BITSAT Mathematics Syllabus

Syllabus for BITSAT Mathematics 2016

January 23, 2016January 23, 2016 by

Part IV: Mathematics

1. Algebra

1.1   Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations; Fundamental theorem of algebra.
1.2   Theory of Quadratic equations, quadratic equations in real and complex number system and their solutions.
1.3   Arithmetic and geometric progressions, arithmetic, geometric and arithmeticogeometric series, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
1.4   Logarithms and their properties.
1.5   Exponential series.
1.6   Permutations and combinations, Permutations as an arrangement and combination as selection, simple applications.
1.7   Binomial theorem for a positive integral index, properties of binomial coefficients, Pascal’s triangle
1.8   Matrices and determinants of order two or three, properties and evaluation of determinants, addition and multiplication of matrices, adjoint and inverse of matrices, Solutions of simultaneous linear equations in two or three variables, elementary row and column operations of matrices, Types of matrices, applications of determinants in finding the area of triangles.
1.9   Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, oneone, into and onto mappings, composition of mappings, binary operation, inverse of function, functions of real variables like polynomial, modulus, signum and greatest integer.
1.10   Mathematical reasoning and methods of proofs , 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 through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words – difference between contradiction, converse and contra positive., Mathematical induction
1.11   Linear Inequalities, solution of linear inequalities in one variable ( Algebraic) and two variables (Graphical).

2. Trigonometry

2.1   Measurement of angles in radians and degrees, positive and negative angles, trigonometric ratios, functions with their graphs and identities.
2.2   Solution of trigonometric equations.
2.3   Inverse trigonometric functions

3. Two-dimensional Coordinate Geometry

3.1   Cartesian coordinates, distance between two points, section formulae, shift of origin.
3.2   Straight lines and pair of straight lines: Equation of straight lines 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, concurrent lines.
3.3   Circles: Equation of circle in standard form, parametric equations of a circle.
3.4   Conic sections : parabola, ellipse and hyperbola their eccentricity, directrices & foci.

4. Three dimensional Coordinate Geometry

4.1   Co-ordinate axes and co-ordinate planes, distance between two points, section formula, direction cosines and direction ratios, equation of a straight line in space and skew lines.
4.2   Angle between two lines whose direction ratios are given, shortest distance between two lines.
4.3   Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines, angles between two planes, angle between a line and a plane.

5. Differential calculus

5.1   Domain and range of a real valued function, Limits and Continuity of the sum, difference, product and quotient of two functions, Differentiability.
5.2   Derivative of different types of functions (polynomial, rational, trigonometric, inverse trigonometric, exponential, logarithmic, implicit functions), derivative of the sum, difference, product and quotient of two functions, chain rule, parametric form.
5.3   Geometric interpretation of derivative, Tangents and Normals.
5.4   Increasing and decreasing functions, Maxima and minima of a function.
5.5   Rolle’s Theorem, Mean Value Theorem and Intermediate Value Theorem.

6. Integral calculus

6.1   Integration as the inverse process of differentiation, indefinite integrals of standard functions.
6.2   Methods of integration: Integration by substitution, Integration by parts, integration by partial fractions, and integration by trigonometric identities.
6.3   Definite integrals and their properties, Fundamental Theorem of Integral Calculus, applications in finding areas under simple curves.
6.4   Application of definite integrals to the determination of areas of regions bounded by simple curves.

7. Ordinary Differential Equations

7.1   Order and degree of a differential equation, formulation of a differential equation whole general solution is given, variables separable method.
7.2   Solution of homogeneous differential equations of first order and first degree
7.3   Linear first order differential equations

8. Probability

8.1   Various terminology in probability, axiomatic and other approaches of probability, addition and multiplication rules of probability.
8.2   Conditional probability, total probability and Baye’s theorem
8.3   Independent events
8.4   Discrete random variables and distributions with mean and variance.

9. Vectors

9.1   Direction ratio/cosines of vectors, addition of vectors, scalar multiplication, position vector of a point dividing a line segment in a given ratio.
9.2   Dot and cross products of two vectors, projection of a vector on a line.
9.3   Scalar triple products and their geometrical interpretations.

10. Statistics

10.1 Measures of dispersion
10.2 Analysis of frequency distributions with equal means but different variances

11. Linear Programming

11.1 Various terminology and formulation of linear Programming
11.2 Solution of linear Programming using graphical method, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (upto three nonitrivial constraints)

12. Mathematical modelling

12.1 Formulation of simple real life problem, solution using matrices, calculus and linear programming.

BITSAT 2015 Chemistry Syllabus

July 17, 2014 by bn Mishra

Chemistry

1. States of Matter

1.1 Measurement: Physical quantities and SI units, Dimensional analysis, Precision, Significant figures.

1.2 Chemical reactions: Laws of chemical combination, Dalton’s atomic theory; Mole concept; Atomic, molecular and molar masses; Percentage composition empirical & molecular formula; Balanced chemical equations & stoichiometry

1.3 Gaseous state: Gas Laws, ideal behavior, empirical derivation of gas equation, Kinetic theory – Maxwell distribution of velocities, Average, root mean square and most probable velocities and relation to temperature, Diffusion; Deviation from ideal behaviour – Critical temperature, Liquefaction of gases, vander Waals equation.

1.4 Liquid state: Vapour pressure, surface tension, viscosity.

1.5 Solid state: Classification; Space lattices & crystal systems; Unit cell – Cubic & hexagonal systems; Close packing; Crystal structures: Simple AB and AB2 type ionic crystals, covalent crystals – diamond & graphite, metals. Imperfections- Point defects, non-stoichiometric crystals; Electrical, magnetic and dielectric properties; Amorphous solids – qualitative description. Band theory of metals, conductors, semiconductors and insulators, and n- and p- type semiconductors.

2. Atomic Structure

2.1 Introduction: Radioactivity, Subatomic particles; Atomic number, isotopes and isobars, Rutherford’s picture of atom; Hydrogen atom spectrum and Bohr model.

2.2 Quantum mechanics: Wave-particle duality – de Broglie relation, Uncertainty principle; Hydrogen atom: Quantum numbers and wavefunctions, atomic orbitals and their shapes (s, p, and d), Spin quantum number.

2.3 Many electron atoms: Pauli exclusion principle; Aufbau principle and the electronic configuration of atoms, Hund’s rule.

2.4 Periodicity: Periodic law and the modern periodic table; Types of elements: s, p, d, and f blocks; Periodic trends: ionization energy, atomic and ionic radii, electron affinity, electro negativity and valency.

3. Chemical Bonding & Molecular Structure

3.1 Ionic Bond: Lattice Energy and Born-Haber cycle; Covalent character of ionic bonds and polar character of covalent bond

3.2 Molecular Structure: Lewis picture & resonance structures, VSEPR model & molecular shapes

3.3 Covalent Bond: Valence Bond Theory- Orbital overlap, Directionality of bonds & hybridization (s, p & d orbitals only), Resonance; Molecular orbital theory- Methodology, Orbital energy level diagram, Bond order, Magnetic properties for homonuclear diatomic species.

3.4 Metallic Bond: Qualitative description.

3.5 Intermolecular Forces: Polarity; Dipole moments; Hydrogen Bond.

4. Thermodynamics

4.1 Basic Concepts: Systems and surroundings; State functions; Intensive & Extensive Properties; Zeroth Law and Temperature

4.2 First Law of Thermodynamics: Work, internal energy, heat, enthalpy, heat capacities; Enthalpies of formation, phase transformation, ionization, electron gain; Thermochemistry; Hess’s Law. Bond dissociation, combustion, atomization, sublimation, dilution

4.3 Second Law: Spontaneous and reversible processes; entropy; Gibbs free energy related to spontaneity and non-mechanical work; Standard free energies of formation, free energy change and chemical equilibrium

4.4 Third Law: Introduction

5. Physical and Chemical Equilibria

5.1 Concentration Units: Mole Fraction, Molarity, and Molality

5.2 Solutions: Solubility of solids and gases in liquids, Vapour Pressure, Raoult’s law, Relative lowering of vapour pressure, depression in freezing point; elevation in boiling point; osmotic pressure, determination of molecular mass; solid solutions.

5.3 Physical Equilibrium: Equilibria involving physical changes (solid-liquid, liquid-gas, solid-gas), Surface chemistry, Adsorption, Physical and Chemical adsorption, Langmuir Isotherm, Colloids and emulsion, classification, preparation, uses.

5.4 Chemical Equilibria: Equilibrium constants (KP, KC), Le-Chatelier’s principle.

5.5 Ionic Equilibria: Strong and Weak electrolytes, Acids and Bases (Arrhenius, Lewis, Lowry and Bronsted) and their dissociation; Ionization of Water; pH; Buffer solutions; Acid-base titrations; Hydrolysis; Solubility Product of Sparingly Soluble Salts; Common Ion Effect.

5.6 Factors Affecting Equilibria: Concentration, Temperature, Pressure, Catalysts, Significance of ∆ G and ∆ G⁰in Chemical Equilibria.

6. Electrochemistry

6.1 Redox Reactions: Oxidation-reduction reactions (electron transfer concept); Oxidation number; Balancing of redox reactions; Electrochemical cells and cell reactions; Electrode potentials; EMF of Galvanic cells; Nernst equation; Factors affecting the electrode potential; Gibbs energy change and cell potential; Secondary cells; Fuel cells; Corrosion and its prevention.

6.2 Electrolytic Conduction: Electrolytic Conductance; Specific and molar conductivities; Kolhrausch’s Law and its application, Faraday’s laws of electrolysis; Coulometer; Electrode potential and electrolysis, Commercial production of the chemicals, NaOH, Na, Al, Cl2 & F2.

7. Chemical Kinetics

7.1 Aspects of Kinetics: Rate and Rate expression of a reaction; Rate constant; Order and molecularity of the reaction; Integrated rate expressions and half life for zero and first order reactions.

7.2 Factor Affecting the Rate of the Reactions: Concentration of the reactants, size of particles; Temperature dependence of rate constant; Activation energy; Catalysis, Surface catalysis, enzymes, zeolites; Factors affecting rate of collisions between molecules.

7.3 Mechanism of Reaction: Elementary reactions; Complex reactions; Reactions involving two/three steps only.

8. Hydrogen and s-block elements

8.1 Hydrogen: Element: unique position in periodic table, occurrence, isotopes; Dihydrogen: preparation, properties, reactions, and uses; Molecular, saline, ionic, covalent, interstitial hydrides; Water: Properties; Structure and aggregation of water molecules; Heavy water; Hydrogen peroxide: preparation, reaction, structure & use, Hydrogen as a fuel.

8.2 s-block elements: Abundance and occurrence; Anomalous properties of the first elements in each group; diagonal relationships; trends in the variation of properties (ionization energy, atomic & ionic radii).

8.3 Alkali metals: Lithium, sodium and potassium: occurrence, extraction, reactivity, and electrode potentials; Biological importance; Reactions with oxygen, hydrogen, halogens water and liquid ammonia; Basic nature of oxides and hydroxides; Halides; Properties and uses of compounds such as NaCl, Na2CO3, NaHCO3, NaOH, KCl, and KOH.

8.4 Alkaline earth metals: Magnesium and calcium: Occurrence, extraction, reactivity and electrode potentials; Reactions with non-metals; Solubility and thermal stability of oxo salts; Biological importance; Properties and uses of important compounds such as CaO, Ca(OH)2, plaster of Paris, MgSO4, MgCl2, CaCO3, and CaSO4; Lime and limestone, cement.

9. p- d- and f-block elements

9.1 General: Abundance, distribution, physical and chemical properties, isolation and uses of elements; Trends in chemical reactivity of elements of a group; electronic configuration, oxidation states; anomalous properties of first element of each group.

9.2 Group 13 elements: Boron; Properties and uses of borax, boric acid, boron hydrides & halides. Reaction of aluminum with acids and alkalis;

9.3 Group 14 elements: Carbon: carbon catenation, physical & chemical properties, uses, allotropes (graphite, diamond, fullerenes), oxides, halides and sulphides, carbides; Silicon: Silica, silicates, silicone, silicon tetrachloride, Zeolites.

9.4 Group 15 elements: Dinitrogen; Reactivity and uses of nitrogen and its compounds; Industrial and biological nitrogen fixation; Ammonia: Haber’s process, properties and reactions; Oxides of nitrogen and their structures; Ostwald’s process of nitric acid production; Fertilizers – NPK type; Production of phosphorus; Allotropes of phosphorus; Preparation, structure and properties of hydrides, oxides, oxoacids (elementary idea only) and halides of phosphorus, phosphine.

9.5 Group 16 elements: Isolation and chemical reactivity of dioxygen; Acidic, basic and amphoteric oxides; Preparation, structure and properties of ozone; Allotropes of sulphur; Production of sulphur and sulphuric acid; Structure and properties of oxides, oxoacids (structures only), hydrides and halides of sulphur.

9.6 Group 17 and group 18 elements: Structure and properties of hydrides, oxides, oxoacids of chlorine (structures only); preparation, properties & uses of chlorine & HCl; Inter halogen compounds; Bleaching Powder; Preparation, structure and reactions of xenon fluorides, oxides, and oxoacids.

9.7 d-Block elements: General trends in the chemistry of first row transition elements; Metallic character; Oxidation state; ionization enthalpy; Ionic radii; Catalytic properties; Magnetic properties; Interstitial compounds; Occurrence and extraction of iron, copper, silver, zinc, and mercury; Alloy formation; Steel and some important alloys; preparation and properties of CuSO4, K2Cr2O7, KMnO4, Mercury halides; Silver nitrate and silver halides; Photography.

9.8 f-Block elements: Lanthanoids and actinoids; Oxidation states and chemical reactivity of lanthanoids compounds; Lanthanide contraction; Comparison of actinoids and lanthanoids.

9.9 Coordination Compounds: Coordination number; Ligands; Werner’s coordination theory; IUPAC nomenclature; Application and importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems e.g. chlorophyll, vitamin B12, and hemoglobin); Bonding: Valence-bond approach, Crystal field theory (qualitative); Stability constants; Shapes, color and magnetic properties; Isomerism including stereoisomerisms; Organometallic compounds.

10. Principles of Organic Chemistry and Hydrocarbons

10.1 Classification: Based on functional groups, trivial and IUPAC nomenclature. Methods of purification: qualitative and quantitative.

10.2 Electronic displacement in a covalent bond: Inductive, resonance effects, and hyperconjugation; free radicals; carbocations, carbanions, nucleophiles and electrophiles; types of organic reactions.

10.3 Alkanes and cycloalkanes: Structural isomerism, general properties and chemical reactions.

10.4 Alkenes and alkynes: General methods of preparation and reactions, physical properties, electrophilic and free radical additions, acidic character of alkynes and (1,2 and 1,4) addition to dienes.

10.5 Aromatic hydrocarbons: Sources; properties; isomerism; resonance delocalization; aromaticity; polynuclear hydrocarbons; mechanism of electrophilic substitution reaction, directive influence and effect of substituents on reactivity; carcinogenicity and toxicity.

10.6 Haloalkanes and haloarenes: Physical properties, chemical reactions and mechanism of substitution reaction. Uses and environmental effects; di, tri, tetrachloromethanes, iodoform, freon and DDT.

10.7 Petroleum: Composition and refining, uses of petrochemicals.

11. Stereochemistry

11.1 Introduction: Chiral molecules; optical activity; polarimetry; R,S and D,L configurations; Fischer projections; enantiomerism; racemates; diastereomerism and meso structures.

11.2 Conformations: Ethane conformations; Newman and Sawhorse projections.

11.3 Geometrical isomerism in alkenes

12. Organic Compounds with Functional Groups Containing Oxygen and Nitrogen

12.1 General: Electronic structure, important methods of preparation, identification, important reactions, physical properties and uses of alcohols, phenols, ethers, aldehydes, ketones, carboxylic acids, nitro compounds, amines, diazonium salts, cyanides and isocyanides.

12.2 Specific: Effect of substituents on alpha-carbon on acid strength, comparative reactivity of acid derivatives, mechanism of nucleophilic addition and dehydration, basic character of amines methods of preparation, and their separation, importance of diazonium salts in synthetic organic chemistry.

13. Biological , Industrial and Environmental chemistry

13.1 The Cell: Concept of cell and energy cycle.

13.2 Carbohydrates: Classification; Monosaccharides; Structures of pentoses and hexoses; Anomeric carbon; Mutarotation; Simple chemical reactions of glucose, Disaccharides: reducing and non-reducing sugars – sucrose, maltose and lactose; Polysaccharides: elementary idea of structures of starch, cellulose and glycogen.

13.3 Proteins: Amino acids; Peptide bond; Polypeptides; Primary structure of proteins; Simple idea of secondary , tertiary and quarternary tructures of proteins; Denaturation of proteins and enzymes.

13.4 Nucleic Acids: Types of nucleic acids; Primary building blocks of nucleic acids (chemical composition of DNA & RNA); Primary structure of DNA and its double helix; Replication; Transcription and protein synthesis; Genetic code.

13.5 Vitamins: Classification, structure, functions in biosystems; Hormones

13.6 Polymers: Classification of polymers; General methods of polymerization; Molecular mass of polymers; Biopolymers and biodegradable polymers; Free radical, cationic and anionic addition polymerizations; Copolymerization: Natural rubber; Vulcanization of rubber; Synthetic rubbers. Condensation polymers.

13.7 Pollution: Environmental pollutants; soil, water and air pollution; Chemical reactions in atmosphere; Smog; Major atmospheric pollutants; Acid rain; Ozone and its reactions; Depletion of ozone layer and its effects; Industrial air pollution; Green house effect and global warming; Green Chemistry.

13.8 Chemicals in medicine, health-care and food: Analgesics, Tranquilizers, antiseptics, disinfectants, anti- microbials, anti-fertility drugs, antihistamines, antibiotics, antacids; Preservatives, artificial sweetening agents, antioxidants, soaps and detergents.

14. Theoretical Principles of Experimental Chemistry

14.1 Volumetric Analysis: Principles; Standard solutions of sodium carbonate and oxalic acid; Acid-base titrations; Redox reactions involving KI, H2SO4, Na2SO3, Na2S2O3and H2S; Potassium permanganate in acidic, basic and neutral media; Titrations of oxalic acid, ferrous ammonium sulphate with KMnO4, K2 Cr2O7/Na2S2O3, Cu(II)/Na2S2O3.

14.2 Qualitative analysis of Inorganic Salts: Principles in the determination of the cations Pb²⁺, Cu²⁺, As³⁺, Mn²⁺,

Zn²⁺, Co²⁺, Ca²⁺, Sr²⁺, Ba²⁺, Mg²⁺, NH4+, Fe³⁺, Ni²⁺ and the anions CO32-, S^2-, SO42-, SO32-, NO2-, NO3-, Cl^–, Br^–, I^–, PO43-, CH3COO^–, C2O42-.

14.3 Physical Chemistry Experiments: preparation and crystallization of alum, copper sulphate, ferrous sulphate, double salt of alum and ferrous sulphate, potassium ferric sulphate; Temperature vs. solubility; pH measurements; Lyophilic and lyophobic sols; Dialysis; Role of emulsifying agents in emulsification. Equilibrium studies involving (i) ferric and thiocyanate ions (ii) [Co(H2O)6]²⁺ and chloride ions; Enthalpy determination for (i) strong acid vs. strong base neutralization reaction (ii) hydrogen bonding interaction between acetone and chloroform; Rates of the reaction between (i) sodium thiosulphate and hydrochloric acid, (ii) potassium iodate and sodium sulphite (iii) iodide vs. hydrogen peroxide, concentration and temperature effects in these reactions.

14.4 Purification Methods: Filtration, crystallization, sublimation, distillation, differential extraction, and chromatography. Principles of melting point and boiling point determination; principles of paper chromatographic separation – Rf values.

14.5 Qualitative Analysis of Organic Compounds: Detection of nitrogen, sulphur, phosphorous and halogens; Detection of carbohydrates, fats and proteins in foodstuff; Detection of alcoholic, phenolic, aldehydic, ketonic, carboxylic, amino groups and unsaturation.

14.6 Quantitative Analysis of Organic Compounds: Basic principles for the quantitative estimation of carbon, hydrogen, nitrogen, halogen, sulphur and phosphorous; Molecular mass determination by silver salt and chloroplatinate salt methods; Calculations of empirical and molecular formulae.

14.7 Principles of Organic Chemistry Experiments: Preparation of iodoform, acetanilide, p-nitro acetanilide, di- benzayl acetone, aniline yellow, beta-naphthol; Preparation of acetylene and study of its acidic character.

BITSAT 2015 Physics Syllabus

July 17, 2014July 17, 2014 by bn Mishra

Physics

1. Units & Measurement

1.1 Units (Different systems of units, SI units, fundamental and derived units)

1.2 Dimensional Analysis

1.3 Precision and significant figures

1.4 Fundamental measurements in Physics (Vernier calipers, screw gauge,

Physical balance etc)

2. Kinematics

2.1 Properties of vectors

2.2 Position, velocity and acceleration vectors

2.3 Motion with constant acceleration

2.4 Projectile motion

2.5 Uniform circular motion

2.6 Relative motion

3. Newton’s Laws of Motion

3.1 Newton’s laws (free body diagram, resolution of forces)

3.2 Motion on an inclined plane

3.3 Motion of blocks with pulley systems

3.4 Circular motion – centripetal force

3.5 Inertial and non-inertial frames

4. Impulse and Momentum

4.1 Definition of impulse and momentum

4.2 Conservation of momentum

4.3 Collisions

4.4 Momentum of a system of particles

4.5 Center of mass

5. Work and Energy

5.1 Work done by a force

5.2 Kinetic energy and work-energy theorem

5.3 Power

5.4 Conservative forces and potential energy

5.5 Conservation of mechanical energy

6. Rotational Motion

6.1 Description of rotation (angular displacement, angular velocity and angular

acceleration)

6.2 Rotational motion with constant angular acceleration

6.3 Moment of inertia, Parallel and perpendicular axes theorems, rotational kinetic

energy

6.4 Torque and angular momentum

6.5 Conservation of angular momentum

6.6 Rolling motion

7. Gravitation

7.1 Newton’s law of gravitation

7.2 Gravitational potential energy, Escape velocity

7.3 Motion of planets – Kepler’s laws, satellite motion

8. Mechanics of Solids and Fluids

8.1 Elasticity

8.2 Pressure, density and Archimedes’ principle

8.3 Viscosity and Surface Tension

8.4 Bernoulli’s theorem

9. Oscillations

9.1 Kinematics of simple harmonic motion

9.2 Spring mass system, simple and compound pendulum

9.3 Forced & damped oscillations, resonance

10. Waves

10.1 Progressive sinusoidal waves

10.2 Standing waves in strings and pipes

10.3 Superposition of waves, beats

10.4 Doppler Effect

11. Heat and Thermodynamics

11.1 Kinetic theory of gases

11.2 Thermal equilibrium and temperature

11.3 Specific heat, Heat Transfer – Conduction, convection and radiation, thermal

conductivity, Newton’s law of cooling

11.4 Work, heat and first law of thermodynamics

11.5 2^nd law of thermodynamics, Carnot engine – Efficiency and Coefficient of

performance

12. Electrostatics

12.1 Coulomb’s law

12.2 Electric field (discrete and continuous charge distributions)

12.3 Electrostatic potential and Electrostatic potential energy

12.4 Gauss’ law and its applications

12.5 Electric dipole

12.6 Capacitance and dielectrics (parallel plate capacitor, capacitors in series and

parallel)

13. Current Electricity

13.1 Ohm’s law, Joule heating

13.2 D.C circuits – Resistors and cells in series and parallel, Kirchoff’s laws,

potentiometer and Wheatstone bridge

13.3 Electrical Resistance (Resistivity, origin and temperature dependence of

resistivity).

14. Magnetic Effect of Current

14.1 Biot-Savart’s law and its applications

14.2 Ampere’s law and its applications

14.3 Lorentz force, force on current carrying conductors in a magnetic field

14.4 Magnetic moment of a current loop, torque on a current loop, Galvanometer and

its conversion to voltmeter and ammeter

15. Electromagnetic Induction

15.1 Faraday’s law, Lenz’s law, eddy currents

15.2 Self and mutual inductance

15.3 Transformers and generators

15.4 Alternating current (peak and rms value)

15.5 AC circuits, LCR circuits

16. Optics

16.1 Laws of reflection and refraction

16.2 Lenses and mirrors

16.3 Optical instruments – telescope and microscope

16.4 Interference – Huygen’s principle, Young’s double slit experiment

16.5 Interference in thin films

16.6 Diffraction due to a single slit

16.7 Electromagnetic waves and their characteristics (only qualitative ideas),

Electromagnetic spectrum

16.8 Polarization – states of polarization, Malus’ law, Brewster’s law

17. Modern Physics

17.1 Dual nature of light and matter – Photoelectric effect, De Broglie wavelength

17.2 Atomic models – Rutherford’s experiment, Bohr’s atomic model

17.3 Hydrogen atom spectrum

17.4 Radioactivity

17.5 Nuclear reactions : Fission and fusion, binding energy

BITSAT 2015 Mathematics Syllabus

July 17, 2014July 17, 2014 by bn Mishra

Mathematics

1. Algebra

1.1 Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations; Fundamental theorem of algebra.

1.2 Theory of Quadratic equations, quadratic equations in real and complex number system and their solutions, relation between roots and coefficients, nature of roots, equations reducible to quadratic equations.

1.3 Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, arithmetico-geometric series, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

1.4 Logarithms and their properties.

1.5 Exponential series.

1.6 Permutations and combinations, Permutations as an arrangement and combination as selection, simple applications.

1.7 Binomial theorem for a positive integral index, properties of binomial coefficients, Pascal’s triangle.

1.8 Matrices and determinants of order two or three, properties and evaluation of determinants, addition and multiplication of matrices, adjoint and inverse of matrices, Solutions of simultaneous linear equations in two or three variables, elementary row and column operations of matrices.

1.9 Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings, binary operation, inverse of function, functions of real variables like polynomial, modulus, signum and greatest integer.

1.10 Mathematical Induction

1.11 Linear Inequalities, solution of linear inequalities in one and two variables.

2. Trigonometry

2.1 Measurement of angles in radians and degrees, positive and negative angles, trigonometric ratios, functions and identities.

2.2 Solution of trigonometric equations.

2.3 Properties of triangles and solutions of triangles

2.4 Inverse trigonometric functions

2.5 Heights and distances

3. Two-dimensional Coordinate Geometry

3.1 Cartesian coordinates, distance between two points, section formulae, shift of origin.

3.2 Straight lines and pair of straight lines: Equation of straight lines 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, concurrent lines.

3.3 Circles and family of circles :Equation of circle in various form, equation of tangent, normal & chords, parametric equations of a circle , intersection of a circle with a straight line or a circle, equation of circle through point of intersection of two circles, conditions for two intersecting circles to be orthogonal.

3.4 Conic sections : parabola, ellipse and hyperbola their eccentricity, directrices & foci, parametric forms, equations of tangent & normal, conditions for y=mx+c to be a tangent and point of tangency.

4. Three dimensional Coordinate Geometry

4.1 Co-ordinate axes and co-ordinate planes, distance between two points, section formula, direction cosines and direction ratios, equation of a straight line in space and skew lines.

4.2 Angle between two lines whose direction ratios are given, shortest distance between two lines.

4.3 Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines, angles between two planes, angle between a line and a plane.

5. Differential calculus

5.1 Domain and range of a real valued function, Limits and Continuity of the sum, difference, product and quotient of two functions, Differentiability.

5.2 Derivative of different types of functions (polynomial, rational, trigonometric, inverse trigonometric, exponential, logarithmic, implicit functions), derivative of the sum, difference, product and quotient of two functions, chain rule.

5.3 Geometric interpretation of derivative, Tangents and Normals.

5.4 Increasing and decreasing functions, Maxima and minima of a function.

5.5 Rolle’s Theorem, Mean Value Theorem and Intermediate Value Theorem.

6. Integral calculus

6.1 Integration as the inverse process of differentiation, indefinite integrals of standard functions.

6.2 Methods of integration: Integration by substitution, Integration by parts, integration by partial fractions, and integration by trigonometric identities.

6.3 Definite integrals and their properties, Fundamental Theorem of Integral Calculus, applications in finding areas under simple curves.

6.4 Application of definite integrals to the determination of areas of regions bounded by simple curves.

7. Ordinary Differential Equations

7.1 Order and degree of a differential equation, formulation of a differential equation whole general solution is given, variables separable method.

7.2 Solution of homogeneous differential equations of first order and first degree

7.3 Linear first order differential equations

8. Probability

8.1 Various terminology in probability, axiomatic and other approaches of probability, addition and multiplication rules of probability.

8.2 Conditional probability, total probability and Baye’s theorem

8.3 Independent events

8.4 Discrete random variables and distributions with mean and variance.

9. Vectors

9.1 Direction ratio/cosines of vectors, addition of vectors, scalar multiplication, position vector of a point dividing a line segment in a given ratio.

9.2 Dot and cross products of two vectors, projection of a vector on a line.

9.3 Scalar triple products and their geometrical interpretations.

10. Statistics

10.1 Measures of dispersion

10.2 Measures of skewness and Central Tendency, Analysis of frequency distributions with equal means but different variances

11.Linear Programming

11.1 Various terminology and formulation of linear Programming

11.2 Solution of linear Programming using graphical method, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (upto three nonitrivial constraints)