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MATHEMATICS (14 topics) Subject

SETS, RELATIONS, AND FUNCTIONS (5 subtopics) Topic

Sets and their representation

Union, intersection, and complement of sets and their algebraic properties

Power set

Relation, Type of relations, equivalence relations, functions

one-one, into and onto functions, the composition of functions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS (5 subtopics) Topic

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 number, modulus, and argument (or amplitude) of a complex number

Quadratic equations in real and complex number system and their solutions

Relations between roots and co-efficient, nature of roots, the formation of quadratic equations with given roots

MATRICES AND DETERMINANTS (5 subtopics) Topic

Matrices, algebra of matrices, type of matrices, determinants

Matrices of order two and three, evaluation of determinants

Area of triangles using determinants

Adjoint and evaluation of inverse of a square matrix using determinants

Test of consistency and solution of simultaneous linear equations in two or three variables using matrices

PERMUTATIONS AND COMBINATIONS (3 subtopics) Topic

The 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 (3 subtopics) Topic

Binomial theorem for a positive integral index

General term and middle term

Simple applications

SEQUENCE AND SERIES (3 subtopics) Topic

Arithmetic and Geometric progressions

Insertion of arithmetic, geometric means between two given numbers

Relation between A.M and G.M

LIMIT, CONTINUITY, AND DIFFERENTIABILITY (6 subtopics) Topic

Real–valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic, and exponential functions, inverse function

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 up to two

Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable

INTEGRAL CALCULUS (7 subtopics) Topic

Integral as an anti-derivative

Fundamental integral involving algebraic, trigonometric, exponential, and logarithmic functions

Integrations by substitution, by parts, and by partial fractions

Integration using trigonometric identities

Evaluation of simple integrals

The 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 (3 subtopics) Topic

Ordinary differential equations, their order, and degree

Solution of differential equation by the method of separation of variables

Solution of a homogeneous and linear differential equation of the type dy/dx + p(x)y = q(x)

CO-ORDINATE GEOMETRY (12 subtopics) Topic

Cartesian system of rectangular coordinates in a plane

Distance formula, section formula, locus, and its equation

Slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis

Straight line

Various forms of equations of a line, intersection of lines, angles between two lines

Conditions for concurrence of three lines, distance of a point from a line

Co-ordinate of the centroid, orthocentre, and circumcentre of a triangle

Circle, conic sections

Standard form of equations of a circle, general form of the equation of a circle

Equation of a circle when the endpoints of a diameter are given

Points of intersection of a line and a circle with the centre at the origin and sections of conics

Equations of conic sections (parabola, ellipse, and hyperbola) in standard forms

THREE DIMENSIONAL GEOMETRY (4 subtopics) Topic

Coordinates of a point in space, the distance between two points, section formula

Direction ratios, and direction cosines, and the angle between two intersecting lines

Skew lines, the shortest distance between them, and its equation

Equations of a line

VECTOR ALGEBRA (3 subtopics) Topic

Vectors and scalars, the addition of vectors

Components of a vector in two dimensions and three-dimensional space

Scalar and vector products

STATISTICS AND PROBABILITY (4 subtopics) Topic

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 variable

TRIGONOMETRY (2 subtopics) Topic

Trigonometric identities and trigonometric functions

Inverse trigonometric functions, and their properties

PHYSICS (20 topics) Subject

PHYSICS AND MEASUREMENT (5 subtopics) Topic

Units of measurements, System of Units, S I Units

Fundamental and derived units

Least count, significant figures

Errors in measurements

Dimensions of Physics quantities, dimensional analysis, and its applications

KINEMATICS (10 subtopics) Topic

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 graph

Relations for uniformly accelerated motion

Scalars and Vectors, Vector addition and subtraction, scalar and vector products

Unit Vector, Resolution of a Vector

Relative Velocity, Motion in a plane, Projectile Motion

Uniform Circular Motion

LAWS OF MOTION (8 subtopics) Topic

Force and inertia, Newton's First law of motion

Momentum, Newton's Second Law of motion, Impulses

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

Vehicle on a level circular road, vehicle on a banked road

WORK, ENERGY, AND POWER (6 subtopics) Topic

Work done by a constant force and a variable force

Kinetic and potential energies, work-energy theorem, power

Potential energy of spring conservation of mechanical energy

Conservative and non-conservative forces

Motion in a vertical circle

Elastic and inelastic collisions in one and two dimensions

ROTATIONAL MOTION (7 subtopics) Topic

Centre of the mass of a two-particle system, the Centre of the 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, the radius of gyration, values of moment of inertia for simple geometrical objects

Parallel and perpendicular axis theorem and their applications

Rigid body rotation

Equations of rotational motion

GRAVITATION (4 subtopics) Topic

The universal law of gravitation

Acceleration due to gravity and its variation with altitude and depth

Kepler's law of planetary motion

Gravitational potential energy, gravitational potential, escape velocity, orbital velocity of a satellite, geostationary satellites

PROPERTIES OF SOLIDS AND LIQUIDS (8 subtopics) Topic

Elastic behavior, Stress-strain relationship

Hooke's Law, Young's modulus, bulk modulus, shear modulus of rigidity

Pressure due to a fluid column, Pascal's law and its applications

Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli's theorem and its applications

Surface energy and surface tension

Angle of contact, applications of surface tension

Heat, temperature, thermal expansion, specific heat capacity, Cp, Cv, latent heat

Heat transfer: conduction, convection, and radiation, Newton's law of cooling

THERMODYNAMICS (4 subtopics) Topic

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, Heat engine and its efficiency

KINETIC THEORY OF GASES (6 subtopics) Topic

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, the law of equipartition of energy, applications to specific heat capacities of gases

Mean free path, Avogadro's number

OSCILLATIONS AND WAVES (9 subtopics) Topic

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 S.H.M

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 wave motion

Displacement relation for a progressive wave

Principle of superposition of waves, the reflection of waves, standing waves in strings and pipes, fundamental mode and harmonics

Beats, Doppler effect

ELECTROSTATICS (10 subtopics) Topic

Electric charges: Conservation of charge, Coulomb's law-forces between two point charges, forces between multiple charges

Superposition principle and continuous charge distribution

Electric field: Electric field due to a point charge, electric field lines

Electric dipole, electric field intensity due to a dipole, behavior of dipole in a uniform electric field

Electric flux, Gauss's law and its applications

Electric potential and its calculation for a point charge, electric dipole, and system of charges

Equipotential surfaces, electrical potential energy of a system of two point charges

Conductors and insulators, dielectrics and electric polarization

Capacitors and capacitance, combination of capacitors in series and parallel, capacitance of a parallel plate capacitor with and without dielectric medium betwe

Energy stored in a capacitor

CURRENT ELECTRICITY (8 subtopics) Topic

Electric current, drift velocity, mobility and their relation with electric current

Ohm's law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity

Carbon resistors, color code for carbon resistors, series and parallel combination of resistors, temperature dependence of resistance

Electromotive force (EMF) and potential difference, internal resistance of a cell

Potential difference and emf of a cell, combination of cells in series and in parallel

Kirchhoff's laws and their applications

Wheatstone bridge, meter bridge

Potentiometer: principle and its applications

MAGNETIC EFFECTS OF CURRENT AND MAGNETISM (13 subtopics) Topic

Biot–Savart law and its application to current carrying circular loop

Ampere's law and its applications to infinitely long current carrying straight wire and solenoid

Force on a moving charge in a uniform magnetic and electric field

Cyclotron

Force on a current-carrying conductor in a uniform magnetic field

Force between two parallel current-carrying conductors-definition of ampere

Torque experienced by a current loop in uniform magnetic field

Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter

Current loop as a magnetic dipole and its magnetic dipole moment

Bar magnet as an equivalent solenoid, magnetic field lines

Earth's magnetic field and magnetic elements

Para-, dia- and ferro-magnetic substances

Magnetic susceptibility and permeability, hysteresis, electromagnets, and permanent magnets

ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS (8 subtopics) Topic

Electromagnetic induction; Faraday's law, induced EMF and current, Lenz's law

Eddy currents, self and mutual inductance

Alternating current: peak and RMS value of alternating current/voltage

Reactance and impedance

LC oscillations (qualitative treatment only)

LCR series circuit, resonance, and Q-factor

Power in AC circuits, power factor

AC generator and transformer

ELECTROMAGNETIC WAVES (4 subtopics) Topic

Electromagnetic waves and their characteristics

Transverse nature of electromagnetic waves

Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays)

Applications of e-m waves

OPTICS (13 subtopics) Topic

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

Refraction of light through a prism

Scattering of light: the blue color of the sky and the reddish appearance of the sun at sunrise and sunset

Wave optics: Wavefront and Huygens's principle

Proof of laws of reflection and refraction using Huygens principle

Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light

Diffraction due to a single slit, width of central maximum

Resolving power of microscope and astronomical telescope, Polarisation, plane-polarized light

Brewster's law, uses of plane polarized light and Polaroids

DUAL NATURE OF MATTER AND RADIATION (6 subtopics) Topic

Dual nature of electromagnetic radiation

Photoelectric effect, Hertz and Lenard's observations

Einstein's photoelectric equation

Particle nature of light

Matter waves-wave nature of particles, de Broglie relation

Davisson-Germer experiment

ATOMS AND NUCLEI (9 subtopics) Topic

Alpha-particle scattering experiments

Rutherford's model of the 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, its variation with mass number

Nuclear fission and fusion

ELECTRONIC DEVICES (7 subtopics) Topic

Semiconductors; semiconductor diode: I-V characteristics in forward and reverse bias

Diode as a rectifier

Special purpose p-n junction diodes: LED, photodiode, solar cell, Zener diode, Zener diode as a voltage regulator

Junction transistor, transistor action, characteristics of a transistor

Transistor as an amplifier (common emitter configuration) and oscillator

Logic gates (OR, AND, NOT, NAND and NOR)

Transistors as a switch

EXPERIMENTAL SKILLS (19 subtopics) Topic

Familiarity with the basic approach and observations of the experiments and activities:

1. Vernier calipers - its use to measure internal and external diameter and depth of a vessel

2. Screw gauge - its use to determine thickness/diameter of thin sheet/wire

3. Simple Pendulum - dissipation of energy by plotting a graph between square of amplitude and time

4. Metre Scale - mass of a given object by principle of moments

5. Young's modulus of elasticity of the material of a metallic wire

6. Surface tension of water by capillary rise and effect of detergents

7. Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body

8. Speed of sound in air at room temperature using a resonance tube

9. Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures

10. Resistivity of the material of a given wire using a metre bridge

11. Resistance of a given wire using Ohm's law

12. Resistance and figure of merit of a galvanometer by half deflection method

13. Focal length of: (i) Convex mirror, (ii) Concave mirror, and (iii) Convex lens, using parallax method

14. Plot of the angle of deviation vs angle of incidence for a triangular prism

15. Refractive index of a glass slab using a travelling microscope

16. Characteristic curves of a p-n junction diode in forward and reverse bias

17. Characteristic curves of a Zener diode and finding reverse breakdown voltage

18. Identification of Diode, LED, Resistor, Capacitor from a mixed collection of such items

CHEMISTRY (20 topics) Subject

SOME BASIC CONCEPTS IN CHEMISTRY (6 subtopics) Topic

Matter and its nature

Dalton's atomic theory

Concept of atom, molecule, element, and compound

Laws of chemical combination

Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae

Chemical equations and stoichiometry

ATOMIC STRUCTURE (14 subtopics) Topic

Nature of electromagnetic radiation, photoelectric effect

Spectrum of the hydrogen atom

Bohr model of a hydrogen atom - its postulates, derivation of relations, limitations

Dual nature of matter, de Broglie's relationship

Heisenberg uncertainty principle

Elementary ideas of quantum mechanics

Quantum mechanical model of the atom

Concept of atomic orbitals as one-electron wave functions

Variation of ψ and ψ2 with r for 1s and 2s orbitals

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

CHEMICAL BONDING AND MOLECULAR STRUCTURE (11 subtopics) Topic

Kossel-Lewis approach to chemical bond formation

Ionic Bonding

Covalent Bonding

Electronegativity, Fajan's rule, dipole moment

Valence Shell Electron Pair Repulsion (VSEPR) theory

Valence bond theory

Concept of hybridization

Resonance

Molecular Orbital Theory

Metallic bonding

Hydrogen bonding

CHEMICAL THERMODYNAMICS (3 subtopics) Topic

Fundamentals of thermodynamics

First law of thermodynamics

Second law of thermodynamics

SOLUTIONS (5 subtopics) Topic

Methods for expressing concentration of solution

Vapour pressure of solutions and Raoult's Law

Colligative properties of dilute solutions

Determination of molecular mass using colligative properties

Abnormal value of molar mass, Van't Hoff factor

EQUILIBRIUM (9 subtopics) Topic

Meaning of equilibrium and concept of dynamic equilibrium

Equilibria involving physical processes

Equilibrium involving chemical processes

Law of chemical equilibrium

Factors affecting equilibrium

Ionic equilibrium

Acids and bases

pH scale

Buffer solutions

REDOX REACTIONS AND ELECTROCHEMISTRY (8 subtopics) Topic

Electronic concepts of oxidation and reduction

Redox reactions, oxidation number

Electrolytic and metallic conduction

Electrochemical cells

Nernst equation and its applications

Relationship between cell potential and Gibbs' energy change

Dry cell and lead accumulator

Fuel cells

CHEMICAL KINETICS (8 subtopics) Topic

Rate of a chemical reaction

Factors affecting the rate of reactions

Order and molecularity of reactions

Rate law, rate constant

Differential and integral forms of zero and first-order reactions

Effect of temperature on rate of reactions

Arrhenius theory, activation energy

Collision theory of bimolecular gaseous reactions

CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES (3 subtopics) Topic

Modern periodic law and present form of the periodic table

s, p, d and f block elements

Periodic trends in properties of elements

P- BLOCK ELEMENTS (3 subtopics) Topic

Group -13 to Group 18 Elements

General Introduction

Electronic configuration and general trends in physical and chemical properties

d - and f- BLOCK ELEMENTS (7 subtopics) Topic

Transition Elements

General introduction, electronic configuration, occurrence and characteristics

General trends in properties of the first-row transition elements

Preparation, properties, and uses of K2Cr2O7 and KMnO4

Inner Transition Elements

Lanthanoids - Electronic configuration, oxidation states, and lanthanoid contraction

Actinoids - Electronic configuration and oxidation states

CO-ORDINATION COMPOUNDS (8 subtopics) Topic

Introduction to coordination compounds

Werner's theory

Ligands, coordination number, denticity, chelation

IUPAC nomenclature of mononuclear co-ordination compounds

Isomerism

Bonding-Valence bond approach and basic ideas of Crystal field theory

Colour and magnetic properties

Importance of co-ordination compounds

PURIFICATION AND CHARACTERISATION OF ORGANIC COMPOUNDS (5 subtopics) Topic

Purification - Crystallization, sublimation, distillation, differential extraction, and chromatography

Qualitative analysis - Detection of nitrogen, sulphur, phosphorus, and halogens

Quantitative analysis - Estimation of carbon, hydrogen, nitrogen, halogens, sulphur, and phosphorus

Calculations of empirical formulae and molecular formulae

Numerical problems in organic quantitative analysis

SOME BASIC PRINCIPLES OF ORGANIC CHEMISTRY (9 subtopics) Topic

Tetravalency of carbon

Shapes of simple molecules - hybridization

Classification of organic compounds

Homologous series

Isomerism - structural and stereoisomerism

Nomenclature (Trivial and IUPAC)

Covalent bond fission - Homolytic and heterolytic

Electronic displacement in a covalent bond

Common types of organic reactions

HYDROCARBONS (5 subtopics) Topic

Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties, and reactions

Alkanes - Conformations, Mechanism of halogenation

Alkenes - Geometrical isomerism, Mechanism of electrophilic addition

Alkynes - Acidic character, Addition reactions

Aromatic hydrocarbons - Nomenclature, benzene structure and aromaticity, Mechanism of electrophilic substitution

ORGANIC COMPOUNDS CONTAINING HALOGENS (4 subtopics) Topic

General methods of preparation, properties, and reactions

Nature of C-X bond

Mechanisms of substitution reactions

Uses and Environmental effects of chloroform, iodoform, freons, and DDT

ORGANIC COMPOUNDS CONTAINING OXYGEN (4 subtopics) Topic

General methods of preparation, properties, reactions, and uses

ALCOHOLS, PHENOLS, AND ETHERS

Aldehydes and Ketones

Carboxylic Acids

ORGANIC COMPOUNDS CONTAINING NITROGEN (3 subtopics) Topic

General methods of preparation, properties, reactions, and uses

Amines: Nomenclature, classification, structure, basic character

Diazonium Salts: Importance in synthetic organic chemistry

BIOMOLECULES (6 subtopics) Topic

General introduction and importance of biomolecules

CARBOHYDRATES - Classification, aldoses and ketoses, monosaccharides

PROTEINS - Elementary Idea of α-amino acids, peptide bond, polypeptides, Proteins structure

VITAMINS – Classification and functions

NUCLEIC ACIDS – Chemical constitution of DNA and RNA, Biological functions

Hormones (General introduction)

PRINCIPLES RELATED TO PRACTICAL CHEMISTRY (6 subtopics) Topic

Detection of extra elements in organic compounds

Detection of functional groups in organic compounds

Chemistry involved in the preparation of inorganic and organic compounds

Chemistry involved in titrimetric exercises

Chemical principles involved in qualitative salt analysis

Chemical principles involved in various experiments

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