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Birla Institute of Technology Syllabus |

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Re: Birla Institute of Technology Syllabus
BITSAT is a computer based online test for admission to all the integrated first degree programmes of Birla Institute of Technology (BITS), Pilani at Pilani Campus, Goa Campus, and Hyderabad Campus BITSAT Entrance Exam PatternPart I Physics 40 Part II Chemistry 40 Part III - (a) English Proficiency 15 (b) Logical Reasoning 10 Part IV Mathematics 45 SyllabusThe examination tests a candidate's ability on basis of NCERT syllabus for class XIth and XIIth. BITSAT 2013 Mathematics Syllabus Algebra 1. Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations. 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. 3. Logarithms and their properties. 4. 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. 5. Exponential series. 6. Permutations and combinations, Permutations as an arrangement and combination as selection, simple applications. 7. Binomial theorem for a positive integral index, properties of binomial coefficients. 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. 9. Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings. 10. Mathematical Induction 11. Linear Inequalities, solution of linear inequalities in one and two variables. Trigonometry 1. Trigonometric ratios, functions and identities. 2. Solution of trigonometric equations. 3. Properties of triangles and solutions of triangles 4. Inverse trigonometric functions 5. Heights and distances Two-dimensional Coordinate Geometry 1. Cartesian coordinates, distance between two points, section formulae, shift of origin. 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. 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. 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. Three dimensional Coordinate Geometry 1. Direction cosines and direction ratios, equation of a straight line in space and skew lines. 2. Angle between two lines whose direction ratios are given 3. Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines. Differential calculus 1. Domain and range of a real valued function, Limits and Continuity of the sum, difference, product and quotient of two functions, Differentiability. 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. 3. Geometric interpretation of derivative, Tangents and Normals. 4. Increasing and decreasing functions, Maxima and minima of a function. 5. Rolle's Theorem, Mean Value Theorem and Intermediate Value Theorem. Integral calculus 1. Integration as the inverse process of differentiation, indefinite integrals of standard functions. 2. Methods of integration: Integration by substitution, Integration by parts, integration by partial fractions, and integration by trigonometric identities. 3. Definite integrals and their properties, Fundamental Theorem of Integral Calculus and its applications. 4. Application of definite integrals to the determination of areas of regions bounded by simple curves. Ordinary Differential Equations 1. Variables separable method. 2. Solution of homogeneous differential equations. 3. Linear first order differential equations Probability 1. Addition and multiplication rules of probability. 2. Conditional probability 3. Independent events 4. Discrete random variables and distributions Vectors 1. Addition of vectors, scalar multiplication. 2. Dot and cross products of two vectors. 3. Scalar triple products and their geometrical interpretations Statistics 1. Measures of dispersion 2. Measures of skewness and Central Tendency Linear Programming 1. Formulation of linear Programming 2. Solution of linear Programming, using graphical method. BITSAT 2013 Physics Syllabus Units & Measurement 1. Units (Different systems of units, SI units, fundamental and derived units) 2. Dimensional Analysis 3. Precision and significant figures 4. Fundamental measurements in Physics (Vernier calipers, screw gauge, Physical balance etc) Kinematics 1. Properties of vectors 2. Position, velocity and acceleration vectors 3. Motion with constant acceleration 4. Projectile motion 5. Uniform circular motion 6. Relative motion Newton's Laws of Motion 1. Newton's laws (free body diagram, resolution of forces) 2. Motion on an inclined plane 3. Motion of blocks with pulley systems 4. Circular motion - centripetal force 5. Inertial and non-inertial frame Impulse and Momentum 1. Definition of impulse and momentum 2. Conservation of momentum 3. Collisions 4. Momentum of a system of particles 5. Center of mass Work and Energy 1. Work done by a force 2. Kinetic energy and work-energy theorem 3. Power 4. Conservative forces and potential energy 5. Conservation of mechanical energy Rotational Motion 1. Description of rotation (angular displacement, angular velocity and angular acceleration) 2. Rotational motion with constant angular acceleration 3. Moment of inertia, Parallel and perpendicular axes theorems, rotational kinetic energy6.4 Torque and angular momentum 4. Conservation of angular momentum Gravitation 1. Newton's law of gravitation 2. Gravitational potential energy, Escape velocity 3. Motion of planets - Kepler's laws, satellite motion Mechanics of Solids and Fluids 1. Elasticity 2. Pressure, density and Archimedes' principle 3. Viscosity and Surface Tension 4. Bernoulli's theorem Oscillations 1. Kinematics of simple harmonic motion 2. Spring mass system, simple and compound pendulum 3. Forced & damped oscillations, resonance Waves 1. Progressive sinusoidal waves 2. Standing waves in strings and pipes 3. Superposition of waves beats Heat and Thermodynamics 1. Kinetic theory of gases 2. Thermal equilibrium and temperature 3. Specific heat 4. Work, heat and first law of thermodynamics Electrostatics 1. Coulomb's law 2. Electric field (discrete and continuous charge distributions) 3. Electrostatic potential and Electrostatic potential energy 4. Gauss' law and its applications 5. Electric dipole 6. Capacitance and dielectrics (parallel plate capacitor, capacitors in series and parallel) Current Electricity 1. Ohm's law, Joule heating 2. D.C circuits - Resistors and cells in series and parallel, Kirchoff's laws, potentiometer and Wheatstone bridge, 3. Electrical Resistance (Resistivity, origin and temperature dependence of resistivity). Magnetic Effect of Current 1. Biot-Savart's law and its applications 2. Ampere's law and its applications 3. Lorentz force, force on current carrying conductors in a magnetic field 4. Magnetic moment of a current loop, torque on a current loop, Galvanometer and its conversion to voltmeter and ammeter Electromagnetic Induction 1. Faraday's law, Lenz's law, eddy currents 2. Self and mutual inductance 3. Transformers and generators 4. Alternating current (peak and rms value) 5. AC circuits, LCR circuits Optics 1. Laws of reflection and refraction 2. Lenses and mirrors 3. Optical instruments - telescope and microscope 4. Interference - Huygen's principle, Young's double slit experiment 5. Interference in thin films 6. Diffraction due to a single slit 7. Electromagnetic waves and their characteristics (only qualitative ideas), Electromagnetic spectrum 8. Polarization - states of polarization, Malus' law, Brewster's law Modern Physics 1. Dual nature of light and matter - Photoelectric effect. De Broglie wavelength 2. Atomic models - Rutherford's experiment, Bohr's atomic model 3. Hydrogen atom spectrum 4. Radioactivity 5. Nuclear reactions: Fission and fusion, binding energy BITSAT 2013 Chemistry Syllabus States of Matter 1. Measurement: Physical quantities and SI units, Dimensional analysis, Precision, Significant figures. 2. Chemical reactions: Laws of chemical combination, Dalton's atomic theory; Mole concept; Atomic, molecular and molar masses; Percentage composition & molecular formula; Balanced chemical equations & stoichiometry 3. Gaseous state: 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, van der Waals equation. 4. Liquid state: Vapour pressure, surface tension, viscosity. 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. Atomic Structure Introduction: Subatomic particles; Rutherford's picture of atom; Hydrogen atom spectrum and Bohr model. 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. 3. Many electron atoms: Pauli exclusion principle; Aufbau principle and the electronic configuration of atoms, Hund's rule. 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, and valency. 5. Nucleus: Natural and artificial radioactivity; Nuclear reactions, Artificial transmutation ofelements. Chemical Bonding & Molecular Structure 1.Ionic Bond: Lattice Energy and Born-Haber cycle 2. Molecular Structure: Lewis picture & resonance structures, VSEPR model & molecular shapes 3. Covalent Bond: Valence Bond Theory- Orbital overlap, Directionality of bonds & hybridistaion (s & p orbitals only), Resonance; Molecular orbital theory- Methodology, Orbital energy level diagram, Bond order, Magnetic properties for homonuclear diatomic species. 4. Metallic Bond: Qualitative description. 5. Intermolecular Forces: Polarity; Dipole moments; Hydrogen Bond. Thermodynamics 1. Basic Concepts: Systems and surroundings; State functions; Intensive & Extensive Properties; Zeroth Law and Temperature 2. First Law of Thermodynamics: Work, internal energy, heat, enthalpy, heat capacities; Enthalpies of formation, phase transformation, ionization, electron gain; Thermochemistry; Hess's Law. 3. Second and Third Laws: 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; Third Law and Absolute Entropies. Physical and Chemical Equilibria 1. Concentration Units: Mole Fraction, Molarity, and Molality 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. 3. Physical Equilibrium: Equilibria involving physical changes (solid-liquid, liquid-gas, solid-gas), Adsorption, Physical and Chemical adsorption, Langmuir Isotherm. 4. Chemical Equilibria: Equilibrium constants (KP, KC), Le-Chatelier's principle. 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. 6. Factors Affecting Equilibria: Concentration, Temperature, Pressure, Catalysts, Significance of DG and DG0 in Chemical Equilibria. Electrochemistry 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; Gibbs energy change and cell potential; Concentration cells; Secondary cells; Fuel cells; Corrosion and its prevention. 2. Electrolytic Conduction: Electrolytic Conductance; Specific, equivalent and molar conductivities; Kolhrausch's Law and its application, Faraday's laws of electrolysis; Electrode potential and electrolysis, Commercial production of the chemicals, NaOH, Na, Al, C12, & F2 Chemical Kinetics 1. Aspects of Kinetics: Rate and Rate expression of a reaction; Rate constant; Order of reaction; Integrated rate expressions for zero and first order reactions; Half-life; Determination of rate constant and order of reaction 2. Factor Affecting the Rate of the Reactions: Temperature dependence of rate constant; Activation energy; Catalysis, Surface catalysis, enzymes, zeolites; Factors affecting rate of collisions between molecules; Effect of light. 3. Mechanism of Reaction: Elementary reactions; Complex reactions; Reactions involving two/three steps only; Photochemical reactions; Concept of fast reactions. 4. Radioactive isotopes: Half-life period; Radiochemical dating. Hydrogen and s-block elements 1. Hydrogen: Element: unique position in periodic table, occurrence, isotopes; Dihydrogen: preparation, properties, reactions, and uses; Molecular, saline, interstitial hydrides; Water: Properties; Structure and aggregation of water molecules; Hard and soft water; Heavy water; Hydrogen peroxide. 2. s-block elements: Abundance and occurrence; Anomalous properties of the first elements in each group; diagonal relationships. 3. Alkali metals: Lithium, sodium and potassium: occurrence, extraction, reactivity, and electrode potentials; Reactions with oxygen, hydrogen, halogens and liquid ammonia; Basic nature of oxides and hydroxides; Halides; Properties and uses of compounds such as NaCl, Na2CO3, NaHCO3, NaOH, KCl, and KOH. 4. Alkaline earth metals: Magnesium and calcium: Occurrence, extraction, reactivity and electrode potentials; Reactions with non-metals; Solubility and thermal stability of oxo salts; Properties and uses of important compounds such as CaO, Ca(OH)2, plaster of Paris, MgSO4, MgCl2, CaCO3, and CaSO4; Lime and limestone, cement. *p- d- and f-block elements 1. General: Abundance, distribution, physical and chemical properties, isolation and uses of elements; Trends in chemical reactivity of elements of a group; Extraction and refining of metals. 2. Group 13 elements: Boron; Properties and uses of borax, boric acid, boron hydrides & halides. Reaction of aluminum with acids and alkalis; 3. Group 14 elements: Carbon: Uses, Allotropes (graphite, diamond, fullerenes), oxides, halides and sulphides, carbides; Silicon: Silica, silicates, silicones; Tin and lead: Extraction, halides and oxides. 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 and halides of phosphorus. 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, hydrides and halides of sulphur. 6. Group 17 and group 18 elements: Structure and properties of hydrides, oxides, oxoacids of chlorine; Inter halogen compounds; Bleaching Powder; Preparation, structure and reactions of xenon fluorides, oxides, and oxoacids. 7. d-block elements: General trends in the chemistry of first row transition elements; Metallic character; Oxidation state; 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. 8. f-block elements: Lanthanides and actinides; Oxidation states and chemical reactivity of lanthanide compounds; Lanthanide contraction; Comparison of actinides and lanthanides. 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. Principles of Organic Chemistry and Hydrocarbons 1. Classification: Based on functional groups, trivial and IUPAC nomenclature. 2 Electronic displacement in a covalent bond: Inductive, resonance effects, and hyperconjugation; free radicals; carbocations, carbanion, nucleophile and electrophile; types of reactions. 3. Alkanes and cycloalkanes: Structural isomerism and general properties. 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. 5. Aromatic hydrocarbons: Sources; Properties; Isomerism; Resonance delocalization; polynuclear hydrocarbons; mechanism of electrophilic substitution reaction, directive influence and effect of substituents on reactivity. 6. Haloalkanes and haloarenes: Physical properties, chemical reactions. 7. Petroleum: Composition and refining, uses of petrochemicals. Stereochemistry 1. Introduction: Chiral molecules; Optical activity; Polarimetry; R,S and D,L configurations; Fischer projections; Enantiomerism; Racemates; Diastereomerism and meso structures. 2. Conformations: Ethane, propane, n-butane and cyclohexane conformations; Newman and sawhorse projections. 3. Geometrical isomerism in alkenes Organic Compounds with Functional Groups Containing Oxygen and Nitrogen Address:Birla Institute of Technology and Science Vidya Vihar,Pilani,Rajasthan,333031, BITS, Pilani, Rajasthan 333031 01596 242 192 Map:
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