NITWET 2011 Syllabus NIT Warangal MSc Entrance Test Exam Date

NITWET 2011 NIT Warangal Entrance Test 

DETAILED SYLLABII FOR ENTRANCE EXAMINATION 

1. For   M.Sc. (Applied Mathematics) and 

M.Sc. (Mathematics and Scientific Computing) programs:

Modern Algebra: Groups-Subgroups-Cosets-Lagrange’s Theorem – Cyclic groups – Quotient groups – Homomorphism of groups – Kernel of a group – Permutation groups – Rings – Integral domains – Ideals – Quotient Rings – Fields – Euclidean rings.

Linear Algebra: Elementary transformation – Rank of a matrix – Normal form - system of homogeneous and non-homogeneous linear equations – Eigen values – Eigen vectors – Cayley – Hamilton theorem – Vector space – Subspace – Linear dependence and independence – Span of a set – Basis, Dimension – Linear Transformation – Rank and nullity - Gram – Schmidt orthogonalization – Quadratic forms.

Mathematical Analysis: Real numbers – Sequences – Series – Tests of convergence – Absolute and conditional convergence – Limits, Continuity and differentiability – Mean value theorems – Taylor’s and Maclaurin’s expansions – Riemann integration - properties of Riemann integrals.

Vector Calculus: Vector differentiation – Gradient, Divergence and Curl – Line, Surface and Volume integrals – Stokes, Green’s and Gauss divergence theorems.

Coordinate Geometry of Three Dimensions: Coordinates – Direction  Ratios and Cosines – Angle between two lines – Plane – Angle between planes – Lines – Coplanarity of lines – Shortest distance between two lines – Spheres – tangent planes – Polar planes – Conjugate planes and lines.

Differential Equations: Formation of differential equation – First order and first degree differential equations – orthogonal trajectories – Linear Differential Equations with constant coefficients – Variation of Parameters – Simultaneous differential equations. 

2. For M.Sc. (Tech.) Engineering Physics Program:

UNIT - I

Geometrical Optics:  Reflection, Refraction at plane and curved surfaces mirrors and lenses.  Thin and thick lenses.  Combination of lenses.  Cardinal points. Unit planes and nodal points. Matrix method in paraxial optics, defects of the images – chromatic, achromatic, monochromatic and spherical aberrations, minimization of spherical aberration, explanation of coma and its elimination, astigmatism and its removal. Optical instruments, vision optics. Dispersion and scattering of light. Velocity of light.

Physical Optics: Huygen’s Wave Theory, Coherence, Superposition of waves, Displacement of fringes-phase change on reflection. Interference by division of wave front – division of amplitude. Young’s interference, Newton’s rings. Michelson interferometer, Fabry perot interferometer. Thin films, interference filters. Diffraction: integral theorem of Helmholtz, Fresnel – Kirchoff’s theory of diffraction. Fresnel and Fraunhoffer diffraction (Fourier approach). Slit –circular apertures.

Polarization and Souble refraction of light – matrix method for polarization analysis, production and detection of polarized light, Nicolprism, Polaroid, Maluslaw – phenomenon of double refraction – mathematical analysis, refraction of a plane wave in a calcite crystal, Waveplates, Compensators, Optical activity, Basics of lasers and Holography.   

UNIT – II

Mechanics, Thermodynamics, Electricity & Magnetism: Motion of variable mass systems. Center of mass kinematics, torque, collisions, Centre of mass – Lab reference frames. Motion in uniformly accelerated frames. Inertial forces in non-inertial frames. Euler’s equation, conservation laws, steady flow, Bernoulli’s equation-applications. Einsten’s special theory of relativity – concepts. Damped oscillations, Q-factor, forced oscillations, resonance, mechanical impedance, Coupled oscillators, wave equation.

Laws of thermodynamics, Entropy changes. Thermodynamic potentials. Thermodynamics of low temperatures. Black body radiation. Different fitment formulae. Maxwell-Boltzman, Fermi-Dirac and Bose–Einstein Statistics.

Electro-statics, Magneto-statics, Current. Electricity, Ohm’s law, Kirchoff’s Laws, Potentiometer,  Wheatstone bridge. Capacitance, dielectrics, Ampere’s law, Biot-Savart Law.  Faraday’s Laws of electro–magnetic induction. Inductance, Transformer – RC, LC, LR & LCR circuits,  Thermoelectricity, Crystal systems, X-ray diffraction, types of magnetism, IH BH curves,  Magnetic materials. Maxwell equations and Electromagnetic waves. Hard and Soft super conductors.

UNIT – III

Modern Physics: Photoelectric effect, Compton effect. Uncertainty principle. Atomic spectra, Bohr’s theory of hydrogen spectra, Vector atom model. Zeeman and Stark effects. X-rays and its applications. Radio activity and its uses. Nuclear detectors. Particle accelerators. Fission. Fusion. Nuclear reactors. Thermo nuclear reactions, Cosmic rays.

Electronics: Basic electronics, band theory of solids, Conductors, semi conductors and insulators. Intrinsic and extrinsic semi conductors. Hall Effect, Fermi levels. Types of PN junction, Junction diode, Zener diode, varicap, tunnel diode, metal semiconductor diode, photodiode, PN diode SCR. CE configuration as a two port network, ‘h’ parameter equivalent circuit, Amplifiers based on frequency ranges. Biasing and load line analysis, thermal runway, types of feed back. Effect of feedback on gain, noise and band width. Phase shift and weinbridge oscillators. Hartley and Colpitt’s oscillators, crystal oscillators and frequency stability. Relaxation oscillators. CRT, CRO.   

3. For  M.Sc. Industrial Chemistry (Dyes, Drugs, Pharmaceuticals and Pesticides) and 

M.Sc. Industrial Chemistry (Modern Methods of Chemical Analysis) programs:

Inorganic Chemistry : s-Block Elements; Group I A, II A, p-Block Elements: Group III B,    IV B, V B, VI B, VII B, Group Zero Elements, Metallurgy; d- Block Elements; f-Block Elements; Coordination Compounds; Nuclear Chemistry.

Organic Chemistry: Structure of Organic Molecules; Reactivity of Organic Molecules; Nomenclature of Organic Compounds; Alkanes, Cyclo Alkanes, Alkenes, Alkynes, Arenes, Halogen Compounds, Hydroxy Compounds, Ethers, Carbonyl Compounds, Monocarboxylic Acids and their Derivative; Organic Synthesis based on Carbanions, Nitrogen Compounds, Optical Isomerism, Classification of Natural Amino Acids; Carbohydrates; Heterocyclic Compounds.

Physical Chemistry: Atomic Structure, Chemical Equilibrium; Colloids; Adsorption; Gaseous State; Liquids, Solids, Solutions; Phase Rules; Colligative Properties; Thermodynamics; Electro Chemistry; Chemical Kinetics.

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