Unit 1: General Physics

Units and Dimensions

• Units and dimensions, dimensional analysis.
• Least count and significant figures.

Experimental Analysis

• Methods of measurement and error analysis for physical quantities pertaining to the following experiments:
• Experiments based on using Vernier calipers and screw gauge (micrometer).
• Determination of g using the simple pendulum.
• Young’s modulus by Searle’s method.
• Specific heat of a liquid using calorimeter, the focal length of a concave mirror and a convex lens using the u-v method.
• The speed of sound using resonance column.
• Verification of Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box.

Unit 2 Mechanics

Kinematics

• Kinematics in one and two dimensions (Cartesian coordinates only), projectiles.
• Uniform Circular motion, relative velocity.

Newton’s laws of motion

• Newton’s laws of motion, Inertial and uniformly accelerated frames of reference.
• Static and dynamic friction, Kinetic and potential energy.
• Work and power.
• Conservation of linear momentum and mechanical energy.

Systems of particles

• Centre of mass and its motion; Impulse.
• Elastic and inelastic collisions.

Gravitation

• Laws of gravitation.
• Gravitational potential and field, acceleration due to gravity.
• The motion of planets and satellites in circular orbits and escape velocity.

Inertia and Momentum

• Rigid body, the moment of inertia, parallel and perpendicular axes theorems, the moment of inertia of uniform bodies with simple geometrical shapes.
• Angular momentum, Torque, Conservation of angular momentum.
• Dynamics of rigid bodies with fixed axis of rotation.
• Rolling without slipping of rings, cylinders, and spheres; Equilibrium of rigid bodies.
• The collision of point masses with rigid bodies.

Harmonic motions

• Linear and angular simple harmonic motions.
• Hooke’s law, Young’s modulus.

The pressure in a fluid

• Pascal’s law; Buoyancy.
• Surface energy and surface tension, capillary rise, viscosity (Poiseuille’s equation excluded).
• Stoke’s law, terminal velocity, Streamline flow, the equation of continuity, Bernoulli’s theorem and its applications.

Waves

• Wave motion (plane waves only), longitudinal and transverse waves, superposition of waves.
• Progressive and stationary waves.
• The vibration of strings and air columns, Resonance, Beats.
• The speed of sound in gases; Doppler effect (in sound).

Thermal Physics

• Thermal expansion of solids, liquids, and gases, calorimetry, latent heat
• .
• Heat conduction in one dimension, elementary concepts of convection and radiation, Newton’s law of cooling; Ideal gas laws.
• Specific heats (Cv and Cp for monatomic and diatomic gases), Isothermal and adiabatic processes, bulk modulus of gases.
• Equivalence of heat and work, First law of thermodynamics and its applications (only for ideal gases).
• Blackbody radiation, absorptive and emissive powers, Kirchhoff’s law.
• Wien’s displacement law, Stefan’s law.

Unit 3 Electricity and magnetism

Electric Fields

• Coulomb’s law; Electric field and potential.
• The electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field.
• Electric field lines; Flux of the electric field.
• Gauss’s law and its application in simple cases, such as, to find field due to the infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.

Capacitance

• Capacitance, Parallel plate capacitor with and without dielectrics.
• Capacitors in series and parallel, Energy stored in a capacitor.

Electric current

• Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells.
• Kirchhoff’s laws and simple applications.
• Heating effect of current.

Magnetic Fields

• Biot Savart’s law and Ampere’s law.
• Magnetic field near a current-carrying straight wire, along with the axis of a circular coil and inside a long straight solenoid.
• Force on a moving charge and on a current-carrying wire in a uniform magnetic field.
• The magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop.
• Moving coil galvanometer, voltmeter, ammeter and their conversions.

Electromagnetic Induction

• Electromagnetic induction, Faraday’s law, Lenz’s law.
• Self and mutual inductance.
• RC, LR and LC circuits with D.C. and A.C. sources.

Unit 4 Optics

Reflection and Refraction

• Rectilinear propagation of light.
• Reflection and refraction at plane and spherical surfaces, total internal reflection.
• Deviation and dispersion of light by a prism.
• Thin lenses, Combinations of mirrors and thin lenses; Magnification.

Wave nature of light

• Huygen’s principle.
• Interference limited to Young’s double-slit experiment.

Unit 5 Modern Physics

Atoms and Nuclei

• Atomic nucleus; Alpha, beta and gamma radiations; Law of radioactive decay.
• Decay constant; Half-life and mean life; Binding energy and its calculation; Fission and fusion processes; Energy calculation in these processes.
• Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Characteristic and continuous X-rays.
• Moseley’s law; de Broglie wavelength of matter waves.

Unit 1 General topics

• The concept of atoms and molecules, Mole concept, Dalton’s atomic theory.
• Balanced chemical equations, Chemical formulas, Calculations on mole concept involving common oxidation and reduction.
• Neutralization and displacement reactions.
• Concentration in terms of mole fraction, molality, molarity, and normality.

Unit 2 Liquid and the Gaseous States

• The absolute scale of temperature, ideal gas equation, Deviation from ideality, van der Waals equation.
• Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature.
• Law of partial pressures, Vapour pressure and Diffusion of gases.

Unit 3 Atomic Structure and Chemical Bonding

• Bohr model, the spectrum of hydrogen atom, quantum numbers, Wave-particle duality, de Broglie hypothesis and Uncertainty principle.
• Qualitative quantum mechanical picture of the hydrogen atom, shapes of s, p and d orbitals, Electronic configurations of elements (up to atomic number 36), Aufbau principle, Pauli exclusion principle and Hund’s rule.
• Orbital overlap and the covalent bond; Hybridization involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond.
• Polarity in molecules, dipole moment (qualitative aspects only), VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral).

Unit 4 Energetics

• First law of Thermodynamics, Internal energy, work, and heat.
• Pressure-Volume work, Enthalpy, Hess’s law; Heat of reaction, fusion, and vaporization.
• The second law of Thermodynamics, Entropy, Free energy, and criterion of spontaneity.

Unit 5 Chemical Equilibrium

• Law of mass action, Equilibrium constant, and Le Chatelier’s principle (effect of concentration, temperature and pressure).
• The significance of Delta G and Delta G0 in chemical equilibrium, Solubility product, common ion effect, pH, and buffer solutions.
• Acids and bases (Bronsted and Lewis concepts) and Hydrolysis of salts.

Unit 6 Electrochemistry

• Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to Delta G.
• Electrochemical series, emf of galvanic cells, Faraday’s laws of electrolysis.
• Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law, and Concentration cells.

Unit 7 Chemical Kinetics

• Rates of chemical reactions, Order of reactions, and Rate constant.
• First order reactions, Temperature dependence of rate constant (Arrhenius equation).

Unit 8 Solid State

• Classification of solids, crystalline state, and seven crystal systems (cell parameters a, b, c, Alpha, Beta, Gamma).
• Close-packed structure of solids (cubic), packing in fcc, bcc and hcp lattices.
• Nearest neighbours, ionic radii, simple ionic compounds, point defects.

Unit 9 Solutions

• Raoult’s law, Molecular weight determination from lowering of vapor pressure, elevation of boiling point and depression of freezing point.
• Surface chemistry: Elementary concepts of adsorption (excluding adsorption isotherms).
• Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants, and micelles (only definitions and examples).

Unit 10 Nuclear chemistry

• Radioactivity: isotopes and isobars, Properties of Alpha, Beta, and Gamma rays.
• Kinetics of radioactive decay (decay series excluded), carbon dating.
• Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions.

Unit 1 Isolation/preparation and properties of the non-metals

• Boron, silicon, nitrogen, phosphorus, oxygen, sulphur, and halogens.
• Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur.

Unit 2 Preparation and properties of the compounds

• Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium.
• Boron: diborane, boric acid, borax, and Aluminium: alumina, aluminium chloride and alums.
• Carbon: oxides and oxyacid (carbonic acid), and Silicon: silicones, silicates and silicon carbide.
• Nitrogen: oxides, oxyacids and ammonia, and Phosphorus: oxides, oxyacids (phosphorus acid phosphoric acid) and phosphine.
• Oxygen: ozone and hydrogen peroxide, and Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate.
• Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.

Unit 3 Transition elements (3d series)

• Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment.
• Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).

Unit 4 Preparation and properties of the following compounds

• Oxides and chlorides of tin, and lead.
• Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+.
• Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate.

Unit 5 Ores and minerals

• Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminum, zinc, and silver.
• Extractive metallurgy: Chemical principles, and reactions only (industrial details excluded).

Unit 6 Reduction Methods

• Carbon reduction method (iron and tin), Self-reduction method (copper and lead), Electrolytic reduction method (magnesium and aluminium), Cyanide process (silver and gold).
• Principles of qualitative analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide.

Unit 1 Basic Concepts

• Hybridization of carbon; _ and _-bonds; Shapes of simple organic molecules, Structural and geometrical isomerism, Optical isomerism of compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded).
• IUPAC nomenclature of simple organic compounds (only hydrocarbons, monofunctional, and bifunctional compounds), Conformations of ethane and butane (Newman projections), Resonance and hyperconjugation.
• Keto-enol tautomerism, Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds: definition and their effects on physical properties of alcohols and carboxylic acids.
• Inductive and resonance effects on acidity and basicity of organic acids and bases, Polarity and inductive effects in alkyl halides.
• Reactive intermediates produced during homolytic and heterolytic bond cleavage, Formation, structure and stability of carbocations, carbanions and free radicals.

Unit 2 Preparation, properties, and reactions of Alkenes and Alkynes

• Physical properties of alkenes and alkynes (boiling points, density and dipole moments); Acidity of alkynes.
• Acid-catalyzed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination), Reactions of alkenes with KMnO4 and ozone.
• Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions.
• Electrophilic addition reactions of alkenes with X2, HX, HOX, and H2O (X=halogen), Addition reactions of alkynes, and Metal acetylides.

Unit 3 Properties, Preparation, and reactions of Alkanes

• Homologous series, physical properties of alkanes (melting points, boiling points and density).
• Combustion and halogenation of alkanes.
• Preparation of alkanes by Wurtz reaction and decarboxylation reactions.

Unit 4 Reactions of Phenol and Benzene

• Structure and aromaticity, Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation, Effect of o-, m- and p-directing groups in monosubstituted benzenes.
• Phenols: Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation); Reimer-Tiemann reaction, and Kolbe reaction.

Unit 5 Characteristic Reactions

• Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution reactions.
• Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and Ketones.
• Ethers: Preparation by Williamson’s Synthesis; Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation; aldol condensation, Perkin reaction; Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard addition).
• Carboxylic acids: formation of esters, acid chlorides, and amides, ester hydrolysis.
• Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, the azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction.
• Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution).

Unit 6 Carbohydrates

• Classification, mono- and disaccharides (glucose and sucrose), Oxidation, reduction, glycoside formation and hydrolysis of sucrose.
• Amino acids and peptides: General structure (only primary structure for peptides) and physical properties.
• Properties and uses of some important polymers: Natural rubber, cellulose, nylon, Teflon, and PVC.

Unit 7 Practical Organic Chemistry

• Detection of elements (N, S, halogens).
• Detection and identification of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino and nitro.
• Chemical methods of separation of mono-functional organic compounds from binary mixtures.

Unit 1 Algebra

Complex Numbers

• Algebra of complex numbers, addition, multiplication, conjugation.
• Polar representation, properties of modulus and principal argument.
• Triangle inequality, cube roots of unity.
• Geometric interpretations.

Quadratic Equations

• Quadratic equations with real coefficients.
• Relations between roots and coefficients.
• Formation of quadratic equations with given roots.
• Symmetric functions of roots.

Sequence and Series

• Arithmetic, geometric, and harmonic progressions.
• Arithmetic, geometric, and harmonic means.
• Sums of finite arithmetic and geometric progressions, infinite geometric series.
• Sums of squares and cubes of the first n natural numbers.

Logarithms

• Logarithms and their properties.

Permutation and Combination

• Problems on permutations and combinations.

Binomial Theorem

• Binomial theorem for a positive integral index.
• Properties of binomial coefficients.

Matrices and Determinants

• Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix.
• Determinant of a square matrix of order up to three, the inverse of a square matrix of order up to three.
• Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties.
• Solutions of simultaneous linear equations in two or three variables.

Probability

• Addition and multiplication rules of probability, conditional probability.
• Bayes Theorem, independence of events.
• Computation of probability of events using permutations and combinations.

Unit 2 Trigonometry

Trigonometric Functions

• Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae.
• Formulae involving multiple and submultiple angles.
• The general solution of trigonometric equations.

Inverse Trigonometric Functions

• Relations between sides and angles of a triangle, sine rule, cosine rule.
• Half-angle formula and the area of a triangle.
• Inverse trigonometric functions (principal value only).

Unit 3 Vectors

Properties of Vectors

• The addition of vectors, scalar multiplication.
• Dot and cross products.
• Scalar triple products and their geometrical interpretations.

Unit 4 Differential Calculus

Functions

• Real-valued functions of a real variable, into, onto and one-to-one functions.
• Sum, difference, product, and quotient of two functions.
• Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
• Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Limits and Continuity

• Limit and continuity of a function.
• Limit and continuity of the sum, difference, product and quotient of two functions.
• L’Hospital rule of evaluation of limits of functions.

Derivatives

• The derivative of a function, the derivative of the sum, difference, product and quotient of two functions.
• Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
• Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative.
• Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function.
• Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Unit 5 Integral calculus

Integration

• Integration as the inverse process of differentiation.
• Indefinite integrals of standard functions, definite integrals, and their properties.
• Fundamental Theorem of Integral Calculus.
• Integration by parts, integration by the methods of substitution and partial fractions.

Application of Integration

• Application of definite integrals to the determination of Areas involving simple curves.

Differential Equations

• Formation of ordinary differential equations.
• The solution of homogeneous differential equations, separation of variables method.
• Linear first order differential equations.