Lalit Narayan Mithila University, Darbhanga B.Sc. part-1 Physics honours syllabus. There will be two theory papers, each of three hours d...
Lalit Narayan Mithila University, Darbhanga B.Sc. part-1 Physics honours syllabus.
There will be two theory papers, each of three hours duration and will carry 75 marks of each paper. There will be one practical paper of 50 marks of three hours duration.
Paper-I
Five questions to be answered. Question number 1 will have six short type questions, out of which three will have to be answered. There will be four questions each from Group A and Group B. Two questions from each Group will have to be answered, besides question number one which will be compulsory. The questions will be of equal value.
Group-A
Mathematical Physics and Properties of Matter
1. Infinite sequence and series-convergence and divergence, Functions of several variables-partial differentiation, Taylor's series, multiple integrals, random variables and probabilities-statistical expectations value, variance, analysis of random errors, probability distribution functions (Binomial, Gaussian and Poisson).
2. Transformation Properties of vectors, Differentiation and integration of vectors; Line integral, volume integral and surface integral involving vector fields; Gradient, divergence and curl of a vector field, Gauss's divergence theorem, Stokes theorem, Green's theorem-application to simple problem; Orthogonal curvilinear co-ordinate systems, unit vectors in each systems, illustration by plane, spherical and cylindrical co-ordinate systems only.
3. Relation between elastic constants, twisting torque on a cylinder of wire. Bending of beam, cantilever, and flat spiral spring. Kinematics of moving fluids, poiseuille's equation for flow of a liquid through a capillary tube, viscosity, experimental determination of coefficient of viscosity of a liquid, Rankine's method for measuring viscosity of gas, surface tension and surface energy, excess pressure inside an air bubble, measurement of surface tension by ripple's method.
Group-B
Special theory of relativity, Oscillations, waves and accoustics
1. Michelson-Morley experiments and it's outcome, postulates of special theory of relativity, Lorentz transformation, simultaneity and order of events, length contraction, time dilation, relativistic transformation of velocity, relativistic addition of velocity, variation of mass with velocity, mass energy equivalence, relativistic Doppler effect.
2. Damped and forced Oscillations, critical damping, resonance, waves in one-dimensional chain of particles, classical wave equation, waves in continuous media, energy transmission in waves, group velocity and phase velocity.
3. Fourier analysis and its applications, intensity of sound waves, acoustic of building, reverberation, Sabine's formula.
Paper-II
Five questions to be answered. Question number 1 will have six short type questions, out of which three will have to be answered. There shall be four questions each from group A and group B. Two questions from each group will have to be answered, besides question number 1 which will be compulsory. The questions will be equal value.
Group-A
Thermal Physics
1. Kinetic theory of gases: Basic assumptions of Kinetic theory, Ideal gas approximation, deduction of perfect gas laws. Maxwell's distribution law (both in terms of velocity and energy), root mean square and most probable speeds.
2. Finite size of molecules: Collision probability. Distribution of free paths and mean free path from maxwell's distribution. Degrees of freedom, equipartition of energy (detailed derivation not required).
3. Transport Phenomena: Viscosity, thermal conduction and diffusion of gases, Brownian motion; Einstein's theory, Perrin's work determination of Avogadro number.
4. Real gases: Nature of intermolecular interaction, Isotherms of real gases. Vander-Waals equation of state, critical constants of a gas, law of corresponding states, Virial coefficients, Boyle's temperature.
5. Conduction of Heat: Thermal conductivity, diffusivity, Fourier's equation for heat conduction-its solution for rectilinear and radial (spherical and cylindrical) flow of heat.
6. Radiation: Spectral emissive and absorptive powers, Kirchoff's law blackbody radiation, energy density, radiation pressure, stefan Boltzman law, Wein's displacement law, Rayleigh-Jeans law, Planck's law (no detailed derivation).
7. Basic Concepts: Microscopic and mac point of views thermodynamic variables of a system, State function. Exact and inexact differentials.
8. First Law of Thermodynamics: Thermal equilibrium. Zeroth law and the concept of temperature. Thermodynamic equilibrium internal energy. external work, qu static process, first law of thermodynamics and applications including magnetic systems, specific heats and their ratio, isothermal and adiabatic changes in perfect and real gases.
9. Second law of thermodynamics: Reversible and irreversible processes, indicator diagram. Carnot's cycles-efficiency, Carnot's theorem, Kelvin's scale of temperature, relation to perfect gas scale. second law of thermodynamics-different formulations and their equivalence, Clauses inequality, entropy change of entropy in simple reversible and irreversible processes, entropy and disorder, equilibrium and entropy principle, principle of degradation of energy.
10. Thermodynamic Functions: Enthalpy, Helmholtz and Gibbs free energies, Legendre transformations, Maxwell's relations and simple deductions using these relations, thermodynamic equilibrium and free energies.
11. Change of State Equilibrium between phases, triple point, Gibb's phase rule (statement only) and simple applications. First and higher order phase transitions, Ehrenfest criterion. Clausius-Clapeyronn's equation. Joule Thomson effect, Temperature of inversion.
Group-B
Electrostatics and Magnetism
1.Gauss' law: Coulomb's law of electrostatics. Intensity and potential theorem-its application, Poisson and Laplace's equation Superposition theorem (statement only) Application of Laplace equation to simple cases of symmetric spherical charge distribution.
2. Multipole expansion: Multipole expansion of scalar potential- monopole, dipole and quadrupole terms: potential and field due to a dipole: work done in deflecting a dipole: dipole-dipole interaction (for both electric and magnetic dipoles): force on dipole in a non- homogenous field.
3. Dielectrics Polarisation, electric displacement vector (D): Gauss theorem in dielectric media: boundary conditions: electrostatic field energy: computation of capacitance in simple cases (parallel plates): spherical and cylindrical capacitors containing dielectrics-uniform and non-uniform, relation between three electric vectors.
4. Electrical images: Solution of field problem in case of a point charge near a grounded conducting infinite plane. Boundary value problem in uniform external field for (i) conducting spherical shell and dielectric sphere.
5. Magnetic effect of steady current: Magnetic field B. Magnetic force between current elements and definition of B. Magnetic flux Biot-Savart's law B due to straight current carrying conductor and (ii) current loop. Current loop as magnetic dipole and its dipole moment (analogy with electric dipole), Ampere's circuital law (integral and differential forms) B due to a Properties of B, Curl and Divergence of B. Vector potential. Forces on an isolated moving charge, Magnetic force on a current carrying wire, Torque on a current loop in a uniform magnetic field.
6. Magnetic Properties of Matter: Magnetism of matter: Gauss's l of magnetism (integral and Differential forms). Magnetization current, Relative permeability of a material, Magnetic susceptibility Magnetization vector (M), Magnetic intensity (H); Relation between B, M and H. Stored magnetic energy in matter, Magnetic circuit. BH curve and energy loss in hysteresis.
7. Electromagnetic induction: Faraday's law (Differential and integral forms), Lenz's law. Self and mutual induction. Energy stored in a magnetic field.
LNMU B.Sc. part-1 Chemistry subsidiary syllabus
Time- 3 hours
Full marks- 75
Pass marks- 23
One question is compulsory which will be very short answer type. Five questions in all to be answered, at least one question from each group to be answered.
Group-A
1. Gaseous state: Equation of state. Postulates of kinetic theory of gas and kinetic equation of gas. RMS average and most probable velocity. Deviation from ideality. Vander Waal's constant. Ideal gas.
2. Chemical Kinetics: Rate of reaction, factors affecting rate of reaction or Molecularity and order of reaction. First and Second order reaction. Half Life Activation energy.
3. Chemical Equation: Law of Mass action. Equilibrium constant (Kp. Ke & Kx) i e. Chaterllier's principle, Relationship between Kp, Kc & kx.
4. Colloidal State: Classification, Preparation of Colloidal Solution. Purification (Dialysis) Protective colloid. Gold no. Emulsion, Stability of Colloids optical and electrical properties, coagulation Hardy-Schulz Law.
Group-B
1. Structure of Atom: Isotope, Isobar & Isotone, J. J. Thomson & Mullican's oil drop methods of determining the charge of an electron Rutherford's model. Bohr Model and defect. Correction. Theory of Atomic Spectra. Albau Principle, Pauli Exclusion Principle, Quantum no. Hund's Rule. Electronic Configuration writing for atom & ions.
2. Periodicity: Electronic layout of the P.T. classification of elements Periodicity Atomic radii. Ionic radii, Ionisation Potential & Energy Electron affinity. Electronegativity, Modern periodic table. Naming of elements having atomic no. more than one hundred, Merit demerits of P.T.
3. Chemical Bonding: Hydrogen bond, Metallic bond, Fajan's rule, Valence bond theory, Hybridisation and shape and structure of simple covalent molecules and ions VSEPR Theory.
4. Chemistry of the elements: Occurrence metallurgy, General Characteristic, General Chemistry and important compounds of Ag Au, Sn, Pb and B.
Group-C
1. General concepts of Hybridisation: Shape and structure of simple organic compounds & ions. Tetravalent of carbon Fission and its kinds. Reaction and its types reagents & types. General Idea of inductive effect. Mesomeric effect & hyper Conjugation.
2. Alcohol: Classification, Nomenclature, Dihydric & Trihydric Alcohol-Glycol, Glycerol General method of preparation. Properties & uses. Their occurrence and isolation, Structure of Glycerol.
3. Aldehydes, Ketones & Carboxylic acid: General methods of Synthesis. Properties and uses. Difference between Aldehyde & Ketones. Reactivity and acid characters of Aldehyde and ketones. Strength of carboxylic acids, preparation of acid derivatives.
4. Amines & Urea: Structure, Nomenclature effect due to substituents classfication and separation of amine mixture (primary. secondary & tertiary) basic strength of amines, method of synthesis. Properties & Urea-Preparation, Properties. Uses.
LNMU B.Sc. part-1 Mathematics subsidiary syllabus
Time- 3 hours
Full marks- 100
Sixteen questions to be set and Eight to be answered. You will have select at least one from each Group.
Group-A
Set theory, Modern Algebra and Linear Algebra (7 questions)
1. Set Theory: - De Morgan's laws, Cartesian product of sets. Equivalence relation, Partition of a set Fundamental theorem on equavalence relation. Countability of rational, real and algebraic number. (2 questions)
2. Abstract Algebra: - Nations of group, abelian group with simple examples, Uniqueness of identity and inverse, Cancellation laws in a group. Reversal rule. Definitions and examples of subgroup and cyclic group (1 question)
3. Definitions, simple examples and simple properties of Ring, integral doman and field (1 question)
4. Matrices, Transpose, Orthogonal, adjoint and in of the matrix Rank of Matrix (2 questions)
5. Definition, examples and properties of vector space, vector subspace. (1 question)
Group-B
1. Real Analysis (Four questions): Sequence and their convergence, Cauchy's general principle of covergence Bounded sequence, Monotonic sequences. (1 question)
2. Convergent and divergent Series. Convergence of the positive term series. comparision test.
3. Cauchy's root test. D' Alembert's ratio test. Raabe's test and Liebnitz's test questions)
4. Continuity and differentiability of real function of single real variable with examples (1 question)
Group-C
Analytic Geometry of Two and Three Dimensions (Five questions)
1. Analytic Geometry of Two dimensions: - System of circles. Coaxial circles. Radical axis, General equation of second degree and its reduction to standard forms of parabola. Ellipse and Hyperbola. Equation of tangents and normal for general equation. (3 questions)
2. Analytic Geometry of three dimensions: - Rectangular Cartesian co-ordinates. Direction cosines. Angle between two straight lines. Equations of plane and straight line. Condition for coplanarity of straight lines. Equation of shortest distance. (2 questions)
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