|
|
i. Complex Numbers: Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number. cube roots of unity, triangle inequality.
ii. Matrices and Determinants: Determinants and matrices of order two and three- properties of determinants, evaluation of determinants, addition and multiplication of matrices, adjoint and the inverse of a matrix. A solution of simultaneous linear equations using determinants.
iii. Quadratic Equations: Quadratic equations and their solutions, the relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.
iv. Permutations and Combinations: The Fundamental principle of counting; permutation as an arrangement and combination as a selection, meaning of P (n, r) and C (n, r), simple applications
v. Sequences and Series: Arithmetic, Geometric and Harmonic progressions. The relation between A.M., G.M. and H.M. Special series’ n, n2, n3, Arithmetic-Geometric series, exponential and logarithmic series.
vi. Vector Algebra: Vectors and scalars, the addition of two vectors, components of a vector in two and three-dimensional space, scalar and vector products, scalar and vector triple products. Application of vectors to plane geometry.
vii. Trigonometry: Trigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles including centroid, incentre, circumcentre and orthocentre. The solution of triangles. Heights and distances.
viii. Measures of Central Tendency and Dispersion: Calculation of mean, median and mode, standard deviation, variance and mean deviation for grouped and ungrouped data.
ix. Probability: Probability of an event, addition and multiplication theorems of probability and their applications. Conditional probability; Bayes’ theorem. Probability distribution of a random variate- Binomial and Poisson distributions and their properties.
x. Differential Calculus: Polynomial, rational, trigonometric, logarithmic and exponential functions. Graphs of simple functions. Limits, continuity and differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two. Applications of derivatives-maxima and minima of functions of one variable, tangents and normals, Rolle’s and Lagrange’s mean value theorems.
xi. Integral Calculus: Integral as an antiderivative, fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Integral as a limit of a sum. Properties of definite integrals. Evaluation of definite integral, determining areas of the regions bounded by simple curves.
xii. Differential Equations: Formation of differential equations. Solutions of first-order differential equations- the method of separation of variables, homogeneous and linear differential equations.
xiii. Two-Dimensional Geometry: Review of the Cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points, the slope of a line, parallel and perpendicular lines, and intercepts of a line on the coordinate axes.
xiv. The Straight Line and Pair of Straight Lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, a distance of a point from a line. Equations of internal and external bisectors of angles between two lines, equation of a family of lines passing through the point of intersection of two lines, point of intersections and angles between two lines. Pair of straight lines- condition for the general second-degree equation to represent a pair of lines, the point of intersection and angle between a pair of lines through the origin, a combined equation of the bisectors of the angles between a pair of lines.
xv. Circles and Family of Circles: Equation of a circle- standard form, general form, parametric form, the equation of a circle when the endpoints of a diameter are given. Radius and center of a circle, points of intersection of a line and a circle. The condition for a line to be tangent, an equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.
xvi. Conic Sections: Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, conditions for a line to be a tangent and point(s) of tangency.
|
|
|
i. Basic Concepts: Atomic and molecular masses; Chemical Equation and stoichiometry.
ii. States of Matter: Gaseous State: Gas laws, Avogadro’s hypothesis & gas equations; Kinetic Theory of Gases; Liquefaction, Critical Phenomena; Liquid State and Solid-state.
iii. Atomic Structure: Bohr’s Model; de Broglie equation; Quantum Mechanical Model; Aufbau’s Principle, Pauli’s Exclusion Principles, Hund’s Rule, Electronic Configuration; Bonding: Lewis structure, SEPR theory, hybridization, ionic, covalent and coordinate covalent bonds, bonding in solid-state, MO theory, bond order and magnetic properties of H2, O2, N2, F2.
iv. Solutions: Types, Units of concentration, Raoult’s Law, colligative properties, abnormal molecular weights.
v. Chemical Energetics and Thermodynamics: Internal Energy, Enthalpy, Hess’s Law, First & Second Laws of thermodynamics & applications; entropy, free energy; the spontaneity of a chemical reaction.
vi. Chemical Kinetics & Chemical Equilibrium: Rate and orders of a reaction; activation energy; catalyst; Rate law; physical & chemical equilibria; Le Chateliers’s principle; acid-base equilibrium; acids and bases; pH; buffers; solubility product.
vii. Redox Reactions, Electrochemistry & Surface Chemistry: Electron Transfer Concepts of Oxidation and reduction; Electrochemical cells; emf; Nernst Equation; Molar conductivity; Kohlrausch’s Law; Fuel Cells; Corrosion. Physical & Chemical adsorption isotherms; Colloids: Preparation & properties; Homogenous and Heterogeneous Catalysis; Enzymes.
viii. Periodic Properties, Chemical Families, Chemistry of Non-Metals & Metals: Modern Periodic Law; Ionization Energy, Electron Affinity, Atomic Radii, Valency, Trends in Groups and periods. Chemistry of s & p block elements; Alkali metals, Alkaline Earth Metals, Boron, Carbon, Nitrogen, Oxygen Halogen and Noble gases families; Hydrogen: Position, Ortho para, Isotopes, hybrids; Oxygen, Water, Hydrogen peroxide, Hard & Soft water; Ammonia, Nitrogen oxides, Nitric acid; Boron, Boric Acid, Borax; Carbides, Allotropy of Carbon; Sodium, Magnesium, Copper, Silver, Zinc, Transition Metals, and Lanthanides: Extraction, properties and uses.
ix. Co-Ordination Chemistry: Nomenclature, isomerism and bonding in coordination compounds; Werner’s Theory.
x. Nuclear Chemistry: Radioactivity, Nuclear reactions, Radiocarbon dating, Radioactive series, Artificial Transmutation.
xi. Organic Chemistry Fundamentals: Purification; detection and estimation of elements; Empirical and Molecular formulae, Classification, Functional Groups, IUPAC Nomenclature, Hemolytic and Heterolytic Bond Fissions, Structural and Stereoisomerism, Free radicals, Carbocations and carbanions; Substitution, addition, elimination and rearrangement reactions.
xii. Hydrocarbons & Halo Alkanes & Halo Alkenes: Alkanes, Alkenes and Alkynes, Haloalkanes & Halo alkenes: Preparation, properties and uses; Aromatic Hydrocarbons: Benzene, Structure, Resonance, Substitution in Benzene. Petroleum: Cracking, reforming, Octane number.
xiii. Organic Compounds Containing Oxygen, Nitrogen: Preparation properties and uses of Aromatic and aliphatic alcohols, Polyhydric alcohols, ethers, aldehydes, ketones, carboxylic acids and their derivatives; Cyanides, isocyanides, nitro compounds and amines.
xiv. Synthetic and Natural Polymers & Bimolecular: Natural and Synthetic polymers; Teflon, PVC, Polystyrene, Nylon 66 Terylene, and Bakelite; carbohydrates, amino acids and peptides, Nucleic Acids, lipids, etc.
xv. Chemistry in Action & Environmental Chemistry: Dyes, Medicines (Antipyretics, Analgesics and Antibiotics), Rocket Propellants; Acid Rain, Ozone Hole, Green House Effect, Global Warming Industrial Pollution.
|
|
|
i. Units and Dimensions: Units for measurement, the system of units, SI, fundamental and derived units, dimensions and their applications.
ii. Mechanics: Motion in a straight line, uniform and non-uniform motion, uniformly accelerated motion and its applications Scalars and Vectors, and their properties; resolution of vectors, scalar and vector products; uniform circular motion and its applications, projectile motion Newton’s Laws of motion; conservation of linear momentum and its applications, laws of friction, Concept of work, energy and power; energy-kinetic and potential; conservation of energy; different forms of energy. Elastic collisions in one and two dimensions. Centre of Mass of a many-particle system; the center of mass of a rigid body, rotational motion and torque.
Angular momentum and its conservation. Moments of inertia, parallel and perpendicular axes theorem, a moment of inertia for a thin rod, ring, disc and sphere. Gravitation: Acceleration due to gravity and its properties. One and two-dimensional motion under gravity. The universal law of gravitation, planetary motion, Kepler’s laws, artificial satellite, geostationary satellite, gravitational potential energy near the surface of the earth, gravitational potential and escape velocity.
C. Solids and Fluids:
Solids: Elastic properties, Hooke’s law, Young’s modulus, bulk modulus, modulus of rigidity.
Liquids: Cohesion and adhesion; surface energy and surface tension; the flow of fluids, Bernoulli’s theorem and its applications; viscosity, Stoke’s Law, terminal velocity.
Oscillations and Waves: Periodic motion, simple harmonic motion and its equation, oscillations of spring and simple pendulum. Wave motion, properties of waves, longitudinal and transverse waves, superposition of waves, Progressive and standing waves. Free and forced oscillations, resonance, the vibration of strings and air columns, beats, Doppler effect.
Heat and Thermodynamics: Thermal expansion of solids, liquids and gases and their specific heats, the relationship between Cp and Cv for gases, first and second laws of thermodynamics, Carnot cycle, the efficiency of heat engines. Transference of heat; thermal conductivity; black body radiations, Kirchoff’s law, Wein’s Law, Stefan’s law of radiation and Newton’s law of cooling.
D. Electrostatics, Current Electricity and Magnetostatics
Coulomb’s law, dielectric constant, electric field, lines of force, field due to dipole, electric flux, Gauss’s theorem and its applications; electric potential, potential due to a point charge; conductors and insulators, distribution of charge on conductors; capacitance, parallel plate capacitor, a combination of capacitors, energy stored in a capacitor.
Electric current: Cells-primary and secondary, the grouping of cells; resistance and specific resistivity and its temperature dependence. Ohm’s law, Kirchoff’s Law. Series and parallel circuits; Wheatstone’s Bridge and a potentiometer with their applications. Heating effects of current, electric power, the concept of thermoelectricity-See beck effect and thermocouple; chemical effect of current- Faraday’s laws of electrolysis.
Magnetic effects: Oersted’s experiment, Biot Savert’s law, magnetic field due to straight wire, circular loop and solenoid, a force on a moving charge in a uniform magnetic field (Lorentz force), forces and torques on a current-carrying conductor in a magnetic field, the force between current-carrying wires, moving coil galvanometer and conversion to ammeter and voltmeter
Magnetostatics: Bar magnet, magnetic field, lines of force, the torque on a bar magnet in a magnetic field, earth’s magnetic field; para, dia and ferromagnetism, magnetic induction, magnetic susceptibility, etc.
E. Electromagnetic Induction and Electromagnetic Waves
Induced e.m.f., Faraday’s law, Lenz’s law, self and mutual inductance; alternating currents, impedance and reactance, power in ac; circuits with LC and R series combination, resonant circuits, transformer and AC generator. Electromagnetic waves and their characteristics; electromagnetic spectrum from gamma to radio waves.
F. Ray and Wave Optics
Reflection and refraction of light at plane and curved surfaces, total internal reflection; optical fiber; deviation and dispersion of light by a prism; lens formula, magnification and resolving power; microscope and telescope Wave nature of light, interference, Young’s double experiment; thin films, Newton’s rings. Diffraction: diffraction due to a single slit; a diffraction grating, polarization and applications.
G. Modern Physics
Charge on an electron, photoelectric effect, Alpha particle scattering experiment, atomic masses, size of the nucleus; radioactivity, alpha, beta and gamma particles/rays. Radioactive decay law, half-life and mean a life of radioactive nuclei; Nuclear binding energy, mass-energy relationship, nuclear fission and nuclear fusion.
Energy bands in solids, conductors, insulators and semiconductors, PN junction, diode, diode as a rectifier, transistor action, transistor as an amplifier.
|
