Dynamics

Newton’s Laws of Motion: First law of motion – force and inertia with examples -momentum – second law of motion, derivation of F=ma, mention of spring force F=kx, mention of basic forces in nature – impulse and impulsive forces with examples – second law as applied to the variable mass situation – third law of motion – Identifying action and reaction forces with examples – derivation of the law of conservation of momentum with examples in daily life – the principle of rocket propulsion – inertial and non-inertial frames – apparent weight in a lift and rocket/satellite – problems.

Fluid Dynamics: Explanation of streamline and turbulent motion – mention of the equation of continuity – mention of expressions for PE, KE and pressure energy of an element of a liquid flowing through a pipe – statement and explanation of Bernoulli’s Theorem and its application to the uplift of an aircraft sprayer.

Surface Tension: Concept of adhesive and cohesive forces – definition of Surface energy and surface tension and angle of contact – explanation of the capillary rise and mention of its expression – mention of application of surface tension to (i) formation of drops and bubbles (ii) capillary action in the wick of a lamp (iii) action of detergents.

Work – Power – Energy: Work done by a force – F.S – unit of work – graphical representation of work done by a constant and variable force – power – units of power – energy – derivation of expression for gravitation potential energy and kinetic energy of a moving body – statement of work-energy theorem – mention of expression for the potential energy of a spring – statement and explanation of the law of conservation of energy – illustration in the case of a body sliding down on an inclined plane – discussion of special case  = 90 degrees, for a freely falling body – explanation of conservative and non-conservative forces with examples – explanation of elastic and inelastic collisions with examples – coefficient of restitution – problems.

Gravitation: Statement and explanation of Law of Gravitation – definition of G – derivation of relation between g and G – mention of expression for the variation of g with altitude, depth and latitude – statement and explanation of Kepler’s Laws of planetary motion – definition of orbital velocity and escape velocity and mention of their expressions – satellites – basic concepts of geostationary satellites, launching of satellites – IRS and communication satellites – a brief explanation of Inertial mass and gravitational mass – weightlessness – remote sensing and essentials of space communication – problems.

Concurrent Co-planner forces: Definition of resultant and equilibrant – statement of the law of parallelogram of forces – derivation of expression for magnitude and direction of two concurrent coplanar forces – law of triangle of forces and its converse – Lami’s Theorem – problems.

Heat

Gas Laws: Statement and explanation of Boyle’s Law and Charles’ Law – definition of Pressure and Volume Coefficient of a gas – absolute zero – Kelvin scale of temperature – mention of the perfect gas equation – explanation of isothermal and adiabatic changes – mention of Van-der-Waal’s equation of state for real gases.

Mode of heat transfer: Conduction of heat – steady-state – temperature gradient – definition of the coefficient of thermal conductivity – basic concepts of convection of heat – radiation – properties of thermal radiation – radiant energy – definition of emissivity and absorptivity – perfect black body – statement and explanation of Kirchhoff’s Law. Newton’s Law of cooling – Stefan’s Law – Wien’s Displacement and Planck’s Law – qualitative explanation of Solar Constant and surface temperature of the sun – principle and working of total radiation pyrometer – problems.

Unit 3- Geometrical Optics

Waves: Waves around us – brief note on light waves, sound waves, radio waves, microwaves, seismic waves – wave as a carrier of energy – classification of waves. (i) based on medium – mechanical and electromagnetic waves (ii) based on the vibration of particles in the medium – Longitudinal & Transverse waves – one, two & three-dimensional waves with an example – definition of wave amplitude, wave frequency, wave period, wavelength and wave velocity – concept to establish the relation between the path of the phase of a wave – derivation v=f difference and phase difference – definition of a progressive wave – and its characteristics – derivation of the equation of a progressive wave – different forms of a progressive wave equation – definition of wave intensity – mention of expression of wave intensity and its unit – statement and explanation of principles of superposition of waves with examples – problems.

Sound: Properties of sound – speed of sound in a gas – explanation of Newton’s Formula for speed of sound – correction by Laplace – Newton – Laplace Formula – discussion of factors affecting speed i.e. pressure, temperature, humidity and wind – definition of sound intensity – explanation of loudness and its unit – definition of intensity level and it’s unit – mention of the relation between intensity and loudness – the distinction between noise and musical note – characteristics of a musical note – the phenomenon of beats and its theory – application of beats (i) to find the frequency of a note (ii) to tune the musical instruments -Doppler Effect – derivation of expression for apparent frequency in general case and discussion to special cases – qualitative comparison of Doppler Effect in sound and light – problems.

Refraction at a plane surface: Refraction through a parallel-sided glass slab – derivation of expressions for lateral shift and normal shift (object in a denser medium) – total internal reflection and its applications -optical fibres and its application in communication – problems.

Refraction through a prism: Derivation of expression for the refractive index in terms of A and D -dispersion through a prism – experimental – arrangement for pure spectrum – deviation produced by a thin prism – dispersive power – mention of condition for dispersion without deviation – problems.

Refraction at a spherical surface: Derivation of the relation – connecting n,u,v and r for refraction at a spherical surface (concave towards a point object in a denser medium) derivation of lens maker’s formula -the power of a lens – magnification – derivation of expression for the equivalent focal length of combination of two thin lenses in contact – mention of expression for the equivalent focal length of two thin lenses separated by a distance – problems.

Physical Optics

Introduction to Theories of Light: A brief explanation of Newton’s corpuscular theory, Huygen’s wave theory and Maxwell’s electromagnetic theory – mention of expression for o, qualitative explanation of Hertz’s experiment – brief eom speed of light C=1/ explanation of Planck’s quantum theory of radiation -dual nature of light.

Interference: Explanation of the phenomenon theory of interference – derivation of conditions for constructive and destructive interference. Young’s Double-slit Experiment, derivation of expression for fringe width – qualitative explanation of interference at thin films and Newton’s rings – problems.

Diffraction: Explanation of the phenomenon – the distinction between Fresnel and Fraunhofer Diffraction -qualitative explanation of diffraction at single slit and analysis of diffraction pattern (Fraunhofer type) – qualitative explanation of plane diffraction grating at normal incidence – limit of resolution – resolving power – Rayleigh’s Criterion – definition and mention of expression for resolving powers of microscope and telescope – problems.

Polarisation: Explanation of the phenomenon – representation of polarized and unpolarised light -explanation of plane of polarization and plane of vibration – methods of producing plane-polarized light: by reflection – Brewster’s Law, refraction, double refraction, selective absorption – construction and application of polaroids – optical activity-specific rotatory power – construction and working of Laurent’s half shade polarimeter – mention of circularly and elliptically polarized light – problems.

Speed of light: Michelson’s rotating mirror experiment to determine of light – the importance of speed of light.

Electrostatics

Electric charges: Concept of charge – Coulomb’s Law, absolute and relative permittivity – SI unit of charge.

Electrostatic Field: Concept of electric field – definition of field strength – derivation of expression for the field due to an isolated change, the concept of dipole – mention of expression for the field due to a dipole -definition of dipole moment – mention of expression for torque on a dipole – explanation of polarization of a dielectric medium – dielectric strength – the concept of lines of force and their characteristics – explanation of electric flux – statement and explanation of Gauss theorem and its applications to derive expressions for electric intensity (a) near the surface of a charged conductor (b) near a spherical conductor – the concept of electric potential – derivation of the relation between electric field and potential – derivation of expression for potential due to an isolated charge – explanation of potential energy of a system of charges – problems.

Capacitors: Explanation of capacity of a conductor and factors on which it depends – definition of capacitance and its unit – derivation of expression for capacity of a spherical conductor – the principle of a capacitor – derivation of expression for the capacitance of parallel plate capacitor – mention of expression for the capacitance of spherical and cylindrical capacitors – derivation of expression for energy stored in a capacitor – derivation of expression for the equivalent capacitance of capacitors in series and parallel – mention of uses of capacitors – problems.

Current Electricity

Electric current: Microscope view of current through conductors (random motion of electrons) – explanation of drift d -velocity and mobility – derivation of expression for current I = neA deduction of  Ohm’s Law – the origin of resistance – definition of resistivity – temperature coefficient of resistance – concept of superconductivity – explanation of critical temperature, critical field and high-temperature superconductors – mention of uses of superconductors – thermistors and mention of their uses – colour code for resistors -derivation of expression for effective resistance of resistances in series and parallel -derivation of expression for branch currents – definition of emf and internal resistance of a cell – Ohm’s law applied to a circuit -problems.

Kirchoff’s Laws: Statement and explanation of Kirchoff’s Laws for the electrical network – explanation of Wheatstone’s network – derivation of the condition for its balance by applying Kirchoff’s laws – the principle of metre bridge – problems.

Magnetic effect of electric current: Magnetic field produced by electric current – statement and explanation of Biot – Savart (Laplace’s) Law – derivation of expression for the magnetic field at any point on the axis of a circular coil carrying current and hence expression for the magnetic field at the centre – current in a circular coil as a magnetic dipole – explanation of magnetic moment of the current loop – mention of expression for the magnetic field due to (i) a straight current-carrying conductor (ii) at a point on the axis of a solenoid – basic concepts of terrestrial magnetism – statement and explanation of Tangent law -construction and theory of tangent galvanometer – problems.

The mechanical effect of electric current: Mention of expression for the force on a charge moving in a magnetic field – mention of expression for force on a conductor carrying current kept in a magnetic field – statement of Fleming’s left hand rule – explanation of magnetic field strength in terms of flux density – derivation of expression for the force between two parallel conductors carrying currents and hence definition of ampere -mention of expression for torque on a current loop kept in an uniform magnetic field – construction and theory of moving coil galvanometer – conversion of a pointer galvanometer into an ammeter and voltmeter -problems.

Electromagnetic Induction: Statement explanation of Faraday’s laws of electromagnetic induction and Lenz’s Law – derivation of expression for emf induced in a rod moving in a uniform magnetic field – explanation of self induction and mutual induction – mention of expression for energy stored in a coil -explanation of eddy currents – alternating currents – derivation of expression for sinusoidal emf – definition of phase and frequency of ac – mention of the expression for instantaneous, peak, rms, and average values – derivation of expression for current in case of ac applied to a circuit containing (i) pure resistor (ii) inductor (iii) capacitor – derivation of expression for impedance and current in LCR series circuit by phasor diagram method – explanation of resonance – derivation of expression for resonant frequency – brief account of sharpness of resonance and Q-factor – mention of expression for power in ac circuits – power factor and wattless current – qualitative description of choke -basic ideas of magnetic hysteresis – construction and working of transformers – mention of sources of power loss in transformers – ac meters – principle and working of moving iron meter – qualitative explanation of transmission of electrical power – advantages of ac and dc – problems.

Atomic Physics

Introduction to atomic physics: Mention of the types of electron emission – description and theory of Dunnington’s method of finding e/m of an electron – explanation of types of spectra: emission and absorption spectra – brief account of Fraunhoffer lines – qualitative explanation of electromagnetic spectrum with emphasis on frequency.

Photo electric effect: Explanation of photo electric effect – experiment to study photo electric effect – experimental observations – Einstein’s photo electric equation and its explanation – principle and uses of photo cells: (i) photo emissive (ii) photo voltaic (iii) photo conductive cells – problems.

Dual nature of matter: Concept of matter waves – arriving at the expression for de Brogile Wave length – principle and working of G.P. Thomson’s experiment – principle of Electron Microscope – Scanning Electron Microscope Transmission Electron Microscope and Atomic -Force Microscope.

Bohr’s Atom model: Bohr’s atomic model for Hydrogen like atoms – Bohr’s postulates – arriving at the expressions for radius, velocity, energy and wave number – explanation of spectral series of Hydrogen -energy level diagram – explanation of ionization and excitation energy – limitations of Bohr’s theory -qualitative explanation of Sommerfeld & Vector atom models – problems.

Scattering of light: Explanation of coherent and incoherent scattering – blue of the sky and sea – red at sunrise and sunset – basic concepts and applications of Raman Effect.

Lasers: Interaction between energy levels and electromagnetic radiation – laser action – population inversion – optical pumping – properties of lasers – construction and working of Ruby laser – mention of applications of lasers – brief account of photonics.

Nuclear Physics: Characteristics of nucleus – qualitative explanation of liquid drop model – qualitative explanation of nuclear magnetic resonance (NMR) and its applications in medical diagnostics as MRI -nuclear forces and their characteristics – explanation of Einstein’s mass – energy relation – definition of amu and eV – arriving at 1amu = 931 Mev – examples to show the conversion of mass into energy and vice-versa – mass defect – binding energy – specific binding energy – BE curve – packing fraction.

Nuclear fission with equations – nuclear chain reaction – critical mass – controlled and un-controlled chain reactions – types of nuclear reactors and mention of their principles – disposal of nuclear waste. Nuclear fusion – stellar energy (carbon & proton cycles) – problems.

Radioactivity: Laws of radioactivity (i)  -mSoddy’s group displacement laws (ii) decay law – derivation of N=NOe- explanation of decay constant – derivation of expression for half life – mention of expression for mean life – relation between half and mean life – units of activity: Bequerrel and Curie – Artificial transmutation: Artificial radioactivity – radio isotopes and mention of their uses – brief account of biological effects of radiations and safety measures – problems.

Elementary particles: Basic concepts of – decay – neutrino hypothesis leptons and hadrons – qualitative explanation of  Quarks.

Solid state electronics: Qualitative explanation of Bond Theory of solids – classification of conductors, insulators and semiconductors – intrinsic and extrinsic semiconductors – p-type and n-type semiconductors – construction and action of pn-junction – forward and reverse biasing – half wave and full wave rectification -function and application of light emitting diodes – photo diode – laser diode – transistors – npn and pnp transistors – action of transistor – npn transistor as an amplifier in CE mode.

Digital Electronics: Logic gates – AND, OR, NOR & NAND symbols and truth table – applications of logic gates (Boolean equations) – half adder and full adder.

Soft condensed matter physics: Liquid crystals – classification, thermotropic ( nematic, cholesteric and smectic) and lyotropic liquid crystals – mention of applications of liquid crystals – basic concepts of emulsions, gels & foams.

Stoichiometry

Atomic Structure

Periodic Properties

Oxidation Number

Gaseous State

Chemical Kinetics

Organic Compounds with Oxygen-2, Amines

Phenols

Uses of phenol.
Classification: Mono, di and tri-hydric Phenols
Isolation from coal tar and manufacture by Cumene Process.
Methods of preparation of phenol from – Sodium benzene sulphonate, Diazonium salts
Chemical properties: Acidity of Phenols-explanation using resonance-Effect of substituents on Acidity (methyl group and nitro group as substituents), Ring substitution reactions-Bromination, Nitration, Friedel-craft’s methylation, Kolbe’s reaction, Reimer-Tiemann reaction.

Aldehydes and Ketones:

Uses of methanol, benzaldehyde and acetophenone
Nomenclature
General methods of preparation of aliphatic and aromatic aldehydes and ketones from Alcohols and Calcium salts of carboxylic acids
Common Properties of aldehydes and ketones
a) Addition reactions with – Hydrogen cyanide, sodium bisulphate
b) Condensation reactions with-Hydroxylamine, Hydrazine, Phenyl hydrazine, Semicarbazide
c) Oxidation.
Special reactions of aldehydes: Cannizzaro’s reaction-mechanism to be discussed, Aldol condensation, Perkin’s reaction, Reducing properties-with Tollen’s and Fehling’s reagents.
Special reaction of ketones-Clemmensen’s reduction

Monocarboxylic Acids

Uses of methanoic acid and ethanoic acid.
Nomenclature and general methods of preparation of aliphatic acids
From Alcohols, Cyanoalkanes and Grignard reagent
General properties of aliphatic acids: Reactions with – Sodium bicarbonate, alcohols, Ammonia, Phosphorus pentachloride and soda lime
Strength of acids-explanation using resonance.
Effect of substituents (alkyl group and halogen as substituents)

Amines

Uses of Aniline
Nomenclature Classification-Primary, Secondary, Tertiary-aliphatic and aromatic.
General methods of preparation of primary amines from – Nitro hydrocarbons, Nitriles (cyano hydrocarbons), Amides(Hoffmann’s degradation)
General Properties – Alkylation,Nitrous acid, Carbyl amine reaction, Acylation
Tests to distinguish between-Primary, secondary, Tertiary amines-Methylation method.
Interpretation of Relative Basicity of-Methylamine, Ammonia and Aniline using inductive effect.

Hydrocarbons-2

Stability of Cycloalkanes-Baeyer’s Strain theory-interpretation of the properties of Cycloalkanes, strain less ring. Elucidation of the structure of Benzene – Valence Bond Theory and Molecular Orbital Theory. Mechanism of electrophilic substitution reactions of Benzene-halogenations, nitration, sulphonation and Friedel Craft’s reaction.

Haloalkanes

Monohalogen derivatives:
Nomenclature and General methods of preparation from-Alcohols and alkenes.
General properties of monohalogen derivatives: Reduction, with alcoholic KOH, Nucleophilic substitution reactions with alcoholic KCN, AgCN and aqueous KOH, with Magnesium, Wurtz Reaction, Wurtz-Fittig’s Reaction, Friedal-Craft’s Reaction
Mechanism of Nucleophilic Substitution reactions- SN1 mechanism of Hydrolysis of tertiary butyl bromide and SN2 mechanism of Hydrolysis of methyl bromide.

Coordination Compounds

Co-ordination compound: Definition, complex ion, ligands, types of ligands-mono, bi, tri and polydentate ligands. Co-ordination number, isomerism (ionization linkage, hydrate), Werner’s Theory, Sidgwick’s Theory, and E A N rule, Nomenclature of coordination, compounds. Valence Bond Theory: sp³, dsp² and d²sp³ hybridisation taking [Ni(Co)4], [Cu(NH₃)₄]SO₄, K₄[Fe(CN)6] respectively as examples.

Chemical Bonding-2

Covalent bonding-molecular orbital theory: linear combination of atomic orbitals (Qualitative approach), energy level diagram, rules for filling molecular orbitals, bonding and anti bonding orbitals, bond order, electronic configuration of H2, Li2 and O2 Non existence of He2 and paramagnetism of O2.

Metallic bond: Electron gas theory (Electron Sea model), definition of metallic bond, correlation of metallic properties with nature of metallic bond using electron gas theory.

Chemical Thermodynamics-2

Spontaneous and non-spontaneous process. Criteria for spontaneity-tendency to attain a state of minimum energy and maximum randomness. Entropy – Entropy as a measure of randomness, change in entropy, unit of entropy. Entropy and spontaneity. Second law of thermodynamics. Gibbs’ free as a driving force of a reaction Gibbs’ Equation. Prediction of feasibility of a process in terms of • G using Gibbs’ Equation. Standard free energy change and its relation to Kp (equation to be assumed). Numerical problems.

Solid State

Crystalline and amorphous solids, differences. Types of crystalline solids – covalent, ionic, molecular and metallic solids with suitable examples. Space lattice, lattice points, unit cell and Co- ordination number.
Types of cubic lattice-simple cubic, body centered cubic, face centered cubic and their coordination numbers. Calculation of number of particles in cubic unit cells. Ionic crystals-ionic radius, radius ratio and its relation to co-ordination number and shape. Structures of NaCl and CsCl crystals.

Electrochemistry

Electrolytes and non-electrolytes. Electrolysis-Faraday’s Laws of electrolysis. Numerical problems. Arrhenius theory of electrolytic dissociation, Merits and limitations. Specific conductivities and molar conductivity-definitions and units. Strong and weak electrolytes-examples. Factors affecting conductivity.Acids and Bases: Arrhenius’ concept, limitations. Bronsted and Lowry’s concept, merits and limitations. Lewis concept, Strengths of Acids and Bases – dissociation constants of weak acids and weak bases. Ostwald’s dilution law for a weak electrolytes-(equation to be derived) – expression for hydrogen ion concentration of weak acid and hydroxyl ion concentration of weak base – numerical problems.

Ionic product of water. pH concept and pH scale. pKa and pkb values-numerical problems. Buffers, Buffer action, mechanism of buffer action in case of acetate buffer and ammonia buffer. Henderson’s equation for pH of a buffer (to be derived). Principle involved in the preparation of buffer of required pH-numerical problems. Ionic equilibrium: common ion effect, solubility. 2B and AB2product, expression for Ksp of sparingly soluble salts of types AB, A B2Relationship between solubility and solubility product of salts of types AB, A. Applications of common ion effect and solubility product in inorganic2and AB qualitative analysis. Numerical problems. Electrode potential: Definition, factors affecting single electrode potential. Standard electrode potential. Nernst’s equation for calculating single electrode potential (to be assumed). Construction of electro-chemical cells-illustration using Daniel cell. Cell free energy change [•Go =-nFEo (to be assumed)]. Reference electrode: Standard Hydrogen Electrode-construction, use of SHE for determination of SRP of other single electrodes. Limitations of SHE.
Electrochemical series and its applications. Corrosion as an electrochemical phenomenon, methods of prevention of corrosion.

Organic Chemistry

Inductive effect, Mesomeric effect and Electromeric effect with illustrations, Conversion of methane to ethane and vice versa and Methanol to ethanol and vice versa

Isomerism -2

Stereo isomerism: geometrical and optical isomerismGeometrical isomerism-Illustration using 2-butene, maleic acid and fumaric acid as example, Optical Isomerism-Chirality, optical activity-Dextro and Laevo rotation (D and L notations).

Carbohydrates

Biological importance of carbohydrates, classification into mono, oligo and poly saccharides. Elucidation of the open chain structure of Glucose. Haworth’s structures of Glucose, Fructose, Maltose and Sucrose (elucidation not required).

Oils and Fats

Biological importance of oils and fats, Fatty acids-saturated, unsaturated, formation of triglycerides. Generic formula of triglycerides.

Chemical nature of oils and fats-saponification, acid hydrolysis, rancidity refining of oils, hydrogenation of oils, drying oils, iodine value.

Amino Acids and Proteins

Aminoacidsa Biological importance of proteins, – General formula
Formulae and unique feature of glycine, alanine, serine, cysteine, aspartic acid, lysine, tyrosine and proline. Zwitter ion, amphiprotic nature, isoelectric point, peptide bond, polypeptides and proteins. Denaturation of proteins
Structural features of Insulin – a natural polypeptide.

Metallurgy -2

Physico-chemical concepts involved in the following metallurgical operations – 
Desilverisation of lead by Parke’s process-Distribution law.Reduction of metal oxides – Ellingham diagrams – Relative tendency to undergo oxidation in case of elements Fe Ag, Hg, Al, C. Cr, and Mg.Blast furnace – metallurgy of iron – Reactions involved and their role, Maintenance of the temperature gradient, Role of each ingredient and Energetics

Industrially Important Compounds

Manufacture of Caustic soda by Nelson’s cell Method, Ammonia by Haber’s process, Sulphuric acid by Contact process and Potassium dichromate from chromite.Uses of the above compounds.
Chemical properties of Sulphuric acid: Action with metals, Dehydrating nature, Oxidation reactions and Reaction with PCIChemical properties of potassium dichromate: With KOH, Oxidation reactions, formation of chromyl chloride.

Group 18, Nobel Gases

Applications of noble gases. Isolation of rare gases from Ramsay and Raleigh’s Method and separation of individual gases from noble gas mixture (Dewar’s charcoal adsorption method). Preparation of Pt XeF6 by Neil Bartlett.

d- Block elements (transition elements)

Definition. 3d series: electronic configurations, size, variable oxidation states, colour, magnetic properties, catalytic behaviour, complex formation and their interpretations.

Theory of Dilute Solutions

Vant Hoffs theory of dilute solutions, colligative property. Examples of colligative properties-lowering of vapour pressure, elevation in boiling points, depression in freezing point and osmotic pressure.
Lowering of vapour pressure-Raoult’s law (mathematical form to be assumed). Ideal and non-ideal solutions (elementary idea) – measurement of relative lowering of vapour pressure-Ostwald and Walker’s dynamic method. Determination of molecular mass by lowering of vapour pressure). Numerical problems.

Colloids

Introduction. Colloidal system and particle size. Types of colloidal systems. Lyophilic and lyiphobic sols, examples and differences. Preparation of sols by Bredig’s arc method and peptisation. Purification of sols-dialysis and electrodialysis. Properties of sols-Tyndall effect, Brownian movement electrophoresis, origin of charge, coagulation, Hardy and Schulze rule, Protective action of sols. Gold number. Gold number of gelatin and starch. Applications of colloids. Electrical precipitation of smoke, clarification of drinking water and formation of delta.

Algebra

Mathematical Induction: Motivation, Principle of mathematical induction,

Numbers and Quadratic Equations: Complex numbers, Algebra of complex numbers, The modulus and the conjugate of a complex number, Argand plane and polar representation and Quadratic equations,

Linear Inequalities: Inequalities, Algebraic solutions of linear inequalities, graphical solution and solution of system of linear inequalities in two variables

Permutations and Combinations: Permutations and Combinations, Derivation of formulae and their connections

Binomial Theorem: Binomial theorem for positive integral indices, General and middle terms, Applications

Sequence and Series: Sequences, Series, Arithmetic progression, Geometric progression, Relationship between AM and GM, sum to n terms of special series

Matrices: Matrix, types, operations, Transpose, Symmetric and skew symmetric matrices, elementary operation, Invertible matrices

Determinants: Properties, Area of a triangle, minors and cofactors, Adjoint and inverse of a matrix, applications

Coordinate Geometry

Straight Lines: Slope of a line, Various forms of the equation of a line, General equation of a line, Distance of a point from a line

Conic Sections: Section of a cone, Circle, Parabola, Ellipse, Hyperbola

Introduction to Three-dimensional Geometry: Coordinate axes and coordinate planes in three-dimensional space, Coordinates of a point in space, Distance between two points, Section formula.

Calculus

Limits and Derivatives: Intuitive idea of derivatives, Limits of trigonometric functions, Derivatives, Continuity and Differentiability: Exponential and logarithmic functions, logarithmic differentiation, Derivatives of functions in parametric forms, Second order derivative, Mean value theorem,

Applications of Derivatives: Rate of change of quantities, Increasing and decreasing functions, Tangents and normals, Approximations, Maxima and Minima,

Integrals and their Application: Integration, methods of integration, Integrals of some particular functions, Integration by partial fractions, Integration by parts, Definite Integral, Fundamental theorem of calculus, Evaluation of definite integrals by substitution, Properties of definite integrals, Area under simple curves and two curves,

Differential equations: Basic concepts, General and particular solutions of a differential equation, formation of a differential equation, methods of solving first order, first degree differential equations

Mathematical Reasoning

Statements, New statements from old, Special words/phrases, Implications, Validating statements,

Statistics and Probability: Measure of dispersion, Range, Mean deviation, Variance and standard deviation, Analysis of frequency distributions, Random experiments, Event, Axiomatic approach to probability, Conditional probability, multiplication theorem on probability, Independent events, Bayes’ theorem, Random variables and its probability distributions, Bernoulli trials and binomial distribution,

Relations and Functions: Types of relations and functions, Composition of functions and invertible function, Binary operations, Inverse Trigonometric Functions: Basic concepts, Properties of inverse trigonometric functions,

Vector algebra: Basic concepts, types of vectors, Addition of vectors, Multiplication of a vector by a scalar, Product of two vectors

Three-Dimensional Geometry: Direction cosines and direction ratios of a line, Equation of a line in space, Angle between two lines, Shortest distance between two lines, Plane, Coplanarity of two lines, Angle between two planes, Distance of a point from a plane, Angle between a line and a plane

Linear programming: Problem and its mathematical formulation, different types of linear programming problems