Part I: Physics
Part II: Chemistry
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)
2.1 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
4.4 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
5.4 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
6.2 Rotational motion with constant angular acceleration
6.3 Moment of inertia, Parallel and perpendicular axes theorems, rotational
6.4 Torque and angular momentum
6.5 Conservation of angular momentum
6.6 Rolling motion
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
8.2 Pressure, density and Archimedes’ principle
8.3 Viscosity and Surface Tension
8.4 Bernoulli’s theorem
9.1 Kinematics of simple harmonic motion
9.2 Spring mass system, simple and compound pendulum
9.3 Forced & damped oscillations, resonance
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
11.4 Work, heat and first law of thermodynamics
11.5 2nd law of thermodynamics, Carnot engine – Efficiency and Coefficient of
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
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
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
16.1 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),
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
17.2 Atomic models – Rutherford’s experiment, Bohr’s atomic model
17.3 Hydrogen atom spectrum
17.5 Nuclear reactions : Fission and fusion, binding energy
1. States of Matter
Part III: (a) English Proficiency and (b) Logical Reasoning
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 & 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: Subatomic particles; 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
2.3 Many electron atoms: Pauli exclusion principle; Aufbau principle and the
electronic configuration of atoms,
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.
2.5 Nucleus: Natural and artificial radioactivity; Nuclear reactions.
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 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.
4.1 Basic Concepts: Systems and surroundings; State functions; Intensive &
Extensive Properties; Zeroth Law and
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 nonmechanical
work; Standard free energies of formation, free energy change and chemical
equilibrium; Third Law
and Absolute Entropies.
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
5.3 Physical Equilibrium: Equilibria involving physical changes (solid-liquid,
liquid-gas, solid-gas), Adsorption,
Physical and Chemical adsorption, Langmuir Isotherm.
5.4 Chemical Equilibria: Equilibrium constants (KP, KC), Le-Chatelier’s
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
6.1 Redox Reactions: Oxidation-reduction reactions (electron transfer concept);
Oxidation number; Balancing of redox
reactions; Electrochemical cells and cell reactions; Electrode potentials; Idea
of heterogeneous equilibria on the
surface of the electrode; EMF of Galvanic cells; Nernst equation; Factors
affecting the electrode potential; Gibbs
energy change and cell potential; Concentration cells; Secondary cells; Fuel
cells; Corrosion and its prevention.
6.2 Electrolytic Conduction: Electrolytic Conductance; Specific, equivalent 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, Al2,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;
Determination of rate constant and order
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; Effect of light.
7.3 Mechanism of Reaction: Elementary reactions; Complex reactions; Reactions
involving two/three steps only;
Photochemical reactions; Concept of fast reactions.
7.4 Radioactive isotopes: Half-life period; Radiochemical dating.
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
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
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
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,.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
9.8 f-block elements: Lanthanides and actinides; Oxidation states and chemical
reactivity of lanthanide compounds;
Lanthanide contraction; Comparison of actinides and lanthanides.
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;
10. Principles of Organic Chemistry and Hydrocarbons
10.1 Classification: Based on functional groups, trivial and IUPAC
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
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.
10.7 Petroleum: Composition and refining, uses of petrochemicals.
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, propane, n-butane and cyclohexane 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
12.2 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
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
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
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
13.5 Lipids, Hormones, Vitamins: Classification, structure, functions in
13.6 Polymers: Classification of polymers; General methods of polymerization;
Molecular mass of polymers;
Biopolymers and biodegradable polymers; Free radical, cationic and anionic
Copolymerization: Natural rubber; Vulcanization of rubber; Synthetic rubbers.
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; Cosmetics: Creams,
perfumes, talcum powder, deodorants;
Preservatives, artificial sweetening agents, antioxidants, and edible colours.
13.9 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.
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,
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: 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; Elementary idea of mass spectrometer for accurate molecular mass
determination; 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.
(a) English Proficiency
This test is designed to assess the test takers’ general proficiency in the use
of English language as a means of selfexpression
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.
1.1 Agreement, Time and Tense, Parallel construction, Relative pronouns
1.2 Determiners, Prepositions, Modals, Adjectives
1.3 Voice, Transformation
1.4 Question tags, Phrasal verbs
2.1 Synonyms, Antonyms, Odd Word, One Word, Jumbled letters,
2.2 Contextual meaning.
3. Reading Comprehension
3.5 Reconstruction (rewording)
4.2 Paragraph Unity
(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
5. Verbal Reasoning
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
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
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
1.1 Complex numbers, addition, multiplication, conjugation, polar
representation, properties of modulus and principal
argument, triangle inequality, roots of complex numbers, geometric
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
1.3 Arithmetic, geometric and harmonic progressions, arithmetic, geometric and
harmonic means, arithmeticogeometric
series, sums of finite arithmetic and geometric progressions, infinite
geometric series, sums of squares
and cubes of the first n natural numbers.
1.4 Logarithms and their properties.
1.5 Exponential series.
1.6 Permutations and combinations, Permutations as an arrangement and
combination as selection, simple applications.
1.7 Binomial theorem for a positive integral index, properties of binomial
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
1.9 Sets, Relations and Functions, algebra of sets applications, equivalence
relations, mappings, one-one, into and onto
mappings, composition of mappings.
1.10 Mathematical Induction
1.11 Linear Inequalities, solution of linear inequalities in one and two
2.1 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
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
4. Three dimensional Coordinate Geometry
4.1 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
4.3 Equation of a plane, distance of a point from a plane, condition for
coplanarity of three lines.
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
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 and its applications.
6.4 Application of definite integrals to the determination of areas of regions
bounded by simple curves.
7. Ordinary Differential Equations
7.1 Variables separable method.
7.2 Solution of homogeneous differential equations.
7.3 Linear first order differential equations
8.1 Addition and multiplication rules of probability.
8.2 Conditional probability
8.3 Independent events
8.4 Discrete random variables and distributions
9.1 Addition of vectors, scalar multiplication.
9.2 Dot and cross products of two vectors.
9.3 Scalar triple products and their geometrical interpretations.
10.1 Measures of dispersion
10.2 Measures of skewness and Central Tendency
11.1 Formulation of linear Programming
11.2 Solution of linear Programming, using graphical method.
Part IV Biology
1: Diversity in Living World
1.1 Biology - its meaning and relevance to mankind
1.2 What is living; Taxonomic categories and aids; Systematics and Binomial system of nomenclature.
1.3 Introductory classification of living organisms (Two-kingdom system, Five-kingdom system);
1.4 Plant kingdom - Salient features of major groups (Algae to Angiosperms);
1.5 Animal kingdom - Salient features of Nonchordates up to phylum, and Chordates up to class level.
2: Cell: The Unit of Life; Structure and Function
2.1 Cell wall; Cell membrane; Endomembrane system (ER, Golgi apparatus/ Dictyosome, Lysosomes, Vacuoles); Mitochondria; Plastids; Ribosomes; Cytoskeleton; Cilia and Flagella; Centrosome and Centriole; Nucleus; Microbodies.
2.2 Structural differences between prokaryotic and eukaryotic, and between plant and animal cells.
2.3 Cell cycle (various phases); Mitosis; Meiosis.
2.4 Biomolecules - Structure and function of Carbohydrates, Proteins, Lipids, and Nucleic acids.
2.5 Enzymes - Chemical nature, types, properties and mechanism of action.
3: Genetics and Evolution
3.1 Mendelian inheritance; Chromosome theory of inheritance; Gene interaction; Incomplete dominance; Co- dominance; Complementary genes; Multiple alleles;
3.2 Linkage and Crossing over; Inheritance patterns of hemophilia and blood groups in humans.
3.3 DNA -its organization and replication; Transcription and Translation;
3.4 Gene expression and regulation; DNA fingerprinting.
3.5 Theories and evidences of evolution, including modern Darwinism.
4: Structure and Function - Plants
4.1 Morphology of a flowering plant; Tissues and tissue systems in plants; Anatomy and function of root, stem (including modifications), leaf, inflorescence, flower (including position and arrangement of different whorls, placentation), fruit and seed; Types of fruit; Secondary growth;
4.2 Absorption and movement of water (including diffusion, osmosis and water relations of cell) and of nutrients; Translocation of food; Transpiration and gaseous exchange; Mechanism of stomatal movement.
4.3 Mineral nutrition - Macro- and micro-nutrients in plants including deficiency disorders; Biological nitrogen fixation mechanism.
4.4 Photosynthesis - Light reaction, cyclic and non-cyclic photophosphorylation; various pathways of carbon dioxide fixation; Photorespiration; Limiting factors.
4.5 Respiration - Anaerobic, Fermentation, Aerobic; Glycolysis, TCA cycle; Electron transport system; Energy relations.
5: Structure and Function - Animals
5.1 Human Physiology - Digestive system - organs, digestion and absorption; Respiratory system - organs, breathing and exchange and transport of gases.
5.2 Body fluids and circulation - Blood, lymph, double circulation, regulation of cardiac activity; Hypertension, Coronary artery diseases.
5.3 Excretion system - Urine formation, regulation of kidney function
5.4 Locomotion and movement - Skeletal system, joints, muscles, types of movement.
5.5 Control and co-ordination - Central and peripheral nervous systems, structure and function of neuron, reflex action and sensory reception; Role of various types of endocrine glands; Mechanism of hormone action.
6: Reproduction, Growth and Movement in Plants
6.1 Asexual methods of reproduction;
6.2 Sexual Reproduction - Development of male and female gametophytes; Pollination (Types and agents); Fertilization; Development of embryo, endosperm, seed and fruit (including parthenocarpy and elminth).
6.3 Growth and Movement - Growth phases; Types of growth regulators and their role in seed dormancy, germination and movement;
6.4 Apical dominance; Senescence; Abscission; Photo- periodism; Vernalisation;
6.5 Various types of movements.
7: Reproduction and Development in Humans
7.1 Male and female reproductive systems;
7.2 Menstrual cycle; Gamete production; Fertilisation; Implantation;
7.3 Embryo development;
7.4 Pregnancy and parturition;
7.5 Birth control and contraception.
8: Ecology and Environment
8.1 Meaning of ecology, environment, habitat and niche.
8.2 Ecological levels of organization (organism to biosphere); Characteristics of Species, Population, Biotic Community and Ecosystem; Succession and Climax. Ecosystem - Biotic and abiotic components; Ecological pyramids; Food chain and Food web;
8.3 Energy flow; Major types of ecosystems including agroecosystem.
8.4 Ecological adaptations - Structural and physiological features in plants and animals of aquatic and desert habitats.
8.5 Biodiversity and Environmental Issues - Meaning, types and conservation strategies (Biosphere reserves, National parks and Sanctuaries), Air and Water Pollution (sources and major pollutants); Global warming and Climate change; Ozone depletion; Noise pollution; Radioactive pollution; Methods of pollution control (including an idea of bioremediation); Deforestation; Extinction of species (Hot Spots).
9: Biology and Human Welfare
9.1 Animal husbandry - Livestock, Poultry, Fisheries; Major animal diseases and their control. Pathogens of major communicable diseases of humans caused by fungi, bacteria, viruses, protozoans and elminthes, and their control.
9.2 Cancer; AIDS.
9.3 Adolescence and drug/alcohol abuse;
9.4 Basic concepts of immunology.
9.5 Plant Breeding and Tissue Culture in crop improvement.
10: Biotechnology and its Applications
10.1 Microbes as ideal system for biotechnology;
10.2 Microbial technology in food processing, industrial production (alcohol, acids, enzymes, antibiotics), sewage treatment and energy generation.
10.3 Steps in recombinant DNA technology - restriction enzymes, NA insertion by vectors and other methods, regeneration of recombinants
10.4 Applications of R-DNA technology in human health -Production of Insulin, Vaccines and Growth hormones, Organ transplant, Gene therapy.
10.5 Applications in Industry and Agriculture - Production of expensive enzymes, strain improvement to scale up bioprocesses, GM crops by transfer of genes for nitrogen fixation, herbicide-resistance and pest-resistance including Bt crops.