Unit of Life : Definition of life, Cell as the basic unit of life. Cell theory, Prokaryotic and Eukaryotic cell structure and differences.
Ultrastructure and functions of cellular components: Cell wall, Plasma membrane, Plastid, Endoplasmic reticulum, Golgi bodies, Mitochondria, Ribosomes, Lysosomes, Nucleus, Centrosomes, Cilia, Flagella.
Microscopy : Components and principles of Simple and Compound Microscope; Electron Microscope : Basic functional principles. Physical and chemical principles involved in maintenance of life processes : Diffusion, Osmosis, Absorption, Osmoregulation.
Biomolecules : Classification and structural properties of carbohydrates, lipids, aminoacids, proteins and nucleic acids.
Carbohydrates : Monosaccharides, digosaccharides, and polysaccharides (starch, glycogen, cellulose).
Proteins : Simple (albumins, globulins, collagen) and conjugated proteins (only examples).
Nucleic acids : Structure of DNA, RNA, types of RNA.
Enzymes : Definition & properties, Examples; Mechanism of Action, Allosterism and Regulation.
Chromosomes and Cell Division : Morphology of chromosomes; Euchromatin and Heterochromatin.
Nucleic acid as genetic material (Examples : Bacterial Transformation and Viral Transduction).
Brief idea of Polytene chromosomes : Cell cycle and phases (excluding control mechanism). Characters of malignant cell; Process & significance of Meiosis.
Genetics : Laws of Heredity : (Monohybrid and dihybrid crosses; Mendels laws). Back cross, Test cross, Linkage, Crossing over, Sex linked inheritance Colour blindness, Haemophilia.
Mutation : Definition and Types; Replication of DNA, Transcription and Translation (Brief idea).Origin, Evolution and Diversity of Life : Haldane and Oparins concept on origin of life. Modern concept of Natural selection, Biological Species concept.
Human evolution: an outline.
Taxonomy and Classification : Definition; Importance of Taxonomy, Binomial Nomenclature, Law of Priority (Homonym & Synonym).
Concept of Biodiversity : Definition of Biodiversity ; Genetic diversity; Species diversity and Ecosystem diversity. Five kingdom classification (only distinct characters).Salient features of major animal phyla with common examples, classification of Chordates (up to Sub Class) with distinctive characters only.
Population Biology : Concept of population growth (logistic and exponential) and population control.
Ecosystem : Concept of ecosystem and Biosphere, Wetland.
Brief idea of Ecological pyramids, Energy flow, Biogeochemical cycle (concept only).
Environmental pollution : Air, water and noise pollution sources effects and probable control strategies; Biomagnification and Bioaccumulation. Cause of Dyslexia, Minamata and Etai etai diseases. Green house effect, BOD, COD, Acid rain and Ozone hole. Virus and Bacteria :Morphological characteristics of Bacteriophage (T2),Plant virus (TMV);Animal virus (influenza),Bacterial cell (E. coli).
Staining : Gram staining for bacteria. Biotechnological application of microbes;
- Agricultural : Rhizobium and other Nitrogen fixing bacteria, Biofertilizers and Bio-pesticides;
- Industrial : Production of curd; tanning and brewery; synthesis of antibiotics, vitamin.
- Cloning of microbial genes.
Tissue and tissue system:
- Plant Tissues: Meristematic and permanent (types with characterization and function).
- Animal Tissue: outline classification and examples.
Functions of life :
Major photosynthetic pigments, outline concept of light and dark reaction phases, basic idea of bacterial photosynthesis, C2, C3, C4 pathways, CAM (in brief), photorespiration.
Respiratory system :
(a) Definition of respiration, Mechanisms of glycolysis, Krebs cycle (Flow chart only; calculation for ATP, CO2 & H2O) Outline idea of Electron Transport system, Relationships of photosynthesis and respiration.
(b) Respiratory system in human : Respiratory tract, Mechanism of breathing, Role of intercostals muscles and diaphragm; Significance of physiological and anatomical dead space. Tidal volume, inspiratory and expiratory reserve volumes, residual volume, vital capacity. Composition of inspired, expired and alveolar air. Common respiratory diseases definition and causes Asthma, Tuberculosis, Hypoxia, Anoxia, Apnoea, Dyspnoea.
Cardiovascular system & Blood : Anatomy of Heart junctional tissues of the heart; origin and propagation of cardiac impulse. Histological structures of arteries, veins and capillaries.
Cardiac cycle : Atrial and ventricular events only; cardiac cycle time, Heart sound.
Cardiac output : definition, Stroke and Minutes volume.
Blood pressure : factors controlling & measurement.
Blood : Composition and functions of blood.Blood coagulation and anticoagulants, Blood group and Rh factor, Blood Transfusion, Lymph and tissue fluid formation and functions, Portal circulation.
Nutrition and Digestive system : Basic constituents of food and their nutritional significance.
Molecules and Chemical Arithmetic : Daltons atomic theory; Gay Lussacs law of gaseous volume; Avogadros Hypothesis and its applications.
Atomic mass; Molecular mass; Equivalent weight; Valency; Gram atomic weight; Gram molecular weight; Gram equivalent weight and mole concept.
Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralization, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality. Percentage composition, empirical formula and molecular formula; Numerical problems.
Atomic Structure : Concept of Nuclear Atom electron, proton and neutron (charge and mass), atomic number; Rutherfords model and its limitations; Extra nuclear structure; Line spectra of hydrogen atom. Quantization of energy (Plancks equation E = hν); Bohrs model of hydrogen atom and its limitations, Sommerfelds modifications (elementary idea); The four quantum numbers, ground state electronic configurations of many electron atoms and mono-atomic ions; The Aufbau Principle;
Paulis Exclusion Principle and Hunds Rule. Uncertainty principle; The concept of atomic orbitals, shapes of s, p and d orbitals (pictorial approach) Radioactivity and Nuclear Chemistry Radioactivity α, Β, γ rays and their properties; Artificial transmutation; Rate of radioactive decay, decay constant, half-life and average life period of radio-elements; Units of radioactivity; Numerical problems. Stability of the atomic nucleus effect of neutronproton (n/p) ratio on the modes of decay, group displacement law, radioisotopes and their uses (C, P, Co and I as examples) isobars and isotones (definition and examples), elementary idea of nuclear fission and fusion reactions.
The Periodic Table and Chemical Families : Modern periodic law (based on atomic number); Modern periodic table based on electronic configurations, groups (Gr. 118) and periods. Types of elements-representative (s-block and p-block), transition (d-block) elements and inner transition (f-block / lanthanides and actinides) and their general characteristics. Periodic trends in physical and chemical propertiesatomic radii, valency, ionization energy, electron affinity, electronegativity, metallic character, acidic and basic characters of oxides and hydrides of the representative elements (up to Z = 36). Position of hydrogen and the noble gases in the periodic table; Diagonal relationships.
Chemical Bonding and Molecular Structure :
Valence electrons, the Octet rule, electrovalent, covalent and coordinate covalent bonds with examples; Properties of electrovalent and covalent compounds. Limitations of Octet rule (examples); Fajans Rule. Directionality of covalent bonds, shapes of poly-atomic molecules (examples); Concept of hybridization of atomic orbitals (qualitative pictorial approach) : sp, sp2, sp3 and dsp2. Molecular orbital energy diagrams for homonuclear diatomic species bond order and magnetic properties. Valence Shell Electron Pair Repulsion (VSEPR) concept (elementary idea) shapes of molecules. Concept of resonance (elementary idea), resonance structures (examples). Elementary idea about electronegativity, bond polarity and dipole moment, inter- and intra- molecular hydrogen bonding and its effects on physical properties (mp, bp and solubility); Hydrogen bridge bonds in diborane. Double salts and complex salts, co-ordination compounds (examples only), co-ordination number (examples of co-ordination number 4 and 6 only).
Gaseous state : Measurable properties of gases. Boyles Law and Charles Law, absolute scale of temperature, kinetic theory of gases, ideal gas equation average, root mean square and most probable velocities and their relationship with temperature. Daltons Law of partial pressure, Grahams Law of gaseous diffusion. Deviations from ideal behavior. Liquefaction of gases, real gases, van der Waals equation; Numerical problems.
Chemical Energetics and Chemical Dynamics : Chemical Energetics conservation of energy principle, energy changes in physical and chemical transformations. First law of thermodynamics; Internal energy, work and heat, pressure-volume work; Enthalpy. Internal energy change (ΔE) and Enthalpy change (ΔH) in a chemical reaction. Hesss Law and its applications (Numerical problems). Heat of reaction, fusion and vapourization; Second law of thermodynamics; Entropy; Free energy; Criterion of spontaneity.
Chemical Equilibria : The Law of mass action, dynamic nature of chemical equilibria. Equilibrium constants, Le Chateliers Principle. Equilibrium constants of gaseous reactions (Kp and Kc) and relation between them (examples). Significance of ΔG and ΔGº.
Chemical Dynamics : Factors affecting the rate of chemical reactions (concentration, pressure, temperature, catalyst). Arrhenius equation and concept of activation energy. Order and molecularity (determination excluded); First order reactions, rate constant, half-life (numerical problems), examples of first order and second order reactions.
Physical Chemistry of Solutions Colloidal Solutions : differences from true solutions; Hydrophobic and hydrophilic colloids (examples and uses); Coagulation and peptization of colloids; Dialysis and its applications; Brownian motion; Tyndall effect and its applications; Elementary idea of emulsion, surfactant and micelle. Electrolytic Solutions Specific conductance, equivalent conductance, ionic conductance, Kohlrauschs law, Faradays laws of electrolysis, applications. Numerical problems. Non-electrolytic Solutions Types of solution, vapour pressure of solutions. Raoults Law; Colligative properties lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure and their relationships with molecular mass (without derivations); Numerical problems. Ionic and Redox Equilibria Ionic equilibria ionization of weak electrolytes, Ostwalds dilution law. Ionization constants of weak acids and bases, ionic product of water, the pH scale, pH of aqueous solutionsof acids and bases; Buffer solutions, buffer action and Henderson equation.
Acid-base titrations, acid-base indicators (structures not required).
Solubility and Solubility Products.
Common ion effect (no numerical problems).
Redox Equilibria : Oxidation-Reduction reactions as electron transfer processes, oxidation numbers, balancing of redox reactions by oxidation number and ion-electron methods. Standard electrode potentials (Eº), Electrochemical series, feasibility of a redox reaction. Significance of Gibbs equation: ΔGº= nFΔGºEº (without derivation), no numerical problems. Redox titrations with (examples); Nernst equations (Numerical problems). Chemistry of Non-metallic Elements and their Compounds Carbon occurrence, isotopes, allotropes (graphite, diamond, fullerene); CO and CO2 production, properties and uses. Nitrogen and Phosphorus occurrence, isotopes, allotopes, isolation from natural sources and purification, reactivity of the free elements. Preparation, properties, reactions of NH3, PH3, NO, NO2 , HNO2, HNO3, P4O10, H3PO3 and H3PO4. Oxygen and Sulfur Occurrence, isotopes, allotropic forms, isolation from natural sources and purification, properties and reactions of the free elements. Water, unusual properties of water, heavy water (production and uses). Hydrogen peroxide and ozone (production, purification, properties and uses).
Halogen : Halogens comparative study, occurrence, physical states and chemical reactivities of the free elements, peculiarities of fluorine and iodine; Hydracids of halogens (preparation, properties, reactions and uses), inter-halogen compounds (examples); Oxyacids of chlorine.
Chemistry of metals : General principles of metallurgy occurrence, concentration of ores, production and purification of metals, mineral wealth of India. Typical metals (Na, Ca, Al, Fe, Cu and Zn) occurrence, extraction, purification (where applicable), properties and reactions with air, water, acids and non-metals. Manufacture of steels and alloy steel (Bessemer, Open-Hearth and L.D. process). Principles of chemistry involved in electroplating, anodizing and galvanizing.
Chemistry in Industry : Large scale production (including physicochemical principles where applicable omitting technical details and uses of individual items).
Heavy chemicals : Sulfuric acid (contact process), Ammonia (Habers process), Nitric acid (Ostwalds process), sodium bi-carbonate and sodium carbonate (Solvey process). Polymers, Polythene, Nylon-66, rubber from natural source, vulcanization.
Electrochemicals : sodium hydroxide, chlorine, bleaching powder as by-products.
Fuel Gases : LPG, CNG. Silicon carbide and silicones. Environmental Chemistry Common modes of pollution of air, water and soil. Ozone layer, ozone hole important chemical reactions. Green House effect; Smog; Pollution of water by domestic and industrial effluents; Pollutantspesticides, fertilizers and plastics.
Chemistry of carbon compounds :
Hybridization of carbon s and p bonds : Isomerism constitutional and stereoisomerism; Geometrical and optical isomerism of compounds containing upto two asymmetric carbon atoms. IUPAC nomenclature of simple organic compoundshydrocarbons, mono and bifunctional molecules only (alicyclic and heterocyclic compounds excluded). Conformations of ethane and n-butane (Newman projection only).
Electronic effects : inductive, resonance and hyperconjugation. Stability of carbocation, carbanion and free radicals; Rearrangement of carbocation; Electrophiles and nucleophiles, tautomerism in _ dicarbonyl compounds, acidity and basicity of simple organic compounds. Aliphatic Compounds Alkanes Preparation from alkyl halides and carboxylic acids;
Reactions : halogenation and combustion. Alkenes and Alkynes Preparation by elimination of alcohols, alkyl halides and quaternary ammonium hydroxides, Saytzeff and Hofmann rules; Reactions electrophilic addition of X2, HX, HOX, H2O (X = halogen), ozonolysis, epoxidation and oxidation with KMno4,oso4(stereochemistry of addition excluded). Markownikoffs and anti-Markownikoffs additions; Hydroboration; Oxymercuration demercuration, reduction of alkenes and alkynes (H2/Lindler catalyst and Na in liquid NH3), metal acetylides.
Alkyl halides : Preparation from alcohols; Formation of Grignard reagents and their synthetic applications for the preparation of alkanes, alcohols, aldehydes, ketones and acids; SN1 and SN2 reactions (preliminary concept).
Alcohols : Preparation from carbonyl compounds and esters. Reaction dehydration, oxidation, esterification, reaction with sodium, ZnCl2 / HCl, phosphorous halides.
Ethers : Preparation by Williamsons synthesis; Cleavage with HCl and HI.
Aldehydes and Ketones : Preparation from esters, acid chlorides, gem-dihalides, Ca-salt of carboxylic acids. Reaction Nucleophilic addition with HCN, hydrazine, hydroxyl amines, semi carbazides, alcohols; Aldol condensation, Clemmensen and Wolff-Kishner reduction, haloform, Cannizzaro and Wittig reactions.
Carboxylic Acids : Hydrolysis of esters (mechanism excluded) and cyanides; Hunsdicker and HVZ reactions.
Aliphatic Amines : Preparation from nitro, cyano and amido compounds. Distinction of 1:, 2: and 3: amines (Hinsberg method); Reaction with HNO2; Carbyl amine reaction. Aromatic Compounds Benzene Kekule structure, aromaticity and Huckel rule. Electrophilic substitution halogenation, sulfonation, nitration, Friedel Crafts reaction, ozonolysis. Directive influence of substituents in monosubstituted benzenes.
Amines : Preparation from reduction of nitro compounds; Formation of diazonium salts and their stability; Replacement of diazonium group with H, OH, X (halogen), CN and NO2, diazocoupling and reduction.
Haloarenes : Nucleophilic substitution, cine substitution (excluding mechanism).
Phenols : halogenation, sulfonation, nitration, Reimer-Tiemann and Kolbe reactions.
Aromatic Aldehydes : Preparation by Gattermann, Gattermann Koch, Rosenmund and Stephens method.
Reaction : Perkin, Benzoin and Cannizzaro. Application Oriented chemistry Main ingredients, their chemical natures (structures excluded) and their side effects, if any, of common antiseptics, analgesics, antacids, vitamin-C.
Introduction to Bio-molecules Carbohydrates : Pentoses and hexoses. Distinctive chemical reactions of glucose.
Aminoacids : glycine, alanine, aspartic acid, cysteine (structures). Zwitterion structures of amino acids, peptide bond. ADP and ATP structures and role in bioenergetics;
Nucleic acids : DNA and RNA skeleton structures. Names of essential elements in biological system.
Principles of qualitative analysis Detection of water soluble noninterfaring Acid and Basic Radicals by dry and wet tests from among :
- Acid Radicals: Cl-, S2-, SO4-, NO3, CO32-
- Basic Radicals: Cu2+, Al3+, Fe3+, Fe22+, Zn2+, Ca2+, Mg2+, Na+, NH42+
Detection of special elements (N, Cl, Br, I and S) in organic compounds by chemical tests.
Identification of functional groups in : phenols, aromatic amines, aldehydes, ketones and carboxylic acids.
Mechanics & General properties of matter :
- Units and dimensions : Units of measurement, system of units, fundamental and derived units, SI units, dimensional analysis. Methods of measurement: Vernier scale, screw gauge, analysis of errors, significant figures.
- Scalars and vectors: Addition, subtraction, multiplication of vectors.
- Kinematics : in one, two and three dimensions, projectiles, uniform circular motion,centripetal force, centrifigual force, relative velocity.
- Dynamics : Newton’s laws of motion; inertial frames, uniformly accelerated frame (pseudoforces), conservation of linear momentum, rocket motion, centre of mass, impulsive forces, friction.
- Work, Power and Energy : conservative and non-conservative forces, conservation of energy, collision(elastic and inelastic)
- Rotational motion : Torque, angular momentum and conservation of angular momentum, moment of inertia, radius of gyration, moment of inertia of objects with simple geometrical shapes, rotational kinetic energy and rolling on horizontal surface.
Gravitation : Laws of gravitation, gravitational field and potential, acceleration due to gravity and its variation, escape velocity, Kepler’s laws and planetary motion, motion of satellites, Geostationary orbit.
Elasticity : Hooke’s law, elastic modulii, Poisson’s ratio, elastic energy.
Hydrostatics and fluid mechanics : Pressure in a fluid, Pascal’s law, Archimedes’ principle, hydraulic press.
Surface energy and surface tension, capillary rise.
Viscosity, streamline and turbulent motion, critical velocity, Reynold’s number, Stoke’s law, Bernoulli’s theorem.
Vibrations : Simple Harmonic Motion, equation of motion, damped and forced vibrations, resonance, superposition of SHM.
Wave motion : Elastic waves, longitudinal and transverse waves. progressive waves, superposition of waves: interference, stationary waves, beats, vibration of strings, air columns, velocity of elastic waves in different media, Doppler effect.
Thermal Physics : Scales of temperature, thermal expansion of solids, liquids and gases, calorimetry, change of state of matter, latent heat, transition temperature, Transmission of heat: conduction, convection, radiation, Black body radiation, absorptive and emissive powers: Kirchoffs law, Wien’s law, Stefan’s law, Newton’s law of cooling, Kinetic theory : mean free path, pressure of an ideal gas, mean and rms velocity of molecules of a gas, kinetic interpretation of temperature, degrees of freedom, equipartition of energy (statement only) — application to monoatomic and diatomic gases.
Thermodynamics : first law of thermodynamics, equivalence of heat and work, intensive and extensive thermodynamic variables, reversible and irreversible processes, specific heats of gases, relation between Cpand Cv.
Optics : reflection and refraction at plane and spherical surfaces, total internal reflection, thin lenses, power of a lens, combination of lenses and mirrors, deviation and dispersion by prisms. Simple and compound microscopes, astronomical telescope, human eye: defects and remedies. Coherent sources, interference of light, Youngs double slit.
Electrostatics : Coulomb’s law, electric field and potential,flux of electric field, Gauss’ law, electric field and potential due to an infinite line charge, charged infinite sheet, solid spheres and spherical shells.Electric dipole and field due to dipole. Capacitance, spherical and parallel plate capacitors, energy stored in a capacitor, series and parallel combination of capacitors,
Current Electricity : Electric current, drift velocity and mobility, Ohm’s law, resistivity, combination of resistances in series and parallel, combination of cells. Kirchoffs laws, Wheatstone bridge, Metre bridge, potentiometer. Heating effect of current, thermoelectricity, Seebeck and Peltier effect. Chemical effect of current, Faradays law of electrolysis,:primary and secondary cells.
Electromagnatism : Magnetic effects of Current, Biot Savart’s law, magnetic field due to an infinite lin e charge, circular coil and solenoid, Amperes circuital law, Lorentz force, Flemings left hand rule, force between two current carrying conductors, magnetic moment of a current loop, magnetic dipole, torque experienced by a current carrying coil in a uniform magnetic field,galvanometer, current sensitivity, conversion of galvanometer to voltmeter and ammeter. Magnetic field of earth, tangent galvanometer, magnetic properties of materials : Dia, para and ferromagnet , permeability, susceptibility.
Electromagnetic induction : Magnetic flux, Faradays laws of electromagnetic induction, Lenz’s law, self and mutual induction, Flemings right hand rule, Alternating current, peak and rms value of alternating current; generator, D.C. motor and transformer Qualitative idea of electromagnetic wave and its spectrum.
Modern Physics : Bohr’s atomic model for hydrogen like atom, hydrogen spectrum, x-ray emission, Moseley’s law, wave particle duality, de Broglies hypothesis, photo electric effect . Constituents of atoms, isotopes, mass defect, mass-energy equivalence, binding energy. radioactivity -α, β, γ radiation, half life, mean life, fission, fusion. Energy bands in solids, intrinsic and doped semiconductors, p-n junction diode, rectifier, pnp and npn transistors, common emitter characteristics. Binary number, AND, OR, NOT, NAND and NOR gates .
A.P., G.P., H.P. : Definitions of A. P. and G.P.; General term; Summation of first n-terms; A.M.and G.M.; Definitions of H.P. (only 3 terms) and H.M.; Finite arithmetico-geometric series.
Logarithms : Definition; General properties; Change of base.
Complex Numbers : Definition and properties of complex numbers; Complex conjugate; Triangle inequality; Square root of complex numbers; Cube roots of unity; DMoivres theorem (statement only) and its elementary applications.
Quadratic Equations : Quadratic equations with real coefficients;
Relations between roots and coefficients; Nature of roots; Formation of a quadratic equation, sign and magnitude of the quadratic expression ax2+bx+c (a,b,c are rational numbers and a≠0).
Permutation and combination : Permutation of n different things taken r at a time (r≤n). Permutation of n things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n different things taken r at a time (r≤n). Combination of n things not all different. Basic properties.Problems involving both permutations and combinations.
Principle of Mathematical Induction : Statement of the principle. Proof by induction for the sum of squares, sum of cubes of first n natural numbers, divisibility properties like 22n-1 is divisible by 3 (n ≥ 1), 7 divides 32 n+1+2n+2(n ≥ 1) .
Binomial theorem (positive integral index) : Statement of the theorem, general term, middle term, equidistant terms, properties of binomial co-efficients. Infinite series :Binomial theorem for negative and fractional index. Infinite G.P. series, Exponential and Logarithmic series with range of validity (statement only), simple applications.
Matrices : Concepts of n mW (m ≤3, n ≤3) real matrices, operations of addition, scalar multiplication and multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants (statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area of a triangle. Solutions of system of linear equations. (Not more than 3 variables).
Sets, Relations and Mappings : Idea of sets, subsets, power set, complement, union, intersection and difference of sets, Venn diagram, De Morgans Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian product of sets. Relation and its properties. Equivalence relation definition and elementary examples, mappings, range and domain, injective, surjective and bijective mappings, composition of mappings, inverse of a mapping.
Probability : Classical definition, addition rule, conditional probability and Bayes theorem, independence, multiplication rule.
Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions.
Co-ordinate geometry of two dimensions Basic Ideas :
Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Polar coordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of axes, concept of locus, elementary locus problems.
Straight line : Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and parallelism of two lines. Distance of a point from a line. Distance between two parallel lines. Lines through the point of intersection of two lines.
Circle : Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y may represent a circle. Equation of a circle in terms of endpoints of a diameter . Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of two intersecting circles.
Conics : Definition, Directrix, Focus and Eccentricity, classification based on eccentricity.
Parabola : Standard equation. Reduction of the form x = ay2+by+c or y = ax2+bx+c to the standard form y2 = 4ax or x2 = 4ay respectively. Elementary properties and parametric equation of a parabola.
Ellipse and Hyperbola : Reduction to standard form of general equation of second degree when xy term is absent. Conjugate hyperbola. Simple properties. Parametric equations. Location of a point with respect to a conic.
Differential calculus : Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives of implicit functions and of functions defined parametrically. Rolles Theorem and Lagranges Mean Value theorem (statement only). Their geometric interpretation and elementary application. LHospitals rule (statement only) and applications. Second order derivative.
Integral calculus : Integration as a reverse process of differentiation, indefinite integral of standard functions. Integration by parts. Integration by substitution and partial fraction. Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its applications. Properties of definite integrals.
Differential Equations : Formulation and solution of differential equations of the forms.
- dy / dx = (x).g(y)
- dy / dx = (y/x)
- dy / dx = (ax+by) / (cx+dy)
- dy / dx = (a1x+b1y+c1 ) / (a2x+b2y+c2) / (a1/a2=b1/b2)
- dy / dx + p(x)y = Q(x)
- d2y / dx2 + p1dy / dx + p2y = 0 with p1and p2 constants.
- d2y / dx2 = (x)
Application of Calculus : Tangents and normals, conditions of tangency. Determination of monotonicity, maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and straight lines. Area of the region included between two elementary curves.
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