**Mathematical Physics:**

- Vectors: Vector operators like DCI & grad, div. & curl. Surface and volume integrals – Theorems of Gauss, Stokes, & Green.
- Matrices : Quality, addition and subtraction, multiplication of matrices, inverse of a matrices, similarity and unitary transformation Characteristic equation of a matrix Eigen values – Eigen vectors Square, diagonal, unit, symmetric, and skewmatrix – Hermitian and unitary matrix.
- Tensors: Tensors of any order –Transformation relation Covariant & Contra-variant tensors-Christoffel symbols.
- Fourier Analysis: Trigonometric Fourier series – Evaluation of coefficients – Exponential Fourier series.

** Classical Mechanics**

- General Theorems of mechanics of mass points – Principals of Virtual work – De-Alember’s principle – Lagrange’s equation of motion – Hamilton’s principle – Hamilton’s Equation of motion – Principle of lest action – Canonical transformations = Poisson bracket. Rigid body motion – Euler’s theorem on rigid body motion – moment of inertia-tensor – heavy Symmetrical top.

** III. Electromagnetic Theory:**

- Generalisation of Ampere’s Law – Derivation of Maxwells equation – Pointing theorem – Transverse nature of Electromagnetic waves – propagation & Conducting and non-conducting media – metallic reflection – Propagation of light in crystalline media – Fresnel’s Theory of double refraction.

** IV. Special Theory of Relativity:**

- Galilean Transformation – Newtonians Relativity – Michelson’s Morley Experiment – Postulates of special theory of relativity Lorentz’s transformation – Relativistic particle mechanics Equivalence of mass & energy – Covariance of Maxwell’s equation.

**V. Statistical Mechanics:**

- Generalised coordinates & momenta-phase space, Liowellies Theorems – Maxwell Boltzman statistics – Distribution of velocities and energy in ideal gas – Equipartition of energy – Vibrational, rotational, and electronic partition functions for diatomic gas – specific heats of gas – Ortho and para hydrogen’s – Bose Einstein & Fermi Dirac statistics – Bose Einstein gas and application to radiation – liquid helium – Free electrons in metals.

**VI. Quantum Mechanics:**

- Shordinger’s wave equation – Born interpretation of wave functions – Expectations values of dynamical variables – Ehrenfests’ Theorem – Uncertainity Principle – Application of Shordinger’s equation to (a) One dimensional squarewell potential (b) Simple harmonic Oscillator (c) Hydrogen atom. Perturbation theory – First order and second order theories for non degenerate & degenerate systems – Application to normal helium atom – Time dependent & time independent perturbation theory – Application for each. Relativistic quantum mechanics – Klenn Garnian equation Dirac’s equation Solution for a free particle meaning of negative energy states – Quantum theory of scattering – Born approximation.

**VII. Electronics: Vacuum:**

- Tubes and semiconductor diodes – Principle and working of rectifier and power supply – Ripple factor L and T section filters voltage stabilisation in power supplies characteristics of triode and pentode and junction transistors their static characteristics – Voltage amplifiers – R.C. coupled amplifiers – and its frequency response Negative feed back in amplifiers – Advantages of – Ve feed back – condition for sinosoidal oscillations in transistor circuits Hartley and Colpitts oscillators – multi vibrators A stable – Monostable and bi-stable type – Pulse generator – Saw tooth voltage generator Cathode – ray oscilloscope (C.R.O).

** VIII. Solid State Physics:**

- Crystallography – Classification of solids – Point group and space group – Crystal systems – Specification of planes and directions – Elements of X-ray diffraction – Various crystal bindings – Metallic, ionic, co-valent molecular and hydrogen bonded crystals – Band theory of solids – motion of electrons in periodic potential Block’s theorem Kronig’s penny model – energy bands – Brillouin zones – distinction between insulators – Metals and Semi-conductors on band theory.

**IX. Nuclear Physics:**

- Radioactivity, Chain dis-integration, transient and secular equilibrium – Age of rocks and Radio carbon dating – alpha decay or Gamow’s theory – Beta decay and nutrino Interaction of gamma rays with matter – Selection rules – nuclear models – Liquid drop model – semi empirical mass formula – criteria for stability against spontaneous decay – Shell model – nuclear detectors – Ionisation – Chambers – G.M. counters – Proportional counters – bubble and spark chambers – Semi-conductor detectors.

**X.Spectroscopy**

- Bohr – Sommerfield theory of Hydrogen atoms – Space quantisation – fine structure of spectral lines – Alkali spectra – Zeeman effect Vector atom model of one electron system – Paschen – Back effect – Stark effect in Hydrogen atoms – Band spectra – Types of band spectra-I.R. and Raman effect. Isotope effect – Franck – Candon Principle.

**SCIENCE AND TECHNOLOGY**

- a) General Science and Technology.

- b) Role and impact of science and Technology on India’s development.

(Questions will cover general appreciation and understanding of matters of everyday observation and experience as may be expected of a well-educated person who has not made a special study of science and technology disciplines).

**INDIAN HISTORY AND CULTURE**

- a) Modern Indian History from the 19th century to the present.

- b) Nationalist Movement and Constitutional development.

- c) Indian Culture and Heritage including architecture, Fine Arts, Dance Forms, Music, Paintings, Folk Arts and performing arts.

d) History of Andhradesa Society, Culture, Geography, and Economic Development.

**INDIAN POLITY**

- General and broad understanding of the structural (institutions) and functional (processes) aspects of Indian Political System. 04. INDIAN ECONOMY AND GEOGRAPHY OF INDIA: a) Structure of National Economy. b) Economic Development (including planning) since independence. c) Economic Reforms. d) Physical, Economic and Social Geography of India. 05. CURRENT EVENTS: Current Events of Regional, National and International importance. 06. General Mental Ability (reasoning and analytical abilities)

**Real Analysis**

- Continuity and differentiability of real functions.; Uniform continuity, Sequences and series of functions. Uniform convergence. Functions of bounded variation. Riemann integration.

** Complex Analysis**

Analytic functions. Cauchy’s theorem Cauchy’s integral formula. Laurent’s series. Singularities. Theory of residues – Conformal mapping.

** Abstract Algebra: **

- Groups – Sub-groups – normal subgroups Quotient group Homomorphism – Fundamental theorem of Homomorphism, Permutation groups: Cayley’s theorem – Rings – Subrings – Ideals – Fields – Polynomial rings.

** Linear Algebra **

Vector spacers – Basis and dimension – Linear transformations – Matrices – Characteristic roots and characteristic vectors – systems of linear equations – Canonicl forms – Cayley – Hamilton theorem.

** Differential Equations**

First order ordinary differential equations (O.D.E) and their solutions – Singular solutions. Initial value problems for first order O.D.E. The general theory of homogeneous and nonhomogeneous linear differential equations, variation of parameters. Elements of first-order partial differential equations (PDE). Co-ordinate Geometry of Three Dimensions: The Plane – The straight-line – Sphere and cone.

Detailed Study of literary age (19th Century) viz.,

The period of English Literature from 1798 to 1900 with special reference to the works of the major writers including Words worth, Coleridge, Byron, Keats, Shelley, Lamb, Hazlitt, Thackeray, Dickens, Tennyson, Browning, Arnold George Eliot, Calyle and Ruskin.

Study of the following Texts:

William Shakespeare | ‘Macbeth’, ‘Hamlet’, ‘Julius Vrsdst’, ‘Tempest’ |

John Milton | ‘Paradise Lost’, -Books I & II |

Alexander Pope | ‘The Rape of the Lock |

William Wordsworth | ‘The Immorality Ode’, ‘The Tin Tern Abbey’ |

John Keats | ‘Ode to a Nightingale’ |

P.B. Shelley | ‘Ode to the West Wing’ |

Jane Austen | ‘Pride and Prejudice’. |

Charles Dickens | ‘A Tale of Two Cities’ |

Thomas Hardy | ‘The mayor of Casterbridge’ |

W.B. Yeats | “Byzantium”, ‘The Second Coming’ |

T.S. Eliot | ‘The Waste Land’. |

D.H. Lawrence | ‘Sons and Lovers’ |

Mulk Raj Anand | ‘The Big heart’ |

R.K. Narayan | ‘The Man-eater of Malgudi’ |

** ANALYSIS OF STRUCTURES**

- Sending stresses and shear stresses in beams, Deflection and slope of beams; Combined bending and direct stresses; axially and eccentrically loaded columns, Close-Coiled and open-coiled; helical springs under axial load and axial twist; carriage springs, Analysis thin and thick cylinders; compound cylinders, Analysis of statically determinate plane trusses; method of joints and method of sections. Analysis of statically indeterminate beams; proposed cantilevers, fixed beams, and continuous beams. Strain energy method, the slope-deflection method, moment distribution method and Kaini’s method of analysis of indeterminate structures.Influence lines and moving loads on beams and simple bridge trusses.

** STRUCTURAL DESIGN**

- Reinforced concrete, concrete technology, R.C.C. Design, working stress method and limit state method,Design of beams, Design of one-way and two-way slabs, design of axially loaded columns, design of continuous beams and slabs; Design of wall footings and isolated footings, combined footings, raft foundations, and retaining walls by limit state method, water tanks, Deck-slab and T-beam bridges by working stress method. Structural Steel – design of revetted and welded joints, the design of tension members, Compression members, simple and compound beams. Design of plate girders, crane girders, and roof trusses. Elements of pre-stressed concrete.

** FLUID MECHANICS AND HYDRAULIC MACHINES**

- Fluid properties; fluid static’s; fluid-flow concepts; Laminar and turbulent flow; steady and unsteady-flow, uniform and non-uniform flow; Fundamental EQUATIONS; CONTINUITY EQUATION; Euler’s equation of motion, Bernoulli’s equation, Analysis of liquid jets; flow through orifice and mouthpieces,radial flow, flow along a curved path; Momentum equation and applications; Moment of Momentum equation. Dimensional analysis and similitude; Viscous flow-laminar flow through circular pipes; velocity distribution in laminar flow.Turbulent flow in pipes, velocity distribution in turbulent flow; Flow measurement – pressure moment,

velocity measurement and discharge measurement, venturi meter, Orifice, meter, notches, and weins.Hydraulic machines; Turbines and pumps; basic equations; Orifice, performance, selection, specific speed.

** WATER RESOURCES ENGINEERING**

- Steady flow through open channels. Uniform flow in channels; Chezy and Manning’s formulae. Specific energy and critical depth. Hydraulic jump – Momentum equation for a hydraulic jump. Surface Water Hydrology, Hydrologic cycle, hydrologic data- measurement of precipitation, evaporation, transpiration, and

infiltration. Runoff, determination of run-off. Steam gauging; floor-Studies, Hydrograph and unit hydrograph, flood routing. Groundwater resources, Darcy’s law, Dupuits equation, the yield of wells, recuperation test.

** SURVEYING**

- Chain surveying; compass surveying, plane table surveying; leveling and contouring, Minor instruments, Areas, and Volumes; Theodolite surveying and traversing; Tachometry; Curve ranging; setting out works.Principles and uses of triangulation, hydrographic surveying, Arial photogrammetry and photo interpretation,

remote sensing, and electromagnetic distance measurement.

** GEOTECHNICAL ENGINEERING**

- Physical properties of soils; identification and classification of soils; permeability and seepage; consolidation, shearing strength of soil; stability of earth slopes; site investigation and subsoil exploration. Stress distribution in soil; soil; compaction; lateral earth pressure and retaining walls; bearing capacity and shallow foundations; pile foundations; well foundations; Machine foundations.

** TRANSPORTATION ENGINEERING**

- Highway Engineering; classification of roads; highway alignment and surveys; geometric design of highways, elements of traffic engineering; highway materials and testing; elements of pavement design, construction, and maintenance of earth gravel, W.B.M., bituminous and concrete roads; highway drainage. Railway Engineering, engineering surveys for a new railway route, gauge, and gauge problem; track components; ballast; sleepers; rails anrail fastenings, Station and station yards, requirements, and requirement for station yards, signaling, and interlocking. Elements of cross drainage works; causeways, culverts, bridges

** ENVIRONMENTAL ENGINEERING:**

- Water supply engineering; sources of water supply, conveyance of water, distribution systems; quality of water; treatment of water, filtration, disinfection; methods of water treatment. Sanitary engineering, sewerage, and sewage disposal; house fittings, the design of sewers, characteristics of sewage, primary and secondary treatment of sewage’ methods of disposal of sewage.

- Network analysis, Topology, Tree Tieset outset, first and Second order Circuits.Steady State and Transient response, Sinusoidal Steady-State Analysis. Series and parallel Resonance, Network Theorems, Laplace Transforms, Fourier series, Fourier Transforms -Applications, Two-port.Network Parameters, Interconnection of two ports, Image Impedance, Image Parameters. Filters – constant K and M derived sections. Electronics Devices – Diodes, Transistors, FET biasing, and characteristics, Frequency, Response, Amplifier circuits.Electro Magnetic Theory – Maxell’s Equations. Coulomb’s law, Amper’s law, Faraday’s law, Poynting Energy Theorem, Stoke’s theorem, uniform plane waves.Transmission Line Theory – Standing waves & Travelling waves, Reflection, VSWR.
- Feedback Amplifiers and oscillator Circuits Wave Shaping circuits, Logic Gates, Boolean Theorems, Adders & Subtractors. Antennas & Propagation – Radiation Principle, Antenna parameters.Definitions. Directional Antennas, Linear Antenna Arrays, Broadside & End fire Arrays, Gain, Directivity, Radiation pattern.Ground Wave, SkyWave, Ionosphere Propagation, Guided Waves, Rectangular Wave-Guide Analysis, Microwave Circuits, and Components.Microwave Tubes, Klystron, Magnetron, and TWT. Modulation Techniques – AM, FM, PM. Channel capacity, Noise, AM, FM, Transmitters, Radio Receivers. TV and Satellite Communication – Principles Radar Equation and Applications of Radar Computer Programming, FORTRAN, BASIC, PASCAL, Are Programming languages.

**ELECTRIC CIRCUITS, FIELDS & MEASUREMENTS**

- Network elements – Ohm’s law and Kirchoff’s laws – formation of mesh and nodal equations – topological description of networks – response of R, L and C elements to arbitrary excitations – Laplace transform method of analyzing networks. Network theorems – superposition, Thevenin’s Norton’s theorems – Maximum power transfer the reciprocity theorem – applications – two port parameters – Z, Y, ABCD, H parameters – their relationships. A.C. Circuits – single phase circuits – J-notation – calculations – resonance – Polyphase – circuits – measurements of polyphase power. Electromagnetic theory – general relations in static fields – potential gradient and field intensity – flux density – Gauss’s law – Poisson and Laplace equations – relations in electromagnetic fields – ampere’s law – flux and flux density – divergence and curl – vector magnetic potential. Electrical measurements – Types of measuring instruments – Principles of operation – an extension of ranges – instrument transformers.

**CONTROL SYSTEMS, COMPUTATION, AND ELECTRONICS**

- Control systems – Types of servomechanisms – equations and models of linear systems – block diagrams – time response of second-order systems – stability criteria – root locus technique – frequency response – Nyquist criterion – Bode plots. Elements of computation: Digital systems – flow charts and algorithms – FORTRAN – types of statements – logical expressions – Assignment statements – program structure – Scientific and Engineering applications. Electronics: Solid-state devices and circuits – small signal amplifier design – feedback amplifiers – Oscillators – FETS – Thyristors.

**ELECTRICAL MACHINES:**

- Principles of Electromechanical Energy Conversion: Basic ideas of production of torque – concepts of generation of voltages – formulae for voltage and torque production. Three phase induction motors: The revolving field theory – Principles of operation of induction motor – torque equation – Computation of performance – torque-speed characteristics – motor starters – conventional and thyristor controllers for speed control of induction motors. Single phase motors: Revolving field theory – types of single-phase motors – equivalent circuits – speed control – applications. Synchronous machines: Generation of 3-phase voltages – types of synchronous machines – equivalent circuit – experimental determination of reactances – voltage regulation and efficiency – parallel operation – transient and subtransient reactances – synchronous motors – theory of operation – -phase of the diagram – equivalent circuit – performance and power factor control – applications. Special machines: Two-phase servomotors – stepper motors – methods of operation – metadyne and amplidyne – operating characteristics and applications. D.C. Machines and Transformers.

**POWER SYSTEMS**

- Generation: Methods of power generation – steam, hydro, nuclear, diesel – a selection of the site for each – general layout of each type – a function of each component – the economics of different types – base and peak load stations – pumped stations – simple calculations in hydro station design. Transmission: A.C. Vs. D.C. transmission – criteria for selection of voltages – transmission line parameters – G.M.D. and G.M.R – concepts for short, medium and long lines – line calculations – A.B.C and D Constance – load flow analysis – surge impedance loading. Corona and insulators: production of corona – disruptive and visual corona – corona loss – methods to avoid corona – types of insulators – string efficiency. Fault analysis: Per unit representation: fault analysis – Symmetrical and unsymmetrical faults – application of symmetrical components – reactors. Protection: Switchgear – methods of arc extinction – classification of circuit breakers – definitions – calculations in switchgear – testing of circuit breakers – Relaying principles – primary and back up relaying – definitions – operation of different types of relays – applications to line, transformer and generator protection – protection of lines and equipment against voltage surges – travelling wave theory. Utilisation: Industrial drives – motors for various applications – braking – methods of heating and welding – welding transformer – Economics and other aspects of track electrification.

**FLUID MECHANICS:**

- Fluid Properties, fluid static’s, Kinematics and Dynamics, Euler’s equation, Bernoulli’s energy equation, the flow of ideal fluids, Viscous incompressible flows – laminar flow, boundary layer, basic features of turbulent flow, flow through pipes, fluid machinery, Specific speed and classification of fluid machines. Performance and operation of pumps, impulse and reaction turbines, velocity triangles and degree of reaction.

**THERMODYNAMICS**

- Thermodynamic systems, measurements of temperature work, heat and internal energy. First law of thermodynamics, ideal gas equation Air standard cycles, Carnot, Otto, Diesel, dual and joule cycle. Energy and Enthalpy. The second law of Thermodynamics. Available and Unavailable energies. Reversible and irreversible processes. Psychrometry, Properties of pure substances.

**MATERIAL SCIENCE**

- Structure of metal and alloys, Binding in solids. Imperfections of metals and in crystals, fracture, creep, fatigue and corrosion. Phase Rule, phase transformation diagrams and lever rule.

**ENGINEERING MECHANICS AND STRENGTH OF MATERIALS**

- Equivalent force systems, free body concepts and equations of equilibrium, frictional forces. Kinematics and dynamics of rigid bodies. Stress and strain, elastic limit, yield point and ultimate stress, shear force and bending moment diagrams for beams. Calculation of stress slope and deflection in beams, theories of failure, torsion of a circular shaft, thin cylinders, the equivalent bending moment for solid and hollow shafts.

**MANUFACTURING PROCESSES**

- Classification of manufacturing processes. Fundamentals of casting. Classification of the casting process. Sand casting – patterns, molding, melting and pouring solidification, cleaning and finishing casting defects. Metal forming – hot and cold working, forging, rolling extrusion, wire and tube drawing, deep drawing, blanking, and stamping processes. Fundamentals of the welding arc and gas welding, brazing and soldering, heat treatment – appealing – normalizing, hardening and tempering.

**APPLIED THERMODYNAMICS**

- Internal combustion engines classification, working, and performance of C.I. and S.I. engines combustion process in I.C. Engines Rating of fuels, pre-ignition and knocking in I.C. Engines, Carburation and injection, Reciprocating air compressors – Single and, multi-stage compressors, inter-cooling, volumetric efficiency. Rotary Compressors – fans blowers and compressors Axial and Centrifugal compressors – merits and demerits. Boilers and condensers – types of boilers and condensers, calculation of boiler efficiency and equivalent evaporation, feedwater heaters. Steam and Gas turbines Impulse and reaction turbines degree of reaction velocity triangles, ranking cycle for steam turbine power plant reheating and regeneration Gas turbine cycles methods of improving gas turbine cycle efficiency.

**HEAT TRANSFER AND REFRIGERATION**

- Modes of heat transfer, one dimensional steady and unsteady heat conduction convective heat transfer forced convection over flat plates and tubes, free convection over cylinders and flat plates radiative heat transfer-black and grey surfaces. Types of heat exchangers – heat exchanger performance LMTD and NTU methods vapor compression cycle analysis. COP; and its estimation vapor absorption refrigeration cycle properties of refrigerators.

**MACHINE DESIGN**

- Design for static and dynamic loading fatigue strength stress concentration, the factor of safety designing of bolted, riveted and welded joints, hydrodynamic lubrication, journal and roller bearings design of spur and helical gears, clutches, and breaks. Belt and rope drive Design of shafts, keys, and couplings.

**THEORY OF MACHINES**

- Constrained motion, plane mechanisms, velocity acceleration analysis, Flywheel, and their applications, Balancing of reciprocating and rotating masses cams and followers, Tooth profiles Types of gears Principles of the gyroscope, vibration of free and forced one degree of freedom systems with and without damping, critical speed of the shaft.

**PRODUCTION ENGINEERING**

- Metal cutting and machining types of chips, chip formation tool wear and tool life, machineability single point and multi-point cutting operations machining processes shaping, planning, turning, milling, grinding, hobbling and drilling operating unconventional machining processes – USM, EDM, ECM, and LBM. Basic features of NC Machines tools linear and angular measurements, Comparators, limit gauges, screw and gear measurements.

**INDUSTRIAL ENGINEERING AND MANAGEMENT**

- Industrial organizations and plant layout production planning and control cost of manufacturing. Break-even analysis. Time and motion study, basic linear programming and queuing theory. PERT / CPM in production systems.