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Physics And Measurement

Physics, technology and society, SI units, Fundamental and derived units Least count, accuracy and precision of measuring instruments, measurement errors, Dimensions of Physical quantities, dimensional analysis and its applications.

Laws Of Motion

Force and Inertia, Newton’s First Law of motion; Momentum, Newton’s Second Law of motion; Impulse; Newton’s Third Law of motion. Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces, Static and Kinetic friction, laws of friction, rolling friction, Dynamics of uniform circular motion: Centripetal force and its applications.

Kinematics

Frame of reference Motion in a straight line: Position-time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion. Scalars and Vectors, Vector addition and Subtraction, Zero Vector, Scalar and Vector products, Unit Vector, Resolution of a Vector Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.

Work, Energy And Power, Work done by a constant force and a variable force; kinetic and potential energies, work energy theorem, Power, Potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces; Elastic and inelastic collisions in one and two dimensions.

Gravitation

The universal law of gravitation, Acceleration due to gravity and its variation with altitude and depth, Kepler’s laws of planetary motion, Gravitational potential energy; gravitational potential, Escape velocity, Orbital velocity of a satellite, Geo-stationary satellites.

Rotational Motion

Centre of mass of a two-particle system, Centre of mass of a rigid body, Basic concepts of rotational motion, moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Rigid body rotation, equations of rotational motion.

Thermodynamics

Thermal equilibrium, zeroth law of thermodynamics, concept of temperature. Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency.

Properties of Solids And Liquids

Elastic behaviour, Stress-strain relationship, Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications. Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, Reynolds number. Bernoulli’s principle and its applications. Surface energy and surface tension, angle of contact, application of surface tension – drops, bubbles and capillary rise. Heat, temperature, thermal expansion; specific heat capacity, calorimetry; change of state, latent heat. Heat transfer-conduction, convection and radiation, Newton’s law of cooling.

Kinetic Theory of Gases

Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases – assumptions, concept of pressure. Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path, Avogadro’s number.

Oscillations And Waves

Periodic motion: period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion (S.H.M.) and its equation; phase; oscillations of a spring -restoring force and force constant; energy in SHM – kinetic and potential energies; Simple pendulum – derivation of expression for its time period; Free, forced and damped oscillations, resonance.

Wave motion: Longitudinal and transverse waves, speed of a wave. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler Effect in sound.

Current Electricity

Electric field, Electric current, Drift velocity, Ohm’s law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and non-ohmic conductors, Electrical energy and power, Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance. Electric Cell and its internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff’s laws and their applications. Wheatstone bridge, Metre bridge. Potentiometer – principle and its applications.

Communication Systems

Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation, Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only).

Atoms and Nuclei

Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity-alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion.

Optics  

Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifying powers, Wave optics.

Sets, relations and functions

Sets and their representation Union, intersection and complement of sets and their algebraic properties Power set; Relation, Types of relations, equivalence relations, functions; One-one, into and onto functions, the composition of functions.

Complex numbers and quadratic equations

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

Matrices and determinants

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

Mathematical induction

Principle of Mathematical Induction and its simple applications

Permutations and combinations

Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

Binomial theorem and its simple applications, Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients simple applications

Sequences and series

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers relation between A.M. and G.M. sum upto n terms of special series: S n, S n2, Sn3 Arithmetic – Geometric progression

Limit, continuity and differentiability

Real – valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions Graphs of simple functions Limits, continuity and differentiability 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 upto two Rolle’s and Lagrange’s Mean Value Theorems Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.

Integral calculus

Integral as an anti – derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities, Evaluation of simple integrals of the type Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

Differential equations

Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy/dx+p(x)y=q(x).

Co-ordinate geometry

Cartesian system of rectangular co-ordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes, Straight lines, Circles, conic sections.

Three-dimensional geometry

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.

Vector algebra

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product.

Statistics and probability

Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

Probability: Probability of an event, addition and multiplication theorems of probability, Bayes’ theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

Trigonometry

Trigonometrical identities and equations, Trigonometrical functions, Inverse trigonometrical functions and their properties, Heights and Distances

Mathematical reasoning, Statements, logical operations and, or, implies, implied by, if and only if Understanding of tautology, contradiction, converse and contrapositive

Some Basic Concepts in Chemistry

Matter and its nature, Dalton’s atomic theory Concept of atom, molecule, element and compound Physical quantities and their measurements in Chemistry, precision and accuracy, significant figures, S.I. Units, dimensional analysis Laws of chemical combination Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae Chemical equations and stoichiometry.

States of Matter

Gaseous State: Measurable properties of gases Gas laws – Boyle’s law, Charle’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial pressure Concept of Absolute scale of temperature; Ideal gas equation Kinetic theory of gases (only postulates) Concept of average, root mean square and most probable velocities Real gases, deviation from Ideal behaviour, compressibility factor and van der Waals equation.

Liquid State: Properties of liquids – vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only).

Solid State: Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea) Bragg’s Law and its applications Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids Electrical, magnetic and dielectric properties.

Chemical Bonding And Molecular Structure

Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy. Kossel – Lewis approach to chemical bond formation, concept of ionic and covalent bonds.

Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple molecules.

Quantum mechanical approach to covalent bonding: Valence bond theory – Its important features, concept of hybridization involving s, p and d orbitals Resonance Molecular Orbital Theory – Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy.

Atomic Structure

Elementary ideas of quantum mechanics, quantum mechanical model of atom, its important features, concept of atomic orbitals as one electron wave functions various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance shapes of s, p and d – orbitals, electron spin and spin quantum number Rules for filling electrons in orbitals – aufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals, Thomson and Rutherford atomic models and their limitations Nature of electromagnetic radiation, photoelectric effect Spectrum of hydrogen atom, Bohr model of hydrogen atom – its postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohr’s model Dual nature of matter, de-Broglie’s relationship, Heisenberg uncertainty principle.

Chemical Thermodynamics

First law of thermodynamics – Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity Hess’s law of constant heat summation Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution Second law of thermodynamics Spontaneity of processes DS of the universe and DG of the system as criteria for spontaneity, Dgo (Standard Gibbs energy change) and equilibrium constant

Solutions

Different methods for expressing concentration of solution – molality, molarity, mole fraction, percentage (by volume and mass both), vapour pressure of solutions and Raoult’s Law – Ideal and non-ideal solutions, vapour pressure – composition, plots for ideal and non-ideal solutions Colligative properties of dilute solutions – relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure Determination of molecular mass using colligative properties; Abnormal value of molar mass, van’t Hoff factor and its significance.

Equilibrium

Equilibria involving physical processes: Solid -liquid, liquid – gas and solid – gas equilibria, Henry’s law, general characterics of equilibrium involving physical processes. Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of DG and DGo in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s principle.

Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius, Bronsted – Lowry and Lewis) and their ionization, acid-base equilibria (including multistage ionization) and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions.

Redox Reactions and Electrochemistry

Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrausch’s law and its applications. Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.

Surface Chemistry

Colloidal state- distinction among true solutions, colloids and suspensions, classification of colloids – lyophilic, lyophobic multi molecular, macromolecular and associated colloids (micelles), preparation and properties of colloids – Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation and flocculation Emulsions and their characteristics. Adsorption- Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids – Freundlich and Langmuir adsorption isotherms, adsorption from solutions.

Environmental Chemistry

Environmental pollution – Atmospheric, water and soil. Atmospheric pollution – Tropospheric and Stratospheric Tropospheric pollutants – Gaseous pollutants: Oxides of carbon, nitrogen and sulphur, hydrocarbons; their sources, harmful effects and prevention; Greenhouse effect and Global warming; Acid rain; Particulate pollutants: Smoke, dust, smog, fumes, mist; their sources, harmful effects and prevention. Stratospheric pollution- Formation and breakdown of ozone, depletion of ozone layer – its mechanism and effects. Water Pollution – Major pollutants such as, pathogens, organic wastes and chemical pollutants; their harmful effects and prevention. Soil pollution – Major pollutants such as: Pesticides (insecticides, herbicides and fungicides), their harmful effects and prevention. Strategies to control environmental pollution.

D – And F – BLOCK ELEMENTS

Transition Elements: General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first row transition elements – physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation; Preparation, properties and uses of K2 Cr2 O7 and KMnO4, Inner Transition Elements: Lanthanoids – Electronic configuration, oxidation states and lanthanoid contraction.

Hydrogen

Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen Physical and chemical properties of water and heavy water Structure, preparation, reactions and uses of hydrogen peroxide Hydrogen as a fuel

S – Block Elements (Alkali and Alkaline Earth Metals)

Group – 1 and 2 Elements: General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships. Preparation and properties of some important compounds – sodium carbonate and sodium hydroxide; Industrial uses of lime, limestone, Plaster of Paris and cement; Biological significance of Na, K, Mg and Ca.

P – Block Elements

Group – 13: Preparation, properties and uses of boron and aluminium; properties of boric acid, diborane, boron trifluoride, aluminium chloride and alums. Group – 14: Allotropes of carbon, tendency for catenation; Structure & properties of silicates, and zeolites. Group – 15: Properties and uses of nitrogen and phosphorus; Allotrophic forms of phosphorus; Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids of phosphorus. Group – 16: Preparation, properties, structures and uses of ozone; Allotropic forms of sulphur; Preparation, properties, structures and uses of sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur. Group – 17: Preparation, properties and uses of hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens. Group –18: Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon. Group – 13 to Group 18 Elements General Introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups; unique behaviour of the first element in each group.

Alcohols, Phenols and Ethers

Alcohols: Identification of primary, secondary and tertiary alcohols; mechanism of dehydration. Phenols: Acidic nature, electrophilic substitution reactions: halogenation, nitration and sulphonation, Reimer – Tiemann reaction. Ethers: Structure. Aldehyde and Ketones: Nature of carbonyl group Nucleophilic addition to >C=O group, relative reactivities of aldehydes and ketones Important reactions such as – Nucleophilic addition reactions (addition of HCN, NH3 and its derivatives), Grignard reagent; oxidation; reduction (Wolff Kishner and Clemmensen); acidity of r – hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction; Chemical tests to distinguish between aldehydes and Ketones.

Organic Compounds Containing Nitrogen

General methods of preparation, properties, reactions and uses. Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character. Diazonium Salts: Importance in synthetic organic chemistry.

Polymers

General introduction and classification of polymers, general methods of polymerization-addition and condensation, copolymerization Natural and synthetic rubber and vulcanization of some important polymers with emphasis on their monomers and uses – polythene, nylon, polyester and Bakelite.

Chemistry in Everyday Life

Chemicals in food – Preservatives, artificial sweetening agents – common examples. Cleansing agents – Soaps and detergents, cleansing action.

Chemicals in medicines – Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines – their meaning and common examples.