Part I: 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 2nd 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
Part II: 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, 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.
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.
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
3.2 Molecular Structure: Lewis picture & resonance structures, VSEPR model & molecular shapes
3.3 Covalent Bond: Valence Bond Theory- Orbital overlap, Directionality of bonds & hybridistaion (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.
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 ÄG and ÄG0 in 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, interstitial hydrides; Water: Properties; Structure
and aggregation of water molecules; Heavy water; Hydrogen peroxide;
Hydrogen as a fuel.
8.2 s-block elements: Abundance and
occurrence; Anomalous properties of the first elements in each group;
diagonal relationships.
8.3 Alkali metals: Lithium, sodium and
potassium: occurrence, extraction, reactivity, and electrode potentials;
Biological importance; 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.
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;.
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:
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 and halides of phosphorus.
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, hydrides
and halides of sulphur.
9.6 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.
9.7 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.
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.
10.2
Electronic displacement in a covalent bond: Inductive, resonance
effects, and hyperconjugation; free radicals; carbocations, carbanion,
nucleophile and electrophile; types of reactions.
10.3 Alkanes and cycloalkanes: Structural isomerism and general properties.
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; polynuclear hydrocarbons; mechanism of electrophilic
substitution reaction, directive influence and effect of substituents on
reactivity.
10.6 Haloalkanes and haloarenes: Physical properties,
chemical reactions. 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,
important reactions and physical properties 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, 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 structures 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.
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-, S2-, 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-benzyl
acetone, aniline yellow, beta-naphthol; Preparation of acetylene and
study of its acidic character.
Part III: (a) English Proficiency and (b) Logical Reasoning
(a) English Proficiency
This
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.
1. Grammar
1.1 Agreement, Time and Tense, Parallel construction, Relative pronouns
1.2 Determiners, Prepositions, Modals, Adjectives
1.3 Voice, Transformation
1.4 Question tags, Phrasal verbs
2. Vocabulary
2.1 Synonyms, Antonyms, Odd Word, One Word, Jumbled letters, Homophones, Spelling
2.2 Contextual meaning.
2.3 Analogy
3. Reading Comprehension
3.1 Content/ideas
3.2 Vocabulary
3.3 Referents
3.4 Idioms/Phrases
3.5 Reconstruction (rewording)
4. Composition
4.1 Rearrangement
4.2 Paragraph Unity
4.3 Linkers/Connectives
(b) Logical Reasoning
The
test is given to the candidates to judge their power of reasoning
spread 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.
5. Verbal Reasoning
5.1 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.
5.2 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.
5.3 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.
5.4 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.
5.5 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.
6. Nonverbal Reasoning
6.1 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.
6.2 Figure Formation and Analysis
The candidate is required to analyze and form a figure from various given parts.
6.3 Paper Cutting
It involves the analysis of a pattern that is formed when a folded piece of paper is cut into a definite design.
6.4 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.
6.5 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.
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, 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.
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, 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
11.Linear Programming
11.1 Various terminology and formulation of linear Programming
11.2 Solution of linear Programming using graphical method.
