**GATE SYLLABUS**

**GATE 2023 Paper-wise Syllabus**

**GATE 2023 Paper-wise Syllabus**

It is highly unlikely that significant changes would be made in the GATE 2023 syllabus, however, no one can be sure regarding the changes in the GATE examination.

Since, the syllabus for GATE 2023 has not been released yet, candidates can check the previous year paper-wise syllabus.

**GATE Mechanical Engineering (ME) Syllabus **

**GATE Mechanical Engineering (ME) Syllabus 2022 **

**Section 1: Engineering Mathematics**

**Linear Algebra :**Matrix algebra, systems of linear equations, eigenvalues and eigenvectors**Calculus :****Differential 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 Methods :**

**Section 2: Applied Mechanics and Design**

Applied Mechanics and Design section from GATE ME Syllabus deals with the application of concepts of mechanics into complex situations and the response of bodies or systems of bodies under the action of external forces.

**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**

Archimedes observed deviation in the mechanics of fluid and forces acting on them long before the term ‘engineering’ was coined. Following the footsteps of Archimedes- Leonardo Da Vinci, Issac Newton, and Blaise Pascal paved the way for Fluid Mechanics with their groundbreaking inventions and indisputable theories. All the advancements in the field of Fluid Mechanics and Thermal Science is condensed in this section of GATE ME syllabus, which is as following:

**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, Stefan- Boltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis.**Thermodynamics :****Applications :**

**Section 4: Materials, Manufacturing, and Industrial Engineering**

Considered the nerve of Mechanical Engineering, Material Science deals with the discovery and design of new elements, with an emphasis over solids.

Manufacturing Engineering deals with the intricacies of manufacturing processes and other considerations involved in it.

Industrial Engineering deals with the work culture of Industries and mechanical processes involved with a clear depiction of managing roles needed.

**Engineering Materials :****Casting, Forming and Joining Processes :**Different types of castings, design of patterns, molds 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 nontraditional 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 (CMM).**Computer Integrated Manufacturing :****Production Planning and Control :**Forecasting models, aggregate production planning, scheduling, materials requirement planning; lean manufacturing**Operations Research :**Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.**Inventory Control :**

**Section 5: General Aptitude**

**Verbal Aptitude :****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 ****Civil**** Engineering (****C****E) Syllabus**

**GATE Civil Engineering Syllabus 2022**

**GATE Civil Engineering Syllabus 2022**

GATE Civil engineering has been neatly divided into 7 Sections with each section comprising of the related subjects. The details of the syllabus is given below :

**Section 1 – Engineering Mathematics**

**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 nonlinear) 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**

**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 undamped 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 centre; 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 – Geomatics Engineering**

**Section 3 – Geomatics 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**

**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 :****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, evapo-transpiration; Gravity Dams and Spillways; Lined and unlined canals, Design of weirs on permeable foundation; cross drainage structure

** Section 5 – Environmental Engineering**

**Section 5 – Environmental Engineering**

**Water and Wastewater :**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 :**

**Section 6 – Transportation Engineering**

**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.**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**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.

**Section 7 – Geotechnical Engineering**

**Section 7 – Geotechnical Engineering**

**Geotechnical Engineering :**

**GATE Computer Science & Information Technology (CS/I****T) ****Syllabus **

**GATE Computer Science & Information Technology Syllabus 2022**

**GATE Computer Science & Information Technology Syllabus 2022**

**Section 1: Engineering Mathematics**

**Section 1: Engineering Mathematics**

**Discrete Mathematics :**Propositional and first-order logic. Sets, relations, functions, partial orders and lattices. Monoids, Groups. Graphs: connectivity, matching, coloring. 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 :**Random variables. Uniform, normal, exponential, poisson and binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem.

**Section 2: Digital Logic**

**Section 2: Digital Logic**

**Section 1 :**Boolean algebra. Combinational and sequential circuits. Minimization.**Section 2 :**Number representations and computer arithmetic (fixed and floating-point).

**Section 3: Computer Organization and Architecture**

**Section 3: Computer Organization and Architecture**

**Section 1 :**Machine instructions and addressing modes. ALU, data‐path and control unit. Instruction pipelining, pipeline hazards.**Section 2 :**Memory hierarchy: cache, main memory and secondary storage; I/O interface (interrupt and DMA mode).

**Section 4: Programming and Data Structures**

**Section 4: Programming and Data Structures**

**Section 1 :**Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.

**Section 5: Algorithms**

**Section 5: Algorithms**

**Section 1 :**Searching, sorting, hashing. Asymptotic worst case time and space complexity. Algorithm design techniques: greedy, dynamic programming and divide‐and conquer.**Section 2 :**Graph traversals, minimum spanning trees, shortest paths

**Section 6: Theory of Computation**

**Section 6: Theory of Computation**

**Section 1 :**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**

**Section 7: Compiler Design**

**Section 1 :**Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code generation.**Section 2 :**Local optimization, Data flow analyses: constant propagation, liveness analysis, common subexpression elimination.

**Section 8: Operating System**

**Section 8: Operating System**

**Section 1 :**System calls, processes, threads, inter‐process communication, concurrency and synchronization.**Section 2 :**Deadlock. CPU and I/O scheduling. Memory management and virtual memory. File systems.

**Section 9: Databases**

**Section 9: Databases**

**Section 1 :**ER‐model. Relational model: relational algebra, tuple calculus, SQL.**Section 2 :**Integrity constraints, normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and concurrency control.

**Section 10: Computer Networks**

**Section 10: Computer Networks**

**Concept of layering :**OSI and TCP/IP Protocol Stacks; Basics of packet, circuit and virtual circuit-switching;**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.

**GATE CSE Syllabus 2023- General Aptitude**

**GATE CSE Syllabus 2023- General Aptitude**

**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 ****Electrical Engineering**** (****EE****) Syllabus**

**GATE Electrical Engineering Syllabus 2022**

**GATE Electrical Engineering Syllabus 2022**

GATE 2022 Syllabus for Electrical Engineering is divided into 10 sections with topics that need to be covered. Candidates can check the Syllabus for GATE Electrical Engineering below:

**Section 1: Engineering Mathematics**

**Section 1: Engineering Mathematics**

Linear Algebra

Calculus

Differential equations

Complex variables

Probability and Statistics

**Section 2: Electric Circuits**

**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**

**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**

**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.

**Section 5: Electrical Machines**

**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**

**Section 6: Power Systems**

Basic concepts of electrical power generation, 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, 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, Economic Load Dispatch (with and without considering transmission losses).

**Section 7: Control Systems**

**Section 7: Control Systems**

Mathematical modeling 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, R.M.S. value, average value calculation for any general periodic waveform.

**Section 8: Electrical and Electronic Measurements**

**Section 8: 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.

**Section 9: Analog and Digital Electronics**

**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, Sallen Key, Butterworth

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**

**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.

**GATE General Aptitude Syllabus 2022**

General Aptitude (GA) is a common section in all GATE Papers and holds 15% of the total marks. The questions in GA are based on verbal ability and numerical ability. The 2 subsections in the GA section are as follows:

Verbal Ability- The following topics are tested in this section: English Grammar, Sentence Completion, Verbal Analogies, Word Groups, Instructions, Critical Reasoning, Verbal Deduction.

Numerical Ability – This section consists of questions that test the basic mathematical skills of candidates. The following subtopics included in this section are: Numerical computation, Numerical Estimation, Numerical Reasoning, Data Interpretation.

**GATE Elect****ronics & Communication**** Engineering (ECE) Syllabus**

**GATE Syllabus for ECE 2022**

**GATE Syllabus for ECE 2022**

GATE Syllabus for ECE 2022 is consists of eight major sections including Engineering Mathematics. These include:

**Section 1: Engineering Mathematics**

**Section 1: Engineering Mathematics**

**Linear Algebra:****Calculus:****Differential Equations:****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:**

**Section 2: Networks, Signals, and Systems**

**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 applications.**Discrete-time signals:**

**Section 3: Electronic Devices**

**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**

**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**

**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, decoders.**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**

**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**

**Section 7: Communications**

**Random processes:**autocorrelation 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, superheterodyne 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**

**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.

**Section 9 - General Aptitude **

**Section 9 - General Aptitude**

**Verbal Ability:**English grammar; Sentence completion, Instructions; Verbal analogies, Word groups; Critical reasoning, Verbal deduction.**Numerical Ability:**Numerical computation; Numerical reasoning; Numerical estimation; Data interpretation.

**GATE ****Instrumentation**** Engineering (****IN****) Syllabus**

**GATE Syllabus for Instrumentation Engineering (IN) 2022**

**GATE Syllabus for Instrumentation Engineering (IN) 2022**

GATE syllabus for Instrumentation Engineering divided into 10 important topics including engineering mathematics. Candidate can check the detailed GATE Syllabus for Instrumentation Engineering (IN) with all the important topics and sub-topics:

**Section 1: Engineering Mathematics**

**Linear Algebra:**Matrix algebra, systems of linear equations, consistency and rank, Eigen values and Eigen vectors.**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 analysis.

**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 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, 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 parameters.

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, P-I, P-I-D, cascade, feedforward, and ratio controllers.

**Section 6: Analog Electronics**

Characteristics and applications of diode, Zener diode, BJT and MOSFET; small signal analysis of transistor circuits, feedback amplifiers. Characteristics of operational amplifiers; applications of op amps: 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.

**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

**Section 8: Measurements**

SI units, systematic and random errors in measurement, expression of uncertainty - accuracy and precision index, propagation of errors. PMMC, MI and dynamometer type instruments; dc potentiometer; bridges for measurement of R, L and C, 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 (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.

**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-, pulse shift keying for digital modulation; optical sources and detectors: LED, laser, photo-diode, light dependent resistor and their characteristics; interferometer: applications in metrology; basics of fiber optic sensing.

**General Aptitude Syllabus for GATE 2022 Instrumentation Engineering**

**Verbal Ability:**English grammar; Sentence completion, Instructions; Verbal analogies, Word groups; Critical reasoning, Verbal deduction.**Numerical Ability:**Numerical computation; Numerical reasoning; Numerical estimation; Data interpretation.

**GATE ****Production & Industrial**** Engineering (PI) Syllabus**

**GATE Syllabus for Production & Industrial Engineering (PI) 2022**

**GATE Syllabus for Production & Industrial Engineering (PI) 2022**

**Section 1 – Engineering Mathematics**

**Section 1 – Engineering Mathematics**

**Linear Algebra:**Matrix algebra, systems of linear equations, consistency and rank, Eigen values and Eigen vectors.**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:****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 nonlinear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis.

**Section 2: General Engineering**

**Section 2: General Engineering**

**Engineering Materials**: Structure, physical and mechanical properties, and applications of common engineering materials (metals and alloys, semiconductors, ceramics, polymers, and composites – metal, polymer and ceramic based); Iron-carbon equilibrium phase diagram; Heat treatment of metals and alloys and its influence on mechanical properties; Stress-strain behavior of metals and alloys.**Applied Mechanics**: Engineering mechanics – equivalent force systems, free body concepts, equations of equilibrium; Trusses; Strength of materials – stress, strain and their relationship; Failure theories; Mohr’s circle (stress); Deflection of beams, bending and shear stresses; Euler’s theory of columns; Thick and thin cylinders; Torsion.**Theory of Machines and Design**: Analysis of planar mechanisms, cams and followers; Governors and flywheels; Design of bolted, riveted and welded joints; Interference/shrink fit joints; Friction and lubrication; Design of shafts, keys, couplings, spur gears, belt drives, brakes and clutches; Pressure vessels.**Thermal and Fluids Engineering**: Fluid mechanics – fluid statics, Bernoulli’s equation, flow through pipes, laminar and turbulent flows, equations of continuity and momentum, capillary action; Dimensional analysis Thermodynamics – zeroth, first and second laws of thermodynamics, thermodynamic systems and processes, calculation of work and heat for systems and control volumes; Air standard cycles; Heat transfer – basic applications of conduction, convection and radiation.

**Section 3: Manufacturing Processes I**

**Section 3: Manufacturing Processes I**

**Casting**: Types of casting processes and applications; Sand casting: patterns – types, materials and allowances; molds and cores–materials, making, and testing; design of gating system and riser; casting techniques of cast iron, steels, and nonferrous metals and alloys; analysis of solidification and microstructure development; Other casting techniques: Pressure die casting, Centrifugal casting, Investment casting, Shell mold casting; Casting defects and their inspection by non-destructive testing.**Metal Forming**: Stress-strain relations in elastic and plastic deformation; von Mises and Tresca yield criteria, Concept of flow stress; Hot, warm and cold working; Bulk forming processes - forging, rolling, extrusion and wire drawing; Sheet metal working processes – blanking, punching, bending, stretch forming, spinning and deep drawing; Ideal work and slab analysis; Defects in metal working and their causes.**Joining of Materials**: Classification of joining processes; Principles of fusion welding processes using different heat sources (flame, arc, resistance, laser, electron beam), Heat transfer and associated losses; Arc welding processes - SMAW, GMAW, GTAW, plasma arc, submerged arc welding processes; Principles of solid state welding processes - friction welding, friction stir welding, ultrasonic welding; Welding defects - causes and inspection; Principles of adhesive joining, brazing and soldering processes.**Powder Processing**: Production of metal/ceramic powders, compaction and sintering of metals and ceramic powders, Cold and hot isostatic pressing.**Polymers and Composites**: Polymer processing – injection, compression and blow molding, extrusion, calendaring and thermoforming; Molding of composites.

**Section 4: Manufacturing Processes II**

**Section 4: Manufacturing Processes II**

**Machining**: Orthogonal and oblique machining, Single point cutting tool and tool signature, Chip formation, cutting forces, Merchant’s analysis, Specific cutting energy and power; Machining parameters and material removal rate; tool materials, Tool wear and tool life; Thermal aspects of machining, cutting fluids, machinability; Economics of machining; Machining processes - turning, taper turning, thread cutting, drilling, boring, milling, gear cutting, thread production; Finishing processes – grinding, honing, lapping and superfinishing.**Machine Tools**: Lathe, milling, drilling and shaping machines – construction and kinematics; Jigs and fixtures – principles, applications, and design.**Advanced Manufacturing**: Principles and applications of USM, AJM, WJM, AWJM, EDM and Wire EDM, LBM, EBM, PAM, CHM, ECM; Effect of process parameters on material removal rate, surface roughness and power consumption; Additive manufacturing techniques.**Computer Integrated Manufacturing**: Basic concepts of CAD and CAM, Geometric modeling, CNC; Automation in Manufacturing; Industrial Robots – configurations, drives and controls; Cellular manufacturing and FMS – Group Technology, CAPP.

**Section 5: Quality and Reliability**

**Section 5: Quality and Reliability**

**Metrology and Inspection**: Accuracy and precision; Types of errors; Limits, fits and tolerances; Gauge design, Interchangeability, Selective assembly; Linear, angular, and form measurements (straightness, flatness, roundness, runout and cylindricity) by mechanical and optical methods; Inspection of screw threads and gears; Surface roughness measurement by contact and non-contact methods.**Quality Management**: Quality – concept and costs; Statistical quality control – process capability analysis, control charts for variables and attributes and acceptance sampling; Six sigma; Total quality management; Quality assurance and certification - ISO 9000, ISO14000.**Reliability and Maintenance**: Reliability, availability and maintainability; Distribution of failure and repair times; Determination of MTBF and MTTR, Reliability models; Determination of system reliability; Preventive and predictive maintenance and replacement, Total productive maintenance.

**Section 6: Industrial Engineering**

**Section 6: Industrial Engineering**

**Product Design and Development**: Principles of product design, tolerance design; Quality and cost considerations; Product life cycle; Standardization, simplification, diversification; Value engineering and analysis; Concurrent engineering; Design for “X”.**Work System Design**: Taylor’s scientific management, Gilbreths’s contributions; Productivity – concepts and measurements; Method study, Micro-motion study, Principles of motion economy; Work measurement – time study, Work sampling, Standard data, PMTS; Ergonomics; Job evaluation and merit rating.**Facility Design**: Facility location factors and evaluation of alternate locations; Types of plant layout and their evaluation; Computer aided layout design techniques; Assembly line balancing; Materials handling systems.

**Section 7: Operations research and Operations management**

**Section 7: Operations research and Operations management**

**Operation Research**: Linear programming – problem formulation, simplex method, duality and sensitivity analysis; Transportation and assignment models; Integer programming; Constrained and unconstrained nonlinear optimization; Markovian queuing models; Simulation – manufacturing applications.**Engineering Economy and Costing:**Elementary cost accounting and methods of depreciation; Break-even analysis; Techniques for evaluation of capital investments; Financial statements; Activity based costing.**Production control**: Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality; Aggregate production planning; Master production scheduling; MRP, MRP-II and ERP; Routing, scheduling and priority dispatching; Push and pull production systems, concepts of Lean and JIT manufacturing systems; Logistics, distribution, and supply chain management; Inventory – functions, costs, classifications, deterministic inventory models, quantity discount; Perpetual and periodic inventory control systems.**Project management:**Scheduling techniques – Gantt chart, CPM, PERT and GERT.

**Section 8 - General Aptitude **

**Section 8 - General Aptitude**

**Verbal Ability:**English grammar; Sentence completion, Instructions; Verbal analogies, Word groups; Critical reasoning, Verbal deduction.**Numerical Ability:**Numerical computation; Numerical reasoning; Numerical estimation; Data interpretation.

**GATE ****Aerospace ****Engineering (****AE****) Syllabus**

**GATE Aerospace Engineering Syllabus 2022**

**GATE Aerospace Engineering Syllabus 2022**

GATE Aerospace Engineering Syllabus consists of 6 sections. In each of the sections, the topics have been divided into two categories – Core Topics and Special Topics. The paper would consist of about 90% of the questions from the core aerospace topics with the rest 10% from the Special Topics for the respective sections

**Section ****1****: ****Engineering Mathematics**

**Section**

**1**

**:**

**Engineering Mathematics**

### Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. It is one of the difficult sections of the paper. This section carries fifteen percent weightage of the total questions. The topics include in this section are -

**CORE TOPIC **

**CORE TOPIC**

Linear Algebra

Calculus

Differential Equations

**SPECIAL TOPIC**

**SPECIAL TOPIC**

Fourier Series, Laplace Transforms, Complex analysis, Probability and statistics.

Numerical methods for linear and nonlinear algebraic equations

Numerical integration and differentiation.

**Section 2: Flight Mechanics**

**Section 2: Flight Mechanics**

Flight mechanics are related to the operations of fixed-wing (gliders, airplanes) and rotary wing (helicopters) aircrafts. An Aeroplane (Airplane in US usage), is defined in ICAO Document 9110. The topics include in this section are -

**CORE TOPIC **

Basics: Atmosphere: Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts. Pressure altitude; equivalent, calibrated, indicated air speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator. Angle of attack, side slip; Roll, pitch & yaw controls. Aerodynamic forces and moments.

Airplane performance: Drag polar; takeoff and landing; steady climb & descent; absolute and service ceiling; range and endurance, load factor, turning flight, V-n diagram. Winds: head, tail & cross winds.

Static stability: Stability & control derivatives; longitudinal stick fixed & free stability; horizontal tail position and size; directional stability, vertical tail position and size; lateral stability. Wing dihedral, sweep & position; hinge moments, stick forces.

**SPECIAL TOPIC**

**SPECIAL TOPIC**

Dynamic stability, Euler angles, Equations of motion

Longitudinal modes, lateral-directional modes.

Decoupling of longitudinal and lateral-directional dynamics

**Section 3: Aerodynamics**

**Section 3: Aerodynamics**

Aerodynamics is the study of the motion of air, particularly its interaction with a solid object, such as an airplane wing. Aerodynamics is a sub-field of fluid dynamics and gas dynamics, and many aspects of aerodynamics theory are common to these fields. The topics include in this section are -

**CORE TOPIC **

Basic Fluid Mechanics: Conservation laws: Mass, momentum and energy (Integral and differential form) Dimensional analysis and dynamic similarity; Potential flow theory: sources, sinks, doublets, line vortex and their superposition. Elementary ideas of viscous flows including boundary layers.

Airfoils and wings: Airfoil nomenclature; Aerodynamic coefficients: lift, drag and moment; Kutta-Joukoswki theorem Thin airfoil theory, Kutta condition, starting vortex; Finite wing theory: Induced drag Prandtl lifting line theory; Critical and drag divergence Mach number.

Compressible Flows: Basic concepts of compressibility, One-dimensional compressible flows, Isentropic flows Fanno flow, Rayleigh flow; Normal and oblique shocks, Prandtl-Meyer flow; Flow through nozzles and diffusers.

**SPECIAL TOPIC**

Shock - boundary layer interaction.

Wind Tunnel Testing

Measurement and visualization techniques

**Section 4: Structures**

**Section 4: Structures**

A structure is an arrangement and organization of interrelated elements in a material object or system. Material structures include man-made objects such as buildings and machines and natural objects such as biological organisms, minerals, and chemicals. Abstract structures include data structures in computer science and musical form. The topics include in this section are -

**CORE TOPIC **

Strength of Materials: Stress and strain: Three-dimensional transformations, Mohr's circle, principal stresses Three-dimensional Hooke's law, Plane stress and strain. Failure theories: Maximum stress, Tresca and von Mises. Strain energy. Castigliano's principles. Statically determinate and indeterminate trusses and beams. Elastic flexural buckling of columns.

Flight vehicle structures: Characteristics of aircraft structures and materials. Torsion, bending and shear of thin-walled sections. Loads on aircraft.

Structural Dynamics: Free and forced vibrations of undamped and damped SDOF systems. Free vibrations of undamped 2-DOF systems.

**SPECIAL TOPIC**

Vibration of beams

Theory of elasticity

Equilibrium and compatibility equations, Airy’s stress function.

**Section 5: Propulsion**

**Section 5: Propulsion**

Propulsion is a means of creating force leading to movement. A propulsion system consists of a source of mechanical power, and a propulsor (means of converting this power into propulsive force). The topics include in this section are -

**CORE TOPIC **

Basics: Thermodynamics, boundary layers, heat transfer, combustion and thermochemistry.

Aerothermodynamics of aircraft engines: Thrust, efficiency, range. Brayton cycle. Engine performance: ramjet, turbojet, turbofan, turboprop and turboshaft engines. Afterburners.

Turbomachinery: Axial compressors: Angular momentum, work and compression, characteristic performance of a single axial compressor stage Efficiency of the compressor and degree of reaction, multi-staging. Centrifugal compressor: Stage dynamics, inducer, impeller and diffuser. Axial turbines: Stage performance.

Rockets: Thrust equation and specific impulse, rocket performance. Multi-staging. Chemical rockets. Performance of solid and liquid propellant rockets.

**SPECIAL TOPIC**

Aerothermodynamics of non-rotating propulsion components such as intakes, combustor and nozzle.

Turbine blade cooling.

Compressor-turbine matching

Surge and stall

**Section 6: Space Dynamics**

**Section 6: Space Dynamics**

Space dynamics is the study of man made objects in space when subjected to natural forces or any artificially induced forces in space. The topics include in this section are -

**CORE TOPIC**

Central force motion, determination of trajectory and orbital period in simple cases. Kepler’s laws; escape velocity.

**SPECIAL TOPIC**

Orbit transfer, in-plane and out-of-plane.

**Section 7 :General Aptitude **

**Section 7 :General Aptitude**

General Aptitude is a common section to all the GATE Papers. It is helpful for testing the analytical skills along with comprehension skills sof the candidate. The topics include in this section are

**CORE TOPIC**

English grammar; Sentence completion, Instructions; Verbal analogies, Word groups; Critical reasoning, Verbal deduction.

**SPECIAL TOPIC**

Numerical computation; Numerical reasoning; Numerical estimation; Data interpretation.

**GATE ****Architecture & Planning**** (A****R****) Syllabus**

**GATE Syllabus for Architecture & Planning (AR) 2022**

**GATE Syllabus for Architecture & Planning (AR) 2022**

GATE Syllabus for Architecture & Planning (AR) will consist of 8 sections. Architecture & Design is the most important section of Architecture and Planning. Candidates can check the Architecture and Planning syllabus as given below:

**GATE Syllabus for Architecture & Planning (AR): Part A Common**

**GATE Syllabus for Architecture & Planning (AR): Part A Common**

**Section 1**: Architecture, Planning and Design Architectural – Graphics; Visual composition in 2D and 3D; Computer application in Architecture and Planning; Anthropometrics; Organization of space; Circulation- horizontal and vertical; Space Standards; Universal design; Building bye laws; Codes and standards;**Section 2**: Construction and Management – Project management techniques e.g. PERT, CPM etc. ; Estimation and Specification; Professional practice and ethics; Form and Structure; Principles and design of disaster resistant structures; Temporary structures for rehabilitation;**Section 3**: Environmental Planning and Design – Natural and man-made ecosystem; Ecological principles; Environmental considerations in planning and design; Environmental pollution- types, causes, controls and abatement strategies; Sustainable development, goals and strategies; Climate change and built environment; Climate responsive design;**Section 4**: Urban Design, landscape and Conservation – Historical and modern examples of urban design; Elements of urban built environment – urban form, spaces, structure, pattern, fabric, texture, grain etc.; Concepts and theories of urban design; Principles, tools and techniques of urban design; Public spaces, character, spatial qualities and Sense of Place; Urban design interventions for sustainable development and transportation; Development controls – FAR, densities and building byelaws. ; Urban renewal and conservation; heritage conservation; historical public spaces and gardens; Landscape design; Site planning.**Section 5**: Planning process – Salient concepts, theories and principles of urban planning; concepts of cities - Eco-City, Smart City; Concepts and theories by trendsetting planners and designers; Ekistics; Urban sociology; Social, Economic and environmental cost benefit analysis; Methods of non-spatial and spatial data analysis; Development guidelines such as URDPFI;**Section 6**: Housing – Housing typologies; Concepts, principles and examples of neighbourhood; Residential densities; Affordable Housing; Real estate valuation;**Section 7**: Services and Infrastructure – Firefighting Systems; Building Safety and Security systems; Building Management Systems; Water treatment; Water supply and distribution system; Water harvesting systems; Principles, Planning and Design of storm water drainage system; Sewage disposal methods; Methods of solid waste management - collection, transportation and disposal; Recycling and Reuse of solid waste; Land-use – transportation - urban form inter- relationships; Design of roads, intersections, grade separators and parking areas; Hierarchy of roads and level of service; Para-transits and other modes of transportation, Pedestrian and slow moving traffic planning;

**GATE Syllabus for Architecture & Planning (AR): Part B1 Architecture**

**GATE Syllabus for Architecture & Planning (AR): Part B1 Architecture**

**Section B1.1**: History and Contemporary Architecture – Principles of Art and Architecture; World History of Architecture: Egyptian, Greco-Roman classical period, Byzantine, Gothic, Renaissance, Baroque-Rococo, etc.; Recent trends in Contemporary Architecture: Art nouveau, Art Deco, Eclecticism, International styles, Postmodernism, Deconstruction in architecture, etc.; Influence of Modern art and Design in Architecture; Indian vernacular and traditional Architecture, Oriental Architecture ; Works of renowned national and international architects**Section B1.2**: Building Construction and Structural systems – Building construction techniques, methods and details; Building systems and prefabrication of building elements; Principles of Modular Coordination; Construction planning and equipment; Building material characteristics and applications; Principles of strength of materials; Alternative building materials; Foundations; Design of structural elements with different materials; Elastic and Limit State design; Structural systems; Principles of Prestressing; High Rise and Long Span structures, gravity and lateral load resisting systems**Section B1.3**: Building Services and Sustainability – Solar architecture; Thermal, visual and acoustic comfort in built environments; Natural and Mechanical ventilation in buildings; Air-Conditioning systems; Sustainable building strategies; Building Performance Simulation and Evaluation; Intelligent Buildings; Water supply; Sewerage and drainage systems; Sanitary fittings and fixtures; Plumbing systems; Principles of internal and external drainage system; Principles of electrification of buildings; Elevators and Escalators - standards and uses

**GATE Syllabus for Architecture & Planning (AR): Part B2 Planning**

**GATE Syllabus for Architecture & Planning (AR): Part B2 Planning**

**Section B2.1**: Regional and Settlement Planning – Regional delineation; settlement hierarchy; Types and hierarchy of plans; Various schemes and programs of central government; Transit Oriented Development (TOD), SEZ, SRZ etc.; Public Perception and user behaviour; National Housing Policies, Programs and Schemes. ; Slums, Squatters and informal housing; Standards for housing and community facilities; Housing for special areas and needs.**Section B2.2**: Planning Techniques and Management – Application of G.I.S and Remote Sensing techniques in urban and regional planning; Tools and techniques of Surveys – Physical, Topographical, Land use and Socio-economic Surveys; Urban Economics, Law of demand and supply of land and its use in planning; Graphic presentation of spatial data; Local self-governance, Panchayatiraj institutions; Planning Legislation and implementation – Land Acquisition Act, PPP etc.; Decision support system and Land Information System; Urban geography and econometrics; Management of Infrastructure Projects; Demography and equity in planning**Section B2.3**: Infrastructure Planning – Process and Principles of Transportation Planning and Traffic Engineering; Road capacity and Travel demand forecasting; Traffic survey methods, Traffic flow Analysis; Traffic analysis and design considerations; Traffic and transport management and control in urban areas; Mass transportation planning; Intelligent Transportation Systems; Urban and Rural Infrastructure System Network

**GATE Syllabus for Architecture & Planning (AR) General Aptitude **

**GATE Syllabus for Architecture & Planning (AR) General Aptitude**

**Verbal Ability**: English grammar; Sentence completion, Instructions; Verbal analogies, Word groups; Critical reasoning, Verbal deduction.**Numerical Ability**: Numerical computation; Numerical reasoning; Numerical estimation; Data interpretation.

**GATE ****Biotechnology**** (****BT****) Syllabus**

**GATE Syllabus for Biotechnology (BT) 2022**

**GATE Syllabus for Biotechnology (BT) 2022**

GATE Biotechnology paper will have questions from topics:

**Section 1 – Engineering Mathematics**

**Section 1 – Engineering Mathematics**

**Linear Algebra:**Matrix algebra, systems of linear equations, consistency and rank, Eigen values and Eigen vectors.**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:****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 nonlinear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis.

**Section 2 – General Biotechnology**

**Section 2 – General Biotechnology**

**Biochemistry**: Biomolecules - structure and function; Biological membranes - structure, membrane channels and pumps, molecular motors, action potential and transport processes; Basic concepts and regulation of metabolism of carbohydrates, lipids, amino acids and nucleic acids; Photosynthesis, respiration and electron transport chain. Enzymes - Classification, catalytic and regulatory strategies; Enzyme kinetics - Michaelis-Menten equation; Enzyme inhibition - competitive, non-competitive and uncompetitive inhibition.**Microbiology**: Bacterial classification and diversity; Microbial Ecology - microbes in marine, freshwater and terrestrial ecosystems; Microbial interactions; Viruses - structure and classification; Methods in microbiology; Microbial growth and nutrition; Nitrogen fixation; Microbial diseases and host-pathogen interactions; Antibiotics and antimicrobial resistance.**Immunology**: Innate and adaptive immunity, humoral and cell mediated immunity; Antibody structure and function; Molecular basis of antibody diversity; T cell and B cell development; Antigen-antibody reaction; Complement; Primary and secondary lymphoid organs; Major histocompatibility complex (MHC); Antigen processing and presentation; Polyclonal and monoclonal antibody; Regulation of immune response; Immune tolerance; Hypersensitivity; Autoimmunity; Graft versus host reaction; Immunization and vaccines.

**Section 3 – Genetics, Cellular, and Molecular Biology**

**Section 3 – Genetics, Cellular, and Molecular Biology**

**Genetics and Evolutionary Biology**: Mendelian inheritance; Gene interaction; Complementation; Linkage, recombination and chromosome mapping; Extra chromosomal inheritance; Microbial genetics - transformation, transduction and conjugation; Horizontal gene transfer and transposable elements; Chromosomal variation; Genetic disorders; Population genetics; Epigenetics; Selection and inheritance; Adaptive and neutral evolution; Genetic drift; Species and speciation.**Cell Biology**: Prokaryotic and eukaryotic cell structure; Cell cycle and cell growth control; Cell-Genetics and Evolutionary Biology: Mendelian inheritance; Gene interaction; Complementation; Linkage, recombination and chromosome mapping; Extra chromosomal inheritance; Microbial genetics - transformation, transduction and conjugation; Horizontal gene transfer and transposable elements; Chromosomal variation; Genetic disorders; Population genetics; Epigenetics; Selection and inheritance; Adaptive and neutral evolution; Genetic drift; Species and speciation.**Molecular Biology:**

**Section 4 – Fundamentals of Biological Engineering**

**Section 4 – Fundamentals of Biological Engineering**

**Engineering principles applied to biological systems:**Material and energy balances for reactive and non-reactive systems; Recycle, bypass and purge processes; Stoichiometry of growth and product formation; Degree of reduction, electron balance, theoretical oxygen demand.**Classical thermodynamics and Bioenergetics**: Laws of thermodynamics; Solution thermodynamics; Phase equilibria, reaction equilibria; Ligand binding; Membrane potential; Energetics of metabolic pathways, oxidation and reduction reactions.**Transport Processes**: Newtonian and non-Newtonian fluids, fluid flow - laminar and turbulent; Mixing in bioreactors, mixing time; Molecular diffusion and film theory; Oxygen transfer and uptake in bioreactor, kLa and its measurement; Conductive and convective heat transfer, LMTD, overall heat transfer coefficient; Heat exchangers

**Section 5 – Bioprocess Engineering and Process Biotechnology**

**Section 5 – Bioprocess Engineering and Process Biotechnology**

**Bioreaction engineering:**Rate law, zero and first order kinetics; Ideal reactors - batch, mixed flow and plug flow; Enzyme immobilization, diffusion effects - Thiele modulus, effectiveness factor, Damkoehler number; Kinetics of cell growth, substrate utilization and product formation; Structured and unstructured models; Batch, fed-batch and continuous processes; Microbial and enzyme reactors; Optimization and scale up.**Upstream and Downstream Processing**: Media formulation and optimization; Sterilization of air and media; Filtration - membrane filtration, ultrafiltration; Centrifugation - high speed and ultra; Cell disruption; Principles of chromatography - ion exchange, gel filtration, hydrophobic interaction, affinity, GC, HPLC and FPLC; Extraction, adsorption and drying.**Instrumentation and Process Control**: Pressure, temperature and flow measurement devices; Valves; First order and second order systems; Feedback and feed forward control; Types of controllers – proportional, derivative and integral control, tuning of controllers.

**Section 6 – Plant, Animal and Microbial Biotechnology**

**Section 6 – Plant, Animal and Microbial Biotechnology**

**Plants**: Totipotency; Regeneration of plants; Plant growth regulators and elicitors; Tissue culture and cell suspension culture system - methodology, kinetics of growth and nutrient optimization; Production of secondary metabolites; Hairy root culture; Plant products of industrial importance; Artificial seeds; Somaclonal variation; Protoplast, protoplast fusion - somatic hybrid and cybrid; Transgenic plants - direct and indirect methods of gene transfer techniques; Selection marker and reporter gene; Plastid transformation.**Animals**: Culture media composition and growth conditions; Animal cell and tissue preservation; Anchorage and non-anchorage dependent cell culture; Kinetics of cell growth; Micro & macro- carrier culture; Hybridoma technology; Stem cell technology; Animal cloning; Transgenic animals; Knock-out and knock-in animals.**Microbes**: Production of biomass and primary/secondary metabolites - Biofuels, bioplastics, industrial enzymes, antibiotics; Large scale production and purification of recombinant proteins and metabolites; Clinical-, food- and industrial- microbiology; Screening strategies for new products.

**Section 7 – Recombinant DNA technology and Other Tools in Biotechnology**

**Section 7 – Recombinant DNA technology and Other Tools in Biotechnology**

**Recombinant DNA technology**: Restriction and modification enzymes; Vectors - plasmids, bacteriophage and other viral vectors, cosmids, Ti plasmid, bacterial and yeast artificial chromosomes; Expression vectors; cDNA and genomic DNA library; Gene isolation and cloning, strategies for production of recombinant proteins; Transposons and gene targeting;**Molecular tools**: Polymerase chain reaction; DNA/RNA labelling and sequencing; Southern and northern blotting; In-situ hybridization; DNA fingerprinting, RAPD, RFLP; Site-directed mutagenesis; Gene transfer technologies; CRISPR-Cas; Biosensing and biosensors.**Analytical tools**: Principles of microscopy - light, electron, fluorescent and confocal; Principles of spectroscopy - UV, visible, CD, IR, fluorescence, FT-IR, MS, NMR; Electrophoresis; Micro- arrays; Enzymatic assays; Immunoassays - ELISA, RIA, immunohistochemistry; immunoblotting; Flow cytometry; Whole genome and ChIP sequencing.**Computational tools**: Bioinformatics resources and search tools; Sequence and structure databases; Sequence analysis - sequence file formats, scoring matrices, alignment, phylogeny; Genomics, proteomics, metabolomics; Gene prediction; Functional annotation; Secondary structure and 3D structure prediction; Knowledge discovery in biochemical databases; Metagenomics; Metabolic engineering and systems biology.

**Section 8 - General Aptitude **

**Section 8 - General Aptitude**

**Verbal Ability**: English grammar; Sentence completion, Instructions; Verbal analogies, Word groups; Critical reasoning, Verbal deduction.**Numerical Ability**: Numerical computation; Numerical reasoning; Numerical estimation; Data interpretation.

**GATE ****Chemical Engineering**** (****CH****) Syllabus**

**GATE Chemical Engineering (CH) Syllabus 2022**

**GATE Chemical Engineering (CH) Syllabus 2022**

Chemical Engineering uses Physics and Chemistry with applied Mathematics to convert chemicals and raw materials into useful substances. Chemical Engineers essentially design large-scale processes for such transformations.

**Section 1: Engineering Mathematics**

**Section 1: Engineering Mathematics**

Engineering Mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. This section carries a 15% weightage of questions. It is one of the important sections of GATE syllabus.

Linear Algebra

Calculus

Differential equations

Complex variables

Probability and Statistics

Numerical Methods

**Section 2: Process Calculations and Thermodynamics**

**Section 2: Process Calculations and Thermodynamics**

Steady and unsteady state mass and energy balances including multiphase, multicomponent, reacting, and non-reacting systems. Use of tie components; recycle, bypass and purge calculations; Gibb’s phase rule and degree of freedom analysis.

First and Second laws of thermodynamics. Applications of first law to close and open systems. Second law and Entropy.

Thermodynamic properties of pure substances: Equation of State and residual properties, properties of mixtures: partial molar properties, fugacity, excess properties, and activity coefficients; phase equilibria: predicting VLE of systems; chemical reaction equilibrium.

**Section 3: Fluid Mechanics and Mechanical Operations**

**Section 3: Fluid Mechanics and Mechanical Operations**

Fluid statics, Newtonian and non-Newtonian fluids, shell-balances including a differential form of Bernoulli equation and energy balance, Macroscopic friction factors, dimensional analysis, and similitude, flow through pipeline systems, flow meters, pumps and compressors, elementary boundary layer theory, flow past immersed bodies including packed and fluidized beds, Turbulent flow: fluctuating velocity, universal velocity profile and pressure drop.

Particle size and shape, particle size distribution, size reduction and classification of solid particles; free and hindered settling; centrifuge and cyclones; thickening and classification, filtration, agitation, and mixing; conveying of solids.

**Section 4: Heat Transfer**

**Section 4: Heat Transfer**

Steady and unsteady heat conduction, convection and radiation, thermal boundary layer and heat transfer coefficients, boiling, condensation, and evaporation; types of heat exchangers and evaporators and their process calculations.

Design of double pipe, shell and tube heat exchangers, and single and multiple effect evaporators.

**Section 5: Mass Transfer**

**Section 5: Mass Transfer**

Fick’s laws, molecular diffusion in fluids, mass transfer coefficients, film, penetration, and surface renewal theories; momentum, heat and mass transfer analogies; stage-wise and continuous contacting and stage efficiencies

HTU & NTU concepts; design and operation of equipment for distillation, absorption, leaching, liquid-liquid extraction, drying, humidification, dehumidification, and adsorption.

**Section 6: Chemical Reaction Engineering**

**Section 6: Chemical Reaction Engineering**

Theories of reaction rates; kinetics of homogeneous reactions, interpretation of kinetic data, single and multiple reactions in ideal reactors, non-ideal reactors; residence time distribution, single parameter model; non-isothermal reactors; kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis.

**Section 7: Instrumentation and Process Control**

**Section 7: Instrumentation and Process Control**

Measurement of process variables; sensors, transducers and their dynamics, process modeling and linearization, transfer functions and dynamic responses of various systems, systems with the inverse response, process reaction curve, controller modes (P, PI, and PID); control valves; analysis of closed-loop systems including stability, frequency response, controller tuning, cascade and feedforward control.

**Section 8: Plant Design and Economics**

**Section 8: Plant Design and Economics**

Principles of process economics and cost estimation including depreciation and total annualized cost, cost indices, rate of return, payback period, discounted cash flow, optimization in process design, and sizing of chemical engineering equipment such as compressors, heat exchangers, multistage contactors.

**Section 9: Chemical Technology**

**Section 9: Chemical Technology**

Inorganic chemical industries (sulfuric acid, phosphoric acid, Chlor-alkali industry), fertilizers (Ammonia, Urea, SSP and TSP); natural products industries (Pulp and Paper, Sugar, Oil, and Fats); petroleum refining and petrochemicals; polymerization industries (polyethylene, polypropylene, PVC, and polyester synthetic fibers).

**GATE Chem****istry**** (CY) Syllabus**

**GATE Chemistry Syllabus 2022**

**GATE Chemistry Syllabus 2022**

GATE Chemistry Syllabus consists of three sections- Physical Chemistry, Inorganic chemistry and Organic Chemistry. Here, we are providing the complete syllabus of Chemistry for GATE which is given below:

**Section 1 - Physical Chemistry**

**Section 1 - Physical Chemistry**

**Subject****: Structure **

**Subject**

**: Structure**

**Topic: **Postulates of quantum mechanics. Operators. Time-dependent and time-independent Schrödinger equations. Born interpretation. Dirac bra- ket notation. Particle in a box: infinite and finite square wells; concept of tunnelling; particle in 1D, 2D and 3D-box; applications. Harmonic oscillator: harmonic and anharmonic potentials; hermite polynomials. Rotational motion: Angular momentum operators, Rigid rotor. Hydrogen and hydrogen-like atoms : atomic orbitals; radial distribution function. Multi-electron atoms: orbital approximation; electron spin; Pauli exclusion principle; slater determinants. Approximation Methods: Variation method and secular determinants; first order perturbation techniques. Atomic units. Molecular structure and Chemical bonding: Born-Oppenheimer approximation; Valence bond theory and linear combination of atomic orbitals – molecular orbital (LCAO-MO) theory. Hybrid orbitals. Applications of LCAO-MO theory to H2 +, H2; molecular orbital theory (MOT) of homo- and heteronuclear diatomic molecules. Hückel approximation and its application to annular π– electron systems

**Subject: ****Group Theory**** **

**Subject:**

**Group Theory**

**Topic: **Symmetry elements and operations; Point groups and character tables; Internal coordinates and vibrational modes; symmetry adapted linear combination of atomic orbitals (LCAO-MO); construction of hybrid orbitals using symmetry aspects.

**Topic:**Symmetry elements and operations; Point groups and character tables; Internal coordinates and vibrational modes; symmetry adapted linear combination of atomic orbitals (LCAO-MO); construction of hybrid orbitals using symmetry aspects.

**Subject: ****Spectroscopy**** **

**Subject:**

**Spectroscopy**

**Topic: **Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules. Line broadening. Einstein’s coefficients. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of nuclear magnetic resonance: gyromagnetic ratio; chemical shift, nuclear coupling.

**Topic:**Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules. Line broadening. Einstein’s coefficients. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of nuclear magnetic resonance: gyromagnetic ratio; chemical shift, nuclear coupling.

**Subject: ****Equilibrium**** **

**Subject:**

**Equilibrium**

**Topic: **Laws of thermodynamics. Standard states. Thermochemistry. Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, Gibbs-Duhem equation, van’t Hoff equation. Criteria of spontaneity and equilibrium. Absolute entropy. Partial molar quantities. Thermodynamics of mixing. Chemical potential. Fugacity, activity and activity coefficients. Ideal and Non-ideal solutions, Raoult’s Law and Henry’s Law, Chemical equilibria. Dependence of equilibrium constant on temperature and pressure. Ionic mobility and conductivity. Debye-Hückel limiting law. Debye-Hückel-Onsager equation. Standard electrode potentials and electrochemical cells. Nernst Equation and its application, relationship between Electrode potential and thermodynamic quantities, Potentiometric and conductometric titrations. Phase rule. Clausius- Clapeyron equation. Phase diagram of one component systems: CO2, H2O, S; two component systems: liquid- vapour, liquid-liquid and solid-liquid systems. Fractional distillation. Azeotropes and eutectics. Statistical thermodynamics: microcanonical, canonical and grand canonical ensembles, Boltzmann distribution, partition functions and thermodynamic properties.

**Topic:**Laws of thermodynamics. Standard states. Thermochemistry. Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, Gibbs-Duhem equation, van’t Hoff equation. Criteria of spontaneity and equilibrium. Absolute entropy. Partial molar quantities. Thermodynamics of mixing. Chemical potential. Fugacity, activity and activity coefficients. Ideal and Non-ideal solutions, Raoult’s Law and Henry’s Law, Chemical equilibria. Dependence of equilibrium constant on temperature and pressure. Ionic mobility and conductivity. Debye-Hückel limiting law. Debye-Hückel-Onsager equation. Standard electrode potentials and electrochemical cells. Nernst Equation and its application, relationship between Electrode potential and thermodynamic quantities, Potentiometric and conductometric titrations. Phase rule. Clausius- Clapeyron equation. Phase diagram of one component systems: CO2, H2O, S; two component systems: liquid- vapour, liquid-liquid and solid-liquid systems. Fractional distillation. Azeotropes and eutectics. Statistical thermodynamics: microcanonical, canonical and grand canonical ensembles, Boltzmann distribution, partition functions and thermodynamic properties.

**Subject: ****Kinetics**** **

**Subject:**

**Kinetics**

**Topic: **Elementary, parallel, opposing and consecutive reactions. Steady state approximation. Mechanisms of complex reactions. Unimolecular reactions. Potential energy surfaces and classical trajectories, Concept of Saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of photochemical and photophysical processes.

**Topic:**Elementary, parallel, opposing and consecutive reactions. Steady state approximation. Mechanisms of complex reactions. Unimolecular reactions. Potential energy surfaces and classical trajectories, Concept of Saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of photochemical and photophysical processes.

**Subject: ****Surfaces and Interfaces**** **

**Subject:**

**Surfaces and Interfaces**

**Topic: **Physisorption and chemisorption. Langmuir, Freundlich and Brunauer–Emmett– Teller (BET) isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity. Self- assembly. Physical chemistry of colloids, micelles and macromolecules.

**Topic:**Physisorption and chemisorption. Langmuir, Freundlich and Brunauer–Emmett– Teller (BET) isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity. Self- assembly. Physical chemistry of colloids, micelles and macromolecules.

**Section 2 - Inorganic Chemistry**

**Section 2 - Inorganic Chemistry**

**Subject: ****Main Group Elements**** **

**Subject:**

**Main Group Elements**

**Topic: **Hydrides, halides, oxides, oxoacids, nitrides, sulfides – shapes and reactivity. Structure and bonding of boranes, carboranes, silicones, silicates, boron nitride, borazines and phosphazenes. Allotropes of carbon, phosphorus and sulphur. Industrial synthesis of compounds of main group elements. Chemistry of noble gases, pseudohalogens, and interhalogen compounds. Acid-base concepts and principles (Lewis, Brønsted, HSAB and acid-base catalysis).

**Topic:**Hydrides, halides, oxides, oxoacids, nitrides, sulfides – shapes and reactivity. Structure and bonding of boranes, carboranes, silicones, silicates, boron nitride, borazines and phosphazenes. Allotropes of carbon, phosphorus and sulphur. Industrial synthesis of compounds of main group elements. Chemistry of noble gases, pseudohalogens, and interhalogen compounds. Acid-base concepts and principles (Lewis, Brønsted, HSAB and acid-base catalysis).

**Subject: ****Transition Elements**** **

**Subject:**

**Transition Elements**

**Topic: **Coordination chemistry – structure and isomerism, theories of bonding (VBT, CFT, and MOT). Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, selection rules, Orgel and Tanabe- Sugano diagrams, nephelauxetic effect and Racah parameter, charge-transfer spectra. Magnetic properties of transition metal complexes. Ray-Dutt and Bailar twists,

**Topic:**Coordination chemistry – structure and isomerism, theories of bonding (VBT, CFT, and MOT). Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, selection rules, Orgel and Tanabe- Sugano diagrams, nephelauxetic effect and Racah parameter, charge-transfer spectra. Magnetic properties of transition metal complexes. Ray-Dutt and Bailar twists,

**Subject: ****Reaction Mechanism**** **

**Subject:**

**Reaction Mechanism**

**Topic: **kinetic and thermodynamic stability, substitution and redox reactions. Metal-metal multiple bond. Lanthanides and Actinides: Recovery. Periodic properties, spectra and magnetic properties.

**Topic:**kinetic and thermodynamic stability, substitution and redox reactions. Metal-metal multiple bond. Lanthanides and Actinides: Recovery. Periodic properties, spectra and magnetic properties.

**Subject: ****Organometallics**** **

**Subject:**

**Organometallics**

**Topic: **18-Electron rule; metal-alkyl, metal-carbonyl, metal-olefin and metal- carbene complexes and metallocenes. Fluxionality in organometallic complexes. Types of organometallic reactions. Homogeneous catalysis - Hydrogenation, hydroformylation, acetic acid synthesis, metathesis and olefin oxidation. Heterogeneous catalysis - Fischer- Tropsch reaction, Ziegler-Natta polymerization.

**Topic:**18-Electron rule; metal-alkyl, metal-carbonyl, metal-olefin and metal- carbene complexes and metallocenes. Fluxionality in organometallic complexes. Types of organometallic reactions. Homogeneous catalysis - Hydrogenation, hydroformylation, acetic acid synthesis, metathesis and olefin oxidation. Heterogeneous catalysis - Fischer- Tropsch reaction, Ziegler-Natta polymerization.

**Subject: ****Radioactivity**** **

**Subject:**

**Radioactivity**

**Topic: **Detection of radioactivity, Decay processes, half-life of radioactive elements, fission and fusion processes. Bioinorganic Chemistry: Ion (Na+ and K+) transport, oxygen binding, transport and utilization, electron transfer reactions, nitrogen fixation, metalloenzymes containing magnesium, molybdenum, iron, cobalt, copper and zinc.

**Topic:**Detection of radioactivity, Decay processes, half-life of radioactive elements, fission and fusion processes. Bioinorganic Chemistry: Ion (Na+ and K+) transport, oxygen binding, transport and utilization, electron transfer reactions, nitrogen fixation, metalloenzymes containing magnesium, molybdenum, iron, cobalt, copper and zinc.

**Subject: ****Solids**** **

**Subject:**

**Solids**

**Topic: **Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg’s law, ionic crystals, structures of AX, AX2, ABX3 type compounds, spinels, band theory, metals and semiconductors. Instrumental Methods of Analysis: UV-visible, fluorescence and FTIR spectrophotometry, NMR and ESR spectroscopy, mass spectrometry, atomic absorption spectroscopy, Mössbauer spectroscopy (Fe and Sn) and X- ray crystallography. Chromatography including GC and HPLC. Electroanalytical methods- polarography, cyclic voltammetry, ion-selective electrodes. Thermoanalytical methods.

**Topic:**Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg’s law, ionic crystals, structures of AX, AX2, ABX3 type compounds, spinels, band theory, metals and semiconductors. Instrumental Methods of Analysis: UV-visible, fluorescence and FTIR spectrophotometry, NMR and ESR spectroscopy, mass spectrometry, atomic absorption spectroscopy, Mössbauer spectroscopy (Fe and Sn) and X- ray crystallography. Chromatography including GC and HPLC. Electroanalytical methods- polarography, cyclic voltammetry, ion-selective electrodes. Thermoanalytical methods.

**Section 3 - Organic Chemistry**

**Section 3 - Organic Chemistry**

**Subject: ****Streochemistry**** **

**Subject:**

**Streochemistry**

**Topic: **Chirality and symmetry of organic molecules with or without chiral centres and determination of their absolute configurations. Relative stereochemistry in compounds having more than one stereogenic centre. Homotopic, enantiotopic and diastereotopic atoms, groups and faces. Stereoselective and stereospecific synthesis. Conformational analysis of acyclic and cyclic compounds. Geometrical isomerism and optical isomerism. Configurational and conformational effects, atropisomerism, and neighbouring group participation on reactivity and selectivity/specificity.

**Topic:**Chirality and symmetry of organic molecules with or without chiral centres and determination of their absolute configurations. Relative stereochemistry in compounds having more than one stereogenic centre. Homotopic, enantiotopic and diastereotopic atoms, groups and faces. Stereoselective and stereospecific synthesis. Conformational analysis of acyclic and cyclic compounds. Geometrical isomerism and optical isomerism. Configurational and conformational effects, atropisomerism, and neighbouring group participation on reactivity and selectivity/specificity.

**Subject: ****Reaction Mechanisms**** **

**Subject:**

**Reaction Mechanisms**

**Topic: **Basic mechanistic concepts – kinetic versus thermodynamic control, Hammond’s postulate and Curtin-Hammett principle. Methods of determining reaction mechanisms through kinetics, identification of products, intermediates and isotopic labelling. Linear free-energy relationship – Hammett and Taft equations. Nucleophilic and electrophilic substitution reactions (both aromatic and aliphatic). Additional reactions to carbon-carbon and carbon-heteroatom (N and O) multiple bonds. Elimination reactions. Reactive intermediates – carbocations, carbanions, carbenes, nitrenes, arynes and free radicals. Molecular rearrangements.

**Topic:**Basic mechanistic concepts – kinetic versus thermodynamic control, Hammond’s postulate and Curtin-Hammett principle. Methods of determining reaction mechanisms through kinetics, identification of products, intermediates and isotopic labelling. Linear free-energy relationship – Hammett and Taft equations. Nucleophilic and electrophilic substitution reactions (both aromatic and aliphatic). Additional reactions to carbon-carbon and carbon-heteroatom (N and O) multiple bonds. Elimination reactions. Reactive intermediates – carbocations, carbanions, carbenes, nitrenes, arynes and free radicals. Molecular rearrangements.

**Subject: ****Organic Synthesis**** **

**Subject:**

**Organic Synthesis**

**Topic: **Synthesis, reactions, mechanisms and selectivity involving the following classes of compounds – alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids, esters, nitriles, halides, nitro compounds, amines and amides. Uses of Mg, Li, Cu, B, Zn, P, S, Sn and Si based reagents in organic synthesis. Carbon-carbon bond formation through coupling reactions - Heck, Suzuki, Stille, Sonogoshira, Negishi, Kumada, Hiyama, Tsuji-Trost, olefin metathesis and McMurry. Concepts of multistep synthesis – retrosynthetic analysis, strategic disconnections, synthons and synthetic equivalents. Atom economy and Green Chemistry, Umpolung reactivity – formyl and acyl anion equivalents. Selectivity in organic synthesis – chemo-, regio- and stereoselectivity. Protection and deprotection of functional groups. Concepts of asymmetric synthesis – resolution (including enzymatic), desymmetrization and use of chiral auxiliaries, organocatalysis. Carbon-carbon and carbon-heteroatom bond forming reactions through enolates (including boron enolates), enamines and silyl enol ethers. Stereoselective addition to C=O groups (Cram, Prelog and Felkin-Anh models).

**Topic:**Synthesis, reactions, mechanisms and selectivity involving the following classes of compounds – alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids, esters, nitriles, halides, nitro compounds, amines and amides. Uses of Mg, Li, Cu, B, Zn, P, S, Sn and Si based reagents in organic synthesis. Carbon-carbon bond formation through coupling reactions - Heck, Suzuki, Stille, Sonogoshira, Negishi, Kumada, Hiyama, Tsuji-Trost, olefin metathesis and McMurry. Concepts of multistep synthesis – retrosynthetic analysis, strategic disconnections, synthons and synthetic equivalents. Atom economy and Green Chemistry, Umpolung reactivity – formyl and acyl anion equivalents. Selectivity in organic synthesis – chemo-, regio- and stereoselectivity. Protection and deprotection of functional groups. Concepts of asymmetric synthesis – resolution (including enzymatic), desymmetrization and use of chiral auxiliaries, organocatalysis. Carbon-carbon and carbon-heteroatom bond forming reactions through enolates (including boron enolates), enamines and silyl enol ethers. Stereoselective addition to C=O groups (Cram, Prelog and Felkin-Anh models).

**Subject:**** Pericyclic Reaction and Photochemistry**** **

**Subject:**

**Pericyclic Reaction and Photochemistry**

**Topic: **Electrocyclic, cycloaddition and sigmatropic reactions. Orbital correlations - FMO and PMO treatments, Woodward-Hoffmann rule. Photochemistry of alkenes, arenes and carbonyl compounds. Photooxidation and photoreduction. Di-π-methane rearrangement, Barton-McCombie reaction, Norrish type-I and II cleavage reaction.

**Topic:**Electrocyclic, cycloaddition and sigmatropic reactions. Orbital correlations - FMO and PMO treatments, Woodward-Hoffmann rule. Photochemistry of alkenes, arenes and carbonyl compounds. Photooxidation and photoreduction. Di-π-methane rearrangement, Barton-McCombie reaction, Norrish type-I and II cleavage reaction.

**Subject: ****Heterocyclic**** **

**Subject:**

**Heterocyclic**

**Topic: **Structure, preparation, properties and reactions of furan, pyrrole, thiophene, pyridine, indole, quinoline and isoquinoline.

**Topic:**Structure, preparation, properties and reactions of furan, pyrrole, thiophene, pyridine, indole, quinoline and isoquinoline.

**Subject: ****Biomolecules**** **

**Subject:**

**Biomolecules**

**Topic: **Structure, properties and reactions of mono- and di-saccharides, physicochemical properties of amino acids, chemical synthesis of peptides, chemical structure determination of peptides and proteins, structural features of proteins, nucleic acids, lipids, steroids, terpenoids, carotenoids, and alkaloids.

**Topic:**Structure, properties and reactions of mono- and di-saccharides, physicochemical properties of amino acids, chemical synthesis of peptides, chemical structure determination of peptides and proteins, structural features of proteins, nucleic acids, lipids, steroids, terpenoids, carotenoids, and alkaloids.

**Subject: ****Experimental Techniques in Organic Chemistry**** **

**Subject:**

**Experimental Techniques in Organic Chemistry**

**Topic: **Optical rotation (polarimetry). Applications of various chromatographic techniques such as thin-layer, column, HPLC and GC. Applications of UV-visible, IR, NMR and Mass spectrometry in the structural determination of organic molecules.

**Topic:**Optical rotation (polarimetry). Applications of various chromatographic techniques such as thin-layer, column, HPLC and GC. Applications of UV-visible, IR, NMR and Mass spectrometry in the structural determination of organic molecules.

**GATE ****Ecology & Evolution**** (****E****Y) Syllabus**

**GATE Syllabus for Ecology & Evolution 2022**

**GATE Syllabus for Ecology & Evolution 2022**

The GATE Syllabus for Ecology & Evolution 2022 is based on graduation level. Applicants are advised to check the complete syllabus before starting the preparation of the exam.

**Section 1: Ecology**

**Section 1: Ecology**

Fundamental concepts: Abiotic and biotic components; scales (population, species, community, ecosystems, biomes); niches and habitats

Population ecology: Population growth rates (density dependent/independent); metapopulation ecology (colonization, persistence, extinction, patches, sources, sinks); age- structured populations

Interactions: Types (mutualism, symbiosis, commensalism, competition, parasitism, predation, etc); ecophysiology (physiological adaptations to abiotic environment); prey- predator interactions (Lotka-Voltera equation etc)

Community ecology: Community assembly, organization and succession; species richness, evenness and diversity indices, species-area relationships; theory of island biogeography

Ecosystems structure and function: trophic levels and their interactions; nutrient cycles; primary and secondary productivity.

**Section 2: Evolution**

**Section 2: Evolution**

History of Evolutionary thought: Lamarckism; Darwinism; Modern Synthesis

Fundamentals: Variation; heritability; natural selection; fitness and adaptation; types of selection (stabilizing, directional, disruptive)

Diversity of life: Origin and history of life on earth; diversity and classification of life; systems of classification (cladistics and phenetics)

Life history strategies: Allocation of resources; trade offs; r/K selection; semelparity and iteroparity

Interactions: Coevolution (co-adaptations, arms race, Red Queen hypothesis, co- speciation); prey-predator interactions (mimicry, crypsis, etc)

Population and Quantitative genetics: Origins of genetic variation; Mendelian genetics; Hardy-Weinberg equilibrium; drift; selection (one-locus two-alleles model); population genetic structure (panmixia, gene flow, FST); polygenic traits; gene-environment interactions (phenotypic plasticity); heritability

Molecular evolution and phylogenetics: Neutral theory; molecular clocks; rates of evolution; phylogenetic reconstruction; molecular systematics

Macroevolution: Species concepts and speciation; adaptive radiation; convergence; biogeography

**Section 3: Mathematics and Quantitative Ecology**

**Section 3: Mathematics and Quantitative Ecology**

Mathematics and statistics in ecology: Simple functions (linear, quadratic, exponential, logarithmic, etc); concept of derivatives and slope of a function; permutations and combinations; basic probability (probability of random events; sequences of events, etc); frequency distributions and their descriptive statistics (mean, variance, coefficient of variation, correlation, etc).

Statistical hypothesis testing: Concept of p-value; Type I and Type II error, test statistics like t-test and Chi-square test; basics of linear regression and ANOVA.

**Section 4: Behavioural Ecology**

**Section 4: Behavioural Ecology**

Classical Ethology: Instinct; fixed action pattern; imprinting; learnt behavior; proximate and ultimate questions

Sensory ecology: Neuroethology; communication (chemical, acoustic and visual signaling); recognition systems

Foraging ecology: Foraging behaviour; optimal foraging theory

Reproduction: Cost of sex; sexual dimorphism; mate choice; sexual selection (runaway selection, good-genes, handicap principle, etc); sexual conflict; mating systems; parental care

Social living: Costs and benefits of group-living (including responses to predators); effect of competition (scramble and contest) on group formation; dominance relationships; eusociality; kin selection; altruism; reciprocity; human behaviour.

**Section 5: Applied Ecology & Evolution**

**Section 5: Applied Ecology & Evolution**

Biodiversity and conservation: Importance of conserving biodiversity; ecosystem services; threats to biodiversity; invasive species; in-situ conservation (endemism, biodiversity hotspots, protected areas); ex-situ conservation; conservation genetics (genetic diversity, inbreeding depression); DNA fingerprinting and DNA barcoding

Disease ecology and evolution: Epidemiology; zoonotic diseases; antibiotic resistance; vector control

Plant and animal breeding: Marker assisted breeding; genetic basis of economically important traits

Global climate change: Causes; consequences; mitigation

**GATE ****Geology & Geophysics**** (****GG****) Syllabus**

**GATE 2022 Geology & Geophysics Syllabus - Common Section**

**GATE 2022 Geology & Geophysics Syllabus - Common Section**

GATE 2022 Geology & Geophysics Syllabus for the common section has to be attempted by all the candidates attempting the subject:

Earth and planetary system – terrestrial planets and moons of the solar system; size, shape, internal structure and composition of the earth; concept of isostasy; elements of seismology – body and surface waves, propagation of body waves in the earth’s interior; Heat flow within the earth; Gravitational field of the Earth; geomagnetism and paleomagnetism; continental drift; plate tectonics – relationship with earthquakes, volcanism and mountain building; continental and oceanic crust – composition, structure and thickness.

Weathering and soil formation; landforms created by river, wind, glacier, ocean and volcanoes.

Basic structural geology - stress, strain and material response; brittle and ductile deformation; nomenclature and classification of folds and faults.

Crystallography – basic crystal symmetry and concept of point groups. Mineralogy – silicate crystal structure and determinative mineralogy of common rock forming minerals.

Petrology of common igneous, sedimentary and metamorphic rocks.

Geological time scale; Geochronology and absolute time. Stratigraphic principles; major stratigraphic divisions of India.

Mineral, coal and petroleum resources of India.

Introduction to remote sensing.

Engineering properties of rocks and soils.

Elements of hydrogeology.

Principles and applications of gravity, magnetic, electrical, electromagnetic, seismic and radiometric methods of prospecting for oil, mineral and groundwater; introductory well logging.

**GATE 2022 Geology Syllabus**

**GATE 2022 Geology Syllabus**

**Geomorphology**- Geomorphic processes and agents; development and evolution of landforms in continental and oceanic settings; tectonic geomorphology.**Structural geology**– Forces and mechanism of rock deformation; primary and secondary structures; geometry and genesis of planar and linear structures (bedding, cleavage, schistosity, lineation); folds, faults, joints and unconformities; Stereographic projection; shear zones, thrusts and superposed folding; basement-cover relationship. Interpretation of geological maps.**Crystallography and mineralogy**- Elements of crystal symmetry, form and twinning; crystallographic projection; crystal chemistry; classification of minerals, physical and optical properties of rock- forming minerals.**Geochemistry**– Cosmic abundance of elements; meteorites; geochemical evolution of the earth; geochemical cycles; distribution of major, minor and trace elements in crust and mantle; elements of high temperature and low temperature geochemical thermodynamics; isotopic evolution of the crust and the mantle, mantle reservoirs; geochemistry of water and water-rock interaction.**Igneous petrology**– Classification, forms, textures and genesis of common igneous rocks; magmatic differentiation; binary and ternary phase diagrams; major and trace elements as monitors of partial melting and magma evolutionary processes. Mantle plumes, hotspots and large igneous provinces.**Sedimentology–****Metamorphic petrology**– Structures and textures of metamorphic rocks. Physico-chemical conditions of metamorphism and concept of metamorphic facies, grade and baric types; chemographic projections; metamorphism of pelitic, mafic and impure carbonate rocks; role of bulk composition including fluids in metamorphism; thermobarometry and metamorphic P-T-t paths, and their tectonic significance.**Paleobiology**- Diversity of life through time, mass extinctions- causes and effects; taphonomy – processes of fossilization. Taxonomy. Morphology and functional morphology of invertebrates (bivalves, brachiopods, gastropods, echinoids, ammonites); microfossils (foraminifera, ostracoda, conodonts, bryozoa); Vertebrate paleontology (Equus, Probicidea, Human); Paleobotany (plant, spores, pollens). Basic concepts of ecology/paleoecology; classification - ecological and taxonomic schemes (diversity and richness). Fossils and paleoenvironments.**Stratigraphy**– Principles of stratigraphy and concepts of correlation; Lithostratigraphy, biostratigraphy and chronostratigraphy. Principles of sequence stratigraphy and applications. Stratigraphy of peninsular and extra-peninsular India. Boundary problems in Indian stratigraphy.**Resource geology**- Ore-mineralogy; ore forming processes vis-à-vis ore-rock association (magmatic, hydrothermal, sedimentary, supergene and meta morphogenic ores); fluid inclusions as ore genetic tools. Coal and petroleum geology; marine mineral resources. Prospecting and exploration of economic mineral deposits - sampling, ore reserve estimation, geostatistics, mining methods. Ore dressing and mineral economics. Distribution of mineral, fossil and nuclear fuel deposits in India.**Global tectonics**– Plate motions, driving mechanisms, plate boundaries, supercontinent cycles.**Applied geology**– Physico-mechanical properties of rocks and soils; rock index tests; Rock failure criteria (Mohr-Coulomb, Griffith and Hoek-Brown criteria); shear strength of rock discontinuities; rock mass classifications (RMR and Q Systems); in-situ stresses; rocks as construction materials; geological factors in the construction of engineering structures including dams, tunnels and excavation sites. Analysis of slope stability. Natural hazards (landslide, volcanic, seismogenic, coastal) and mitigation. Principles of climate change**Hydrogeology**– Groundwater flow and exploration, well hydraulics and water quality.**Basic principles of remote sensing**– energy sources and radiation principles, atmospheric absorption, interaction of energy with earth’s surface, aerial-photo interpretation, multispectral remote sensing in visible, infrared, thermal IR and microwave regions, digital processing of satellite images. GIS – basic concepts, raster and vector mode operations.

**GATE 2022 Geophysics Syllabus**

**GATE 2022 Geophysics Syllabus**

**Solid-Earth Geophysics**- The earth as a planet; different motions of the earth; gravity field of the earth, Clairaut’s theorem, size and shape of earth; geomagnetic field, paleomagnetism; Geothermics and heat flow; seismology and interior of the earth; variation of density, velocity, pressure, temperature, electrical and magnetic properties of the earth.**Geodesy**- Gravitational Field of the Earth; Geoid; Ellipsoid; Geodetic Reference Systems; Datum; Everest (1830) and WGS 84 (1984) systems; GPS and DGPS; Levelling and Surveying.**Earthquake Seismology**- Elements of elasticity theory- stress and strain tensors, Generalized Hooke’s Law; Body and Surface Waves; Rotational, dilatational, irrorational and equivolumnal waves. Reflection and refraction of elastic waves; Homogeneous and evanescent waves and bounded waves; Eikonal Equation and Ray theory; earthquakes-causes and measurements, magnitude and intensity, focal mechanisms; earthquake quantification, source characteristics, seismotectonics and seismic hazards; digital seismographs, Earthquake statistics, wave propagation in elastic media, quantifying earthquake source from seismological data. Elements of Seismic Tomography.**Potential and Time Varying Fields**- Scalar and vector potential fields; Laplace, Maxwell and Helmholtz equations for solution of different types of boundary value problems in Cartesian, cylindrical and spherical polar coordinates; Green’s theorem; Image theory; integral equations in potential and time- varying field theory.**Gravity Methods**- Absolute and relative gravity measurements; Gravimeters; Land, airborne, shipborne and bore-hole gravity surveys; Tensorial Gravity sensors and surveys; various corrections for gravity data reduction – free air, Bouguer and isostatic anomalies; density estimates of rocks; regional and residual gravity separation; principle of equivalent stratum; data enhancement techniques, upward and downward continuation; derivative maps, wavelength filtering; preparation and analysis of gravity maps; gravity anomalies and their interpretation – anomalies due to geometrical and irregular shaped bodies, depth rules, calculation of mass.**Magnetic Methods**- Elements of Earth’s magnetic field, units of measurement, magnetic susceptibility of rocks and measurements, magnetometers and magnetic gradiometers, Land, airborne and marine magnetic and magnetic gradiometer surveys, Various corrections applied to magnetic data, IGRF, Reduction to Pole transformation, Poisson’s relation of gravity and magnetic potential field, preparation of magnetic maps, upward and downward continuation, magnetic anomalies due to geometrical and irregular shaped bodies; Image processing concepts in processing of magnetic anomaly maps; Depth rules; Interpretation of processed magnetic anomaly data; derivative, analytic signal and Euler Depth Solutions. Applications of gravity and magnetic methods for mineral and oil exploration.**Electrical Methods**- Conduction of electricity through rocks, electrical conductivities of metals, non- metals, rock forming minerals and different rocks, concepts of D.C. resistivity measurement and depth of investigation; Apparent Resistivity and Apparent Chargeability, Concept of Negative Apparent Resistivity and Negative Apparent Chargeability; Theory of Reciprocity, Sounding and Profiling, Various electrode arrangements, application of linear filter theory, Sounding curves over multi-layered earth, Dar-Zarrouk parameters, reduction of layers, Triangle of anisotropy, interpretation of resistivity field data, Principles of equivalence and suppression, self-potential method and its origin; Electrical Resistivity Tomography (ERT); , Induced polarization, time and frequency domain IP measurements; interpretation and applications of SP, resistivity and IP data sets for ground-water exploration, mineral exploration, environmental and engineering applications.**Electromagnetic Methods**- Geo-electromagnetic spectrum; Biot Savart’s Law; Maxwell’s Equation, Helmholtz Equation, Basic concept of EM induction in the earth, Skin-depth, elliptic polarization, in- phase and quadrature components, phasor diagrams; Response function and response parameters; Ground and Airborne Methods, measurements in different source-receiver configurations; Earth’s natural electromagnetic methods-tellurics, geomagnetic depth sounding and magnetotellurics; Electromagnetic profiling and Sounding, Time domain EM method; EM scale modeling, processing of EM data and interpretation; Ground Penetrating Radar (GPR) Methods; Effect of conducting overburden; Geological applications including groundwater, mineral environmental and hydrocarbon exploration.**Seismic methods**- Elastic properties of earth materials; Reflection, refraction and CDP surveys; land and marine seismic sources, generation and propagation of elastic waves, velocity – depth models, geophones, hydrophones, digital recording systems, digital formats, field layouts, seismic noise and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D, 3D and 4D seismic data acquisition, processing and interpretation; CDP stacking charts, binning, filtering, static and dynamic corrections, Digital seismic data processing, seismic deconvolution and migration methods, attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismics, VSP, AVO, multi-component seismics and seismic interferometry. Reservoir geophysics- Rock Physics and Petrophysics. Geophysical Survey Design.**Geophysical signal processing**- sampling theorem, Nyquist frequency, aliasing, Fourier series, periodic waveform, Fourier and Hilbert transform, Z-transform and wavelet transform; power spectrum, delta function, autocorrelation, cross correlation, convolution, deconvolution, principles of digital filters, windows, poles and zeros.**Geophysical Well Logging**- Principles and techniques of geophysical well-logging, SP, resistivity, induction, gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic resonance- longitudinal and transverse relaxation, CPMG sequence, porosity characterization, cement bond logging, micro-logs. Pulsed Neutron Devices and Spectroscopy; Multi-Array and Triaxial Induction Devices; Quantitative evaluation of formations from well logs; Logging while drilling; High angle and horizontal wells; Clay Quantification; Lithology and Porosity Estimation; Saturation and Permeability Estimation; application of borehole geophysics in groundwater, mineral and oil exploration.**Radioactive Methods**- Prospecting and assaying of mineral (radioactive and non-radioactive) deposits, half-life, decay constant, radioactive equilibrium, G M counter, scintillation detector, semiconductor devices, application of radiometric for exploration, assaying and radioactive waste disposal.**Geophysical Inversion**- Basic concepts of forward and inverse problems, Ill-posedness of inverse problems, condition number, non-uniqueness and stability of solutions; L1, L2 and Lp norms, overdetermined, underdetermined and mixed determined inverse problems, quasi- linear and non-linear methods including Tikhonov’s regularization method, Singular Value Decomposition, Backus-Gilbert method, simulated annealing, genetic algorithms, swarm intelligence, machine learning and artificial neural networks. Statistics of misfit and likelihood, Bayesian construction of posterior probabilities, sparsity promoting L1 optimization. Ambiguity and uncertainty in geophysical interpretation.

**GATE ****Mathematics**** (****MA****) Syllabus**

**GATE Mathematics Syllabus 2022 **

**GATE Mathematics Syllabus 2022**

There are 11 chapters in the GATE Mathematics Syllabus. Each chapter has many subtopics. The complete syllabus of Mathematics paper is given below.

**Section 1: Calculus**

**Section 1: Calculus**

Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers;

Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

**Section 2: Linear Algebra**

**Section 2: Linear Algebra**

Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial

Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric

Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.

**Section 3: Real Analysis**

**Section 3: Real Analysis**

Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence, Ascoli-Arzela theorem;Weierstrass approximation theorem; contraction mapping principle

Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem.

**Section 4: Complex Analysis**

**Section 4: Complex Analysis**

Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula

Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence

Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.

**Section 5: Ordinary Differential equations**

**Section 5: Ordinary Differential equations**

First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients

Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first order ordinary differential equations

Sturm's oscillation and separation theorems, Sturm-Liouville eigenvalue problems, Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions.

**Section 6: Algebra**

**Section 6: Algebra**

Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups,Group action,Sylow’s theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains

Principal ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.

**Section 7: Functional Analysis**

**Section 7: Functional Analysis**

Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces

Hilbert spaces, orthonormal bases, projection theorem,Riesz representation theorem, spectral theorem for compact self-adjoint operators.

**Section 8: Numerical Analysis**

**Section 8: Numerical Analysis**

Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson method, fixed point iteration; Interpolation

Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error.

Numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2.

**Section 9: Partial Differential Equations**

**Section 9: Partial Differential Equations**

Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable

Wave equation: Cauchy problem and d'Alembert formula, domains of dependence and influence, non-homogeneous wave equation; Heat equation: Cauchy problem; Laplace and Fourier transform methods.

**Section 10: Topology**

**Section 10: Topology**

Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

**Section 11: Linear Programming**

**Section 11: Linear Programming**

Linear programming models, convex sets, extreme points;Basic feasible solution,graphical method, simplex method, two phase methods, revised simplex method ; Infeasible and unbounded linear programming models, alternate optima; Duality theory, weak duality and strong duality; Balanced and unbalanced transportation problems

Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, Vogel’s approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method.

**GATE M****ining Engineering**** (M****N****) Syllabus**

**GATE Syllabus for Mining Engineering (MN) 2022**

**GATE Syllabus for Mining Engineering (MN) 2022**

**Section 1 – Engineering Mathematics**

**Section 1 – Engineering Mathematics**

**Linear Algebra:**Matrix algebra, systems of linear equations, consistency and rank, Eigen values and Eigen vectors.**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 nonlinear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis.

**Section 2: Mining Geology, Mine Development and Surveying**

**Section 2: Mining Geology, Mine Development and Surveying**

**Mining Geology:**Minerals, Rocks and their Origin, Classification, Ore Genesis; Structural Geology.**Mine Development:**Methods of access to deposits; Underground drivages; Drilling methods and machines; Explosives and energetics, blasting devices, blast design practices; Rock-Tool Interaction applicable to mechanical cutting systems and their selection.**Mine Surveying:**Levels and levelling, theodolite, tacheometry, triangulation; Contouring; Errors and adjustments; Correlation; Underground surveying; Curves; Photogrammetry; EDM, Total Station, GPS, Basics of GIS and remote sensing.

**Section 3: Geomechanics and Ground Control**

**Section 3: Geomechanics and Ground Control**

**Engineering Mechanics:**Equivalent force systems; Equations of equilibrium; Two dimensional frames and trusses; Free body diagrams; Friction forces; Particle kinematics and dynamics; Beam analysis.**Geomechanics:**Geo-technical properties of rocks; Rock mass classification; Instrumentation and in-situ stress measurement techniques; Theories of rock failure; Ground vibrations; Stress distribution around mine openings;

Subsidence; Slope stability.**Ground Control:**Design of pillars; Roof supporting systems; Mine filling. Strata Control and Monitoring Plan.

**Section 4: Mining Methods and Machinery**

**Section 4: Mining Methods and Machinery**

**Mining Methods:**Surface mining: layout, development, loading, transportation and mechanization, continuous surface mining systems; highwall mining; Underground coal mining: bord and pillar systems, room and pillar

mining, longwall mining, thick seam mining methods, Underground metal mining: open, supported and caved stopping methods, stope mechanization, ore handling systems.**Mining Machinery:**Generation and transmission of mechanical, hydraulic and pneumatic power; Materials handling: wire ropes, haulages, conveyors, face and development machinery, hoisting systems, pumps;comminution methods and machinery.

**Section 5: Surface Environment, Mine Ventilation, and Underground Hazards**

**Section 5: Surface Environment, Mine Ventilation, and Underground Hazards**

**Surface Environment:**Air, water and soil pollution: Standards of quality, causes and dispersion of contamination and control; Noise pollution and control; Land reclamation; EIA.**Mine Ventilation:**Underground atmosphere; Heat load sources and thermal environment,; air cooling; Mechanics of airflow, distribution, natural and mechanical ventilation; Mine fans and their usage; Auxiliary ventilation; Ventilation survey and planning; Ventilation networks.**Underground Hazards:**Mine Gases, Methane drainage; Underground hazards from fires, explosions, dust and inundation; Rescue apparatus and practices; Safety management plan; Accident data analysis; assessment; Mine lighting; Mine legislation; Occupational health and safety.

**Section 6: Mine Economics, Mine Planning, Systems Engineering**

**Section 6: Mine Economics, Mine Planning, Systems Engineering**

**Mineral Economics:**Mineral resource classification; Discounted cash flow analysis; Mine valuation; Mineral taxation.**Mine Planning:**Sampling methods, practices and interpretation; Reserve estimation techniques: Basics of geostatistics and quality control; Optimization of facility location; Mine planning and its components, Determination of mine size and mine life; Ultimate pit configuration and its determination, Optimum mill cut-off grade and its determination, Stope planning, Design of haul road, Selection of mining system vis-à-vis equipment

system.**Systems Engineering:**Concepts of reliability; Reliability of simple systems; Maintainability and availability; Linear programming, transportation and assignment problems; Network analysis; Inventory models; Queuing theory; Decision trees.

**Section 7 - General Aptitude **

**Section 7 - General Aptitude**

**Verbal Ability****:**English grammar; Sentence completion, Instructions; Verbal analogies, Word groups; Critical reasoning, Verbal deduction.**Numerical Ability****:**Numerical computation; Numerical reasoning; Numerical estimation; Data interpretation.

**GATE ****Architecture & Marine ****Engineering (N****M****) Syllabus**

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Important Topics**

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Important Topics**

GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022 comprises five sections - Engineering Mathematics, Applied Mechanics and Structures, Fluid Mechanics and Marine Hydrodynamics, Naval Architecture and Ocean Engineering, Thermodynamics and Marine Engineering. The topics included in each section are given below.

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 1 (Engineering Mathematics)**

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 1 (Engineering Mathematics)**

**Engineering Mathematics :**Determinants and matrices, Systems of linear equations, Eigenvalues and eigenvectors. Functions, gradient, divergence, curl, chain rules, partial derivatives, directional derivatives, definite and indefinite integrals, line surface and volume integrals, theorems of Stokes, Gauss and Green. Linear, non-linear, first and higher order ordinary and partial differential equations, separation of variables. Laplace transformation, analytical functions of complex variables, Fourier series, numerical methods for differentiation and integration, complex analysis, probability and statistics

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 2 (Applied Machines and Structures)**

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 2 (Applied Machines and Structures)**

**Engineering Mechanics :**Free-body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations.**Mechanics of Materials :**Stress and strain, elastic constants, Poisson’s ratio; Mohr’s circle for plane stress and plane strain; shear force and bending moment diagrams; bending and shear stresses; torsion; Euler’s theory of columns; energy methods; theories and failure, material testing methods.**Vibrations :**Free and forced vibration of damped and undamped systems, single and multi DOF systems.**Machine Design :**Design for static and dynamic loading; Design of machine elements such as shafts, gears, rolling and sliding contact bearings; Joining technics such as bolting, riveting and welding.

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 3 (Fluid Mechanics and Marine Hydrodynamics)**

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 3 (Fluid Mechanics and Marine Hydrodynamics)**

**Fluid Mechanics :**Fluid properties; fluid statics, stability of floating bodies; Conservation laws: Mass, momentum and energy (Integral and differential form); Dimensional analysis and dynamic similarity; sources, sinks, doublets, line vortex and their superposition; Stoke’s integral theorem. Generalised Bernoulli’s equation, sources, sinks, dipole, Flow with circulation, potential flow with rotational symmetry, hydrodynamical lift, Kutta-Joukowski theorem. Vortex motion- Fundamental concepts, vortex analogy to Biot-Savart’s law, straight parallel vortex filaments, vortex sheets. Viscous flowNavier-Stokes equations, Couette flow, Plane poiseuille flow. Equation of continuity, Euler‘s equation, Bernoulli‘s equation, Viscous flow of incompressible fluids, elementary turbulent flow, boundary layer, flow through pipes**Boundary layer theory :**Prandtl’s boundary layer equations, criterion for separation, Blasius solution, Skin friction, displacement thickness, momentum thickness, Turbulent boundary layer, Boundary layer control. Airfoils- Lift, drag, circulation, pressure distribution-theory of thin aerofoils, wings of infinite and finite span, circulation distribution, Cavitation**Hydrodynamics :**Vorticity and Kelvin’s theorem, Potential flow theory, Sources, Sinks and Doublets, hydrodynamic forces in potential flow, D’Alembert’s paradox, added-mass, slender-body theory, hydrodynamic model testing, scaling laws, application of potential theory to surface waves, energy transport, wave/body forces, linearised theory of lifting surfaces.

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 4 (Naval Architecture and Ocean Engineering)**

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 4 (Naval Architecture and Ocean Engineering)**

**Ship geometry and physical fundamentals :**Archimedes’ principle, buoyancy and weight of ship, laws of flotation, heel and trim, stable and unstable equilibrium of ships, importance of streamlined hull shape, ship main particulars, hydrostatic calculations,**Stability and trim of Ships :**Statical stability at small angles of heel, Inclining experiment. Shift of centre of gravity due to addition or removal of mass, transverse movement of mass and effect, Free surface effect, Effect of suspended mass, Stability at large angles of heel, angle of loll, curves of statical stability, dynamical stability, Probabilistic and deterministic Damage Stability Different Characteristic curves of dynamic stability. Floodable length calculations and curves. Loss of stability due to grounding, docking stability.**Resistance & Propulsion :**Components of ship resistance, form factor, hull roughness, model testing and ship resistance prediction methods, tank wall effects, determination of ship resistance different series test results, resistance of advanced vehicles, appendage and added resistance. Geometry of screw propeller, propeller theories, hull-propeller interactions, different propulsive efficiency definitions. Propeller cavitation and effects. Propeller design and series. Open water and selfpropulsion model tests. Different types of propellers and their working principles. Propeller material, strength and manufacturing.Unconventional propellers**Ship Manoeuvring and Motions :**Ship path keeping and changing, equations of motion, linearised equations and control fixed stability indexes, model tests. Stability and control in the horizontal and vertical planes – definitive manoeuvres and sea trials. Rudder hydrodynamics, design and operation. Influence of propeller, hull, appendages etc. on rudder performance. Experimental methods for the determination of hydrodynamic derivatives.**Ocean waves :**Regular, irregular, trochoidal. Wave spectrum, encounter frequency. Types of ship motions, coupled and non-coupled motions, equations of motion. Dynamic effects of ship motion in seaway. Different ship motion stabilisers – passive and active. Different numerical and experimental methods to determine ship motions – strip theory, BEM, FEM. Seakeeping features of high performance marine vehicles.**Ship Structures & Strength :**Shipbuilding materials, joining techniques, ship structural and framing systems – bottom, side, deck, bulkhead, end structures, and structural connections. Primary and secondary structural members, superstructure, hatch covers, machinery foundations, cargo handling systems and support structures Loads acting on ships in seaway, longitudinal and transverse strength considerations and estimation methods. Strength of hull girder, stiffened plate analysis, torsion of hull girder, deformation and stresses, local strength analysis; Reliability analysis and ultimate strength of hull girder, structural vibrations, fatigue and fracture.**Physical Oceanography :**Physical properties of seawater, Different types of ocean waves - tides and wind waves, and their importance. Offshore Structures: Fixed offshore platforms - Jackets, Gravity platforms; Floating platforms - semi-submersibles, jack-ups, TLPs, FPSOs; Mooring, station keeping. Port and Harbour Engineering: Ports and Harbours, Port structures - Jetties, Dolphins, Liquid berths, Dredging, Navigation

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 5 (Thermodynamics and Marine Engineering)**

**GATE Naval Architecture & Marine Engineering (NM) Syllabus 2022: Section 5 (Thermodynamics and Marine Engineering)**

**Thermodynamics :**First law of thermodynamics - Closed system undergoing a cycle; closed system undergoing a change of state; Internal energy of a system; Expansion work; Process using ideal gas - constant pressure, constant volume, isothermal; adiabatic and polytropic process -work done and heat added in different process; First law applied to one - dimensional steady flow process, flow energy, steady flow energy equation (ID). Second law of Thermodynamics - Different statements; Reversible and irreversible process; Corollaries of second law - Absolute temperature scale; Carnot cycle - Carnot engine, refrigerator and heat pump. Clausius inequality and definition of entropy, change of entropy of an ideal gas; Gas power cycles and I.C.Engines; Gas power cycles: Carnot cycle, Brayton cycle, Erricson cycle, Sterling cycle etc.; Air standard cycles- Otto- Diesel, Dual and Joule cycle; Evaluation of thermal efficiency and mean effective pressure; Internal Combustion engine - Classification of I.C. engines -Principle of operation of spark Ignition and Compression Ignition engines both two stroke and four stroke; Stages of combustion in S.I. and C.I. engines Knocking and detonation- factors controlling knock and detonation, methods of preventing Knocking and detonation; Refrigeration - principle of operation of Simple vapour compression system, Comparison with vapour compression systems; Air conditioning principles - Sensible heating and cooling, Humidification and dehumidification, Cooling and humidification, Cooling and dehumidification- Heating and humidification, Heating and dehumidification, Adiabatic mixing of air streams –cooling and heating load calculation.**Marine Diesel Engines :**General engine principles, Low speed and medium speed diesel engines, Two and Four stroke engines, Scavenging and turbocharging, Fuel oil system, Lubricating oil systems, cooling systems, torque and power measurement, Starting air systems and reversing systems, controls and safety devices, Couplings and Gearboxes, Specific Fuel Consumption. Waste heat recovery system, MARPOL regulations and Energy Efficiency Design Index (EEDI), Ship Energy Efficiency Management Plan (SEEMP).