JEEADVANCED Mock Test

PHYSICS

General

Units and dimensions, dimensional analysis

Least count, significant figures

Methods of measurement and error analysis for physical quantities

Experiments using Vernier calipers and screw gauge

Determination of g using simple pendulum

Young's modulus - elasticity of the material

Surface tension of water by capillary rise and effect of detergents

Specific heat of a liquid using calorimeter

Focal length of concave mirror and convex lens using u-v method

Speed of sound using resonance column

Verification of Ohm's law using voltmeter and ammeter

Specific resistance of the material of a wire using meter bridge and post office box

Mechanics

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles

Uniform circular motion

Relative velocity

Newton's laws of motion

Inertial and uniformly accelerated frames of reference

Static and dynamic friction

Kinetic and potential energy

Work and power

Conservation of linear momentum and mechanical energy

Systems of particles

Centre of mass and its motion

Impulse

Elastic and inelastic collisions

Rigid body, moment of inertia, parallel and perpendicular axes theorems

Angular momentum

Torque

Conservation of angular momentum

Dynamics of rigid bodies with fixed axis of rotation

Rolling without slipping of rings, cylinders and spheres

Equilibrium of rigid bodies

Collision of point masses with rigid bodies

Forced and damped oscillation, resonance

Linear and angular simple harmonic motions

Hooke's law, Young's modulus

Law of gravitation

Gravitational potential and field

Acceleration due to gravity

Kepler's laws

Geostationary orbits

Motion of planets and satellites in circular orbits

Escape velocity

Pressure in a fluid

Pascal's law

Buoyancy

Surface energy and surface tension, angle of contact, drops, bubbles and capillary rise

Viscosity (Poiseuille's equation excluded), Modulus of rigidity and bulk modulus in mechanics

Stoke's law

Terminal velocity

Streamline flow, equation of continuity, Bernoulli's theorem and its applications

Wave motion (plane waves only), longitudinal and transverse waves

Superposition of waves

Progressive and stationary waves

Vibration of strings and air columns

Resonance

Beats

Speed of sound in gases

Doppler effect (in sound)

Thermal Physics

Thermal expansion of solids, liquids and gases

Calorimetry, latent heat

Heat conduction in one dimension

Elementary concepts of convection and radiation

Newton's law of cooling

Ideal gas laws

Specific heats (Cv and Cp for monoatomic and diatomic gases)

Isothermal and adiabatic processes

Bulk modulus of gases

Equivalence of heat and work

First law of thermodynamics and its applications (only for ideal gases)

Second law of thermodynamics

Reversible and irreversible processes

Carnot engine and its efficiency

Blackbody radiation: absorptive and emissive powers

Kirchhoff's law

Wien's displacement law

Stefan's law

Electricity and Magnetism

Coulomb's law

Electric field and potential

Electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field

Electric field lines

Flux of electric field

Gauss's law and its applications

Capacitance

Parallel plate capacitor with and without dielectrics

Capacitors in series and parallel

Energy stored in a capacitor

Electric current

Ohm's law

Series and parallel arrangements of resistances and cells

Kirchhoff's laws and simple applications

Heating effect of current

Biot–Savart's law and Ampere's law

Magnetic field near a current-carrying straight wire, along the axis of a circular coil and inside a long straight solenoid

Force on a moving charge and on a current-carrying wire in a uniform magnetic field

Magnetic moment of a current loop

Effect of a uniform magnetic field on a current loop

Moving coil galvanometer, voltmeter, ammeter and their conversions

Electromagnetic induction: Faraday's law, Lenz's law

Self and mutual inductance

RC, LR, LC and LCR circuits with d.c. and a.c. sources

Electromagnetic Waves

Electromagnetic waves and their characteristics

Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses

Optics

Rectilinear propagation of light

Reflection and refraction at plane and spherical surfaces

Total internal reflection

Deviation and dispersion of light by a prism

Thin lenses

Combinations of mirrors and thin lenses

Magnification

Wave nature of light: Huygen's principle, interference limited to Young's double slit experiment

Diffraction due to a single slit

Polarization of light, plane polarized light

Brewster's law, Polaroids

Modern Physics

Atomic nucleus

α, β and γ radiations

Law of radioactive decay

Decay constant

Half-life and mean life

Binding energy and its calculation

Fission and fusion processes

Energy calculation in these processes

Photoelectric effect

Bohr's theory of hydrogen-like atoms

Characteristic and continuous X-rays

Moseley's law

de Broglie wavelength of matter waves

CHEMISTRY

General Topics

Concept of atoms and molecules

Dalton's atomic theory

Mole concept

Chemical formulae

Balanced chemical equations

Calculations (based on mole concept and stoichiometry) involving common oxidation-reduction, neutralisation, and displacement reactions

Concentration in terms of mole fraction, molarity, molality and normality

States of Matter: Gases and Liquids

Gas laws and ideal gas equation

Absolute scale of temperature

Deviation from ideality, van der Waals equation

Kinetic theory of gases

Average, root mean square and most probable velocities and their relation with temperature

Law of partial pressures

Diffusion of gases

Intermolecular interactions: types, distance dependence, and their effect on properties

Liquids: vapour pressure, surface tension, viscosity

Atomic Structure

Bohr model, spectrum of hydrogen atom

Wave-particle duality, de Broglie hypothesis

Uncertainty principle

Qualitative quantum mechanical picture of hydrogen atom: Energies, quantum numbers, wave function and probability density (plots only), shapes of s, p and d orbitals

Aufbau principle

Pauli's exclusion principle and Hund's rule

Chemical Bonding and Molecular Structure

Orbital overlap and covalent bond

Hybridisation involving s, p and d orbitals only

Molecular orbital energy diagrams for homonuclear diatomic species (up to Ne2)

Hydrogen bond

Polarity in molecules, dipole moment

VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral)

Chemical Thermodynamics

Intensive and extensive properties, state functions

First law of thermodynamics

Internal energy, work (pressure-volume only) and heat

Enthalpy, heat capacity, standard state, Hess's law

Enthalpy of reaction, fusion and vapourization, and lattice enthalpy

Second law of thermodynamics

Entropy

Gibbs energy

Criteria of equilibrium and spontaneity

Chemical and Ionic Equilibrium

Law of mass action

Significance of ΔG and ΔG° in chemical equilibrium

Equilibrium constant (Kp and Kc) and reaction quotient

Le Chatelier's principle (effect of concentration, temperature and pressure)

Solubility product and its applications, common ion effect

pH and buffer solutions

Acids and bases (Bronsted and Lewis concepts)

Hydrolysis of salts

Electrochemistry

Electrochemical cells and cell reactions

Standard electrode potentials

Electrochemical work, Nernst equation

Electrochemical series, emf of galvanic cells

Faraday's laws of electrolysis

Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch's law

Batteries: Primary and Secondary, fuel cells

Corrosion

Chemical Kinetics

Rates of chemical reactions

Order and molecularity of reactions

Rate law, rate constant, half-life

Differential and integrated rate expressions for zero and first order reactions

Temperature dependence of rate constant (Arrhenius equation and activation energy)

Catalysis: Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism

Solid State

Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, α, β, γ)

Close packed structure of solids (cubic and hexagonal)

Packing in fcc, bcc and hcp lattices

Nearest neighbours, ionic radii and radius ratio

Point defects

Solutions

Henry's law

Raoult's law

Ideal solutions

Colligative properties: lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure

van't Hoff factor

Surface Chemistry

Elementary concepts of adsorption: Physisorption and Chemisorption

Freundlich adsorption isotherm

Colloids: types, methods of preparation and general properties

Elementary ideas of emulsions, surfactants and micelles (only definitions and examples)

Classification of Elements and Periodicity in Properties

Modern periodic law and the present form of periodic table

Electronic configuration of elements

Periodic trends in atomic radius, ionic radius, ionization enthalpy, electron gain enthalpy, valence, oxidation states, electronegativity, and chemical reactivity

Hydrogen

Position of hydrogen in periodic table

Occurrence, isotopes, preparation, properties and uses of hydrogen

Hydrides – ionic, covalent and interstitial

Physical and chemical properties of water, heavy water

Hydrogen peroxide-preparation, reactions, use and structure

Hydrogen as a fuel

s-Block Elements

Alkali and alkaline earth metals-reactivity towards air, water, dihydrogen, halogens

Their reducing nature including solutions in liquid ammonia

Uses of these elements

General characteristics of their oxides, hydroxides, halides, salts of oxoacids

Anomalous behaviour of lithium and beryllium

Preparation, properties, and uses of compounds of sodium and calcium

p-Block Elements

Oxidation state and trends in chemical reactivity of elements of groups 13-17

Anomalous properties of boron, carbon, nitrogen, oxygen, and fluorine with respect to other elements in their respective groups

Preparation, properties, and uses of important compounds of groups 13-17 elements

Environmental chemistry

d- and f-Block Elements

Oxidation states and their stability

Standard electrode potentials

Interstitial compounds

Alloys

Catalytic properties

Applications

Preparation, structure, and reactions of oxoanions of chromium and manganese

Lanthanoid and actinoid contractions

General characteristics

Coordination Compounds

Werner's theory

Nomenclature, cis-trans and ionization isomerism

Hybridization and geometries of mononuclear coordination compounds

Bonding [VBT and CFT (octahedral and tetrahedral fields)]

Magnetic properties (spin-only) and colour of 3d-series coordination compounds

Ligands and spectrochemical series

Stability

Importance and applications

Metal carbonyls

Isolation of Metals

Metal ores and their concentration

Extraction of crude metal from concentrated ores

Thermodynamic and electrochemical principles of metallurgy

Cyanide process (silver and gold)

Refining

Principles of Qualitative Analysis

Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+)

Nitrate, halides (excluding fluoride), carbonate and bicarbonate, sulphate and sulphide

Environmental Chemistry

Atmospheric pollution

Water pollution

Soil pollution

Industrial waste

Strategies to control environmental pollution

Green chemistry

Basic Principles of Organic Chemistry

Hybridisation of carbon

σ and π-bonds

Shapes of simple organic molecules

Aromaticity

Structural and geometrical isomerism

Stereoisomers and stereochemical relationship

Determination of empirical and molecular formulae

IUPAC nomenclature of organic molecules

Hydrogen bonding effects

Inductive, Resonance and Hyperconjugative effects

Acidity and basicity of organic compounds

Reactive intermediates

Formation, structure and stability of carbocations, carbanions and free radicals

Alkanes

Homologous series

Physical properties and effect of branching

Conformations of ethane and butane

Preparation from alkyl halides and aliphatic carboxylic acids

Reactions: combustion, halogenation, oxidation

Alkenes and Alkynes

Physical properties

Preparation by elimination reactions

Acid catalysed hydration

Metal acetylides

Reactions with KMnO4 and ozone

Reduction of alkenes and alkynes

Electrophilic addition reactions

Effect of peroxide on addition reactions

Cyclic polymerization reaction of alkynes

Benzene

Structure

Electrophilic substitution reactions

Effect of directing groups

Phenols

Physical properties

Preparation

Electrophilic substitution reactions

Reimer-Tiemann reaction

Kolbe reaction

Esterification

Etherification

Aspirin synthesis

Oxidation and reduction reactions

Alkyl Halides

Rearrangement reactions of alkyl carbocation

Grignard reactions

Nucleophilic substitution reactions and their stereochemical aspects

Alcohols

Physical properties

Reactions: esterification, dehydration

Reactions with: sodium, phosphorus halides, ZnCl2/concentrated HCl, thionyl chloride

Conversion of alcohols into aldehydes, ketones and carboxylic acids

Ethers

Preparation by Williamson's synthesis

C-O bond cleavage reactions

Aldehydes and Ketones

Preparation methods

Reactions: oxidation, reduction, oxime and hydrazone formation

Aldol condensation

Cannizzaro reaction

Haloform reaction

Nucleophilic addition reactions

Carboxylic Acids

Physical properties

Preparation: from nitriles, Grignard reagents, hydrolysis of esters and amides

Preparation of benzoic acid from alkylbenzenes

Reactions: reduction, halogenation, formation of esters, acid chlorides and amides

Amines

Preparation from nitro compounds, nitriles and amides

Reactions: Hoffmann bromamide degradation, Gabriel phthalimide synthesis

Reaction with nitrous acid

Azo coupling reaction of diazonium salts of aromatic amines

Sandmeyer and related reactions of diazonium salts

Carbylamine reaction

Hinsberg test

Alkylation and acylation reactions

Haloarenes

Reactions: Fittig, Wurtz-Fittig

Nucleophilic aromatic substitution in haloarenes and substituted haloarenes

Biomolecules

Carbohydrates: Classification; Mono- and di-saccharides; Oxidation; Reduction; Glycoside formation and hydrolysis; Anomers

Proteins: Amino acids; Peptide linkage; Structure of peptides; Types of proteins

Nucleic acids: Chemical composition and structure of DNA and RNA

Polymers

Types of polymerization

Homo and copolymers

Natural rubber

Cellulose

Nylon

Teflon

Bakelite

PVC

Bio-degradable polymers

Applications of polymers

Chemistry in Everyday Life

Drug-target interaction

Therapeutic action and examples of antacids, antihistamines, tranquilizers, analgesics, antimicrobials, and antifertility drugs

Artificial sweeteners

Soaps, detergents, and cleansing action

Practical Organic Chemistry

Detection of elements (N, S, halogens)

Detection and identification of functional groups: hydroxyl, carbonyl, carboxyl, amino and nitro

MATHEMATICS

Sets, Relations and Functions

Sets and their representations

Different kinds of sets (empty, finite and infinite)

Algebra of sets

Intersection, complement, difference and symmetric difference of sets and their algebraic properties

De-Morgan's laws on union, intersection, difference (for finite number of sets)

Practical problems based on set theory

Cartesian product of finite sets

Ordered pair

Relations

Domain and codomain of relations

Equivalence relation

Function as a special case of relation

Functions as mappings

Domain, codomain, range of functions

Invertible functions

Even and odd functions

Into, onto and one-to-one functions

Special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer etc.)

Sum, difference, product and composition of functions

Algebra

Algebra of complex numbers

Addition, multiplication, conjugation of complex numbers

Polar representation of complex numbers

Properties of modulus and principal argument

Triangle inequality

Cube roots of unity

Geometric interpretations of complex numbers

Statement of fundamental theorem of algebra

Quadratic equations with real coefficients

Relations between roots and coefficients of quadratic equations

Formation of quadratic equations with given roots

Symmetric functions of roots

Arithmetic and geometric progressions

Arithmetic and geometric means

Sums of finite arithmetic and geometric progressions

Infinite geometric series

Sum of the first n natural numbers

Sums of squares and cubes of the first n natural numbers

Logarithms and their properties

Permutations and combinations

Binomial theorem for a positive integral index

Properties of binomial coefficients

Matrices

Matrices as a rectangular array of real numbers

Equality of matrices

Addition of matrices

Multiplication of matrices by a scalar

Product of matrices

Transpose of a matrix

Elementary row and column transformations

Determinant of a square matrix of order up to three

Adjoint of a matrix

Inverse of a square matrix of order up to three

Properties of matrix operations

Diagonal, symmetric and skew-symmetric matrices and their properties

Solutions of simultaneous linear equations in two or three variables

Probability and Statistics

Random experiment

Sample space

Different types of events (impossible, simple, compound)

Addition and multiplication rules of probability

Conditional probability

Independence of events

Total probability

Bayes Theorem

Computation of probability of events using permutations and combinations

Measure of central tendency and dispersion

Mean, median, mode

Mean deviation

Standard deviation and variance of grouped and ungrouped data

Analysis of frequency distribution with same mean but different variance

Random variable

Mean and variance of the random variable

Trigonometry

Trigonometric functions

Periodicity and graphs of trigonometric functions

Addition and subtraction formulae

Formulae involving multiple and sub-multiple angles

General solution of trigonometric equations

Inverse trigonometric functions (principal value only)

Elementary properties of inverse trigonometric functions

Analytical Geometry

Two dimensions: Cartesian coordinates

Distance between two points

Section formulae

Shift of origin

Equation of a straight line 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

Concurrency of lines

Centroid, orthocentre, incentre and circumcentre of a triangle

Equation of a circle in various forms

Equations of tangent, normal and chord of a circle

Parametric equations of a circle

Intersection of a circle with a straight line or a circle

Equation of a circle through the points of intersection of two circles and those of a circle and a straight line

Equations of a parabola, ellipse and hyperbola in standard form

Foci, directrices and eccentricity of parabola, ellipse and hyperbola

Parametric equations of parabola, ellipse and hyperbola

Equations of tangent and normal to parabola, ellipse and hyperbola

Locus problems

Three dimensions: Distance between two points

Direction cosines and direction ratios

Equation of a straight line in space

Skew lines

Shortest distance between two lines

Equation of a plane

Distance of a point from a plane

Angle between two lines

Angle between two planes

Angle between a line and a plane

Coplanar lines

Differential Calculus

Limit of a function at a real number

Continuity of a function

Limit and continuity of the sum, difference, product and quotient of two functions

L'Hospital rule of evaluation of limits of functions

Continuity of composite functions

Intermediate value property of continuous functions

Derivative of a function

Derivative of the sum, difference, product and quotient of two functions

Chain rule

Derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions

Tangents and normals

Increasing and decreasing functions

Derivatives of order two

Maximum and minimum values of a function

Rolle's theorem

Lagrange's mean value theorem

Geometric interpretation of Rolle's theorem and Lagrange's mean value theorem

Derivatives up to order two of implicit functions

Geometric interpretation of derivatives

Integral Calculus

Integration as the inverse process of differentiation

Indefinite integrals of standard functions

Definite integrals as the limit of sums

Definite integral and their properties

Fundamental theorem of integral calculus

Integration by parts

Integration by the methods of substitution

Integration by partial fractions

Application of definite integrals to the determination of areas bounded by simple curves

Formation of ordinary differential equations

Solution of homogeneous differential equations of first order and first degree

Separation of variables method

Linear first order differential equations

Vectors

Addition of vectors

Scalar multiplication

Dot and cross products

Scalar and vector triple products

Geometrical interpretations of vector operations

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