IIT JEE FOUNDATION MAINS TO ADVANCE

Syllabus for JEE (Main) - 2025

Syllabus for JEE Main Paper 1 (B.E./B.Tech.)- Mathematics, Physics and Chemistry

MATHEMATICS UNIT 1: SETS, RELATIONS AND FUNCTIONS:

Sets and their representation; Union, intersection and complement of sets and

their algebraic properties; Power set; Relations, type of relations, equivalence

relations, functions; one-one, into and onto functions, the composition of

functions.

UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals, Representation of complex numbers

in the form a + ib and their representation in a plane, Argand diagram, algebra of

complex numbers, modulus and argument (or amplitude) of a complex number,

Quadratic equations in real and complex number systems and their solutions;

Relations between roots and coefficients, nature of roots, the formation of

quadratic equations with given roots.

UNIT3: MATRICES AND DETERMINANTS:

Matrices, algebra of matrices, type of matrices, determinants and matrices of

order two and three, evaluation of determinants, area of triangles using

determinants; Adjoint and inverse of a square matrix; Test of consistency and

solution of simultaneous linear equations in two or three variables using matrices.

UNIT 4: PERMUTATIONS AND COMBINATIONS:

The fundamental principle of counting, permutations and combinations; Meaning

of P(n, r) and C(n, r). Simple applications.

UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for a positive integral index, general term and middle term and

simple applications.

UNIT 6: SEQUENCE AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means

between two given numbers, Relation between A.M and G.M.

UNIT 7: LIMIT, CONTINUITY AND DIFFERENTIABILITY:

Real–valued functions, algebra of functions; polynomial, rational, trigonometric,

logarithmic and exponential functions; inverse functions. Graphs of simple

functions. Limits, continuity and differentiability. Differentiation of the sum,

difference, product and quotient of two functions. Differentiation of

trigonometric, inverse trigonometric, logarithmic, exponential, composite and

implicit functions; derivatives of order upto two, Applications of derivatives:

Rate of change of quantities, monotonic-Increasing and decreasing functions,

Maxima and minima of functions of one variable.

UNIT 8: INTEGRAL CALCULAS:

Integral as an anti-derivative, Fundamental integrals involving algebraic,

trigonometric, exponential and logarithmic functions. Integration by substitution,

by parts and by partial fractions. Integration using trigonometric identities.

Evaluation of simple integrals of the type

The fundamental theorem of calculus, properties of definite integrals.

Evaluation of definite integrals, determining areas of the regions bounded by

simple curves by simple curves in standard forms.

UNIT 9: DIFFRENTIAL EQUATIONS :

Ordinary differential equations, their order and degree, the solution of differential

equation by the method of separation of variables, solution of a homogeneous

and linear differential equation of the type 𝑑

𝑑 + � � � = �(�).

UNIT 10: CO-ORDINATE GEOMETRY :

Cartesian system of rectangular coordinates in a plane, distance formula, sections

formula, locus and its equation, the slope of a line, parallel and perpendicular

lines, intercepts of a line on the co-ordinate axis.

Straight line: Various forms of equations of a line, intersection of lines, angles

between two lines, conditions for concurrence of three lines, the distance of a

point form a line, co-ordinate of the centroid, orthocentre and circumcentre of a

triangle.

Circle, conic sections: A standard form of equations of a circle, the general

form of the equation of a circle, its radius and centre, equation of a circle when

the endpoints of a diameter are given, points of intersection of a line and a circle

with the centre at the origin and sections of conics, equations of conic sections

(parabola, ellipse and hyperbola) in standard forms.

UNIT 11: THREE DIMENSIONAL GEOMETRY :

Coordinates of a point in space, the distance between two points, section

formula, direction ratios and direction cosines and the angle between two

intersecting lines. Equation of a line; Skew lines, the shortest distance between

them and its equation.

UNIT 12: VECTOR ALGEBRA :

Vectors and scalars, the addition of vectors, components of a vector in two

dimensions and three-dimensional spaces, scalar and vector products.

UNIT 13: STATISTICS AND PROBABILITY :

Measures of dispersion; calculation of mean, median, mode of grouped and

ungrouped data, calculation of standard deviation, variance and mean

deviation for grouped and ungrouped data. Probability: Probability of an event,

addition and multiplication theorems of probability, Baye's theorem, probability

distribution of a random variable.

UNIT 14: TRIGONOMETRY :

Trigonometrical identities and trigonometrical functions, inverse trigonometrical

functions their properties.

Syllabus for JEE (Main) - 2025

PHYSICS

UNIT 1: Units and Measurements

Units of measurements, System of units, SI Units, fundamental and derived units,

least count, significant figures, Errors in measurements. Dimensions of Physics

quantities, dimensional analysis and its applications.

UNIT 2: Kinematics

The frame of reference, motion in a straight line, speed and velocity, uniform

and non-uniform motion, average speed and instantaneous velocity, uniformly

accelerated motion, velocity-time, position-time graph, relations for uniformly

accelerated motion, relative velocity.

Motion in a plane, projectile motion, uniform circular motion.

UNIT 3: Laws of Motion

Force and inertia, Newton’s first law of motion, momentum, Newton’s second

Law of motion, impulse, Newton’s third Law of motion. Law of conservation of

linear momentum and its applications, equilibrium of concurrent forces.

Static and Kinetic friction, laws of friction, rolling friction.

Dynamics of uniform circular motion, centripetal force and its applications:

vehicle on a level circular road, vehicle on a banked road.

UNIT 4: Work, Energy and Power

Work done by a constant force and a variable force, kinetic and potential energies,

work-energy theorem, power.

The potential energy of a spring, conservation of mechanical energy,

conservative and non- conservative forces, motion in a vertical circle. Elastic

and inelastic collisions in one and two dimensions.

UNIT 5: Rotational Motion

Centre of mass of a two-particle system, centre of mass of a rigid body. Basic

concepts of rotational motion, moment of a force, torque, angular momentum,

conservation of angular momentum and its applications.

The moment of inertia, the radius of gyration, values of moments of inertia for

simple geometrical objects, parallel and perpendicular axes theorems and their

applications. Equilibrium of rigid bodies, rigid body rotation and equations of

rotational motion, comparison of linear and rotational motions.

UNIT 6: Gravitation

The universal law of gravitation. Acceleration due to gravity and its variation

with altitude and depth. Kepler’s law of planetary motion. Gravitational potential

energy, gravitational potential. Escape velocity, motion of a satellite, orbital

velocity, time period and energy of satellite.

UNIT 7: Properties of Solids and Liquids

Elastic behaviour, stress-strain relationship, Hooke's Law, Young's modulus,

bulk modulus and modulus of rigidity.

Pressure due to a fluid column, Pascal's law and its applications, effect of gravity

on fluid pressure, viscosity, Stoke’s law, terminal velocity, streamline and

turbulent flow, critical velocity, Bernoulli's principle and its applications.

Surface energy and surface tension, angle of contact, excess of pressure across a

curved surface, application of surface tension: drops, bubbles and capillary rise.

Heat, temperature, thermal expansion, specific heat capacity, calorimetry,

change of state, latent heat. Heat transfer: conduction, convection and radiation.

UNIT 8: Thermodynamics

Thermal equilibrium and the concept of temperature, zeroth law of

thermodynamics, heat, work and internal energy. The first law of

thermodynamics, isothermal and adiabatic processes. The second law of

thermodynamics: reversible and irreversible processes.

UNIT 9: Kinetic Theory of Gases

Equation of state of a perfect gas, work done on compressing a gas, kinetic

theory of gases: assumptions, the concept of pressure, kinetic interpretation of

temperature, RMS speed of gas molecules, degrees of freedom, law of

equipartition of energy and applications to specific heat capacities of gases,

mean free path, Avogadro's number.

UNIT 10: Oscillations and Waves

Oscillations and periodic motion: time period, frequency, displacement as a

function of time, periodic functions. Simple harmonic motion (S.H.M.) and its

equation, phase, oscillations of a spring: restoring force and force constant,

energy in S.H.M.: kinetic and potential energies, simple pendulum: derivation

of expression for its time period.

Wave motion, longitudinal and transverse waves, speed of the travelling wave,

displacement relation for a progressive wave, principle of superposition of

waves, reflection of waves, standing waves in strings and organ pipes,

fundamental mode and harmonics, beats.

UNIT 11: Electrostatics

Electric charges: conservation of charge, Coulomb's law forces between two

point charges, forces between multiple charges, superposition principle and

continuous charge distribution.

Electric field: electric field due to a point charge, electric field lines, electric

dipole, electric field due to a dipole, torque on a dipole in a uniform electric

field.

Electric flux, Gauss's law and its applications to find field due to infinitely long

uniformly charged straight wire, uniformly charged infinite plane sheet and

uniformly charged thin spherical shell.

Electric potential and its calculation for a point charge, electric dipole and

system of charges, potential difference, equipotential surfaces, electrical

potential energy of a system of two point charges and of electric dipole in an

electrostatic field.

Conductors and insulators, dielectrics and electric polarization, capacitors and

capacitance, the combination of capacitors in series and parallel and capacitance

of a parallel plate capacitor with and without dielectric medium between the

plates, energy stored in a capacitor.

UNIT 12: Current Electricity

Electric current: drift velocity, mobility and their relation with electric current,

Ohm's law, electrical resistance, I-V characteristics of Ohmic and non-ohmic

conductors, electrical energy and power, electrical resistivity and conductivity,

series and parallel combinations of resistors, temperature dependence of

resistance.

Internal resistance, potential difference and emf of a cell, a combination of cells

in series and parallel.

Kirchhoff’s laws and their applications, Wheatstone bridge, Metre Bridge.

UNIT 13: Magnetic Effects of Current and Magnetism

Biot - Savart law and its application to the current carrying circular loop,

Ampere's law and its applications to infinitely long current carrying straight

wire and solenoid.

Force on a moving charge in uniform magnetic and electric fields, force on a

current-carrying conductor in a uniform magnetic field, the force between two

parallel currents carrying conductors-definition of ampere, torque experienced

by a current loop in a uniform magnetic field: Moving coil galvanometer, its

sensitivity and conversion to ammeter and voltmeter.

Current loop as a magnetic dipole and its magnetic dipole moment, bar magnet as

an equivalent solenoid, magnetic field lines, magnetic field due to a magnetic

dipole (bar magnet) along its axis and perpendicular to its axis, torque on a

magnetic dipole in a uniform magnetic field, para-, dia- and ferromagnetic

substances with examples, the effect of temperature on magnetic properties.

UNIT 14: Electromagnetic Induction and Alternating Currents

Electromagnetic induction: Faraday's law, induced emf and current, Lenz’s law,

eddy currents, self and mutual inductance.

Alternating currents, peak and RMS value of alternating current/voltage,

reactance and impedance, LCR series circuit, resonance, power in AC circuits,

wattless current, AC generator and transformer.

UNIT 15: Electromagnetic Waves

Displacement current, electromagnetic waves and their characteristics,

transverse nature of electromagnetic waves, electromagnetic spectrum (radio

waves, microwaves, infrared, visible, ultraviolet, X-rays, Gamma rays),

applications of electromagnetic waves.

UNIT 16: Optics

Reflection of light, spherical mirrors, mirror formula. Refraction of light at

plane and spherical surfaces, thin lens formula and lens maker formula, total

internal reflection and its applications, magnification, power of a lens,

combination of thin lenses in contact, refraction of light through a prism,

microscope and astronomical telescope (reflecting and refracting ) and their

magnifying powers.

Wave optics: wavefront and Huygens ‘Principle, laws of reflection and

refraction using Huygens principle. Interference: Young's double-slit

experiment and expression for fringe width, coherent sources and sustained

interference of light. Diffraction due to a single slit, width of central maximum.

Polarization: plane-polarized light, Brewster's law, uses of plane- polarized

light and Polaroid.

UNIT 17: Dual Nature of Matter and Radiation

Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations,

Einstein's photoelectric equation, particle nature of light. Matter waves: wave

nature of particle, de- Broglie relation.

UNIT 18: Atoms and Nuclei

Alpha-particle scattering experiment, Rutherford's model of atom, Bohr model,

energy levels, hydrogen spectrum. Composition and size of nucleus, atomic

masses, mass-energy relation, mass defect, binding energy per nucleon and its

variation with mass number, nuclear fission and fusion.

UNIT 19: Electronic Devices

Semiconductors, semiconductor diode: I-V characteristics in forward and

reverse bias, diode as a rectifier; I-V characteristics of LED, the photodiode,

solar cell, Zener diode, Zener diode as a voltage regulator.

Logic gates (OR. AND. NOT. NAND and NOR).

UNIT 20: Experimental Skills

Familiarity with the basic approach and observations of the experiments and

activities:

1. Vernier calipers -its use to measure the internal and external diameter and

depth of a vessel.

2. Screw gauge-its use to determine the thickness/ diameter of thin sheet/wire.

3. Simple pendulum-dissipation of energy by plotting a graph between the

square of amplitude and time.

4. Metre scale - the mass of a given object by the principle of moments.

5. Young's modulus of elasticity of the material of a metallic wire.

6. Surface tension of water by capillary rise and effect of detergents,

7. Co-efficient of viscosity of a given viscous liquid by measuring the

terminal velocity of a given spherical body.

8. Speed of sound in air at room temperature using a resonance tube,

9. Specific heat capacity of a given (i) solid and (ii) liquid by method of

mixtures.

10. The resistivity of the material of a given wire using a metre bridge.

11. The resistance of a given wire using Ohm's law.

12. Resistance and figure of merit of a galvanometer by half deflection method.

13. The focal length of

(i) Convex mirror

(ii) Concave mirror and

(iii)Convex lens, using the parallax method.

14. The plot of the angle of deviation vs angle of incidence for a triangular

prism.

15. The refractive index of a glass slab using a travelling microscope.

16. Characteristic curves of a p-n junction diode in forward and reverse bias.

17. Characteristic curves of a Zener diode and finding reverse breakdown

voltage.

18. Identification of diode, LED, resistor, a capacitor from a mixed collection

of such items

CHEMISTRY

PHYSICAL CHEMISTRY

UNIT I: SOME BASIC CONCEPTS IN CHEMISTRY

Matter and its nature, Dalton's atomic theory, Concept of atom, molecule, element and compound, Laws of

chemical combination, Atomic and molecular masses, mole concept, molar mass, percentage composition,

empirical and molecular formulae, Chemical equations and stoichiometry.

UNIT 2: ATOMIC STRUCTURE

Nature of electromagnetic radiation, photoelectric effect, spectrum of the hydrogen atom, Bohr model of a

hydrogen atom - its postulates, derivation of the relations for the energy of the electron and radii of the

different orbits, limitations of Bohr's model, dual nature of matter, de Broglie's relationship, Heisenberg

uncertainty principle, elementary ideas of quantum mechanics, the quantum mechanical model of the atom

and its important features, concept of atomic orbitals as one-electron wave functions, variation of � and �

2 with r for 1s and 2s orbitals, various quantum numbers (principal, angular momentum and magnetic

quantum numbers) and their significance, shapes of s, p and d - orbitals, electron spin and spin quantum

number, rules for filling electrons in orbitals – Aufbau principle, Pauli's exclusion principle and Hund's

rule, electronic configuration of elements and extra stability of half-filled and completely filled orbitals.

UNIT 3: CHEMICAL BONDING AND MOLECULAR STRUCTURE

Kossel-Lewis approach to chemical bond formation, the concept of ionic and covalent bonds.

Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of

lattice enthalpy.

Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment, Valence Shell Electron Pair

Repulsion (VSEPR ) theory and shapes of simple molecules.

Quantum mechanical approach to covalent bonding: Valence bond theory - its important features, the

concept of hybridization involving s, p and d orbitals, resonance.

Molecular Orbital Theory - Its important features, LCAOs, types of molecular orbitals (bonding,

antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic

molecules, the concept of bond order, bond length and bond energy.

Elementary idea of metallic bonding, hydrogen bonding and its applications.

UNIT 4: CHEMICAL THERMODYNAMICS

Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state

functions, entropy, types of processes.

The first law of thermodynamics - Concept of work, heat, internal energy and enthalpy, heat capacity,

molar heat capacity, Hess’s law of constant heat summation, Enthalpies of bond dissociation,

combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution.

The second law of thermodynamics - Spontaneity of processes, Δ S of the universe and Δ G of the

system as criteria for spontaneity. ΔG°(Standard Gibbs energy change) and equilibrium constant.

UNIT 5: SOLUTIONS

Different methods for expressing the concentration of solution - molality, molarity, mole fraction,

percentage (by volume and mass both), the vapour pressure of solutions and Raoult's Law - Ideal and nonideal

solutions, vapour pressure - composition, plots for ideal and non- ideal solutions, Colligative

properties of dilute solutions - a relative lowering of vapour pressure, depression of freezing point, the

elevation of boiling point and osmotic pressure, determination of molecular mass using colligative

properties, abnormal value of molar mass, van’t Hoff factor and its significance.

UNIT 6: EQUILIBRIUM

Meaning of equilibrium is the concept of dynamic equilibrium.

Equilibria involving physical processes: Solid-liquid, liquid-gas, gas-gas and solid-gas equilibria,

Henry's law. General characteristics of equilibrium involving physical processes.

Equilibrium involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and

Kc) and their significance, the significance of Δ G and Δ G ° in chemical equilibrium, factors affecting

equilibrium concentration, pressure, temperature, the effect of catalyst, Le Chatelier’s principle.

Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and

bases (Arrhenius, Bronsted - Lowry and Lewis) and their ionization, acid-base equilibria (including

multistage ionization) and ionization constants, ionization of water, pH scale, common ion effect,

hydrolysis of salts and pH of their solutions, the solubility of sparingly soluble salts, solubility products

and buffer solutions.

UNIT 7: REDOX REACTIONS AND ELECTROCHEMISTRY

Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning

oxidation number and balancing of redox reactions.

Electrolytic and metallic conduction, conductance in electrolytic solutions, molar conductivities and their

variation with concentration, Kohlrausch’s law and its applications.

Electrochemical cells - Electrolytic and Galvanic cells, different types of electrodes, electrode potentials

including standard electrode potential, half-cell and cell reactions, emf of a Galvanic cell and its

measurement, Nernst equation and its applications, relationship between cell potential and Gibbs' energy

change, dry cell and lead accumulator, fuel cells.

UNIT 8: CHEMICAL KINETICS

Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure

and catalyst, elementary and complex reactions, order and molecularity of reactions, rate law, rate

constant and its units, differential and integral forms of zero and first-order reactions, their

characteristics and half-lives, the effect of temperature on the rate of reactions, Arrhenius theory,

activation energy and its calculation, collision theory of bi-molecular gaseous reactions (no derivation).

INORGANIC CHEMISTRY

UNIT 9: CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES

Modern periodic law and present form of the periodic table, s, p. d and f block elements, periodic trends in

properties of elements atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence,

oxidation states and chemical reactivity.

UNIT 10: p- BLOCK ELEMENTS

Group -13 to Group 18 Elements

General Introduction: Electronic configuration and general trends in physical and chemical properties of

elements across the periods and down the groups, unique behaviour of the first element in each group.

UNIT 11: d - and f- BLOCK ELEMENTS

Transition Elements - General introduction, electronic configuration, occurrence and characteristics,

general trends in properties of the first-row transition elements - physical properties, ionization enthalpy,

oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation,

interstitial compounds, alloy formation, preparation, properties and uses of K2Cr2O7 and KMnO4.

Inner Transition Elements

Lanthanoids - Electronic configuration, oxidation states and Lanthanoid contraction.

Actinoids - Electronic configuration and oxidation states.

UNIT 12: COORDINATION COMPOUNDS

Introduction to coordination compounds. Werner's theory, ligands, coordination number, denticity,

chelation, IUPAC nomenclature of mononuclear co-ordination compounds, isomerism, Bonding: Valence

bond approach and basic ideas of Crystal field theory, colour and magnetic properties, importance of

coordination compounds (in qualitative analysis, extraction of metals and in biological systems).

ORGANIC CHEMISTRY

UNIT 13: PURIFICATION AND CHARACTERISATION OF ORGANIC COMPOUNDS

Purification - Crystallization, sublimation, distillation, differential extraction and chromatography -

principles and their applications.

Qualitative analysis - Detection of nitrogen, sulphur, phosphorus and halogens.

Quantitative analysis (basic principles only) - Estimation of carbon, hydrogen, nitrogen, halogens,

sulphur and phosphorus.

Calculations of empirical formulae and molecular formulae, numerical problems in organic quantitative

analysis,

UNIT 14: SOME BASIC PRINCIPLES OF ORGANIC CHEMISTRY

Tetravalency of carbon, shapes of simple molecules - hybridization (s and p): classification of organic

compounds based on functional groups and those containing halogens, oxygen, nitrogen and sulphur,

homologous series: Isomerism - structural and stereoisomerism.

Nomenclature (Trivial and IUPAC)

Covalent bond fission - Homolytic and heterolytic, free radicals, carbocations and carbanions, stability of

carbocations and free radicals, electrophiles and nucleophiles.

Electronic displacement in a covalent bond

- Inductive effect, electromeric effect, resonance and hyperconjugation.

Common types of organic reactions- Substitution, addition, elimination and rearrangement.

UNITS 15: HYDROCARBONS

Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.

Alkanes - Conformations: Sawhorse and Newman projections (of ethane), mechanism of halogenation of

alkanes.

Alkenes - Geometrical isomerism, mechanism of electrophilic addition, addition of hydrogen, halogens,

water, hydrogen halides (Markownikoffs and peroxide effect), Ozonolysis and polymerization.

Alkynes - Acidic character, addition of hydrogen, halogens, water and hydrogen halides, polymerization.

Aromatic hydrocarbons - Nomenclature, benzene - structure and aromaticity, mechanism of electrophilic

substitution, halogenation, nitration.

Friedel-Craft's alkylation and acylation, directive influence of the functional group in mono- substituted

benzene.

UNIT 16: ORGANIC COMPOUNDS CONTAINING HALOGENS

General methods of preparation, properties and reactions, nature of C-X bond, mechanisms of

substitution reactions.

Uses, environmental effects of chloroform, iodoform, freons and DDT.

UNIT 17: ORGANIC COMPOUNDS CONTAINING OXYGEN

General methods of preparation, properties, reactions and uses.

ALCOHOLS, PHENOLS AND ETHERS

Alcohols: Identification of primary, secondary and tertiary alcohols, mechanism of dehydration.

Phenols: Acidic nature, electrophilic substitution reactions, halogenation, nitration and sulphonation,

Reimer - Tiemann reaction.

Ethers: Structure.

Aldehyde and Ketones: Nature of carbonyl group, nucleophilic addition to >C=O group, relative

reactivities of aldehydes and ketones, important reactions such as - Nucleophilic addition reactions

(addition of HCN, NH3 and its derivatives), Grignard reagent, oxidation, reduction (Wolf Kishner and

Clemmensen), the acidity of � -hydrogen. Aldol condensation, Cannizzaro reaction, Haloform reaction,

chemical tests to distinguish between aldehydes and ketones.

Carboxylic Acids: Acidic strength and factors affecting it.

UNIT 18: ORGANIC COMPOUNDS CONTAINING NITROGEN

General methods of preparation, properties, reactions and uses.

Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary

and tertiary amines and their basic character.

Diazonium Salts: Importance in synthetic organic chemistry.

UNIT 19: BIOMOLECULES

General introduction and importance of biomolecules.

CARBOHYDRATES – Classification, aldoses and ketoses, monosaccharides (glucose and fructose) and

constituent monosaccharides of oligosaccharides (sucrose, lactose and maltose).

PROTEINS - Elementary idea of � -amino acids, peptide bond, polypeptides, proteins: primary,

secondary, tertiary and quaternary structure (qualitative idea only), denaturation of proteins, enzymes.

VITAMINS – Classification and functions.

NUCLEIC ACIDS – Chemical constitution of DNA and RNA, biological functions of nucleic acids.

Hormones (General introduction)

UNIT 20: PRINCIPLES RELATED TO PRACTICAL CHEMISTRY

Detection of extra elements (Nitrogen, sulphur, halogens) in organic compounds, detection of the

following functional groups, hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketones) carboxyl

and amino groups in organic compounds.

 The chemistry involved in the preparation of the following:

Inorganic compounds, Mohr’s salt, potash alum.

Organic compounds: Acetanilide, p-nitro acetanilide, aniline yellow, iodoform.

 The chemistry involved in the titrimetric exercises – acids, bases and the use of indicators,

oxalic-acid vs KMnO4, Mohr’s salt vs KMnO4

 Chemical principles involved in the qualitative salt analysis:

Cations – Pb2+, Cu2+, Al3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH4+

Anions- CO32−, S2-, SO42−, NO3-, NO2-, Cl-, Br-, I- ( Insoluble salts excluded).

Chemical principles involved in the following experiments:

1. Enthalpy of solution of CuSO4

2. Enthalpy of neutralization of strong acid and strong base.

3. Preparation of lyophilic and lyophobic sols.

4. Kinetic study of the reaction of iodide ions with hydrogen peroxide at room temperature.

Syllabus for JEE (Main) Paper 2A (B.Arch.) - Mathematics, Aptitude Test and Drawing Test

Part - I MATHEMATICS

UNIT 1: SETS, RELATIONS AND FUNCTIONS:

Sets and their representation; Union, intersection and complement of sets and their algebraic properties;

Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions,

the composition of functions.

UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a + ib and

their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or

amplitude) of a complex number, Quadratic equations in real and complex number systems and their

solutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equations

with given roots.

UNIT3: MATRICES AND DETERMINANTS:

Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three,

evaluation of determinants, area of triangles using determinants; Adjoint and inverse of a square matrix;

Test of consistency and solution of simultaneous linear equations in two or three variables using matrices.

UNIT 4: PERMUTATIONS AND COMBINATIONS:

The fundamental principle of counting, permutations and combinations; Meaning of P(n, r) and C(n, r).

Simple applications.

UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for a positive integral index, general term and middle term and simple applications.

UNIT 6: SEQUENCE AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given

numbers, Relation between A.M and G.M.

UNIT 7: LIMIT, CONTINUITY AND DIFFERENTIABILITY:

Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic and

exponential functions; inverse functions. Graphs of simple functions. Limits, continuity and

differentiability. Differentiation of the sum, difference, product and quotient of two functions.

Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit

functions; derivatives of order upto two, Applications of derivatives: Rate of change of quantities,

monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable.

UNIT 8: INTEGRAL CALCULAS:

Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and

logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using

trigonometric identities.

Evaluation of simple integrals of the type

The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals,

determining areas of the regions bounded by simple curves in standard forms.

UNIT 9: DIFFRENTIAL EQUATIONS :

Ordinary differential equations, their order and degree, the solution of differential equation by the method

of separation of variables, solution of a homogeneous and linear differential equation of the type

𝑑

𝑑 + � � � = �(�).

UNIT 10: CO-ORDINATE GEOMETRY :

Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its

equation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.

Straight line: Various forms of equations of a line, intersection of lines, angles between two lines,

conditions for concurrence of three lines, the distance of a point form a line, co-ordinate of the centroid,

orthocentre and circumcentre of a triangle.

Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle,

its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection

of a line and a circle with the centre at the origin and sections of conics, equations of conic sections

(parabola, ellipse and hyperbola) in standard forms.

UNIT 11: THREE DIMENSIONAL GEOMETRY :

Coordinates of a point in space, the distance between two points, section formula, direction ratios and

direction cosines and the angle between two intersecting lines. Equation of a line; Skew lines, the shortest

distance between them and its equation.

UNIT 12: VECTOR ALGEBRA :

Vectors and scalars, the addition of vectors, components of a vector in two dimensions and threedimensional

spaces, scalar and vector products.

UNIT 13: STATISTICS AND PROBABILITY :

Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data, calculation of

standard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probability

of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a

random variable.

UNIT 14: TRIGONOMETRY :

Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions and their

properties.

Part –II APTITUDE TEST

UNIT - 1 Awareness of persons: Buildings, Materials.

Objects, Texture related to Architecture and Build-environment, Visualizing three- dimensional objects

from two-dimensional drawings. Visualizing. Different sides of three- dimensional objects. Analytical

Reasoning Mental Ability (Visual, Numerical and Verbal)

UNIT – 2 Three dimensional- perception: Understanding and appreciation of scale and proportions of

objects, building forms and elements, colour texture harmony and contrast Design and drawing of

geometrical or abstract shapes and patterns in pencil. Transformation of forms both 2D and 3D union,

subtraction rotation, development of surfaces and volumes, Generation of plans, elevations and 3D views

of objects, creating two-dimensional and three-dimensional compositions using given shapes and forms.

Part – III DRAWING TEST

Sketching of scenes and activities from memory of urbanscape (public space, market, festivals, street

scenes, monuments, recreational spaces, etc.). landscape (riverfronts. Jungle. Gardens, trees. Plants, etc.)

and rural life.

To be conducted in a Drawing sheet.

Note: Candidates are advised to bring pencils, own geometry box set, crasets and colour pencils and

crayons for the Drawing Test.

Syllabus for JEE (Main) Paper 2B (B.Planning) - Mathematics, Aptitude Test and Planning

Part - I MATHEMATICS

UNIT 1: SETS, RELATIONS AND FUNCTIONS:

Sets and their representation; Union, intersection and complement of sets and their algebraic properties;

Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions,

the composition of functions.

UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a + ib and

their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or

amplitude) of a complex number, Quadratic equations in real and complex number systems and their

solutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equations

with given roots.

UNIT3: MATRICES AND DETERMINANTS:

Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three,

evaluation of determinants, area of triangles using determinants; Adjoint and inverse of a square matrix;

Test of consistency and solution of simultaneous linear equations in two or three variables using matrices.

UNIT 4: PERMUTATIONS AND COMBINATIONS:

The fundamental principle of counting, permutations and combinations; Meaning of P(n, r) and C(n, r),

Simple applications.

UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for a positive integral index, general term and middle term and simple applications.

UNIT 6: SEQUENCE AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given

numbers, Relation between A.M and G.M.

UNIT 7: LIMIT, CONTINUITY AND DIFFERENTIABILITY:

Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic and

exponential functions; inverse functions. Graphs of simple functions. Limits, continuity and

differentiability. Differentiation of the sum, difference, product and quotient of two functions.

Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit

functions; derivatives of order upto two, Applications of derivatives: Rate of change of quantities,

monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable.

UNIT 8: INTEGRAL CALCULAS:

Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and

logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using

trigonometric identities.

Evaluation of simple integrals of the type

The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals,

determining areas of the regions bounded by simple curves.

UNIT 9: DIFFRENTIAL EQUATIONS :

Ordinary differential equations, their order and degree, the solution of differential equation by the method of

separation of variables, solution of a homogeneous and linear differential equation of the type

𝑑

𝑑 + � � � = �(�).

UNIT 10: CO-ORDINATE GEOMETRY :

Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its

equation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.

Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for

concurrence of three lines, the distance of a point form a line, co-ordinate of the centroid, orthocentre and

circumcentre of a triangle.

Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its

radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a

line and a circle with the centre at the origin and sections of conics, equations of conic sections (parabola,

ellipse and hyperbola) in standard forms.

UNIT 11: THREE DIMENSIONAL GEOMETRY :

Coordinates of a point in space, the distance between two points, section formula, direction ratios and

direction cosines and the angle between two intersecting lines. Equation of a line; Skew lines, the shortest

distance between them and its equation.

UNIT 12: VECTOR ALGEBRA :

Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional

spaces, scalar and vector products.

UNIT 13: STATISTICS AND PROBABILITY :

Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data, calculation of

standard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probability of an

event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random

variable.

UNIT 14: TRIGONOMETRY :

Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions and their properties.

Part –II APTITUDE TEST

Expert Vector Algebra and Integral Calculus Tutors in Mangalore

IIT JEE Foundation to Advanced (JEE Main & Advanced) by ASHWANI RAJ SACHIN