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BITSAT Mathematics Syllabus

Algebra

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

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.    

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.

Logarithms and their properties.

Exponential series.

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

Binomial theorem for a positive integral index, properties of binomial coefficients.

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.

Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings.

Mathematical Induction.

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

Trigonometry

Trigonometric ratios, functions and identities. Solution of trigonometric equations.Properties of triangles and solutions of triangles. Inverse trigonometric functions. Heights and distances

Two-dimensional Coordinate Geometry

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

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.

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.

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

Direction cosines and direction ratios, equation of a straight line in space and skew lines.
Angle between two lines whose direction ratios are given. Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines.

Differential Calculus

Domain 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), derivative of 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.

Integral Calculus

Integration as the inverse process of differentiation, indefinite integrals of standard 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 Integral Calculus and its applications. Application of definite integrals to the determination of areas of regions bounded by simple curves.

Ordinary Differential Equations

        Variables separable method.
        Solution of homogeneous differential equations.
        Linear first order differential equations

Probability

Addition and multiplication rules of probability. Conditional probability. Independent events        Discrete random variables and distributions

Vectors

Addition of vectors, scalar multiplication. Dot and cross products of two vectors. Scalar triple products and their geometrical interpretations.

BITSAT 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

1. 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, Cl2, & 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, physical properties, electrophilic and free radical additions, acidic character of alkynes and (1,2 and 1,4) addition to dienes.
5. Aromatic hydrocarbons: Sources; 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

1. General: Electronic structure, important methods of preparation, important reactions and physical properties of alcohols, phenols, ethers, aldehydes, ketones, carboxylic acids, nitro compounds, amines, diazonium salts, cyanides and isocyanides.
2. Specific: Effect of substituents on alpha-carbon on acid strength, comparative reactivity of acid derivatives, basic character of amines and their separation, importance of diazonium salts in synthetic organic chemistry

Biological and Industrial chemistry

1. The Cell: Concept of cell and energy cycle.
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 and cellulose.
3. Proteins: Amino acids; Peptide bond; Polypeptides; Primary structure of proteins; Simple idea of secondary and tertiary structures of proteins; Denaturation of proteins and enzymes.
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.
5. Lipids, Hormones, Vitamins: Classification, structure, functions in biosystems.
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.
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.
8. Chemicals in medicine, health-care and food: Analgesics, Tranquilizers, antiseptics, disinfectants, anti-microbials, anti-fertility drugs, antihistamines, antibiotics, antacids; Cosmetics: Creams, perfumes, talcum powder, deodorants; Preservatives, artificial sweetening agents, antioxidants, and edible colours.
9. Other Industrial Chemicals: Dyes: Classification with examples – Indigo, methyl orange, aniline yellow, alizarin, malachite green; Advanced materials: Carbon fibers, ceramics, micro alloys; Detergents; Insect repellents, pheromones, sex attractants; Rocket Propellants.

Theoretical Principles of Experimental Chemistry

1. Volumetric Analysis: Principles; Standard solutions of sodium carbonate and oxalic acid; Acidbase titrations; Redox reactions involving KI, H2SO4, Na2SO3 and H2S; Potassium permanganate in acidic, basic and neutral media; Titrations of oxalic acid, ferrous ammonium sulphate with KMnO4; Estimation of calcium and magnesium by EDTA titrations.
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-, S2-, SO42-, SO32-, NO2-, NO3-, Cl-, Br-, I-, PO43-, CH3COO-, C2O42-.
3. Physical Chemistry Experiments: 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;
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.
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.
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; Elementary idea of mass spectrometer for accurate molecular mass determination; Calculations of empirical and molecular formulae.
7. Principles of Organic Chemistry Experiments: Preparation of iodoform, acetanilide, p-nitro acetanilide, di-benzyl acetone, aniline yellow, beta-naphthol; Preparation of acetylene and study of its acidic character.

BITSAT Physics Syllabus

Units & Measurement

Units (Different systems of units, SI units, fundamental and derived units)
Dimensional Analysis
Precision and significant figures
Fundamental measurements in Physics (Vernier calipers, screw gauge, Physical balance etc)

Kinematics

Properties of vectors
Position, velocity and acceleration vectors
Motion with constant acceleration
Projectile motion
Uniform circular motion
Relative motion

Newton’s Laws of Motion

Newton’s laws (free body diagram, resolution of forces)
Motion on an inclined plane
Motion of blocks with pulley systems
Circular motion – centripetal force
Inertial and non-inertial frames

Impulse and Momentum

Definition of impulse and momentum
Conservation of momentum
Collisions
Momentum of a system of particles
Center of mass

Work and Energy

Work done by a force
Kinetic energy and work-energy theorem
Power
Conservative forces and potential energy
Conservation of mechanical energy

Rotational Motion

Description of rotation (angular displacement, angular velocity and angular acceleration)
Rotational motion with constant angular acceleration
Moment of inertia, Parallel and perpendicular axes theorems, rotational kinetic energy6.4 Torque and angular momentum
Conservation of angular momentum
Rolling motion

Gravitation

Newton’s law of gravitation
Gravitational potential energy, Escape velocity
Motion of planets – Kepler’s laws, satellite motion

Mechanics of Solids  and Fluids

Elasticity
Pressure, density and Archimedes’ principle
Viscosity and Surface Tension
Bernoulli’s theorem

Oscillations

Kinematics of simple harmonic motion
Spring mass system, simple and compound pendulum
Forced & damped oscillations, resonance

Waves

Progressive sinusoidal waves
Standing waves in strings and pipes
Superposition of waves, beats

Heat and Thermodynamics

Kinetic theory of gases
Thermal equilibrium and temperature
Specific heat
Work, heat and first law of thermodynamics
2nd law of thermodynamics, Carnot engine – Efficiency and Coefficient of performance

Electrostatics

Coulomb’s law
Electric field (discrete and continuous charge distributions)
Electrostatic potential and Electrostatic potential energy
Gauss’ law and its applications
Electric dipole
Capacitance and dielectrics (parallel plate capacitor, capacitors in series and parallel)

Current Electricity

Ohm’s law, Joule heating
D.C circuits – Resistors and cells in series and parallel, Kirchoff’s laws, potentiometer and Wheatstone bridge,
Electrical Resistance (Resistivity, origin and temperature dependence of resistivity).

Magnetic Effect of Current

Biot-Savart’s law and its applications
Ampere’s law and its applications
Lorentz force, force on current carrying conductors in a magnetic field
Magnetic moment of a current loop, torque on a current loop, Galvanometer and its conversion to voltmeter and ammeter

Electromagnetic Induction

Faraday’s law, Lenz’s law, eddy currents
Self and mutual inductance
Transformers and generators
Alternating current (peak and rms value)
AC circuits, LCR circuits

Optics

Laws of reflection and refraction
Lenses and mirrors
Optical instruments – telescope and microscope
Interference – Huygen’s principle, Young’s double slit experiment
Interference in thin films
Diffraction due to a single slit
Electromagnetic waves and their characteristics (only qualitative ideas), Electromagnetic spectrum
Polarization – states of polarization, Malus’ law, Brewster’s law

Modern Physics

Dual nature of light and matter – Photoelectric effect. De Broglie wavelength
Atomic models – Rutherford’s experiment, Bohr’s atomic model
Hydrogen atom spectrum
Radioactivity
Nuclear reactions : Fission and fusion, binding energy

BITSAT English and Logical Reasoning Syllabus

English Proficiency test is designed to assess the test takers’ general proficiency in the use of English language as a means of self-expression in real life situations and specifically to test the test takers’ knowledge of basic grammar, their vocabulary, their ability to read fast and comprehend, and also their ability to apply the elements of effective writing.

Grammar

Agreement, Time and Tense, Parallel construction, Relative pronouns
Determiners, Prepositions, Modals, Adjectives
Voice, Transformation
Question tags, Phrasal verbs

Vocabulary

Synonyms, Antonyms, Odd Word, One Word, Jumbled letters, Homophones, Spelling, Contextual meaning, Analog

Reading Comprehension

Content/ideas
Vocabulary
Referents
Idioms/Phrases
Reconstruction (rewording)

Composition

Rearrangement
Paragraph Unity
Linkers/Connectives

Logical Reasoning test is given to the candidates to judge their power of reasoning in verbal and nonverbal areas. The candidates should be able to think logically so that they perceive the data accurately, understand the relationships correctly, figure out the missing numbers or words, and to apply rules to new and different contexts. These indicators are measured through performance on such tasks as detecting missing links, following directions, classifying words, establishing sequences, and completing analogies.

Verbal Reasoning

1. Analogy

Analogy means correspondence. In the questions based on analogy, a particular relationship is given and another similar relationship has to be identified from the alternatives provided.

2. Classification

Classification means to assort the items of a given group on the basis of certain common quality they possess, and then spot the odd option out.

3. Series Completion

Here series of numbers or letters are given and one is asked to either complete the series, or find out the wrong part in the series.

4. Logical Deduction – Reading Passage

Here a brief passage is given and based on the passage, the candidate is required to identify the correct or incorrect logical conclusions.

5. Chart Logic

Here a chart or a table is given that is partially filled in, and asks to complete it in accordance with the information given either in the chart / table or in the question.

Nonverbal Reasoning

1. Pattern Perception

Here a certain pattern is given and generally a quarter is left blank. The candidate is required to identify the correct quarter from the given four alternatives.

2. Figure Formation and Analysis

The candidate is required to analyze and form a figure from various given parts.

3. Paper Cutting

It involves the analysis of a pattern that is formed when a folded piece of paper is cut into a definite design.

4. Figure Matrix

In this, more than one set of figures is given in the form of a matrix, all of them following the same rule. The candidate is required to follow the rule and identify the missing figure.

5. Rule Detection

Here a particular rule is given and it is required to select from the given sets of figures, a set of figures, which obeys the rule and forms the correct series.