Physics

MEASUREMENT

Concept of length and time. Atomic astronomical range of variation of these physical quantities, different methods of measurement for different magnitudes of the same physical quantity. SI Units. Statement of all SI units. Dimensions and dimensional equations of mechanical quantities: area, volume, velocity, acceleration, momentum, force, energy, and work. Accuracy and errors in measurements.

MOTION

Displacement as a vector quantity, vectors, addition and subtraction of vectors, scalar (dot) and vector (cross) product (not to be done in depth). Newton’s first law of motion, conservation of energy and momentum, collisions, kinematics,Newton’s second law and definition of force. Inertial and gravitational mass, impulse, equations of motion, projectiles, work, relation between work and energy, power, Newton’s third law, friction, law of friction, sliding and rolling friction.

CIRCULAR MOTION

Angular velocity, motion of a body in circular orbits, centripetal force, banking of roads, planetary motion, statement of Kepler’s laws. Newton’s law of gravitation, gravitational field, gravitational potential energy. Earth’s satellites, orbital and escape velocity. Rigid body rotation, moment of inertia-definition and expression for a ring and a circular disc.torque, angular momentum and conservation of angular momentum.

LIQUIDS

General ideas of intermolecular forces, nature of liquids, cohesion and adhesion, surface tension, surface energy, angle of contact, capillary. Types of flow– Laminar and turbulent. Reynolds number. Bernoulli’s equation and its applications, viscosity. Stoke’s law (derivation from dimensional analysis) and its application.

ELASTICITY

Elastic and plastic behaviour of solids, stress, strain, Young’s modulus, bulk modulus, pure shear.

UNIVERSE

The constituents of universe, planets, stars determination of their distances and masses. Concept of parallax, brightness, magnitude scale, luminosity, surface temperature, stellar spectra (classification), energy source of stars (concept).

OSCILLATIONS AND WAVES

Periodic motion, simple harmonic motion (SHM) kinetic and potential energy in SHM, SHM oscillations due to spring, simple pendulum. Wave motion, speed of wave. Principal of superposition, reflection of waves, standing waves, beats, Doppler effect.

KINETIC THEORY OF GASES

Basic assumption, derivation of expression for pressure, temperature. Translational degrees of freedom, mean energy, gas equation, specific heats of Gases, relation between Cp and Cv and (Cp-Cv=R/J)

THERMODYNAMICS

Work and heat, First law of thermodynamics, reversible and irreversible processes. Carnot cycle (qualitative), efficiency of Carnot engine, Second law of thermodynamics, absolute scale of temperature, refrigerators, laws of radiation, emissive power, absorptive power, black-body radiation, Kirchhoff’s law. Stefan’s law, energy distribution of black body radiation, Wein’s law.

ELECTROSTATICS

Frictional electricity, Charges (+ – ),conservation of charges, elementary unit, Coulomb’s law, dielectric constant, electric field, electric field due to a point charge, dipole field and dipole behaviour in uniform two- dimensional electric field, flux, Gauss’s law in simple geometries, Conductors and insulators, presence of free charges and bound charges inside a conductor, capacitance (parallel plate series and parallel , energy of a capacitor, high voltage generators, atmospheric electricity (concept only).

CURRENT ELECTRICITY

Introduction (flow of current), sources of e. m .f. (cell: simple, secondary, chargeable), electric current, resistance of different materials, temperature dependence. thermistor, specific resistivity, colour, code for carbon resistances, Ohm’s law, Kirchhoff’s law, resistance in series and parallel, series and parallel circuits, Wheatstone’s bridge, measurement of voltages and currents, potentiometer.

THERMAL AND CHEMICAL EFFECTS OF CURRENTS

Electric power, heating effects of currents, chemical effects and laws of electrolysis,simple concepts of thermoelectricity.

MAGNETIC EFFECTS OF CURRENTS

Oersted’s observation., Biot-Savart law (magnetic field due to a current element), magnetic field due to a straight wire, circular loop an a solenoid . Forces on moving charge in a magnetic field (Lorentz force) example, forces and torques on currents in a magnetic field, Forces between two currents, definition of ampere, moving coil galvanometer, ammeter and voltmeter.

MAGNETISM

Bar magnet (comparison with solenoid), lines of force, torque on a bar magnet in magnetic field, earth’s magnetic field, tangent galvanometer.

ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

Induced e.m.f., Faraday’s law, self and mutual . Inductance. Alternating currents, impedance and resistance, power in a.c. circuits with L.C.R. series circuit, resonant circuit, phasor diagram, electrical machines and devices (transformer, induction coil, generator and simple motor, choke and starter).

ELECTRO MAGNETIC WAVES

Electromagnetic oscillation some history of e.m. waves. (Maxwell, Hertz, Bose, Marconi) Electromagnetic spectrum (radio, microwaves, infrared, optical, ultraviolet, X-rays and gamma rays) including elementary facts about their uses and propagation, properties of the atmosphere w.r.t. various parts of electromagnetic spectrum.

RAY OPTICS

Ray optics as a limiting case of wave optics, reflection, refraction, total internal reflection, optical fibres, curved mirrors, lenses, mirror and lens formulae. Dispersion, prisms, spectrometer and spectra –absorption and emission: scattering,rainbow. Punjab Technical University

WAVE OPTICS

Wave front and Huygen’s principle, concept of interference, Diffraction and polarization, Young’s double slit experiment & expression, Diffraction from a single slit (qualitative treatment).

OPTICAL INSTRUMENTS

Magnification and resolving power, telescope, microscope.

ELECTRONS AND PHOTONS

Discovery of electron, e/m for an electron charge of an electron, electrical conduction in gases, particle nature of light, Einstein’s photoelectric equation.

ATOMS AND NUCLEI

Rutherford model of the atom, Bohr’s model, Energy quantization, hydrogen spectrum, composition of a nucleus, atomic masses, isotopes, size of a nucleus, radioactivity, Mass-energy relation, fission, fusion, nuclear reactor, nuclear holocaust.

SOLIDS

Structure of crystalline solids, idea of a lattice, cubic and hexagonal crystal structures, packing in crystals.

SEMINCONDUCTOR DEVICES

Energy bands in solids conductor, insulators and semiconductors, p – n junction Diode, Junction Transistor, Logic gate and composition of gate, Diode as a rectifier, transistor as an amplifier and oscillator.

Mathematics Syllabus

NUMBER SYSTEM

Statements of algebraic and order properties of the system of natural numbers, integers, rational numbers and real numbers and simple basic deductions from theses properties.

Complex numbers. Representation of complex numbers as points in a plane. Algebra of complex numbers. Real and imaginary parts. Modulus and argument of a complex number. Conjugate of a complex number, cube roots of unity. Statements of the principal of mathematical induction in respect of natural numbers and simple applications.

CO-ORDINATE GEOMETRY

Distance formula and section formula. Equation of line in a plane. General equation of first degree. Angle between two lines. Parallel and perpendicular lines.Distance of a point from a line. Family of lines. Equation of a circle. General equation. Equation of tangent and normal to a circle. Radical axis of two circles. Family of circles. Parametric representation of a circle.Conic section. Equations of parabola, ellipse and hyperbola in standard form.

VECTORS

Vector as a directed line segment. Addition of Vector Multiplication of a Vector by a real number. Position Vector of a point. Section formula. Application of Vector to some geometrical results. Scalar and Vector product of two vectors. Scalar triple product, vector triple product.

THREE DIMENSIONAL GEOMETRY

Decomposition of a vector into three non-coplanar directions i, j, k as base in 3-dimensons. Angle between two vectors. Distance between two points. Section formula.Equations of lines and planes in 3-D. Angle between two lines, between a line and a plane as also between two planes. Distance of a point from a line and from a plane. Shortest distance between two lines. Equation of any plane passing through the intersection of two planes. Equation of a sphere in the form (r-C)2=a2, Equation of a sphere with the position Vector On the extremities of diameter.

TRIGONOMETRY

Angles and their measure in degrees and radians. Trigonometric functions of angles of arbitrary magnitude. Addition formulae. Sine, cosine, and tangent of multiples and sub multiples of angles. Periodicity and graph of sine, cosine and tangent functions. Trigonometrical ratios of related angles. Solutions of simple trigonometric equations.Sine and cosine formulae for triangles and simple cases of solutions of triangles, problems on heights and distances. Inverse trigonometric functions.

QUADRATIC EQUATIONS

Quadratic equations and their solutions. Relationship between the roots and the coefficients. Formation of quadratic equations with given roots. Criteria for the nature of the roots of quadratic equation.

SEQUENCES AND SERIES

AP, GP, n2, n3 and their sums.

EXPONENTIAL AND LOGARITHMIC SERIES.

The infinite series for e, log (1+x), log[1+x)/(1-x)]

PERMUTATIONS, COMBINATIONS AND BINOMIAL THEOREM

Elementary study of combinations. Values of npr and ncr, simple applications including circular permutations. Binomial theorem for a positive integral index and its proof.Statement only for the binomial theorem for an arbitrary index and its application to approximations. Properties of binomial co-efficient.

MATRICES AND DETERNINANTS

Addition, scalar multiplication and multiplication of matrices, non-computability of matrix multiplication. Singular and non-singular matrices. Linear equations in matrix notations. Determinants: minors and cofactors. Expansion of determinant, properties of elementary transformation of determinants. Application of determinants in solutions of equations. Cramer’s rule. Adjoint and inverse of a matrix and its properties. Applications of matrices in solving simultaneous equations in three variables.

DIFFERENTIAL CALCULUS

Concept of real function, its domain and range, one-one and inverse functions, composition of functions. Notions of right hand and left hand limits and the limits of a function. Fundamental theorems on limits. Continuity of a function. Properties of continuous functions. Continuity of polynomial, trigonometric, exponential,logarithmic and inverse trigonometric functions. Derivative of a function, its geometrical and physical significance, relationship between continuity and differentiability.

Derivative of sum, difference, product, quotient function and of the functions of a function(chain rule), derivatives of trigonometric functions. Logarithmic and exponential functions. Differentiation of functions expressed in parametric form, derivatives of higher order. Applications of the derivative: increasing and decreasing functions, maxima and minima, Rolle’s and Mean value theorems(without proof).

DIFFERENTIAL EQUATIONS

Order and degree, formation of differential equation, general and particular solution, solution by the method of variables, separable. Homogeneous equations and their solutions. Solution of the linear equation of the first order with constant coefficients. Integration as the inverse of differentiation, indefinite integral, properties of integrals, fundamental integrals involving algebraic trigonometric and exponential functions, integration by substitution and by parts. Definition of definite integrals as the limit of a sum illustrated by simple examples, fundamental theorem of Calculus, evaluation of definite integrals, transformation of definite integrals by substitution, properties of definite integrals. Application to determination of area under plane curves in simple cases.

STATISTICS

Population and sample, Measures of central tendency and dispersion, Point and internal estimation(of mean only), Scatter diagrams and Pearson’s correlation coefficients. Calculations of the regression coefficients and the two lines of regression by the method of least squares.

PROBABILITY

Random experiments and sample space, Events. Probability on a discrete sample space, addition theorem. Conditional Probability, multiplication theorem. Independent events. Random variables (discrete) , Binomial distributions

 Chemistry Syllabus

ATOMS AND ATOMIC STRUCTURE

Measurements in Chemistry (Significant figures, S.I. Units), Mole concept, Nature of light and electromagnetic waves, atomic spectra, Bohr model, line spectra ( a brief idea). In adequacy of Bohr’s Model, concept of an atomic orbital, quantum numbers and its application to electronic structures of atoms).Paulo’s exclusion principle. Aufbau principle, Stability of filled an half filled orbital Configuration of transition elements in 3d series. Dual nature of particle and radiation (photoelectric effect etc.) de-Brogile equation, uncertainty principle (simple numerical problems), Hund’s rule.

PERIODIC PROPERTIES OF ELEMENTS

Periodic law, long form of periodic table. Periodicity in properties like atomic radii and volume, ionic radii, ionization energy, electron affinity. Division of elements into s, p, d and f blocks.

CHEMICAL BONDING ANDMOLECULAR STRUCTURE

Concept of orbital overlap in bond formation, sigma and pi bonds shapes. Of molecules (VSEPR) Theory, hybridization (sp, sp2, sp3, dsp2, sp3d, sp3d2), properties of covalentcompounds, shapes of simple molecules like H2O, NH3, CH4, PF5, SF6, C2H4 and C2H2. Coordinate bond formation with a few examples, Ionic bonds; definition, factors influencing the formation of ionic compounds. An elementary treatment of metallic and hydrogen bonds. Idea of molecular orbital, bonding and anti bonding, molecular orbital picture in hydrogen and oxygen molecules only.

CHEMISTRY OF REPRESENTATIVE ELEMENTS

The chemistry of s and p block elements with reference to general trends in physical and chemical properties, anomalous behavior of first member of each group, diagonal relationship.

Group 1 Elements: – Alkali metals;

Group 2 Elements: – Alkali earth metals;

Group 13 Elements: – Boron family;

Group 14 Elements:- Carbon and silicon family;

Group 15 Elements:- Nitrogen family;

Group 16 Elements:- Oxygen family;

Group 17 Elements:- Halogen family; hydrogen

Group 18 Elements:- Noble gases;

Preparation and properties of a few important compounds of representative elements (like halides, oxides and oxyacids etc.)

TRANSITION METALS INCLUDING LANTHANIDES

Electronic configuration: General characteristics properties with special reference to color, magnetism, complex formation and oxidation states. First row transition metals and general properties of their compounds (oxides, halides and suplhides), Inner transition elements, general feature: Chemistry of iron, copper, silver, gold zinc and mercury (occurrence and extraction without technical details). Preparation of few compounds: Potassium dichromate, Potassium permanganate.

COORDINATION CHEMISTRY AND ORGANOMETALLICS

Coordination Compounds nomenclature; Isomerism in Coordination compounds; Bonding in Coordination compounds; Valence Bond Theory Application of Coordination Compounds: Compounds containing metal carbon bonds; Application of organometallics.

CHEMICAL THERMODYNAMICS

Energy changes during a chemical reaction. First law of thermodynamics. Concepts of internal energy and enthalpy. Application of first law of thermodynamics. Hess’s law of constant heat summation, Heat of reaction, Heat of neutralization, heat of combustion, heat of fusion and vapourisation). Numericals based on the above concepts.

Second law of Thermodynamics : Entropy, free energy, spontaneity of a chemical reaction, free energy and chemical equilibrium, free energy available for useful work.

Third law of Thermodynamics (concept of zero entropy only)

CHEMICAL EQUILIBRIUM

Law of mass action and its application to chemical equilibrium. Effect of changing the conditions of system at equilibrium-Le- chatelier’s principle. Equilibrium involving ions. Ionisation of electrolytes, weak and strong electrolytes acid –base equilibrium, Bronsted & Lowry’s concept of acids and bases on these concepts.

CHEMICAL KINETICS

Rate of reaction-symbolic expressions, rate expression. Units of rates and specific rate constants. Order of reaction (n suitable examples).  etermination of order of reaction and concentration(first order reactions only). Temperature dependence of rate constant. Activation energy, Photochemical reactions.

STATES OF MATTER

Gaseous state: Properties of a gas, gas laws, kinetic molecular theory of gases. Solid state: classification of solids, X –ray studies of crystal lattices & unit cell. Liquid state; Properties of liquids like vapour pressure, surface tension, viscosity.

NUCLEAR & RADIOCHEMISTRY

Nature of radiation from radioactive substances: nuclear structure and nuclear properties. Nuclear reaction; radioactive disintegration series; artificial transmutation of elements. Isotopes and their uses. Radio carbon dating. Synthetic elements.

SOLUTIONS

Types of solutions, Vapour pressure of solutions and Raoults’ law. Colligative properties of solutions. Calculation of molecular masses. Electrolyte solutions.

ELECTROCHEMISTRY

Electrolysis, electrolytic conduction ( specific, equivalent and molar conductance ) Kohlrausch law. Voltaic/galvanic cell, electrode potential and electromotive force, Gibbs free energy and cell potential. Dependence of EMF on concentration and temperature (Nernst Equation). Electrode potential and electrolysis. Some commercial cells (batteries and fuel cells ). Corrosion.

SURFACE AND CATALYSIS

Absorption, colloids, emulsions, micelles, modern developments. Interfaces, STEM and technology. Homogeneous and heterogeneous catalysis, structure of a catalyst. Structure of a catalyst.

CARBON AND ITS COMPOUNDS INTRODUCTION TO CARBON COMPOUNDS

Elemental Carbon. Inorganic compounds of carbon (oxides, and carbides).

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