B.Sc.-I (Physics, Chemistry, Mathematics)
Solved Paper (English)
For Rajasthan University
SYLLABUS COVERED IN BOOK
PHYSICS PAPER I: MECHANICS AND OSCILLATIONS
UNIT—1 Physical Law and Frame of Reference
(a) Inertial and non-inertial frames, Transformation of displacement, velocity, acceleration between different frames of reference involving translation.Galilean transformation and invariance of Newton's laws.
(b) Coriolis Force: Transformation of displacement, velocity and acceleration between rotating frame, Pseudo forces, Coriolis force, Motion relative to earth, Focult's pendulum.
(c) Conservative Forces : Introduction about conservation and non conservation forces, Rectilinear motion under conservation forces, Discussion of potential energy curve and motion of particle.
UNIT-II Centre of Mass : Introduction about Centre of Mass, Centre of Mass Frame: Collision of two particles in one and two dimensions (elastic and inelastic), Slowing down of neutrons in a moderator, Motion of a system with varying mass, Angular momentum concept, conservation and charge
Rigid body: Equation of a motion of a rotating body, Inertial coefficient, Case of J not parallel to o, Kinetic energy of rotation and idea of principal axes, Processional motion of a spinning top.
UNIT- III : Motion under Central Forces Introduction about Central Forces, Motion under central forces, Gravitational interaction, Inertia and gravitational mass, General solution under gravitational interaction, Keplers Laws, Discussion of trajectories, Cases of elliptical and circular orbits, Rutherford scattering. Damped Harmonic Oscillations: Introduction about oscillations in a potential well, Damped force and motion under damping, Damped Simple Harmonic Oscillator, Power dissipation, Anharmonic oscillator and simple pendulum as an example.
UNIT- IV : Driven Harmonic Oscillations
Driven harmonic oscillator with damping, Frequency response, Phase relation, Quality factor, Resonance, Series and parallel of LCR circuit, Electromechamical system-Ballistic Galvanometer.
Coupled Oscillations : Equation of motion of two coupled Simple Harmonic Oscillators, Normal modes, mdtion in mixed modes, Transient behavior, Dynamics of a number of oscillators with neighbor interactions.
UNIT — 1: Scalar and Vector Fields
Concept of Field, Scalar and Vector Fields, Gradient of scalar field, Physical significance and formalism of Gradient,Her Divergence and Curl of a vector field in Cartesian coordinates system, Problems based on Gradient, Divergence and curl operators. Concept of Solid angle, Gauss divergence and Stoke's theorem. Gauss law from inverse square law. Differential form of Gauss law.
Electric Field and Potential Energy : Invariance of charge, Potential energy of system if (i) Discreate N-charges (ii) Continuous charge distribution. Energy required to built a uniformaly charged sphere. classical radious of electron. Electric field due to short electric dipole. Interaction of electric dipole with external uniform and non uniform electric field, potential due to a uniformaly charged spherical shell. org Poission 's and Laplace equations in cartesian co-ordinates and their applications to solve the problems of electrostatics. Electric field measured in moving frames, Electric field of a point charge moving with constant velocity.
UNIT- II: Electric Field in Matter
Multipole expansion, defination of moments of charge distribution, Dielectrics, Induced dipole moments, polar non polar molecules, Free and bound charges, Polarization, Atomic polarizabilty, electric displacement” vector, electric susceptibility, dielectric constant, relation between them. Electric potential and electric field due to a uniformly polarized sphere (i) out side the sphere (ii) at the surface of the sphere (iii) inside the sphere, Electric field due to a dielectric sphere placed in a uniform electric field (a) out side the sphere (b) inside the sphere, Electric field due to a charge placed in dielectric medium and Gauss law, ClausiusMossorti relation in dielectrics. mobi
UNIT—III: Magnetostatics and Magnetic Field in Matter
Lorentz force, properties of magnetic field, Ampere's law, field due to a current carrying solid conducting cylinder (a) out side (b) at the surface and (H) inside the cylinder. Ampere's law in differential form, Introduction of Magnetic Vector potential, Poisson's equation for vector potential, Deduction of Bio-Savart law using Magnetic Vector potentials, Differential form of Ampere's law. Atomic magnet, Gyromagnetic ratio, Bohr-magneton, Larmor frequency, induced mangnentic moment and diamagnetism, spin magnetic moment, para and ferro magnetism, Intensity of Magnetization, Magnetic permeability and Susceptibility, free and boun'd current dences, Magnetio field due to a uniformly magnetized material and Non-uniformly magnetized material.
UNIT IV: Manwell's Equations and Electromagnetic Waves : Displacement current Maxwel's equations Electromagnetic waves. Electromagnetic waves in an Isotrophie medium, Properties of Electromagnetic waves. Energy density of Electromagnetic waves, Pointing vector Radiation pressure of free space, Electromagnetic waves in Despersive modrum Spectrum of Electromagnetic waves.
PAPER III: OPTICS
UNIT-II Diffraction Fresnel's diffraction, Half period zones, Fresnel's diffraction at a circular aperture, straight edge and Y a rectangular slit, Zone plate, Multiple foci of zone plate, comparison between zone plate and convex lens, Fraunhofer diffraction by single slit and a circular aperture, Fraunhofer diffraction by N parallel slits with two slits as a special case,Missing order, Plane diffraction grating and its use in determining wavelength, Dispersion by a grating, Rayleigh's criterion of resolution, Resolving power of a Telescope and a Grating.
(I) Polarization :
(III) (ii) Holography
Unit-IV Quantum optics & Photonics
(III) Fiber Optics
Paper-1 Inorganic Chemistry
*Molecular Orbital Theory
*Periodicity of p-block elements
*Some Important compounds of p-block Elements
*Chemistry of Noble Gases
Paper-II Organic Chemistry
*Mechanism of Organic Reactions
*Stereochemistry of Organic Compounds
*Alkenes, Cycloalkenes, Dienes and Methods of formation mechanism of dehydaration of alchohols and dehydrohalogenation of alkyl halides, regioselecticity in alcohols dehydration.
*Arenes and Aromaticity
*Aromatic Electrophilic substitution
*Alkyl and Aryl
Paper-II Physical Chemistry
*Solid State: Definition of space lattice,unit cell:
Paper I: DISCRETE MATHEMATICS
Unit-I Sets and Proposition-Cardinality, Principle of inclusion and exclusion, Mathematical induction. Relations and Functions-Binary relations, Equibalence relations and Prtitions, Partial ordered relations and Lattices, Chains and Antichains, Pigeon Hole principle.
Unit-II Boolean Algebrs- Lattices and Algebraic Structure, Duality, Distributive and Complemented Lattices. Boolean Lattices, Boolean functions and expressions. Fundamental theorem of arithmetic, divisibility in Z, Congruences, Chinese Remainder Theorem, Euler's : Function, primitive roots.
Unit-III Ligic and propositional calculus, proositions, simple and compound, basic logial operations, truth tables, tautologies and contradictions, propositional functions, quantifiers. Discrete numeric functions and Generating functions. Recurrence relationas and Recursibe Algorithms-Linear Recurrence relations with constant coefficients. Homogeneous solutions. Particular functions.
solution. Total solution. Solution by the method of generating
Unit-IV Basic consept of Graph Theory, Type of Graph (Connected Graph,
Unit-I Series-Infinite series and Convergent series. To ncentration convergence of a series-Comparison test, D'Alember centrationtest, Cauchy's ; condensation test, Gauss's test. De of simple er, pseudo
tests is not required). Alternating series. Absolute cor or reaction Taylor's theorem. Maclaurin's theorem. Powerseries e of half life (1+x)". of a tunction. Power series expansion of sin x, cos x, ex 1001
eries. Tests for lembert Bertrands test. (Derivation of osolute convergence rerseries expansion
s x, et, log (1+x).
Unit-II Derivative of the length of an arc. Pedal equations. Curvata Various formulae, Centre of curvature and Chord of curvat Partial differentiation. Euler's theorem for homogeneous function Chain rule of partial differentiation. Differentiation of implin functions.
Unit-III Envelopes, Maxima and minima of functions of two variables Lagrange's metod of undetermined multipliers, Asymptotes. Multiple points. Curve traching of standard curves. (Cartesian and Polar curves).
Unit-IV Beta and Gama functions, Reduction forumlae (simple standard forumlae), Double integrals in Certesian and Polar Coordinates, Change of order of integration. Triple integrals. Derichlet's integral.
Unit-V Areas, Rectification, volumes and surfaces of solids of revolutions
Paper III:ANALYTIC GEOMETRYAND OPTIMIZATION THEORY
Unit-I Polar equation of conics, Polar equaiton of tangent, normal and asymptotes, chord of contact, auxilliary circle, director circle of conics.
Unit-III Cylinder, Central Conicoids-Ellipsoid, Hyperboloid of one and two sheets, Tangent planes, Direct sphere, Normals.
Unit-IV Generating lines of hyperboloid of one sheet system of genrating lines and its properties. Reduction of a general equation of second degree in three-dimensions to standard forms.
Unit-V The linear programming problem. Basic solution. Some basic properties and theorems on convex sets. Fundamental theroem of L.P.P. Theory of simplex method only Duality. Fundamental theorem of duality, Properties and elementary theorems of duality only.