BCECE Pharmacy Syllabus 2024: Check Latest Syllabus Here

Physics: scope and excitement, nature of physical laws; Physics, technology and society.

Need for measurement: Units of measurement, systems of units. S.I. units, fundamental and derived units, length, mass and time measurements, accuracy and precision of measuring instruments, errors in measurement, significant figures, regular and irregular errors.

Dimensions of physical quantities, dimensional analysis and its applications

Frame of reference, Motion in straight line, position time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity.

Uniformly accelerated motion, velocity time and position time graphs, relations for uniformly accelerated motion

(graphical treatment) Elementary concepts of differentiation and integration for describing motion.

Scalar and vector quantities: Position and displacement vectors, general vectors and notation, equality of vectors, multiplication of vectors by a real number, addition and subtraction of vectors, relative velocity, Unit vector, Resolution of a vector in a plane-rectangular component., Motion in a plane, Cases of uniform velocity and uniform acceleration - projectile motion, uniform circular motion.

Intuitive concept of force, Inertia, Newton's first law of motion, momentum and 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, lubrication, dynamics of uniform circular motion: centripetal force examples of circular motion (vehicle on level circular road, vehicle on banked road).

Scalar product of Vector work done by a constant force and a variable force, kinetic energy, work-energy theorem,

Power Notion of potential energy, potential energy of a spring, conservative forces; conservation of mechanical energy

(Kinetic and potential energies), non-conservative forces, elastic and inelastic collisions in one and two dimension.

Centre of mass of two-particle system, momentum, conservation and centre of mass motion, centre of mass of a rigid body, centre of mass of circular ring, disc, rod and sphere.

Vector product of vectors; momentum of a force, torque angular momentum, conservation of angular momentum with some examples.

Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motion, moment of inertia, radius of gyration. Values of M.I. for simple geometrical objects (no derivation), statement of parallel and perpendicular axes theorems and their applications

Kepler’s laws of planetary motion, The universal law of gravitation, Acceleration due to gravity and its variation with altitude and depth.

Gravitational potential energy, gravitational potential, escape velocity, orbital velocity of satellite, Geo-stationary satellites.

Elastic behaviour, stress-strain relationship, Hooke's law, Young's modulus, Bulk modulus, Deformation, Shear modulus of rigidity.

Pressure due to fluid column, pascal's law and its applications / hydraulic lift and hydraulic brakes).

Effect of gravity on fluid pressure, Viscosity, stokes’ law terminal velocity, Reynold's number, Streamline and turbulent flow, Bernoulli's theorem and its applications. Surface energy and surface tension, angle of contact, application of surface tension, ideas to drop bubbles and capillary rise

Heat, temperature, thermal expansion, specific heat capacity, Calorimetry, change of state, latent heat.

Heat transfer - conduction, convection and radiation, thermal conductivity, Newton's law of cooling.

Thermal equilibrium and definition of temperature (Zeroth law of thermodynamics). Heat, work and internal energy.

First law of thermodynamics.

Second law of thermodynamics, Reversible and irreversible processes. Heat engines and refrigerator.

Behaviour of Perfect Gas and Kinetic Theory

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 (statement only) and application to specific heat capacities of gases, concept of mean free path, Avogadro's number.

Oscillations and Waves

Periodic motion - period, frequency, displacement as a function of time, periodic functions, simple harmonic motion

(SHM) and its equation, phase, oscillation 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 (qualitative ideas only), resonance.

Wave motion, Longitudinal and transverse waves, speed of wave motion, Displacement relation for progressive waves, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.

Electrostatics

Electric Charge; Conservation of charge, Coulomb's law-force 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 due to a dipole; torque on a dipole in uniform electric field.

Electric flux, statement of Gauss's theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).

Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges;

Equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.

Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation,

capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graff generator.

Current Electricity

Electric current, flow of electric charges in a metallic conductor, 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, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance.

Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel.

Kirchhoff's laws and simple applications. Wheatstone bridge, metre bridge.

Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.

Magnetic effects of current & Magnetism

Concept of magnetic field, Oersted's experiment.

Biot - Savart law and its application to current carrying circular loop.

Ampere's law and its applications to infinitely long straight wire, straight and toroidal solenoids.

Force on a moving charge in uniform magnetic and electric fields. 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. Magnetic dipole moment of a revolving electron.

Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth's magnetic field and magnetic elements. Para-, dia- and ferro- magnetic substances, with examples.

Electromagnets and factors affecting their strengths. Permanent magnets.

Electromagnetic Induction and Alternating currents

Electromagnetic induction; Faraday's law, induced emf and current; Lenz's Law, Eddy currents. Self and mutual inductance.

Need for displacement current.

Alternating currents, peak and rms value of alternating current/ voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current.

AC generator and transformer.

Electromagnetic Waves

Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves.

Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays gamma rays) including elementary facts about their uses.

Optics

Reflection of light, spherical mirrors, mirror formula, Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker's formula. Magnification, power of a lens, combination of thin lenses in contact, Refraction and dispersion of light through a prism.

Scattering of light-blue colour of the sky and reddish appearance of the sun at sunrise and sunset.

Optical instruments; Human eye, image formation and accommodation, correction of eye defects (myopia, hyper-metropia, presbyopia and astigmatism) using lenses. Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.

Wave optics: wave front and Huygens' principle, reflection and refraction of plane wave at a plane surface using wave fronts. 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 microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster's law, uses of plane polarised light and Polaroids.

Dual Nature of Matter and 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. Davission-Germer experiment.

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.

Electronic Devices

Semiconductors; semiconductor diode - I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and 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). Transistor as a switch.

Communication Systems

General Introduction: Importance and scope of chemistry. Historical approach to particulate nature of matter, laws of chemical combination, Dalton's atomic theory; the concept of elements, atoms and molecules, Atomic and molecular masses, Mole concept and molar mass; percentage composition, empirical and molecular formula; chemical reactions, stoichiometry and calculations based on stoichiometry

Three states of matter, Intermolecular interactions, type of bonding, melting and boiling points, Role of gas laws in elucidating the concept of the molecule, Boyle's law, Charle's law, Gay Lussac's law Avogadro's law, Ideal behaviour, empirical derivation of gas equation, Avogadro's number. Ideal gas equation, Derivation from ideal behaviour, liquification of gases, critical temperature, Liquid State - Vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations)

Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, the polar character of the covalent bond, Covalent characters of Ionic bond, valence bond theory, resonance, the geometry of covalent molecules, VSEPR theory, the concept of hybridization involving s, p and d orbitals and shapes of some simple molecules, molecular orbital, the theory of homonuclear diatomic molecules (qualitative idea only) Hydrogen bonding

Concepts of system, types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions, First law of thermodynamics - internal energy and enthalpy, heat capacity and specific heat, Hess's law of constant heat summation enthalpy of bond dissociation, combustion, formation, atomization, Sublimation, phase transformation, ionization and solution. Introduction of entropy as a state function, free energy change for the spontaneous and non-sponteneous process, criteria for equilibrium

Group 1 and Group 2 elements:

General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii) trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses

Preparation and properties of some important compounds:

Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate, biological importance of 25 sodium and potassium.

CaO, CaCO3 and industrial use, lime and limestone Biological importance of Mg and Ca

Some p-Block Elements:

General Introduction p-Block Elements

Group 3 elements: General introduction, electronic configuration, occurrence, Variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; Boron-physical and chemical properties, some important compounds : borax, boric acids, boron hydrides

Aluminium: uses, reactions with acids and alkalies.

Group 4 elements: General introduction, electronic configuration, occurrence, a variation of properties, oxidation states, trends in chemical reactivity, anomalous behaviour of first element, Carbon - catenation, allotropic forms, physical and chemical properties;

uses of some important compounds: oxides

Important compounds of Silicon and a few uses: Silicon tetrachloride, silicons, silicates and zeolite. (Part-I)

p-Block Elements:

Group - 5 elements:

General introduction, electronic configuration, occurrence, oxidation states, trends in physical

and chemical properties; nitrogen - preparation, properties and uses; compounds of nitrogen: preparation, properties and uses; compounds of nitrogen: preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); Phosphorous-allotropic forms; compounds of phosphorous: preparation and properties of phosphine, halides (PCl3, PCl5) and oxoacids (elementary idea only)

Group - 6 elements:

General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen: preparation, properties and uses; simple oxdides; Ozone, Sulphur-allotropic forms; compounds of sulphur: preparation, properties and uses of sulphur dioxide; sulphuric acid: industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only)

Group - 7 elements:

General introduction, electronic configuration, oxidation states, occurrence, trends in physical

and chemical properties; compounds of halogens; preparation, properties and uses of chlorine and hydrochloric acid, inter-halogen compounds, oxoacids of halogens (structures only)

Group - 8 elements:

General introduction, electronic configuration. Occurrence, trends in physical and chemical

properties, uses (Part-II)

d- and f- Block Elements:

General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals - metallic character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial compounds, alloy formation

Preparation and properties of K2Cr2O7 and KMnO4

Lanthanides: electronic configuration, oxidation states, chemical reactivity and lanthanide contraction.

Actinides: Electronic configuration, oxidation states

Coordination Compounds:

Introduction, ligands, coordination number, colour, magnetic properties and shapes,

IUPAC nomenclature of mononuclear coordination compounds, bonding; isomerism, importance of coordination

Compounds (in qualitative analysis, extraction of metals and biological systems)

General introduction, methods of qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds

Electronic displacements in a covalent bond; inductive effect, electrometric effect, resonance and hyper conjugation

Haemolytic and heterolysis fission of a covalent bond: free radicals, carbocation’s, carbanions; electrophiles and nucleophiles, types of organic reactions

Hydrocarbons:

Classification of hydrocarbons

Alkanes: Nomenclature, isomerism, conformations (ethane only), methods of preparation, physical properties, chemical reactions including halogenation, free radical mechanism, combustion and pyrolysis

Alkenes: Nomenclature, the structure of the double bond

(ethane), geometrical isomerism, methods of preparation, physical properties, chemical reaction: addition of hydrogen, halogen, water, hydrogen halides (Markovnikov's addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition

Alkynes: Nomenclature, the structure of triple bond (ethyne), methods of preparation, physical properties, chemical reactions; the acidic character of alkynes, addition reactions of hydrogen, halogens, hydrogen halides and water

Aromatic hydrocarbons: Introduction, IUPAC nomenclature, Benzene: resonance, aromaticity: methods of preparation, chemical properties

Mechanism of electrophilic substitution: nitration, sulphonation, halogenation, Friedel Craft's alkylation and acylation; directive influence of the functional group in mono-substituted benzene; carcinogenicity and toxicity

Environmental Chemistry

Environmental pollution - Air, water and soil pollution, chemical reactions in atmosphere smogs, major atmospheric

pollutants: acid rain, ozone and its reactions, effects of depletion of ozone layer, greenhouse effect and global warming - pollution due to industrial wastes, green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution*

Solid State:

Classification of solids based on different binding forces: molecular, ionic covalent and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties

Solutions:

Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties-relative lowering of vapour pressure, elevation of Boiling Point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass

Electrochemistry:

Redox reactions, conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch's law, electrolysis and laws of electrolysis (elementary idea), dry cell electrolytic cells and Galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, fuel cells; corrosion

Chemical Kinetics:

Rate of a reaction (average and instantaneous), factors affecting rates of reaction; concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant, integrated rate equations and half

life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment)

Surface Chemistry:

Adsorption - physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis: homogenous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: distinction between true solutions, colloids and suspensions; lyophilic, lyophobic, multi-molecular and macromolecular colloids: properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsion - types of emulsions

General Principles and Processes of Isolation of Elements

Principles and methods of extraction - Concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and Iron

Haloalkanes and Haloarenes

Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions

Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for mono substituted compounds only)

Uses and environmental effects of - dichloromethane, tri-chloro-methane, tetra-chloro-methane, iodoform, freons, DDT

Alcohols, Phenols and Ethers

Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses of methanol and ethanol

Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophilic substitution reactions, uses of phenols

Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses

Aldehydes, Ketones and Carboxylic acids

Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses

Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses

Organic compounds containing Nitrogen

Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines

Cyanides and Isocyanides will be mentioned at relevant places in context

Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry

Biomolecules

Carbohydrates: Classification (aldoses and ketoses), monosaccharides (glucose and fructose), oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); the importance

Proteins: Elementary idea of a-amino acids, peptide bond, polypeptides proteins, primary structure, secondary structure, tertiary structure and quaternary structure (qualitative idea only), denaturation of proteins; enzymes

Vitamins: Classification and functions

Nucleic Acids: DNA & RNA

Polymers

Classification: Natural and synthetic, methods of polymerization (addition and condensation), copolymerization, Some important polymers: Natural and synthetic like polythene, nylon, polyesters, bakelite, rubber

Chemistry in Everyday life

Chemicals in medicines - analgesics, tranquillizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines. Chemicals in food - preservatives, artificial sweetening agents, Cleansing agents - soaps and detergents, cleansing action

Diversity of living organism, Classification of the living organisms (five kingdom classification, major groups principles of classification within each kingdom), Systematics and binomial system of nomenclature, Salient features of animal (non-chordates up to phylum level, and chlordates up to class level) and plant (major groups; Angiosperms up to subclass) classification, Botanical garden, herbaria, zoological parks museums

Tissues in animals and plants. Morphology, anatomy and functions of different parts of flowering plants: Root, stem, leaf, inflorescence, flower,

Fruit and seed, Morphology, anatomy and functions of different systems of an annelid (earthworm), an insect (cockroach) and an Amphibian (frog)

Cell: Cell wall, cell membrane and cell organelles (plastids, mitochondria, endoplasmic reticulum, Golgi bodies/ dictyosomes, ribosomes, lysosomes, vacuoles, centrioles) and nuclear organisation, Mitosis, meiosis, cell cycle, Basis chemical constituents of living bodies, Structure and functions of carbohydrates, proteins, lipids and nucleic acids, Enzymes: Types, properties and function

Movement of water, food, nutrients and gases. Plants and Water : Mineral nutrition, Respiration, Photosynthesis, Plant growth and development

Digestion and absorption, Breathing and respiration, Body fluids and circulation, Excretory products and elimination, Locomotion and movement, Control and coordination

Pollination and fertilization in flowering plants, Development of seeds and fruits, Human reproduction: reproductive system in male and female, menstrual cycle. Production of gametes, fertilization, Implantation, embryo development, pregnancy and parturition, Reproductive health-birth control, contraception and sexually transmitted diseases

Mendelian inheritance, Chromosome theory of inheritance, deviations from Mendelian ratio (gene interaction-Incomplete dominance, codominance, Complementary genes, multiple alleles ), Sex determination in human beings: XX, XY, Linkage and crossing over, Inheritance pattern of haemophilia and blood groups in human beings

DNA: replication, transcription, translation, Gene expression and regulation, Genome and Human Genome Project, DNA fingerprinting

Evolution: Theories and evidences

Animal husbandry, Basic concepts of immunology, vaccines, Pathogens, Parasites, Plant breeding, tissue culture, food production, Microbes in household food processing, industrial production, sewage treatment and energy generation, Cancer and AIDS. Adolescence and drug/alcohol abuse

Recombinant DNA technology, Applications in Health, Agriculture and Industry, Genetically modified (GM) organism; biosafety issues, Insulin and Bt cotton

Ecosystems: components, types and energy flow, Species, population and community., Ecological adaptations, Centres of diversity and conservation of biodiversity, national parks, and sanctuaries, Environmental issues

Sets and their representations, Empty set, Finite & Infinite sets, Equal sets, Subsets, Subsets of the set of real number especially intervals (with notations), Power set, Universal set, Venn diagrams, Union and Intersection of sets, Difference of sets, Complement of a set, Relation & Functions: Ordered pairs, Cartesian product of sets, Number of elements in the Cartesian product of two finite sets, Cartesian product of the reals with itself (upto R X R X R) Definition of relation, pictorial diagrams, domain, condomain and range of a relation, Function as a special kind of relation from one set to another, Pictorial representation of a function, domain, co-domain & range of a function, Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs, Sum, difference, product and quotients of functions Trigonometric Functions: Positive and negative angles, Measuring angles in radians & in degrees and conversion from one measure to another, Definition of trigonometric functions with the help of unit circle

Truth of the identify sin2x + cos2 x = 1, for all x, Signs of trigonometric functions and sketch of their graphs, Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x, & cos y., Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x, General solution of trigonometric equations of the type sin? = sin A, cos? = cos A and tan? = tan A, Proof and simple application of sine and cosine formula

Principle of Mathematical Induction: Processes of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers, The principle of mathematical induction and simple applications

Complex Numbers and Quadratic Equations: Need for complex numbers, especially v-1, to be motivated by inability to solve every quadratic equations, Brief description of algebraic properties of complex numbers, Argand plane and polar representation of complex numbers, Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system

Linear inequalities: Algebraic solutions of linear inequalities in one variable and their representation on the number Line, Graphical solution of linear, inequalities in two variable, Solution of system of linear inequalities in two variables - graphically

Permutation & Combination: Fundamental principle of counting, Factorial n (n!) Permutation and combinations, derivation of formulae and their connections, simple applications

Binomial Theorem: History, statement and proof of the binomial theorem for positive integral indices, Pascal's triangle, General and middle term in binomial expansion, simple applications

Sequence and Series: Arithmetic progression (A.P.) arithmetic mean (A.M.) Geometric progression (G.P.), general term of a G.P., Sum of n terms of a G.P., geometric mean (G.M.), relation between A.M. and G. M., Sum to n terms of the special series, ?n and ?n2 and ?n3

Straight Lines: Brief recall of 2D from earlier classes, Slope of a line and angle between two lines

Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form

General equation of a line, Distance of a point from a line

Conic Section: Sections of a cone: circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a

degenerated case of a conic section, Standard equations and simple properties of parabola, ellipse and hyperbola, Standard equation of a circle

Introduction to Three Dimensional Geometry: Coordinate axes and coordinate planes in three dimensions, Coordinates of a point, Distance between two points and section formula

Limits and Derivatives: Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit, Definition of derivative, relate it to the slope of the tangent of the curve, derivatives of the sum, difference, product and quotient of functions, Derivatives of polynomial and trigonometric functions

Mathematically acceptable statements. Connecting words / phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and / or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics, Validating the statements involving the connecting words - difference between contradiction, converse and contrapositive

The measure of dispersion; mean deviation, variance and standard deviation of ungrouped / grouped data, Analysis of frequency distributions with equal means but different variances

Random experiments: outcomes, sample spaces (set representation), Events: occurrence of events, 'not', 'and' 'or' events, exhaustive events, mutually exclusive events Axiomatic (set theoretic) probability, connections with the theories of earlier classes, Probability of an event, probability of 'not' 'and' & 'or' events

Types of relations: reflexive, symmetric, transitive and equivalence relations, One to one and onto functions, composite functions inverse of a function, Binary operations

Definition, range, domain principal value branches, Graphs of inverse trigonometric functions, Elementary properties of inverse trigonometric functions

Matrices: Concept, notation, order, equality types of matrices zero matrix transpose of a matrix, symmetric and skew symmetric, matrices, Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication, Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2), Concept of elementary row and column operations, Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries)

Determinants: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle, Adjoin and inverse of a square matrix, Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

Continuity and differentiability, the derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function, Concept of exponential and logarithmic functions and their derivatives Logarithmic differentiation, derivative of functions expressed in parametric forms, Second-order derivatives, Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretations

Applications of derivatives: Rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool), Simple problems (that illustrate basic principle and understanding of the subject as well as real-life situations)

Integrals: Integration as inverse process of differentiation, Integration of a variety of functions by substitution by partial fractions and by parts, only simple integrals, Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof), Basic properties of definite integrals and evaluation of definite integrals

Applications of the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable)

Differential Equations: Definition, order and degree, general and particular solutions of a differential equation, Formation of differential equation whose general solution is given, Solution of differential equations by the method of separation of variables, homogeneous differential equations of the first order and first degree, Solutions of the linear differential equation of the type: dy/ dx + py = q, where p and q are functions of

Vectors and scalars, magnitude and direction of a vector, Direction cosines/ratios of vectors, Types of vectors (equal unit zero parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio Scalar (dot) product of vectors, projection of a vector on a line, Vector (cross) product of vectors

Direction cosines / ratios of a line joining two points Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines, Cartesian and vector equation of a plane, Angle between (i) Two lines, (ii) Two planes, (iii) A line and a plane, Distance of a point from a plane

Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints)

Multiplication theorem on probability, Conditional probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of haphazard variable, Repeated independent (Bernoulli) trials and Binomial distribution