## General Section

There is no specific syllabus for the General section. The aim is to test candidate’s aptitude for a career in science. Questions are designed to test the candidate’s familiarity with (and not a detailed understanding of) major historical milestones in mathematics, physics, chemistry, biology, astronomy, computer science and environment. There will be some questions designed to test the grasp of mathematics up to 10th standard and application capabilities of the same to simple problems. Some questions in this section aim to test the

candidate’s general ability to comprehend qualitative and quantitative aspects of a given scientific passage. This is done by giving a passage on some scientific topic and questions based on the concepts elaborated in the passage will be asked. Some questions may aim to find whether the candidates can interpret graphical and/or tabular representation of information.

## Biology

Cell Biology: Cell theory and cells as unit of life. Basic concepts of biomolecules – Proteins, Carbohydrates, Lipids, Nucleic acids. Tools and techniques of cell studies – use of microscope and calibration (microscopy), elements of microscope. Biomembranes – transport mechanism, cellular respiration. Cell organelles – structure and functions. Discovery and structure of DNA, processes of replication, transcription, genetic code and translation. Principles of the basic techniques in molecular biology. Enzymes– catalysis, kinetics, activation energy, competitive and non– competitive inhibition.

Genetics and Evolution: Fundamentals of genetics and evolution. Evidences and theories of organic evolution. Organization of the heredity material in chromosomes. Equational division. Reduction division. Mitosis and meiosis compared and contrasted. Significance of meiosis. Mendel’s laws of inheritance. Discovery of linkage, sex–linked inheritance. Crossing– over, stage at which crossing– over occurs. Neurospora genetics. Mutation – discovery, types of Mutation and Mutations in diploids. Role of mutations in evolution. Elaboration of Mendel’s laws of inheritance. Monohybrid or Dihybrid crosses. Human genetics – human chromosomes, sex–determination, sex–linked inheritance.

Ecology: Physical and biological factors in influencing organisms. Food chains, pyramids of numbers and biomass. Biological equilibrium. Interspecific associations. Bio–diversity. Flora and fauna. Basics of microbial systems, Ecosystems.

Humans and Environment: Soil, rainfall and temperature with reference to natural resources. Our natural resources – their uses and abuses. Environmental pollution and preventive measures. Biodiversity and conservation.

Biotechnology: Principles of recombinant DNA technology. Applications of biotechnology.

Biology of Animal systems:

Digestive System – Modes of nutrition. Different vitamin compounds and their deficiencies.Structure of alimentary canal and associated glands, digestive enzymes and gastrointestinal hormones. Absorption of products of digestion, peristalsis, balanced diet.Respiratory System – Gaseous exchange in animals. Structure of respiratory organs,mechanism of breathing, gaseous transport, tissue respiration.

Circulatory System – Open and closed systems. Functions of blood and 1ymph. Microscopic,structure of blood and blood vessels. Structures and working of heart. Distribution of arteries and veins. Circulation of blood coagulation. Blood groups.

Excretory System – Elimination of nitrogenous waste. Osmoconformers and osmoregulators. Structure and function of kidney tubules. Arrangement of excretory organs.

Nervous System – General account of brain, spinal cord and nerves. Re ex actions (simple and conditioned). Sense organs (eye and ear).

Reproductive System – Sexual and asexual reproduction. General arrangement and functions of reproductive organs.

Developmental Biology: Basic features of development in animals. Types of eggs, fertilization, cleavage, blastula. Stem cells– definition, types, uses, advantages and disadvantages, induced pluripotent stem cells. Different hormones and their roles. Diversity of Animal Life — Principles of classification, binomial nomenclature. General classification of animal phyla up to classes (invertebrates) and up to sub–classes / order (vertebrates), General characters of fishes, amphibians, reptiles, birds and mammals.

Immunology: Basics of immune mechanisms and diseases– active and passive immunity, Tand B-cell responses, antigen presentation, principles of vaccination, monoclonal antibodies and their uses, immunology of AIDS.

Biology of Plant systems: Anatomy and Physiology of Plants – Meristems. Plant growth and development. Internal and external regulators of growth and development in plant. Plant reproduction. Internal structure of root, stem, secondary growth and leaves. Xylem and Phloem – their cell elements and functions. Internal structure of dicot and monocot leaves. Photosynthesis – history, importance, factors and mechanism, stomatal mechanism, transpiration and respiration. Comparative study of dicot and monocot anatomy. Absorption and cell–water relations, transport of water and minerals, tropic and turgor movements. Significance of life–cycles with special reference to alternation of generations as exemplified in Funaria, Selaginella and Pinus (no structural details). Plant hormones.

Systematics: Principles of classical and new systematics. Binomial nomenclature. Familiarity with taxa. Plant breeding and tissue culture.

## Physics

General: Units and dimensions, dimensional analysis, least count, significant figures.

Methods of measurement (Direct, Indirect, Null) and measurement of length, time, mass,

temperature, potential difference, current and resistance.

Design of some simple experiments, such as: i) Searle’s method to determine Young’s

modulus, ii) determination of ‘g’ by simple pendulum, iii) speed of sound using resonance

tube, iv) coefficient of friction using angle of repose, v) determination of focal length of a

convex lens by plotting a graph between ‘u’ and ‘v’, vi) refractive index of material of prism

using the method of minimum deviation, vii) verification of Ohm’s law, viii) resistance of

galvanometer using half deflection method, ix) specific heat of a liquid using calorimeter,

x) I–V characteristic curve for p–n junction in forward and reverse bias.

Graphical representation and interpretation of data. Errors in the measurements and error

analysis.

Mechanics: Kinematics in one and two dimensions (Cartesian coordinates only), projectiles.

Uniform circular motion. Relative velocity. Newton’s laws of motion. Inertial and uniformly

accelerated (linear only) frames of reference. Static and dynamic friction. Kinetic and

potential energy. Linear and circular simple harmonic motion. Work and power.

Conservation of linear momentum and mechanical energy.

Systems of particles. Centre of mass and its motion. Centre of gravity. Impulse. Elastic and

inelastic collisions.

Law of gravitation. Centripetal acceleration and centrifugal force. Gravitational potential

and field. Acceleration due to gravity. Motion of planets and satellites in circular orbits.

Escape velocity.

Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia

of uniform bodies with simple geometrical shapes. Angular momentum, Torque.

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Conservation of angular momentum. Dynamics of rigid bodies with fixed axis of rotation.

Rolling without slipping of rings, cylinders and spheres. Equilibrium of rigid bodies. Collision of

point masses with rigid bodies.

Hooke’s law and stress – strain relations. Elastic limit, plastic deformation. Young’s modulus,

bulk and shear moduli.

Pressure in a fluid. Pascal’s law. Buoyancy. Surface energy and surface tension, capillary

rise. Viscosity – Stoke’s and Poiseuille’s law, Terminal velocity. Qualitative understanding of

turbulence. Reynolds number. Streamline ow, equation of continuity. Bernoulli’s theorem.

Sound and mechanical waves: Plane wave motion, longitudinal and transverse waves,

superposition of waves. Progressive and stationary waves. Vibration of strings and air

columns. Resonance (qualitative understanding). Beats. Speed of sound in gases. Doppler

effect.

Thermal physics: Thermal expansion of solids, liquids and gases. Calorimetry, latent heat.

Heat conduction in one dimension. Elementary concepts of convection and radiation.

Newton’s law of cooling. Ideal gas laws. Specific heats (CV and CP for monoatomic and

diatomic gases). Isothermal and adiabatic processes, bulk modulus of gases. Equivalence

of heat and work. First and second law of thermodynamics and its applications (only for

ideal gases). Entropy. Blackbody radiation – absorptive and emissive powers. Kirchhoff’s

law. Wien’s displacement law, Stefan’s law.

Electricity and magnetism: Coulomb’s law. Electric field and potential. Electrical potential

energy of a system of point charges and of electrical dipoles in a uniform electrostatic field;

Electric field lines. Flux of electric field. Gauss’s law and its application in simple cases, such

as to find field due to infinitely long straight wire. uniformly charged infinite plane sheet and

uniformly charged thin spherical shell.

Capacitance – Calculation of capacitance with and without dielectrics. Capacitors in

series and parallel. Energy stored in a capacitor.

Electric current. Ohm’s law. Series and parallel arrangements of resistances and cells.

Kirchhoff’s laws and simple applications; Heating effect of current.

Biot–Savart’s law and Ampere’s law. Magnetic field near a current carrying straight wire,

along the axis of a circular coil and inside a long straight solenoid. Force on a moving

charge and on a current carrying wire in a uniform magnetic field.

Magnetic moment of a current loop. Effect of a uniform magnetic field on a current loop.

Moving coil galvanometer, voltmeter, ammeter and their conversions.

Electromagnetic induction – Faraday’s law, Lenz’s law. Self and mutual inductance. RC, LR

and LC circuits with and A.C. Sources.

Optics: Rectilinear propagation of light. Reflection and refraction at plane and spherical

surfaces, Deviation and dispersion of light by a prism. Thin lenses. Combination of mirrors

and thin lenses. Magnification. Wave nature of light – Huygen’s principle, interference

limited to Young’s double slit experiment. Elementary idea of diffraction – Rayleigh criterion.

Elementary idea of polarization – Brewster’s law and the law of Malus.

Modern physics: Atomic nucleus. Alpha, beta and gamma radiations. Law of radioactive

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decay. Decay constant. Half–life and mean life. Binding energy and its calculation. Fission

and fusion processes. Energy calculation in these processes.

Photoelectric effect. Bohr’s theory of hydrogen like atoms. Characteristic and continuous

X–rays, Moseley’s law. de Broglie wavelength of matter waves. Heisenberg’s uncertainty

principle.

## Chemistry

Physical Chemistry:

Measurements in chemistry – SI units for fundamental quantities, significant figures in

calculations.

Mole concept – Avogadro number and mole concept, molar masses, mole fraction,

molarity, molality, percent composition, stoichiometry. Equivalent weight and normality.

Calculations based on mole concept and stoichiometry of different reactions. Oxidation–

reduction reactions.

Gaseous and liquid states – Absolute scale of temperature. Gas laws, ideal gas equation,

real gases and deviation from ideality, liquefaction of gases, van der Waals equation.

Kinetic theory of gases; average, root mean square and most probable velocities and their

relation with temperature. Law of partial pressures. Vapour pressure. Diffusion of gases.

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Atomic structure and chemical bonding – Bohr model, spectrum of hydrogen atom,

quantum numbers. Wave particle duality, de Broglie hypothesis. Uncertainty principle.

Orbitals and quantum numbers; shapes and energy of s, p and d orbitals. Electronic

configurations of elements (up to atomic number 36), filling of orbitals – Aufbau principle.

Pauli’s exclusion principle and Hund’s rule. Hybridization involving s, p and d orbitals. Atomic

orbital overlap and chemical bonds; ionic, covalent and coordinate bonds; bond

parameters. Orbital energy diagrams for homo–nuclear diatomic species. Lewis structures.

Hydrogen bond. Polarity in molecules, dipole moment (qualitative aspects). VSEPR theory

and shapes of molecules. Valence Bond Theory. Molecular orbital theory of homo–nuclear

diatomic molecules (qualitative idea).

Thermodynamics – Thermodynamic states. First law of thermodynamics. Internal energy,

work and heat, pressure–volume work. Enthalpy and enthalpy change, Hess’s law, heat of

– reaction, fusion and vaporisation. Second law of thermodynamics, entropy, free energy,

criterion of spontaneity.

Chemical equilibrium – Laws of chemical Equilibrium, law of mass action. Equilibrium

constant – factors affecting equilibrium constant and its applications. Le Chatelier’s

principle – effect of concentration, temperature and pressure. Significance of ΔG and ΔGo

in chemical equilibrium. Relationship of K and ΔG. Ionic equilibrium. Acids and bases

(Bronsted and Lewis concepts), salts. Ka, Kb, Kw, degree of dissociation, pH and their

relationships. Solubility product, common ion effect. Hydrolysis of salts. Buffer solutions.

Electrochemistry – Redox reactions and electrode potential, Electrochemical cells,

Galvanic cells and cell reactions. Standard electrode potential. Nernst equation and its

relation to ΔG and K. Electrochemical series, emf of galvanic cells. Electrolysis and Faraday’s

laws of electrolysis. Electrolytic conductance, specific, equivalent and molar conductivity,

Kohlrausch’s law. Concentration cells. Batteries (primary and secondary), fuel cells,

corrosion.

Chemical kinetics – Rates of chemical reactions. Order of reaction, rate constant. First order

and pseudo first order reactions. Factors affecting rate of reaction – concentration,

temperature (Arrhenius equation), catalyst.

Solid state – Classification of solids, amorphous and crystalline solids, crystalline state, crystal

lattice and unit cells; seven crystal systems (cell parameters a, b, c, α, β, ), close packed

structure of solids (cubic), packing in fcc, bcc and hcp lattices. Packing efficiency, nearest

neighbours, ionic radii. Simple ionic compounds, Imperfection in solids, point defects.

Electrical and magnetic properties, band theory of metals.

Solutions – Solution of solid and gas in liquid. Concentration of solution. Ideal and non-ideal

solutions. Colligative properties. Vapour pressure of solution, Raoult’s law. Molecular weight

determination from lowering of vapour pressure, elevation of boiling point and depression

of freezing point. Abnormal molecular mass, vant Hoff factor. Osmosis – Osmotic pressure,

reverse osmosis.

Surface chemistry:

(a) Adsorption – Physisorption and chemisorptions. Factors affecting adsorption of gases on

solids. Adsorption isotherm. Catalysis – homogeneous and heterogeneous, Activity and

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selectivity. Enzyme catalysis.

(b) Colloidal state – Types, preparation and properties of colloids. Tyndall effect, Brownian

movement, electrophoresis, coagulation. Application of colloids. Micelles.

Inorganic Chemistry:

Classification of elements and periodicity in properties – Modern periodic table,

classification of elements, periodic trends in properties of elements – valence, oxidation

state, atomic/ionic radius, ionization energy, electron gain energy, electronegativity,

valency, chemical reactivity. Diagonal relationship. Anomalous behaviours of Li, Be, B, C.

Hydrogen – Isotopes, preparation, isolation, properties and uses. Hydrides – ionic, covalent

and interstitial. Properties of water and heavy water. Hydrogen peroxide – Preparation,

structure, reactions, uses. Hydrogen as fuel cell.

s– Block elements (Alkali and alkaline earth elements) – General characteristics and trends

in properties.

(a) Group 1: Preparation, properties and reactions of alkali metals with emphasis on

chemistry of Na and K and their compounds – oxides, peroxides, hydroxides, carbonates,

bicarbonates, chlorides and sulphates. Uses.

(b) Group 2: Preparation, properties and reactions alkaline earth metals with emphasis on

the chemistry of Mg and Ca and their compounds – oxides, peroxides, hydroxides,

carbonates, bicarbonates, chlorides and sulphates. Uses.

p– Block elements – General characteristics and trends in properties.

(a) Group 13: Chemistry of Boron and its compounds – borax, boric acid and diborane.

(b) Group 14, 15 and 16: Chemistry of carbon, sulphur, nitrogen and phosphorus. Allotropy.

Chemistry of oxides and oxyacids of these elements. Phosphines, phosphorus chlorides,

ammonia, peroxide and ozone; silicones, silicon tetrachloride and silicates.

(c) Group 17: Chemistry of halogens, chemistry of chlorine in detail. Interhalogen

compounds. HX and oxyacids of halogens.

(d) Group 18: Isolation, properties and reactions of inert gases with emphasis on chemistry

of Xenon.

d–Block elements – (Mainly 3d elements) General characteristics and trends in properties.

Variable oxidation states and their stabilities, colour (excluding the details of electronic

transitions) and calculation of spin–only magnetic moment. Catalytic properties. Interstitial

compounds, alloy formation. Preparation and properties of potassium dichromate and

permanganate.

f–Block elements- (mainly lanthanides) General characteristics and trends in properties.

Variable oxidation states. Lanthanide contraction and its consequences.

Coordination compounds -Nomenclature of mononuclear coordination compounds.

Isomerism. Hybridization and geometries of mononuclear coordination compounds.

Magnetic properties. Werner’s theory, VBT, CFT.

Metals and metallurgy – Occurrence of metals. General methods of extraction involving

chemical principles – thermodynamic, electrochemical and redox principles. General

operation stages involved in metallurgical operation. Metallurgy of p–block element

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(emphasis on Al). Metallurgy of Fe–triad (more emphasis on Fe metallurgy). Metallurgy of

coinage metals (Cu, Ag with more emphasis on Cu). Refining.

Organic Chemistry:

Basic concepts – Representation of organic compounds. Hybridisations of carbon. Sigma

and pi– bonds. Shapes of simple organic molecules. Inductive effect, electromeric effect,

resonance effect, hyperconjugation. Keto–enol tautomerism. Determination of empirical

and molecular formulae (only combustion method). Hydrogen bond – definition and effect

on physical properties of alcohols and carboxylic acids. Acidity and basicity of organic

acids and bases. Methods of purification of compounds.

Reactive intermediates – Homolytic and heterolytic bond cleavages. Formation, structure

and stability of – carbocation, carbanion and free radical.

Isomerism – Structural and stereoisomerism. Geometrical isomerism. Chirality. Enantiomers.

Optical isomerism of compounds containing up to two asymmetric centres, (R, S and E, Z

nomenclature excluded). Racemic mixture. Conformations of ethane and butane

(Newman projections).

Nomenclature – IUPAC nomenclature of simple organic compounds (only hydrocarbons,

mono– functional and bi–functional compounds), including benzene derivatives.

Alkanes – Preparation, properties and reactions. Idea of homologous series Combustion

and halogenation of alkanes. Mechanism of photohalogenation, Wurtz reaction.

Alkenes and Alkynes – Preparation, properties and reactions of alkenes and alkynes.

Isomerization. Acidity of alkynes. Acid catalysed hydration of alkenes and alkynes

(excluding the stereochemistry), Reactions of alkenes with KMnO4, sulphuric acid,

Reduction of alkenes and alkynes, Preparation of alkenes and alkynes by elimination

reactions (excluding stereochemistry), Electrophilic addition reactions of alkenes with X2,

HX, HOX and H2O (X=halogen). Makowniko rule. Peroxide effect. Polymerization of alkenes,

Addition reactions of alkynes, Metal acetylides, Ozonolysis

Aromatic compounds – Aromaticity. Huckel theory of aromaticity. Structure of benzene.

Isomerism in substituted benzenes. Electrophilic substitution reaction on benzene– General

mechanism. Orientating influence of substituents in electrophilic substitution reaction of

monosubstituted benzenes. Electrophilic substitution reactions of benzene and substituted

benzenes – halogenation, nitration, sulphonation, Friedel–Crafts alkylation and acylation

(No mechanism).

Haloalkanes (Alkyl halides) – Preparation from alkanes, alcohols, ole ns. Grignard reagents

and their reaction with aldehydes/ketones/esters/nitriles. Nucleophilic substitution reactions

of alkyl halides with different nucleophilic species. SN1 and SN2 reactions with mechanism.

Halogen exchange reaction. Polyhalogen compounds.

Haloarenes – Nucleophilic aromatic substitution in haloarenes and substituted haloarenes

(excluding Benzyne mechanism and Cine substitution).

Alcohols – Preparation from – ole ns, alkyl halides, carboxylic acids, aldehydes/ketones.

Hydroboration reaction. Dehydration, oxidation to aldehydes and ketones. Reaction with

sodium, phosphorus halides, ZnCl2/ HX, H2SO4. Identification of p–, sec– and tert– alcohols.

Uses of methanol and ethanol.

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Phenols – Preparation of phenol from halobenzene, cumene and benzene sulphonic acid.

Acidity. Reactions of phenols – halogenation, nitration, sulphonation, with Zn. Reimer–

Tieman reaction, Kolbe reaction.

Ethers – Preparation by Williamson’s Synthesis, dehydration of alcohols. Reaction with H2O,

HX.

Aldehydes and Ketones – Preparation of aldehydes and ketones from – Alcohols, olefins,

acid chlorides, arylalkanes, nitriles, esters, Friedel–Crafts reaction. Reactions with – Alcohols,

HCN, NaHSO3. Reactions– oxidation, reduction, oxime and hydrazone formation. Aldol

condensation, Perkin reaction. Cannizzaro reaction. Haloform reaction. Tests to distinguish

aldehydes and ketones.

Carboxylic acids – Acidity and structure–acidity relationship. Preparation of acids.

Preparation of amides, acid chlorides, esters and anhydrides. ester hydrolysis. Reactions of

acids with – thionyl chloride, P–halides, ammonia, alkalis, metals, halogens, reducing

agents. Decarboxylation. Halogenation.

Amines – Basicity and structure–basicity relationship. Identification of p–, sec– and tert–

amines. Preparation of amines from – nitro compounds, nitriles, amides,

haloalkanes/aromatic compounds. Reaction with – Acids, alkylating agents, acylating

agents, nitrous acid. Diazotization of aromatic primary amines – Reactions of aromatic

diazonium salts – azo coupling reaction, Sandmeyer and related reactions. Carbylamine

reaction of p–amines.

Carbohydrate – Classification of carbohydrates. mono– and di– saccharides (glucose and

sucrose). Characteristic tests. Structure of glucose. Reactions of glucose– Oxidation,

reduction, hydroxylamine, HI, acetic anhydride. Cyclic structure of glucose. Structures of –

Sucrose, maltose, starch and cellulose. Glycoside formation and hydrolysis of sucrose.

Amino acids and proteins – α–amino acids. General structure of peptides and proteins.

Peptide bond. Characteristic tests. Separation of amino acids using physical properties.

Denaturation of proteins. Enzymes.

Polymers: Classification. Homo and co–polymers, Addition and condensation

polymerizations. Polythene, nylons, polyesters, Bakelite, melamine–formaldehyde, rubber –

natural and synthetic.

## Mathematics

Algebra:

Algebra of complex numbers, addition, multiplication, conjugation, polar representation,

properties of modulus and principal argument, triangle inequality, cube roots of unity,

geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients,

formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic

means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums

of squares and cubes of the first n natural numbers.

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Logarithms and their properties.

Permutations and combinations, Binomial theorem for positive integral index, properties of

binomial coefficients. Matrices as a rectangular array of real numbers, equality of matrices,

addition, multiplication by a scalar and product of matrices, transpose of a matrix,

determinant of a square matrix of order up to three, inverse of a square matrix of order up

to three, properties of these matrix operations, diagonal, symmetric and skew–symmetric

matrices and their properties, solutions of simultaneous linear equations in two or three

variables.

Addition and multiplication rules of probability, conditional probability, Bayes Theorem,

independence of events, computation of probability of events using permutations and

combinations.

Trigonometry:

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae,

formulae involving multiple and sub–multiple angles, general solution of trigonometric

equations.

Relations between sides and angles of a triangle, sine rule, cosine rule, half–angle formula

and the area of a triangle, inverse trigonometric functions (principal value only).

Analytical geometry:

Two dimensions – Cartesian coordinates, distance between two points, section formulae,

shift of origin. Equation of a straight line in various forms, angle between two lines, distance

of a point from a line. Lines through the point of intersection of two given lines, equation of

the bisector of the angle between two lines, concurrency of lines. Centroid, orthocentre,

incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord. Parametric

equations of a circle, intersection of a circle with a straight line or a circle, equation of a

circle through the points of intersection of two circles and those of a circle and a straight

line.

Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and

eccentricity, parametric equations, equations of tangent and normal. Locus Problems.

Three dimensions – Direction cosines and direction ratios, equation of a straight line in

space, equation of a plane, distance of a point from a plane.

Differential calculus:

Real valued functions of a real variable, into, onto and one–to–one functions, sum,

difference, product and quotient of two functions, composite functions, absolute value,

polynomial, rational, trigonometric, exponential and logarithmic functions.

Limit and continuity of a function, limit and continuity of the sum, difference, product and

quotient of two functions, L’Hospital rule for evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions,

intermediate value property of continuous functions. Derivative of a function, derivative of

the sum, difference, product and quotient of two functions, chain rule, derivatives of

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polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic

functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of

the derivative, tangents and normals, increasing and decreasing functions, maximum and

minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus:

Integration as the inverse process of differentiation, indefinite integrals of standard

functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.

Integration by parts, integration by the methods of substitution and partial fractions,

application of definite integrals to the determination of areas involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential

equations, separation of variables method, linear first order differential equations.

Vectors:

Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and

their geometrical interpretations