Your SlideShare is downloading. ×
Vishu
Vishu
Vishu
Vishu
Vishu
Vishu
Vishu
Vishu
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Vishu

124

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
124
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
1
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. BITSAT 2013 Mathematics Syllabus1. AlgebraComplex numbers, addition, multiplication, conjugation, polar representation,properties of modulus and principal argument, triangle inequality, roots ofcomplex numbers, geometric interpretations; Fundamental theorem of algebra.Theory of Quadratic equations, quadratic equations in real and complex numbersystem and their solutions, relation between roots and coefficients, nature ofroots, equations reducible to quadratic equations.Logarithms and their properties.Arithmetic, geometric and harmonic progressions, arithmetic, geometric andharmonic means, arithmetic-geometric series, sums of finite arithmetic andgeometric progressions, infinite geometric series, sums of squares and cubes ofthe first n natural numbers.Exponential series.Permutations and combinations, Permutations as an arrangement and combination asselection, simple applications.Binomial theorem for a positive integral index, properties of binomialcoefficients, Pascal’s triangle.Matrices and determinants of order two or three, properties and evaluation ofdeterminants, addition and multiplication of matrices, adjoint and inverse ofmatrices, Solutions of simultaneous linear equations in two or three variables,elementary row and column operations of matricesSets, Relations and Functions, algebra of sets applications, equivalencerelations, mappings, one-one, into and onto mappings, composition of mappings,binary operation, inverse of function, functions of real variables likepolynomial, modulus, signum and greatest integer.Mathematical InductionLinear Inequalities, solution of linear inequalities in one and two variables.2. TrigonometryMeasurement of angles in radians and degrees, positive and negative angles,trigonometric ratios, functions and identities.Solution of trigonometric equations.Properties of triangles and solutions of trianglesInverse trigonometric functionsHeights and distances3. Two-dimensional Coordinate GeometryCartesian coordinates, distance between two points, section formulae, shift oforigin.Straight lines and pair of straight lines: Equation of straight lines in variousforms, angle between two lines, distance of a point from a line, lines throughthe point of intersection of two given lines, equation of the bisector of theangle between two lines, concurrent lines.Circles and family of circles : Equation of circle in various form, equation oftangent, normal & chords, parametric equations of a circle , intersection of acircle with a straight line or a circle, equation of circle through point ofintersection of two circles, conditions for two intersecting circles to beorthogonal.Conic sections : parabola, ellipse and hyperbola their eccentricity, directrices& foci, parametric forms, equations of tangent & normal, conditions for y=mx+cto be a tangent and point of tangency.4. Three dimensional Coordinate GeometryCo-ordinate axes and co-ordinate planes, distance between two points, sectionformula, direction cosines and direction ratios, equation of a straight line inspace and skew lines.
  • 2. Angle between two lines whose direction ratios are given, shortest distancebetween two lines.Equation of a plane, distance of a point from a plane, condition for coplanarityof three lines, angles between two planes, angle between a line and a plane.5. Differential calculusDomain and range of a real valued function, Limits and Continuity of the sum,difference, product and quotient of two functions, Differentiability.Derivative of different types of functions (polynomial, rational, trigonometric,inverse trigonometric, exponential, logarithmic, implicit functions), derivativeof the sum, difference, product and quotient of two functions, chain rule.Geometric interpretation of derivative, Tangents and Normals.Increasing and decreasing functions, Maxima and minima of a function.Rolle’s Theorem, Mean Value Theorem and Intermediate Value Theorem.6. Integral calculusIntegration as the inverse process of differentiation, indefinite integrals ofstandard functions.Methods of integration: Integration by substitution, Integration by parts,integration by partial fractions, and integration by trigonometric identities.Definite integrals and their properties, Fundamental Theorem of IntegralCalculus, applications in finding areas under simple curves.Application of definite integrals to the determination of areas of regionsbounded by simple curves.7. Ordinary Differential EquationsOrder and degree of a differential equation, formulation of a differentialequation whole general solution is given, variables separable method.Solution of homogeneous differential equations of first order and first degreeLinear first order differential equations8. ProbabilityVarious terminology in probability, axiomatic and other approaches ofprobability, addition and multiplication rules of probability.Conditional probability, total probability and Baye’s theoremIndependent eventsDiscrete random variables and distributions with mean and variance.9. VectorsDirection ratio / cosines of vectors, addition of vectors, scalarmultiplication, position vector of a point dividing a line segment in a givenratio.Dot and cross products of two vectors, projection of a vector on a line.Scalar triple products and their geometrical interpretations.10. StatisticsMeasures of dispersionMeasures of skewness and Central Tendency, Analysis of frequency distributionswith equal means but different variances.11.Linear ProgrammingVarious terminology and formulation of linear ProgrammingSolution of linear Programming using graphical method, feasible and infeasibleregions, feasible and infeasible solutions, optimal feasible solutions ( uptothree nonitrivial constraints ).
  • 3. BITSAT 2013 Chemistry Syllabus ’ Page 21. States of MatterMeasurement : Physical quantities and SI units, Dimensional analysis, Precision,Significant figures.Chemical reactions: Laws of chemical combination, Dalton’s atomic theory; Moleconcept; Atomic, molecular and molar masses; Percentage composition empirical &molecular formula; Balanced chemical equations & stoichiometryGaseous state : Gas Laws, Kinetic theory ’ Maxwell distribution of velocities,Average, root mean square and most probable velocities and relation totemperature, Diffusion; Deviation from ideal behaviour ’ Critical temperature,Liquefaction of gases, van der Waals equation.Liquid state : Vapour pressure, surface tension, viscosity.Solid state : Classification; Space lattices & crystal systems; Unit cell ’Cubic & hexagonal systems; Close packing; Crystal structures: Simple AB and AB2type ionic crystals, covalent crystals ’ diamond & graphite, metals.Imperfections- Point defects, non-stoichiometric crystals; Electrical, magneticand dielectric properties; Amorphous solids ’ qualitative description.2. Atomic StructureIntroduction : Radioactivity, Subatomic particles; Atomic number, isotopes andisobars, Rutherford’s picture of atom; Hydrogen atom spectrum and Bohr model.Quantum mechanics : Wave-particle duality ’ de Broglie relation, Uncertaintyprinciple; Hydrogen atom: Quantum numbers and wavefunctions, atomic orbitals andtheir shapes (s, p, and d), Spin quantum number.Many electron atoms : Pauli exclusion principle; Aufbau principle and theelectronic configuration of atoms, Hund’s rule.Periodic law and the modern periodic table; Types of elements: s, p, d, and fblocks; Periodic trends: ionization energy, atomic and ionic radii, electronaffinity, electro negativity and valency.3. Chemical Bonding & Molecular StructureIonic Bond: Lattice Energy and Born-Haber cycle, Covalent character of ionicbonds and polar character of covalent bond.Molecular Structure: Lewis picture & resonance structures, VSEPR model &molecular shapesCovalent 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 forhomonuclear diatomic species.Metallic Bond: Qualitative description.Intermolecular Forces: Polarity; Dipole moments; Hydrogen Bond.4. ThermodynamicsBasic Concepts : Systems and surroundings; State functions; Intensive &Extensive Properties; Zeroth Law and TemperatureFirst Law of Thermodynamics : Work, internal energy, heat, enthalpy, heatcapacities; Enthalpies of formation, phase transformation, ionization, electron
  • 4. gain; Thermochemistry; Hess’s Law.Bond dissociation, combustion, atomization,sublimation, dilutionSecond Law : Spontaneous and reversible processes; entropy; Gibbs free energyrelated to spontaneity and non-mechanical work; Standard free energies offormation, free energy change and chemical equilibrium.Third Law: Introduction5. Physical and Chemical EquilibriaConcentration Units : Mole Fraction, Molarity, and MolalitySolutions : Solubility of solids and gases in liquids, Vapour Pressure, Raoult’slaw, Relative lowering of vapour pressure, depression in freezing point;elevation in boiling point; osmotic pressure, determination of molecular masssolid solutions.Equilibria involving physical changes ( solid-liquid, liquid ’ gas, solid ’gas ), Surface chemistry, Adsorption, Physical and Chemical adsorption, LangmuirIsotherm, Colloids and emulsion, classification, preparation, uses.Chemical Equilibria : Equilibrium constants ( KP, KC ), Le ’ Chatelier’sprinciple.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 ofSparingly Soluble Salts; Common Ion Effect.Factors Affecting Equilibria : Concentration, Temperature, Pressure, Catalysts,Significance of ?G and ?G° in Chemical Equilibria.6. ElectrochemistryRedox Reactions : Oxidation-reduction reactions (electron transfer concept);Oxidation number; Balancing of redox reactions; Electrochemical cells and cellreactions; Electrode potentials; EMF of Galvanic cells; Nernst equation; Factorsaffecting the electrode potential; Gibbs energy change and cell potential;Secondary cells; Fuel cells; Corrosion and its prevention.Electrolytic Conduction: Electrolytic Conductance; Specific and molarconductivities; Kolhrausch’s Law and its application, Faraday’s laws ofelectrolysis; Coulometer; Electrode potential and electrolysis, Commercialproduction of the chemicals, NaOH, Na, Al, Cl2 & F2.7. Chemical KineticsAspects of Kinetics: Rate and Rate expression of a reaction; Rate constant;Order and molecularity of the reaction; Integrated rate expressions and halflife for zero and first order reactions.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 ofcollisions between molecules.Mechanism of Reaction : Elementary reactions; Complex reactions; Reactionsinvolving two/three steps only;8. Hydrogen and s-block elementsHydrogen: Element: unique position in periodic table, occurrence, isotopes;Dihydrogen: preparation, properties, reactions, and uses; Molecular, saline,interstitial hydrides; Water: Properties; Structure and aggregation of watermolecules; Heavy water; Hydrogen peroxide; Hydrogen as a fuel.s-block elements : Abundance and occurrence; Anomalous properties of the firstelements in each group; diagonal relationships.Alkali metals : Lithium, sodium and potassium: occurrence, extraction,reactivity, and electrode potentials; Biological importance; Reactions withoxygen, hydrogen, halogens and liquid ammonia; Basic nature of oxides andhydroxides; Halides; Properties and uses of compounds such as NaCl, Na2CO3,NaHCO3, NaOH, KCl, and KOH.Alkaline earth metals: Magnesium and calcium: Occurrence, extraction, reactivityand electrode potentials; Reactions with non-metals; Solubility and thermalstability of oxo salts; Biological importance; Properties and uses of important
  • 5. compounds such as CaO, Ca(OH)2, plaster of Paris, MgSO4, MgCl2, CaCO3, andCaSO4; Lime and limestone, cement.9. p- d- and f-block elementsGeneral: Abundance, distribution, physical and chemical properties, isolationand uses of elements; Trends in chemical reactivity of elements of a group.Group 13 elements: Boron; Properties and uses of borax, boric acid, boronhydrides & halides. Reaction of aluminum with acids and alkalis;Group 14 elements: Carbon: Uses, Allotropes (graphite, diamond, fullerenes),oxides, halides and sulphides, carbides; Silicon: Silica, silicates, silicone,silicon tetrachloride, Zeolites.Group 15 elements: Dinitrogen; Reactivity and uses of nitrogen and itscompounds; Industrial and biological nitrogen fixation; Ammonia: Haber’sprocess, properties and reactions; Oxides of nitrogen and their structures;Ostwald’s process of nitric acid production; Fertilizers ’ NPK type; Productionof phosphorus; Allotropes of phosphorus; Preparation, structure and propertiesof hydrides, oxides, oxoacids and halides of phosphorus.Group 16 elements: Isolation and chemical reactivity of dioxygen; Acidic, basicand amphoteric oxides; Preparation, structure and properties of ozone;Allotropes of sulphur; Production of sulphur and sulphuric acid; Structure andproperties of oxides, oxoacids, hydrides and halides of sulphur.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.d-block elements: General trends in the chemistry of first row transitionelements; Metallic character; Oxidation state; Ionic radii; Catalyticproperties; Magnetic properties; Interstitial compounds; Occurrence andextraction of iron, copper, silver, zinc, and mercury; Alloy formation; Steeland some important alloys; preparation and properties of CuSO4, K2Cr2O7, KMnO4,Mercury halides; Silver nitrate and silver halides; Photography.f-block elements: Lanthanides and actinides; Oxidation states and chemicalreactivity of lanthanide compounds; Lanthanide contraction; Comparison ofactinides and lanthanides.Coordination Compounds: Coordination number; Ligands; Werner’s coordinationtheory; 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 andmagnetic properties; Isomerism including stereoisomerisms; Organometalliccompounds
  • 6. BITSAT 2013 Physics Syllabus1. Units & MeasurementUnits (Different systems of units, SI units, fundamental and derived units)Dimensional AnalysisPrecision and significant figuresFundamental measurements in Physics (Vernier calipers, screw gauge, Physicalbalance etc)2. KinematicsProperties of vectorsPosition, velocity and acceleration vectorsMotion with constant accelerationProjectile motionUniform circular motionRelative motion3. Newton’s Laws of MotionNewton’s laws ( free body diagram, resolution of forces )Motion on an inclined planeMotion of blocks with pulley systemsCircular motion ’ centripetal forceInertial and non-inertial frames4. Impulse and MomentumDefinition of impulse and momentumConservation of momentumCollisionsMomentum of a system of particlesCenter of mass5. Work and EnergyWork done by a forceKinetic energy and work-energy theoremPowerConservative forces and potential energyConservation of mechanical energy6. Rotational MotionDescription of rotation (angular displacement, angular velocity and angularacceleration)Rotational motion with constant angular accelerationMoment of inertia, Parallel and perpendicular axes theorems, rotational kineticenergyTorque and angular momentumConservation of angular momentumRolling motion7. GravitationNewton’s law of gravitationGravitational potential energy, Escape velocity
  • 7. Motion of planets ’ Kepler’s laws, satellite motion8. Mechanics of Solids and FluidsElasticityPressure, density and Archimedes’ principleViscosity and Surface TensionBernoulli’s theorem9. OscillationsKinematics of simple harmonic motionSpring mass system, simple and compound pendulumForced & damped oscillations, resonance10. WavesProgressive sinusoidal wavesStanding waves in strings and pipesSuperposition of waves, beatsDoppler Effect11. Heat and ThermodynamicsKinetic theory of gasesThermal equilibrium and temperatureSpecific heat, Heat Transfer ’ Conduction, convection and radiation, thermalconductivity, Newton’s law of coolingWork, heat and first law of thermodynamics2nd law of thermodynamics, Carnot engine ’ Efficiency and Coefficient ofperformance12. ElectrostaticsCoulomb’s lawElectric field (discrete and continuous charge distributions)Electrostatic potential and Electrostatic potential energyGauss’ law and its applicationsElectric dipoleCapacitance and dielectrics (parallel plate capacitor, capacitors in series andparallel)13. Current ElectricityOhm’s law, Joule heatingD.C circuits ’ Resistors and cells in series and parallel, Kirchoff’s laws,potentiometer and Wheatstone bridge,Electrical Resistance (Resistivity, origin and temperature dependence ofresistivity).14. Magnetic Effect of CurrentBiot-Savart’s law and its applicationsAmpere’s law and its applicationsLorentz force, force on current carrying conductors in a magnetic fieldMagnetic moment of a current loop, torque on a current loop, Galvanometer andits conversion to voltmeter and ammeter15. Electromagnetic InductionFaraday’s law, Lenz’s law, eddy currentsSelf and mutual inductanceTransformers and generatorsAlternating current ( peak and rms value )AC circuits, LCR circuits16. OpticsLaws of reflection and refractionLenses and mirrorsOptical instruments ’ telescope and microscope
  • 8. Interference ’ Huygen’s principle, Young’s double slit experimentInterference in thin filmsDiffraction due to a single slitElectromagnetic waves and their characteristics (only qualitative ideas),Electromagnetic spectrumPolarization ’ states of polarization, Malus’ law, Brewster’s law17. Modern PhysicsDual nature of light and matter ’ Photoelectric effect. De Broglie wavelengthAtomic models ’ Rutherford’s experiment, Bohr’s atomic modelHydrogen atom spectrumRadioactivityNuclear reactions : Fission and fusion, binding energy

×