RPET 2012 SYLLABUS
(SI system of units to be used)

## PHYSICS

Measurement  and  Units : Dimensions  of  a  physical  quantity,  uses  of  dimensional  analysis,  Errors  in measurement.

Dynamics  of  a  Particle: Newton's laws, motion in one, two and three dimensions, relative  motion, inertial  frames, circular motion, spring force, gravitational force, law of gravitation, variation of gravity with altitude, escape velocity, satellite motion, work, kinetic and potential energies, conservation of energy, momentum and angular momentum, elastic collisions in one and two dimensions.

Dynamics of a System of Particles : Centre of mass, motion under external forces, rigid bodies, rotation of a rigid body about a fixed axis, torque, angular acceleration, angular momentum, moment of inertia, radius of gyration, kinetic energy of rotation, combined translational and rotational motions, parallel and perpendicular axes theorems, moment of inertia of a ring, disc, cylinder and sphere.

Simple  Harmonic  Motion:  Basic  equation,  displacement,  velocity  and  acceleration,  graphical  and mathematical  representation,  kinetic  and  potential  energies,  Lissajous  figures,  simple  pendulum,  compound pendulum as a rigid oscillating body. Mass-spring system, damped harmonic oscillations, forced oscillations and resonance.

Intermolecular Forces : Attractive and repulsive forces, three states of matter, ionic, covalent, Van der Waals and metallic bondings, surface tension, angle of contact, capillarity, pressure difference across a spherical film, determination  of  surface  tension  by  capillary  rise  and  Jaeger's  methods,  elasticity,  Hooke's  law,  Young's modulus, shear and bulk moduli.

Kinetic Theory of Gases : Basic postulates, derivation of an expression for pressure exerted by an ideal gas, interpretation of temperature, equipartition of energy, specific heats of monoatomic and diatomic gases.

First Law of Thermodynamics : Dependence of work and heat on path, internal energy, isothermal, isobaric, isochoric and adiabatic processes, specific heats of an ideal gas, Mayer's relation.

Radiation : Black-body, Kirchhoff's law, Stefan's law, Newton's law of cooling, black-body spectrum, Wien's law.

Wave  Motion : Progressive  waves,  superposition  principle,  beats,  stationary  waves,  vibration  of  strings,  air columns, resonance, Doppler's principle and its applications to sound and light waves.

Nature  of  Light :  Light  as  wave  motion,  plane  and  spherical  waves,  Huygen's  principle,  reflection  and refraction at a plane surface, electromagnetic nature of light waves, quantum nature of light, coherent sources; Fresnel's  biprism,  measurement  of  wavelength,  Fresnel's  half  -period  zones,  rectilinear  propagation  of  light, diffraction at a circular obstacle, aperture and a slit for plane waves.

Electrostatics : Conservation and quantization of charge, Coulomb's law, electric field, superposition principle, electric flux, Gauss's law and its applications in simple cases, electric potential and potential difference, electric field and potential due to a dipole, capacitance, capacitors in series and parallel, energy stored in a capacitor.

Electric Circuits: Kirchhoff's laws, Wheat-stone bridge and its applications, potentiometer and its applications.

Magnetic  Field: Biot-Savart and Ampere's laws, magnetic field along the axis of a current carrying circular coil, inside a torroid, due to a straight wire, magnetic moment of a current loop, force on a moving charge and on a current carrying wire in a magnetic field, moving coil galvanometer, voltmeter, ammeter, electromagnetic induction, Faraday's and Lenz's laws, self and mutual inductances, transformer, energy stored in an inductor.

Alternating  Current  Circuits : Rotating coil in a magnetic field, ac, rms and peak values, phase relations between  voltage  and  current  in  a  resistor,  inductor,  capacitor  and  their  series  combinations,  impedance  and reactance (definitions only), instantaneous and average power in ac circuits, power factor, wattless current and choke  coil.

Modern  Physics :  Photons,  photoelectric  effect,  Bohr's  theory  of  hydrogen-like  atoms,  X-rays-production and properties, de Broglie hypothesis, Davisson and Germer  experiment, Thomson's  experiment, explanation of Bohr's orbits, uncertainty principle. radioactivity, nature of alpha, beta and gamma rays, laws of disintegration, half and mean lives, atomic nucleus, binding energy, nuclear energy by fission and fusion.

Electronics : Thermionic emission, work function, diode rectification and triode amplification, bands in solids (descriptive ideas only), conductors, semiconductors and insulators, intrinsic and extrinsic semiconductors, pn junction and its rectification properties.

## CHEMISTRY

Development of Classical Model of an Atom : Bohr model of an atom, calculation of radius of the Bohr's orbit, quantisation  of  electronic  energy  levels,  Spectral  evidence  for  quantisation,  introductory  concept  of  four quantum numbers, Pauli's exclusion principle, Hund's rule, AufBau principle, concept of the spatial distributions of s and p orbitals. Isotope

The  Periodic  Law :  Long  form  of  the  Periodic  Table.  Electronic  configuration  and  the  Periodic  Table. Periodicity  in  properties,  elementary  ideas  about  ionisation  potential,  electron  affinity,  electronegativity  and atomic radii. Position of hydrogen.

The  Theory  of  Chemical  Bonding :  The  ionic  bond,  characteristic  properties  of  ionic  compounds.  The covalent bond. Introductory concept of overlapping of orbitals, σ and π bonds, Co-ordinate bond. Oxidation number. Characteristic properties of covalent compounds, hybridisation as illustrated by common molecules like NH3, H2O, CH4, C2H4 and C2H2.

Chemical  Equilibrium  and  Ionic  Equillibria :  Generalised  expression  of  law  of  mass  action  and  its applications.  Arhenius  theory,  evidence  in  favour  of  dissociation  theory,  ionic  product  of  water,  hydrolysis, relation between hydrolysis constant, ionic product of water and dissociation constant, solubility product and its applications to analytical chemistry.

Chemical  Kinetics  :  Order  and  Molecularity  of  reaction.  Photochemical  reactions.  Expression  for  first  and second order reactions.

Acids and Bases : Hydrogen and hydroxyl ions in aqueous solution, Lewis concept of acids, dissociation of acids, pH value, Buffer solution, Theory of indicators for acid- alkali titrations, choice of indicators for acid-alkali  titrations.Oxidation-reduction,  ion  electron  concept.  Solid  and  liquid  state  of  matter,  Crystalline  and amorphus solids, Four types of crystalline solids, crystal lattice and unit cell. Types of solutions, properties of solutions, osmosis and osmotic pressure, preparation and properties of colloidal solutions.

Metals :  Nature  of  metallic  state.  The  metallic  bond.  Occurrence  of  metals  in  nature.  General  principle  of metallurgy as illustrated by methods used for the extraction of iron, copper, aluminium and silver from various types of ores. Preparation and properties of heavy water, ozone and hydrogen peroxide.

s-Block  Elements  :  General characteristics, Trends in variation of properties in periodic table of alkali and alkaline earth metals.

d-Block Elements : General characteristics, Elementary idea about paramagnetism and diamagnetism, different oxidation states of transition elements as illustrated by chromium, manganese and iron. Classification  of  organic  compounds,  nomenclature,  Homologous  series.  Functional  groups;  Isomerism (position,  chain,  functional,  metamerism).  Petroleum  as  the  commercial  source  of  hydrocarbon  and  organic chemicals, petroleum refining practice, octane number. General methods of preparation, properties and uses of alkanes (upto five carbon atoms). Isomerism of butanes and  pentanes.  Substitution  reaction  (free  radical  mechanism).

Alkenes  :  General  method  of  preparation, properties and uses, Ethylene: Electrophillic addition (Mechanism). Markownikoff's rule, Peroxide effect.

Alkynes  :  General  methods  of  preparation,  properties  and  uses,  Acetylene:  Substitution  reaction; Polymerisation. General  method  of  preparation,  properties  and  uses  of  mono,  di-  and  tri-halogen  derivatives  (excluding unsaturated)  upto  two  carbon  atoms,  haloform  reaction,  synthetic  uses  of  alkyl  halides,  polarity  of  carbon-halogen bond: Elementary concept of nucleophilic substitution. Freons preparation and uses. Grignard reagents and their synthetic applications. General methods of preparation, properties and uses of alcohols with reference to methyl and ethyl alcohols; Absolute alcohol and power alcohol. Fermentation. General methods of preparation, properties and uses of ether with reference to diethyl ether. General methods of preparation, properties and uses of aldehydes and ketones with reference to formaldehyde, acetaldehyde and acetone, Polymerization and condensation reaction (No mechanism). General  methods  of  preparation,  properties  and  uses  of  monocarboxylic  acids  with  reference  to  formic  and acetic acids. Derivatives of fatty acids; acetyl chloride, acetamide, acetic anhydride and ethyl acetate, Soaps and detergents. General methods of preparation, properties and  uses of aliphatic amines with reference to methyl and ethyl amines. Urea. Preparation,  properties  and  uses  of  Benzene  (structure  excluded),  nitrobenzene,  aniline  and  phenol, benzaldehyde, benzoic acid. Polymers, Examples of natural and synthetic polymers and their importance. Preparation and uses of nylon, terylene and Buna-S.

## MATHEMATICS

Algebra : Complex number as an ordered pair of real numbers; real and imaginary parts, absolute value,
graphical representation of complex numbers, triangle inequality, complex conjugate co-ordinates, roots of a complex number.

Theory of quadratic equations and expressions; relation between roots and coefficients. Arithmetic, geometric and harmonic progressions. Permutations and combinations. Elementary applications of mathematical induction. Binomial theorem. Determinants of order two and three and their elementary properties.

Matrices : definition, addition, subtraction and multiplication, transpose and adjoint of a matrix, inverse of a matrix.

Trigonometry : De Moivre's theorem and its applications; hyperbolic and inverse hyperbolic functions, separation of real and imaginary parts of a complex quantity.

Co-ordinateGeometry : Rectangular cartesian co- ordinates, distance between two points, area of a triangle. Straight lines, angle between two lines, parallel and perpendicular lines. Circle, equation of tangent and normal to a circle. Pole, polar, radical axis. Parametric representation. Parabola, tangent and normal, its properties. Coordinate axes and planes in three-dimensional space, coordinates of point in space, distance between two points, section formula, direction cosines & direction ratios of a line joining two points, projection of the join of two points on a line, angle between two lines, whose direction ratios are given.

Calculus : Functions; into, onto and one-one function, polynomial, rational, trigonometric, logarithmic and exponential functions.

Notion of limit and continuity of a function, derivative of a function at a point; derivatives of sum, difference, product and quotient of functions, derivatives of composite functions, implicit functions and inverse trigonometrical, logarithmic and exponential functions. Logarithmic differentiations. Geometrical interpretation of derivative; successive differentiation, tangents and normals. Sign of the derivative and monotonicity. Maximum and minimum values of a function.

Integration as the inverse process of differentiation; integration by parts and by substitutions; definite integral and its application for the determination of areas (simple cases), properties of definite integrals.