of irrigation systems, irrigation methods; Water logging and drainage; Canal regulatory works, cross-drainage structures, outlets and escapes.

### Environmental Engineering

**Water and Waste Water**

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

**Air Pollution**

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

**Municipal Solid Waste**

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

**Noise Pollution**

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

### Transportation Engineering

**Transportation Infrastructure**

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

**Highway Pavements**

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

**Traffic Engineering**

Microscopic and macroscopic parameters of traffic flow, fundamental relationships; Control devices, signal design by Webster’s method; Types of intersections and channelization; 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; Highway level and capacity of service of rural highway and urban road.

**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).

## GATE Mechanical Syllabus

The GATE Syllabus for Mechanical disciplines is given below, where it is used here for covering all the topics that require for qualifying the GATE Exam are given here. Once before preparing for your GATE Exam go through the Syllabus of your department.

### Engineering Mathematics

**Linear Algebra**

Matrix Algebra, Eigenvalues, Systems of linear equations and Eigenvectors.

**Calculus**

Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; double and triple integrals; evaluation of definite and improper integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; vector identities, directional derivatives, line, gradient, divergence and curl, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.

**Differential equations**

First order equations linear and nonlinear; Euler-Cauchy equation; initial and boundary value problems; linear differential equations with constant coefficients; higher order linear differential equations with constant coefficients; The Laplace transform; 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 distributions.

**Numerical Method**

Numerical solution of the linear and non-linear algebraic equation; single and multi-step methods for differential equations; integration by trapezoidal and Simpson’s rules.

## GATE IE Syllabus

The GATE Syllabus for IE disciplines is given below, where it is used here for covering all the topics that require for qualifying the GATE Exam are given here. Once before preparing for your GATE Exam go through the Syllabus of your department.

### Engineering Mathematics

**Linear Algebra**

Matrix Algebra, Systems of linear equations, Eigenvalues and Eigenvectors.

**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, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

**Differential equations**

First order equation (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchy’s and Euler’s equations, initial and boundary value problems, a solution of partial differential equations: variable separable method.

**Analysis of complex variables**

Analytic functions, Cauchy’s integral formula and integral theorem, Taylor’s and Laurent’ series, Residue theorem, a solution of integrals.

**Probability and Statistics**

Sampling theorems, random variables, conditional probability, mean, median, mode and standard deviation, discrete and continuous distributions: normal, Poisson and binomial distributions.

**Numerical Methods**

Matrix inversion, iterative methods for solving differential equations, numerical integration, solutions of non-linear algebraic equations, regression and correlation analysis.

### Instrumentation Engineering

**Electrical Circuits**

Voltage and current sources: independent, dependent, ideal and practical; v-i relationships of resistor, inductor, mutual inductor and capacitor; transient analysis of RLC circuits with dc excitation. 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, a realization of basic filters with R, L and C elements. One-port and two-port networks, driving point impedance and admittance, open-, and short circuit parameters.

**Signals and Systems**

Periodic, aperiodic and impulse signals; Laplace, Fourier and z-transforms; transfer function, the frequency response of first and second order linear time-invariant systems, the 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.

**Control Systems**

Feedback principles, signal flow graphs, transient response, steady-state-errors, Routh and Nyquist criteria, Bode plot, phase and gain margins, root loci, design of lead, lag and lead-lag compensators, state-space representation of systems; on-off, P, P-I, P-I-D, cascade, feedforward, and ratio controllers time-delay systems; mechanical, hydraulic and pneumatic system components, synchro pair, servo and stepper motors, servo valves.

**Analog Electronics**

Characteristic and application of the diode, Zener diode, BJT and MOSFET; small signal analysis of transistor circuits, feedback amplifiers. Characteristics of operational amplifiers; applications of opamps: difference amplifier, adder, subtractor, integrator, differentiator, instrumentation amplifier, precision rectifier, active filters and other circuits. Oscillators, signal generators, voltage controlled oscillators and phase locked loop.

**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, analogue-to-digital

(successive approximation, integrating, flash and sigma-delta) And digital-to-analogue 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, 8-bit microprocessor and microcontroller: applications, memory and input-output interfacing; basics of data acquisition systems.

**Measurements**

SI units, systematic and the random errors in measurement, propagation of errors. PMMC, expression of uncertainty – accuracy and precision index, MI and dynamometer type instruments; bridges for measurement of R, L and C, Q-meter. Measurement of voltage, current and power in single and three phase circuits; dc potentiometer; ac and DC 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.

**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 (differential pressure, 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.

**Communication and Optical Instrumentation**

Amplitude- and frequency modulation and demodulation; frequency and time division multiplexing, amplitude-, phase-, frequency-, pulse shift keying for digital modulation; Shannon’s sampling theorem, pulse code modulation; optical sources and detectors: LED, laser, photo-diode, light dependent resistor and their characteristics; interferometer: applications in metrology; basics of fiber optic sensing.

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