Section-A

Linear Algebra : Vector, space, linear dependance and independance, subspaces, bases, dimensions. Finite dimensional vector spaces.

Matrices, Cayley-Hamiliton theorem, eigenvalues and eigenvectors, matrix of linear transformation, row and column reduction, Echelon form, eqivalence, congruences and similarity, reduction to cannonical form, rank, orthogonal, symmetrical, skew symmetrical, unitary, hermitian, skew-hermitian forms-their eigenvalues. Orthogonal and unitary reduction of quadratic and hermitian forms, positive definite quardratic forms.

Calculus: Real numbers, limits, continuity, differerentiability, mean-value theorems, Taylors theorem with remainders, indeterminate forms, maximas and minima, asyptotes. Functions of several variables: continuity, differentiability, partial derivatives, maxima and minima, Lagranges method of multipliers, Jacobian. Riemanns definition of definite integrals, indefinite integrals, infinite and improper intergrals, beta and gamma functions. Double and triple integrals (evaluation techniques only). Areas, surface and volumes, centre of gravity.

Analytic Geometry:Cartesian and polar coordinates in two and three dimesnipns, second degree equations in two and three dimensions, reduction to cannonical forms, straight lines, shortest distance between two skew lines, plane, sphere, cone, cylinder., paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

Ordinary Differential Equations:Formulation of differential equations, order and degree, equations of first order and first degree, integrating factor, equations of first order but ndt of first degree, Clariauts equation, singular solution.

Higher order linear equations, with constant coefficients, complementary function and particular integral, general solution, Euler-Cauchy equation.

Second order linea: equations with variable coefficients, determination of complete solution when one solution is known, method of variation of parameters.

Dynamics, Statics and Hydrostatics:Degree of freedom and constraints, rectilinerar motion, simple harmonic motion, motion in a plane, projectiles, constrained motion, work and energy, conservation of energy, motion under impulsive forces, Keplers laws, orbits under central forces, motion of varying mass, motion under resistance. Equilibrium of a system of particles, work and potential energy, friction, common catenary, principle of virtual work, stability of equilibrium, equilibrium of forces in three dimensions.

Pressure of heavy fluids, equilibrium of fluids under given system of forces Bernoullis equation, centre of pressure, thrust on curved surfaces, equilibrium of floating bodies, stability of equilibrium, metacentre, pressure of gases.

Vector Analysis :Scalar and vector fields, triple, products, differentiation of vector function of a scalar variable, Gradient, divergence and curl in cartesian, cylindrical and spherical coordinates and their physical interpretations. Higher order derivatives, vector identities and vector quations.

Application to Geometry: Curves in space, curvature and torision. Serret-Frenets formulae, Gauss and Stokes theorems, Greens identities.

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1. Theory of Machines: Kinematic and dynamic analysis of planar mechanisms. Cams, Gears and gear trains, Flywheels, Governors, Balancing of rigid rotors, Balancing of single and multicylinder engines, Linear vibration analysis of mechanical systems (single degree and two degrees of freedom), Critical speeds and whirling of shafts, Automatic Controls, Belts and chain drives. Hydrodynamic bearings.

2. Mechanics of Solids : Stress and strain in two dimensions. Principal stresses and strains, Mohrs construction, linear elastic materials, isotropy and an isotropy, Stress-strain relations, unilaxial loading, thermal stresses. Beams : Banding moment and shear force diagrams, bending stresses and deflection of beams, Shear stress distribution. Torsion of shafts, helical springs. Combined stresses, Thick and thin walled pressure vessels. Struls and columns, Strain energy concepts and theories of failure. Rotating discs. Shrink fits.

3. Engineering Materials : Basic concepts on structure of solids, Crystalline materials, Defects in crystalline materials, Alloys and binary phase diagrams, structure and properties of common engineering materials. Heat treatment of steels. Plastics, Ceramics and composite Materials, common applications of various materials.

4. Manufacturing Science : Marchants force analysis, Taylors tool life equation, machinability and machining economics, Rigid, small and flexible automation, NC, CNC. Recent machining methods- EDM, ECM and ultrasonics. Application of lasers and plasmas, analysis of forming processes. High energy rate forming. Jigs, fixtures, tools and gauges. Inspection of length, position, profile and surface finish.

5. Manufacturing management :Production Planning and Control, Forecastmg-Moving average, exponential smoothing, Operations sheduling; assembly line balancing. Product development. Breakeven analysis, Capacity planning. PERT and CPM.

Control Operations : Inventory control-ABC analysis. EOQ model. Materials requirement planning. Job design, Job standards, work measurement, Quality management-Quality control. Operations Research : Linear programming-Graphical and Simplex methods. Transportation and assignment models. Single server queuing model.

Value Engineering : Value analysis; for cost/value. Total quality management and forecasting techniques. Project management.

6. Elements of Computation : Computer Organisation, Flow charting. Features of Common Computer Languages-FORTRAN d Base III, Lotus 1-2-3 C and elementary programming.

1. Thermodynamics : Basic concept Open and closed systems, Applications of Thermodynamic Laws, Gas equations, Clapeyron equation, Availability, Irreversibility and Tds relations.

2. I.C. Engines, Fuels and Combustion : Spark Ignition and compression ignition engines, Four stroke engine and Two stroke engines, mechnical, thermal and volumetric efficiency, Heat balance.

Combustion process in S.I. and C.I. engines, preignition detonation in S.I. engine Diesel knock in C.I. engine. Choice of engine fuels, Octance and Cetane retings. Alternate fuels Carburration and Fuel injection, Engine emissions and control. Solid, liquid and gaseous fuels, stoichometric air requirements and excess air factor, fuel gas analysis, higher and lower calorific values and their measurements.

3. Heat transfer, Refrigeration and Air conditioning : One and two dimensional heat conduction. Heat transfer from extended surfaces, heat transfer by forced and free convection. Heat exchangers. Fundamentals for diffusive and connective mass transfer, Radiation laws, heat echange between black and non baick surfaces, Network Analysis. Heat pump refrigeration cycles and systems, Condensers, evaporators and expansion devices and controls. Properties and choice of refrigerant, Refrigeration Systems and components, psychometrics, comfort indices, cooling loading calculations, solar refrigeration.

4. Turbo-Machines and Power plants : Continuity, momentum and Energy Equations. Adiabatic and Isentropic flow, fanno lines, Raylegh lines. Theory and design of axial flow turbines and compressors, Flow through turbo-machine balde, cascades, centrifugal compressor. Dimensional analysis and modelling. Selection of site for steam, hydro, nuclear and stand-by power plants,

Selection base and peak load power plants, Modern High pressure, High duly boilers, Draft and dust removal equipment, Fuel and cooling water systems, heat balance, station and plant heat rates, operation and maintenance of various power plants, preventive maintenance, economics of power generation.

Section-A

I. Human Anatomy : Gross and microscopic anatomy and movements of shoulder, hip and knee joints; Blood supply, nerve innervation of hand, Lymphatic system; Karyotyping, medical genetics; Electron microscopic structure of glomerulous and muscle; Gross and microscopic anatomy and blood supply of lungs, heart, kidneys, liver, testis and uterus; Gross anatomy of pelvis, perineum and inguinal region. Cross-sectional anatomy of the body and mid-thoracic, upper abdominal, mid-abdominal and pelvic regions.

Embryology : Major steps in the development of lung, heart, kidney, urinary bladder, uterus, ovary, testis and their common congenital abnoirmalities; Placenta and placental barrier. Anatomy of central and peripheral autonomic nervous system : Neural pathways for cutaneous sensations and vision; Cranial nerves, distribution and clinical significance; Anatomy of autonomic control of gastronintestinal, respiratory and reproductive systems.

II. Human Physiology : Central, peripheral and autonomic nervous, system; Nerve and muscle excitation, conduction and transmission of impulse, mechanism of contraction, neurovascular transmission, EMG; Synaptic transmission, reflexes, control of equilibrium, posture and muscle tone descendig pathways, functions of creebellum, basal ganglia, reticular formation, hypothalamus limbic system and cerebral cortex; Physiology of sleep and consciousness, EEC; Higher functions of the. brain; Vision and hearing.

Endocrine system : Mechanism of action of hormones, formation, secretion, transport, metabolism, functions and regulations of secretion of pancreas and pituitary glands.
Physiology of reproductive system : menstrual cycle, lactation, pregnancy.

Blood : Development, regulations and fate of blood cells. Cardio-vascular, respiratory, gastro-intestinal and renal physiology : Cardiac excitation, spread of cardiac impulse, ECG., cardiac output, blood pressure, regulation of cardiovascular functions; Mechanics of respiration and regulation of respiration; Digestion and absorption of food, regulation of secretion and motiltty of gastrointesinal tract; Glomerular and tubular fucntions of kidney.

III. Biochemistry : pH and pK Hendrson-Hassebalch Equation; Properties and regulation of enzyme activity, role of high energy phosphates in bioenergetics; Sources, daily requirements, action and toxicity of vitamins; Metabolism of lipids, carbohydrates, proteins, disorders of their metaboilism; Chemical nature, structure, synthesis and fucntions of nucleic acids and proteins; Distribution and regulation of body water and minerals including trace elements; Blood Gas Analysis, GTT, Immuno electrophorises, molecular structure of muscle contractile protein, oestrogen receptors.

I. Pathology : Rection of cell and tissue of injury, inflammation and repair, disturbances of growth and cancer, genetic diseases; Pathogenesis and histopathology of Rheumatic and ischaemic heart disease; Bronchogenic carcinoma, carcinoma breast, oral cancer, cancer colon. Lymphoma, leukaemia, liver cancer, meningioma and meningitis; Etiology, pathognesis and histopathology of - Peptic ulcer, cirrhosis liver glomerulonephritis, lobar pneumonia, acute osteomyelitis, hepatitis, acute pancreatitis.

II. Microbiology : Growrth of micro-organisms, sterilization and
disinfection, bacterial genetics, virus-cell interactions; Immunological principles, acquired immunity, immunity in infections cause by viruses; Diseases caused by and laboratory diagnosis of Staphylococcus, enterococcus, salmonella, shigella, secheichiza, pseudomonos, vibrio, adenoviruses, herpes viruses (including rubella fungi, protozoa, helminths, leptospiral infection.

III. Pharmacology : Drug receptor instruction, mechanism of drug action; Mechanism of action, dosage, metabolism and side effects of- Pilocarpine, terbutaline, metoprolol diazepam, acetylsalicylic acid, ibuprofen, furosemide, metronidazole. Chloroquin. Mechanism of action, dosage and toxicity of- Ampicillin, Cephalosponns, l,2,3,4,th generations, Aminoglycoside, Doxycycline, chloramphenicol, rifampin, Calcium channel blocker, beta blocker, ace inhibitors, immunosuppressive therapy. Indications, dosage, side-effects and contraindictions of-Methortrexate, vincristin, tamoxifen. Classification, route of administration, mechanism of action and side effects of - General anaesthetics, hypnotics, analgesics, Anti-viral, anti-fungal drugs.

IV. Forensic Medicine and Toxicology : Forensic examination of injuris and wounds; Physical and chemical examination of blood and seminal stains; Organo phosphorous poisoning, sedative overdose, hanging, drowning, burns, snake envenomation.

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History and Problems of Philosophy

Section A

1. Plato: Theory of Ideas.

2. Aristotle: Form, Matter and causation.

3. Descartes: Cartesian Method and certain knowledge, God, Mind-Body Dualism.

4. Spinoza: Substance, Attributes and Modes, Pantheism; Bondage and Freedom.

5. Leibnitz: Monads; Theory of Perception God.

6. Locke: Theory of Knowledge, Rejection of Innate Ideas; substance and qualities.

7. Berkeley: Immaterialism, God, Criticism of representative Theory of Perception.

8. Hume: Theory of knowledge, Scepticism, Self, Causality.

9. Kant: Distinctions between synthetic and analytic judgements and between apriori and aposteriori judgements, Space, Time Categories, Possibility of Synthetic Apriori Judgements, Ideas of Reason and Antinomies; Criticism of the Proofs for the Existence of God.

10. Hegel: Dialectical Method, Absolute Idealism.

11. Precursors of Linguistic Analysis: Moore (Defence of common sense, Reputation of idealism), Russell (Theory of Descriptions).

12. Logical Atomisms: Atomic Facts, Atomic sentences, Logical Constructions and Incomplete Symbols (Russell), Distinction of saying and showing (Wittgenstein).

13. Logical Positivism: Verification theory and rejection of Metaphysics, Linguistic Theory of Necessary Propositions.

14. Phenomenology: Husserl.

15. Existentialism: Kierkegaard, Sartre.

16. Quine: Radical empiricism.

17. Strawson: Theory of person..

Section B

1. Carvaka: Theory of Knowledge, Materialism.

2. Jainism: Theory of Reality, Saptabhangi Naya, Bondage and Liberation.

3. Buddhism: Pratityasamutpada, Ksanikavyda, Nairatmyavada, Schools of Buddhism, Sautrantika Theory of Pramana, Ideal of Bodhisattva.

4. Samkhya: Prakriti, Purusa, Theory of Causation, Liberation.

5. Naya-Vaisesika: Theory of Pramana, Self, Liberation, God and Proofs for Gods Existence, Categories, Theory of Causation, Atomistic theory of Creation.

6. Mimansa: Theory of Knowledge.

7. Vedanta: Schools of Vedanta, Sankara, Ramaunja, Madhva (Brahman, Isvara, Atman, Jiva, Jagat, Maya, Avidya, Adhyasa, Moksa).

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Section-A

1. Classical Mechanics

(a) Particle dynamics
Centre of mass and laboratory coordinates, conservation of linear and. angular momentum. The rocket equation.. Rutherford scattering, Galilean transformation, intertial and non-inertial frames, rotating frames, centrifugal and Coriolis forces, Foucault pendulum.

(b) System of particles
Constraints, degrees of freedom, generalised coordinates and momenta. Lagranges equation and applications to linear harmonic oscillator, simple pendulum and central force problems. Cyclic coordinates, Hamilitonian Lagranges equation from Hamiltons principle.

(c) Rigid body dynamics
Eulerian angles, inertia tensor, principal moments of inertia. Eulers equation of motion of a rigid body, force-free motion of a rigid body. Gyroscope.

2. Special Relativity, Waves & Geometrical Optics

(a) Special Relativity
Michelson-Morley experiment and its implications. Lorentz transformations-length contraction, time dilation, addition of velocities, aberration and Doppler effect, mass-energy relation, simple applications to a decay process. Minkowski diagram, four dimensional momentum vector. Covariance of equations of physics.

(b) Waves
Simple harmonic motion, damped oscillation, forced oscillation and resonance. Beats-. Stationary waves in a string. Pulses and wave packets. Phase and group velocities. Reflection and Refraction from Huygens principle.

(c) Geometrical Optics
Laws of relfection and refraction from Fermats principle. Matrix method in paraxial optic-thin lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.

3. Physical Optics

(a) Interference
Interference of light-Youngs experiment, Newtons rings, interference by thin films, Michelson interferometer. Multiple beam interference and Fabry-Perot interferometer. Holography and simple applications.

(b) Diffraction
Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power. Fresnel diffraction: - half-period zones and zones plates. Fresnel integrals. Application of Cornus spiral to the analysis of diffraction at a straight edge and by a long narrow slit. Diffraction by a circular aperture and the Airy pattern.

(c) Polarisation and Modern Optics
Production and detection of linearly and circularly polarised light. Double refraction, quarter wave plate. Optical activity. Principles of fibre optics attenuation; pulse dispersion in step index and parabolic index fibres; material dispersion, single mode fibres. Lasers-Einstein A and B coefficients. Ruby and He-Ne lasers. Characteristics of laser light-spatial and temporal coherence. Focussing of laser beams. Three-level scheme for laser operation.

4. Electricity and Magnetism

(a) Electrostatics and Magnetostatics
Laplace ad Poisson equations in electrostatics and their applications. Energy of a system of charges, multipole expansion of scalar potential. Method of images and its applications. Potential and field due to a dipole, force and torque on a dipole in an external field. Dielectrics, polarisation. Solutions to bounary-value problems-conducting and dielectric spheres in a uniform electric field. Magentk shell, uniformly magnetised sphere. Ferromagnetic materials, hysteresis, .energy loss.

(b) Current Electricity
Kirchhoffs laws and their applications. Biot-Savart law, Amperes law, Faradays law, Lenz law. Self-and mutual-inductances. Mean and rms values in AC circuits. LR CR and LCR circuits- series and parallel resonance. Quality factor. Principal of transformer.

5. Electromagnetic Theory & Black Body Radiation

(a) Electromagnetic Theory
Displacement current and Maxwells equatons. Wave equations in vacuum, Poynting theorem. Vector and scalar potentials. Gauge invariance, Lorentz and Coulomb gauges. Electromagnetic field tensor, covariance of Maxwells equations. Wave equations in isotropic dielectrics, reflection and refraction at the boundary of two dielectrics. Fresnels relations. Normal and anomalous dispersion. Rayleigh scattering.

(b) Blackbody radiation .
Balckbody radiation ad Planck radiation law- StefaivBoltzmann law, Wien displacement law and Rayleigh-Jeans law. Planck mass, Planck length, Planck time,. Planck temperature and Planck energy.

6. Thermal and Statistical Physics

(a) Thremo dynamics
Laws of thermodynamics, reversible and irreversible processes, entropy. Isothermal, adiabatic, isobaric, isochoric processes and entropy change. Otto and Diesel engines, Gibbs phase rule and chemical potential, van der Waals equation of state of a real gas, critical constants. Maxwell-Boltzman distribution of molecular velocities, transport phenomena, equipartition and virial theorems. Dulong-Petit, Einstein, and Debyes theories of specific heat of solids. Maxwell lllrelations and applications. Clausius- Clapeyron equation. Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of gases.

(b) Statistical Physics
Saha ionization formula. Bose-Einstein condenssation. Thermodynamic behaviour of an ideal Fermi gas, Chandrasekhar limit, elementary ideas about neutron stars and pulsars. Brownian motion as a random walk, diffusion process. Concept of negative temperatures.

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Political Theory and Indian Politics

Section-A

1, Approaches to the study of political theory: historical, normative and empirical.

2. Theories of state: Social contract, Liberal, Neo-liberai, Marxist, communitarian, post-colonial,

3. State Sovereignty: Marxist and pluralistic theories; globalisation and the State.

4 Democracy and Human Rights: Democratic theory-classical and contemporary Theories of Human Rights; Theories- of Justice, Equality and Revolution, political obligation; New Social Movements.

5. Theories of Political Culture; Culture and politics in Third World countries.

6. Theories of Political Economy-Classical and contemporary.

7. Political Ideologies: Nature of Ideology; Liberalism, Socialism, Marxism, Fascism, Gandhism and Anarchism.

8. Theories of Power and Hegemony: Pareto, Mosca, Mitchels, C. Wright Mills, Weber, Gramsci, Hannah Arendt.

9. Indian Political Thought: Manu, Kautilya M.N. Roy Gandhi Ambedkar and E V Ramswami Naicker.

10. Political Thought: Plato, Aristotle, Machiavelli, Hobbes, J S Mill, Hegel and Marx, Lenin, Rosa Luxemberg and Mao Zedong.

Indian Government and Politics

1. Indian Nationalism: Dadabhai Naoroji, Tilak, Savarkar, Gandhi, Jayaprakash Narain, Nehru, Subhas Bose, Ambedkar, Ram Manohar Lohia.

2. Nature and struggle of Indian freedom struggle : From constitutionalism to Mass Satyagraha, Revolutionary movements Non Co-operation, Civil disobedience and Quit India, Indian Naval uprising, Indian National Army; role of women in freedom struggle.

3. Socio- economic dimensions of the nationalist movement: The communal question and the demand for partition; backward caste movements, Trade union and Peasant movements, Civil rights movement.

4. Landmarks in Constitutional Development during British Rule: Morley-Miito Reforms; Montagu-Chelmsford Reforms; Simon Commission; Government of India Act, 1935; Cripps Mission : Indian Independence Act, 1947.

5. Salient Features of the Indian Constitution: The Preamble, Fundamental Rights and Duties, Directive Principles; federalism, parliamentary system; amending procedures; judicial review.

6. The Executive System in theory and practice: President, Prime Minister and the Council of Ministers; Governor, Chief. Minister and the State Council of Ministers. The Bureaucracy.

7. Role and function of the Parliament and Parlimentary Committee-Lok Sabha and Rajya Sabha; changing socio economic profile.

8. The Supreme Court and the High Courts; Judicial Activism; PIL.

9. Statutory institutions/commis sions-UPSC, Election Commission, Comptroller and Auditor General, Backward Classes Commission, National Commission for women; National Human Rights Commission; Minorities Commission.

10. Party system : ideology and social base of parties; fragmentation and regionalisation. Pressure groups; patterns of coalition politics; trends in electoral behaviour.

11. Class, caste, ethnicity and gender in Indian politics; politics of regionalism, comnumalism, backward class and Dalit movements, Tribal people movements, struggle for gender justice.

12. Planning and Economic Development: Role of the Planning Commission; Planning in the era of liberalisation; political dimensions of economic reforms.

13. Grassroots democracy : Panchayati Raj and municipal government; significance of 73rd and 74th Amendements. Grass root movement and womens empowerment.

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Foundations of Psychology Section-A

1. Introduction : Psychology as a Science : Definitions and perspective. Psychology in relation to other social and natural sciences. Use of interdiciplinary approach.

2. Methods of Psychology : Characteristics and componets of methods in psychology (induction, deduction and introspection). Observation, Survey, Laboratory and field experiments. Clinical and Case study. Experimental and quasi experimental methods.

3. Research methods and quantitative analysis : Major steps in psychological research (problem statement, hypothesis formulation, research design, sampling, tools of data collection, analysis and interpretation and report writing). Fundamental versus applied research. Methods of data collection (interview, observation, questionnaire and case study). Research Designs (Ex-post facto and experimental). Application of statistical techniques (t-test, one-way ANOVA correlation and regression and chi-square tests).

4. Development of Human Behaviour : The nature, origin and development. Role of genetic and environmental factors in determining human behaviour. Influence of cultural factors and socialisation. Life span development-the critical periods and their handling, Mastery of the developmental tasks. Influence of child rearing practices and its impact on the growth and development of the individual, concept of national character.

5. Attention and perception : Attention- factors, influencing attention including set and characteristics- of stimulus. Sensation-concepts of threshold, absolute and difference thresholds, signal detection and vigilance. Definition and concept of perception, biological factors in perception. Perceptual organisation-influence of past experiences, Perceptual-defence-factors influencing. Space and depth perception, size estimation and perceptual readiness.

6. Learning : Concepts and theories of learning (Pavlov, Skimer and Piaget). The processes of extinction, discrimination and generalisation. Programmed learning, probability learning, self instructional learning, concepts, types and the schedules of reinforcement. Modelling and social learning.

7. Memory : Concepts and definition of memory and forgetting, 7+/-2 concept and clumking Encoding, storage and retrieval. Factors influencing retention.and foregetting. Theories of forgetting (Repression, Decay and Interference theories). The concept cf reminiscence.

8. Thinking and Problem Solving: Concept formation processes. Resoning and problem solving. Creative thinking and fostering creativity. Information processing. Decision making and judgement.

9. Intelligence and Aptitude : Concept and definition of Intelligence and aptitude, Nature and theories of intelligence. Measurement of Intelligence and aptitude Concepts and measurement of emotional and multiple intelligence.

10. Motivation and Emotion : Definition and concepts. Theories and physiological basis of motivation and emotion. Measurement of motivation and emotion Motivation and emotion-their effects on behaviour.

11. Personality : Concept and definition of personality. Theories of personality {psychoanalytical, socio-cultural, interpersonal and developmental, humanistic, behaviouristic, trait and type approaches). Measurement of personality (projective tests, pencil-paper tet). The Indian approach to Personality. Training for personality development.

12. Language and Communication: Human language-properties, structure , and linguistic hierarchy, Language acquisition-predisposition, critical period hypothesis. Theories of language development (Skinner, Chomsky), Process and types of communication. Effective communication and training.

13. Attitudes, Values and Interests : Definitions, concepts of attitudes, values and interests. Components ofattitudes, values and interests. Formation and maintenance of attitudes. Measurement of attitudes, values and interests. Theories of attitudes, and attitudes changes, strategies for fostering values.

14. Recent Trends : Computer application in the Psychological laboratory and psychological testing. Articial Intelligence. Psychocybernetics. Study of consciousness-sleep-wake schedules; dreams, stimulus deprivation, meditation, hypnoti c/drug induced states. Extrasensory perception. Intersensory perception Simulation studies.

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