National Testing Agency (JEE) Main-2023 Joint Entrance Examination Syllabus Details

National Testing Agency :

JEE (Main) Exam Syllabus: The National Testing Agency (NTA) Joint Entrance Examination (JEE (Main)-2023 syllabus The examination will happen in stages. The syllabus for the Paper I and Paper II exams is provided here.

Syllabus for JEE (Main) 2023 Paper-I Exam (B.E/B.Tech) – Mathematics, Physics & Chemistry:

I. Mathematics: 

UNIT 1: SETS, RELATIONS &  FUNCTIONS:
Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.

UNIT 2: COMPLEX NUMBERS & QUADRATIC EQUATIONS:
Complex numbers represented as sorted real pair Complex number representation in the form of a + ib and its representation on a plane, Triangle inequality, complex number algebra, modulus and argument (or amplitude) of a complex number, complex number square root, Real and complex number system quadratic equations and their answers The nature of roots, the relationship between roots and coefficients, and how quadratic equations with specified roots are formed.

UNIT 3: MATRICES &  DETERMINANTS:
Area of triangles utilizing determinants, determinants, determinants, algebra of matrices, types of matrices, determinants, and matrices of order two and three Adjacent, and utilizing determinants and simple transformations to evaluate the inverse of a square matrix, Using determinants and matrices, solve simultaneous linear equations in two or three variables to test consistency.

UNIT 4: PERMUTATIONS &  COMBINATIONS:
The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications.

UNIT 5: MATHEMATICAL INDUCTIONS:
Principle of Mathematical Induction and its simple applications.

UNIT 6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients, and simple applications.

UNIT 7: SEQUENCE AND SERIES:
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression.

UNIT 8: LIMIT, CONTINUITY & DIFFERENTIABILITY:

Inverse functions, polynomials, rational, trigonometric, logarithmic, exponential, and real-valued functions are all included in the algebra of functions. Simple function graphs. Differentiability, continuity, and limits. differentiation of two functions’ product, quotient, difference, and sum. Differentiation of logarithmic, exponential, composite, implicit, inverse, and trigonometric functions; derivatives up to order two; Rolle’s and Lagrange’s Average amount Theorems and Derivative Applications: Rate of monotonic quantity change Functions that increase and decrease, maxima and minima of tangents, normal, and functions of a single variable.

UNIT 9: INTEGRAL CALCULUS:
Integral as an anti-derivative, Fundamental Integrals involving algebraic, trigonometric, exponential, and logarithms functions. Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities. Integral as limit of a sum. The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

UNIT 10: DIFFRENTIAL EQUATIONS: 
Ordinary differential equations, their order, and degree, the formation of differential equations, solution of differential equation by the method of separation of variables, solution of a homogeneous and linear differential equation of the type

dy/dx+P(x)y=q(x)

UNIT 11: CO-ORDINATE GEOMETRY
Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus, and its equation, translation of axes, 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, equations of internal and external by sectors of angles between two lines co-ordinate of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.

Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, 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 condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency.

UNIT 12: THREE DIMENSIONAL GEOMETRY
Coordinates of a point in space, the distance between two points, section formula, directions ratios, and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them, and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

UNIT 13: VECTOR ALGEBRA
Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product.

UNIT 14: STATISTICS AND PROBABILITY
Measures of discretion; calculation of mean, median, mode of grouped and un grouped data calculation of standard deviation, variance and mean deviation for grouped and un grouped data.
Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials, and binomial distribution.

UNIT 15: TRIGONOMETRY
Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions, and their properties, heights, and distance.

UNIT 16: MATHEMATICAL REASONING
Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse, and contrapositive.

PHYSICS:

UNIT 1: PHYSICS AND MEASUREMENT
Physics, technology, and society, S I Units, fundamental and derived units, least count, accuracy and precision of measuring instruments, Errors in measurement, Dimensions of Physics quantities, dimensional analysis, and its applications.

UNIT 2: KINEMATICS
The frame of reference, motion in a straight line, Position- time graph, 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, Scalars and Vectors, Vector. Addition and subtraction, zero vector, scalar and vector products, Unit Vector, Resolution of a Vector. 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, Impulses; 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.

UNIT 4: WORK, ENERGY, AND POWER
Work done by a content force and a variable force; kinetic and potential energies, work-energy theorem, power.
The potential energy of spring conservation of mechanical energy, conservative and neoconservative forces; Elastic and inelastic collisions in one and two dimensions.

UNIT 5: ROTATIONAL MOTION
Centre of the mass of a two-particle system, Centre of the mass of a rigid body; Basic concepts of rotational motion; a 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. Rigid body rotation equations of rotational motion.

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, Orbital velocity of a satellite. Geo stationary satellites.

UNIT 7: PROPERTIES OF SOLIDS AND LIQUIDS
Adaptive behavior, link between stress and strain, Hooke’s Law. Bulk modulus, stiffness modulus, and Young’s modulus. Pascal’s law: pressure resulting from a fluid column and its applications. viscosity. Stokes’ law. turbulent flow, streamline, and terminal velocity. Reynolds figure. The principle of Bernoulli and its uses. Surface tension and energy, contact angle, surface tension application—drops, bubbles, and capillary rise—all play a role. Heat, temperature, thermal expansion; calorimetry; change of state; specific heat capacity; latent heat. radiation, convection, and conduction of heat. The cooling law of Newton.

UNIT 8: THERMODYNAMICS
Thermal equilibrium, zeroth law of thermodynamics, the concept of temperature. Heat, work, and internal energy. The first law of thermodynamics. The second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency.

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 energy and temperature: RMS speed of gas molecules: Degrees of freedom. Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path. Avogadro’s number.

UNIT 10: OSCILLATIONS AND WAVES
Period, frequency, and displacement as a function of time define periodic motion. periodic activities. Energy in simple harmonic motion (S.H.M.) – Kinetic and potential energies; phase: oscillations of a spring -restoring force and force constant; Simple pendulum: formula for determining its period of time Resonance, forced, damped, and free oscillations. motion of waves. Wave speed, both transverse and longitudinal. Relation of displacement for a wave that is progressive. Wave superposition principle and wave reflection. Standing waves in harmonics, fundamental mode, and organ pipes. Beats. Doppler Sound effect

UNIT 11: ELECTROSTATICS
Charge conservation applies to electric charges. Coulomb’s law describes the forces that exist between two point charges, as well as the superposition principle and continuous charge dispersion between numerous charges.
Electricity domain: Point charge-induced electric field; electric field lines. electrical dipole A dipole’s electric field. torque in a consistent electric field applied to a dipole.
electrical flow. Gauss’s law and its applications to the determination of field caused by an evenly charged thin spherical shell, an indefinitely long straight wire, and a uniformly charged infinite flat sheet. The computation of electric potential for a point charge, an electric dipole, and a system of charges; surfaces equipotential, A system with two point charges in an electrostatic field has electrical potential energy.
insulators and conductors. Electric polarization and dielectrics, capacitors, and series combinations of capacitors

UNIT 12: CURRENT ELECTRICITY
Electric current. Drift velocity. Ohm’s law. Electrical resistance. Resistances of different materials. V-l characteristics of Ohmic and non-ohmic conductors. Electrical energy and power. Electrical resistivity. Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance.
Electric Cell and its 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. Potentiometer – principle and its applications.

UNIT 13: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM

The current-carrying circular loop and the application of Biot-Savart law. Ampere’s law and its applicability to infinitely long current carrying straight wire and solenoid. force in uniform electric and magnetic fields applied to a moving charge. cyclotron.
force in a homogeneous magnetic field on a conductor carrying electricity. The definition of an ampere is the force between two parallel currents carrying conductors. A current loop’s torque in a uniform magnetic field is measured using a moving coil galvanometer, which also converts to an ammeter and voltmeter based on its current sensitivity.
The magnetic dipole moment of the current loop as a dipole. The Earth’s magnetic field, magnetic elements, and bar magnets as analogous solenoids. Materials that are para-, dia-, and ferromagnetic. Permeability and susceptibility to magnetic fields. Hysteresis. Permanent magnets and electromagnets.

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: Quality factor, power in AC circuits, wattless current. AC generator and transformer.

UNIT 15: ELECTROMAGNETIC WAVES
Electromagnetic waves and their characteristics, Transverse nature of electromagnetic waves, Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet. X-rays. Gamma rays), Applications of e.m. waves.

UNIT 16: OPTICS
The mirror formula for light reflection and refraction on spherical and planar surfaces. Wholehearted introspection and its uses. Lens Formula: Deviation and Dispersion of Light by a Prism. Enlargement. The Strength of a Lens. combination of interconnected tiny lenses. The magnification abilities of an astronomical telescope and a microscope, both of which reflect and refractive.
Huygens’ principle and wavefront in wave optics. Huygens’ principle applied to the laws of reflection and refraction. Young’s double-slit experiment, fringe width, coherent sources, and continuous light interference are all examples of interference. Diffraction from a single slit, maximal width in the center. astronomy telescopes’ and microscopes’ resolution. Brewster’s law, polarization, plane-polarized light applications, 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. Davisson-Germer experiment.

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, isotopes, isobars: isotones. Radioactivity- alpha. beta and gamma particles/rays and their properties; radioactive decay law. 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: 1-V characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED. the photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor: transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR. AND. NOT. NAND and NOR). Transistor as a switch.

UNIT 20: COMMUNICATION SYSTEMS
Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation. Need for modulation. Amplitude and Frequency Modulation, Bandwidth of signals. the bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only).

UNIT 21: 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 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. Surf ace tension of water by capillary rise and effect of detergents,
7. Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body,
8. Plotting a cooling curve for the relationship between the temperature of a hot body and time. 9. Speed of sound in air at room temperature using a resonance tube,
10. Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.
11. The resistivity of the material of a given wire using a metre bridge.
12. The resistance of a given wire using Ohm’s law.
13. Potentiometer- i. Comparison of emf of two primary cells.
ii. Determination of internal resistance of a cell.
14. Resistance and figure of merit of a galvanometer by half deflection method.
15. The focal length of;
(i) Convex mirror
(ii) Concave mirror, and
(iii) Convex lens, using the parallax method
16. The plot of the angle of deviation vs angle of incidence for a triangular prism.
17. Refractive index of a glass slab using a travelling microscope.
18. Characteristic curves of a p-n junction diode in forward and reverse bias.
19. Characteristic curves of a Zener diode and finding reverse break down voltage.
20. Characteristic curves of a transistor and finding current gain and voltage gain.
21. Identification of Diode. LED, Transistor. IC. Resistor. A capacitor from a mixed collection of such items.
22. Using a multimeter to:
(i) Identify the base of a transistor
(ii) Distinguish between NPN and PNP type transistor
(iii) See the unidirectional current in case of a diode and an LED.
(iv) Check the correctness or otherwise of a given electronic component (diode, transistor, or IC).

PHYSICAL CHEMISTRY:

UNIT I: SOME BASIC CONCEPTS IN CHEMISTRY
Matter and its nature, Dalton’s atomic theory: Concept of atom, molecule, element, and compound: Physical quantities and their measurements in Chemistry, precision, and accuracy, significant figures. S.I.Units, dimensional analysis: Laws of chemical combination; Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae: Chemical equations and stoichiometry.

UNIT 2: STATES OF MATTER
Classification of matter into solid, liquid, and gaseous states.
Gaseous State:
Measurable properties of gases: Gas laws – Boyle’s law, Charle’s law. Graham’s law of diffusion. Avogadro’s law, Dalton’s law of partial pressure; Concept of Absolute scale of temperature; Ideal gas equation; Kinetic theory of gases (only postulates); Concept of average, root mean square and most probable velocities; Real gases, deviation from Ideal behaviour, compressibility factor, and van der Waals equation.
Liquid State:
Properties of liquids – vapour pressure, viscosity and surface tension, and effect of temperature on them (qualitative treatment only).
Solid State:
Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea); Bragg’s Law and its applications: Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, an imperfection in solids; Electrical and magnetic properties.
UNIT 3: ATOMIC STRUCTURE
The shortcomings of the Rutherford and Thomson atomic models; the photoelectric effect and the nature of electromagnetic radiation Atomic hydrogen’s spectrum. The postulates of the Bohr model of a hydrogen atom, the derivation of the relations for the energy of the electron and the radii of the various orbits, and the model’s constraints The duality of matter and the de Broglie connection. The principle of Heisenberg uncertainty. Concepts fundamental to quantum mechanics, quantum mechanical model of the atom, and key aspects of it. Atomic orbitals as one-electron wave functions conceptualization: Variation of and 2 with r for 1s and 2s orbitals; different quantum numbers and their meanings (principal, angular momentum, magnetic quantum numbers); orbitals, electron spin, and spin quantum number of the s, p, and d shapes: Guidelines for orbital electron filling the Aufbau principle. Electronic element configuration, Pauli’s exclusion principle, Hund’s rule, and additional stability of fully and partially filled orbitals.

UNIT 4: 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 5: CHEMICAL THERMODYNAMICS
Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, 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; S of the universe and G of the system as criteria for spontaneity. G (Standard Gibbs energy change) and equilibrium constant.

UNIT 6: SOLUTIONS
Several techniques to express the concentration of a solution include the vapour pressure of solutions, Raoult’s Law, molality, molarity, mole fraction, and percentage (by both volume and mass). Plots for ideal and nonideal solutions, composition of vapour pressure, ideal and nonideal solutions; Colligative features of diluted solutions include an increase in boiling point, a decrease in freezing point, a relative decrease in vapour pressure, and an increase in osmotic pressure; molecular mass calculation based on colligative characteristics; The van’t Hoff factor, abnormal molar mass, and its importance.

UNIT 7: EQUILIBRIUM
Definition of dynamic equilibrium and equilibrium.
Henry’s law and the solid-liquid, liquid-gas, and solid-gas equilibria are examples of equilibrium involving physical processes. general properties of physical processes-based equilibrium.
equilibrium pertaining to chemical reactions: Chemical equilibrium law, equilibrium constants (Kp and Kc) and their importance, the role of G and G in chemical equilibrium, temperature, pressure, and catalyst impact, as well as Le Chatelier’s principle, are all discussed.
Ionic equilibrium includes the following topics: ionization of water, ionization of weak and strong electrolytes, ionization of electrolytes, and different ideas of acids and bases (Arrhenius, Bronsted, Lowry, and Lewis) and their ionization. The solubility of salts and their products that are sparingly soluble, buffer solutions, the common ion effect, the hydrolysis of salts and pH of their solutions, among other things.

UNIT 8: REDOX REACTIONS AND ELECTROCHEMISTRY
Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, 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 9: 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 bimolecular gaseous reactions (no derivation).

UNIT 10: SURFACE CHEMISTRY
Adsorption- Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids – Freundlich and Langmuir adsorption isotherms, adsorption from solutions.
Catalysis – Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis, and its mechanism.
Colloidal state- distinction among true solutions, colloids, and suspensions, classification of colloids – lyophilic. lyophobic; multi-molecular. macromolecular and associated colloids (micelles), preparation and properties of colloids – Tyndall effect. Brownian movement, electrophoresis, dialysis, coagulation, and flocculation: Emulsions and their characteristics.

INORGANIC CHEMISTRY

UNIT 11: CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES
Modem 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 12: GENERAL PRINCIPLES AND PROCESSES OF ISOLATION OF METALS
Modes of occurrence of elements in nature, minerals, ores; Steps involved in the extraction of metals – concentration, reduction (chemical and electrolytic methods), and refining with special reference to the extraction of Al. Cu, Zn, and Fe; Thermodynamic and electrochemical principles involved in the extraction of metals.

UNIT 13: HYDROGEN
Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen; Physical and chemical properties of water and heavy water; Structure, preparation, reactions, and uses of hydrogen peroxide; Classification of hydrides – ionic, covalent, and interstitial; Hydrogen as a fuel.

UNIT 14: S -BLOCK ELEMENTS (ALKALI AND ALKALINE EARTH METALS)
Group -1 and 2 Elements
General introduction, electronic configuration, and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships.
Preparation and properties of some important compounds – sodium carbonate and sodium hydroxide and sodium hydrogen carbonate; Industrial uses of lime, limestone. Plaster of Paris and cement: Biological significance of Na, K. Mg, and Ca.

UNIT 15: 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.
Groupwise study of the p – block elements Group -13
Preparation, properties, and uses of boron and aluminum; Structure, properties, and uses of borax, boric acid, diborane, boron trifluoride, aluminum chloride, and alums.
Group -14
The tendency for catenation; Structure, properties, and uses of Allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites, and silicones.
Group -15
Properties and uses of nitrogen and phosphorus; Allotrophic forms of phosphorus; Preparation, properties, structure, and uses of ammonia, nitric acid, phosphine, and phosphorus halides, (PCl3. PCl5); Structures of oxides and oxoacids of nitrogen and phosphorus.
Group -16
Preparation, properties, structures, and uses of ozone: Allotropic forms of sulphur; Preparation, properties, structures, and uses of sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur.
Group-17
Preparation, properties, and uses of hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens.
Group-18 
Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon.

UNIT 16: 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 17: CO-ORDINATION 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 co-ordination compounds (in qualitative analysis, extraction of metals and in biological systems).

UNIT 18: ENVIRONMENTAL CHEMISTRY
Pollution of the soil, water, and atmosphere.
Tropospheric and stratospheric pollution of the atmosphere
Gaseous pollutants in the troposphere, including hydrocarbons, nitrogen, sulfur, and carbon oxides; their sources, detrimental effects, and mitigation Global warming and the greenhouse effect: acid rain
Particulate pollution: the causes, detrimental effects, and prevention of smoke, dust, smog, fumes, and mist.
The mechanism and effects of stratospheric pollution include ozone formation and breakdown as well as ozone layer depletion.
Water pollution: negative effects and prevention of major pollutants such diseases, organic wastes, and chemical pollutants.
Major pollutants including pesticides (herbicides, fungicides, and insecticides), their deleterious effects, and prevention are examples of soil pollution. Techniques for reducing pollution in the environment.

ORGANIC CHEMISTRY:

UNIT 19: 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, phosphorus.
Calculations of empirical formulae and molecular formulae: Numerical problems in organic quantitative analysis,

UNIT 20: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 21: 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 monosubstituted benzene.

UNIT 22: 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 23: 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 24: 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 25: POLYMERS
General introduction and classification of polymers, general methods of polymerization, – Addition and condensation, copolymerization.
Natural and synthetic, rubber and vulcanization, some important polymers with emphasis on their monomers and uses – polythene, nylon, polyester, and bakelite.

UNIT 26: 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.

UNIT 27: CHEMISTRY IN EVERYDAY LIFE 
Chemicals in Medicines – Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, anti-fertility drugs, antibiotics, antacids. Anti-histamines -their meaning and common examples.
Chemicals in food – Preservatives, artificial sweetening agents – common examples.
Cleansing Agents – Soaps and detergents, cleansing action

UNIT 28: 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+
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) 2023 Paper-2A Exam (B.Arch) – Mathematics:

UNIT 1: SETS, RELATIONS, AND FUNCTIONS:

Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, 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 number, modulus and argument (or amplitude) of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions Relations between roots and co-efficient, nature of roots, the formation of quadratic equations with given roots.

UNIT 3: MATRICES AND DETERMINANTS:
Matrices, algebra of matrices, type of matrices, determinants, and matrices of order two and three, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint, and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

UNIT4:PERMUTATIONS AND COMBINATIONS:
The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications.

UNIT 5: MATHEMATICAL INDUCTIONS:
Principle of Mathematical Induction and its simple applications.

UNIT 6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients, and simple applications.

UNIT 7: SEQUENCE AND SERIES:
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression.

UNIT 8: LIMIT, CONTINUITY, AND DIFFERENTIABILITY:
Inverse functions, polynomials, rational, trigonometric, logarithmic, exponential, and real-valued functions are all included in the algebra of functions. Simple function graphs. boundaries, consistency, and uniqueness. differentiation of two functions’ product, quotient, difference, and sum. Differentiation of logarithmic, exponential, composite, implicit, inverse, and trigonometric functions; derivatives up to order two; Rolle’s and Lagrange’s Average amount Theorems and Derivative Applications: Rate of monotonic quantity changeFunctions that increase and decrease, maxima and minima of tangents, normal, and functions of a single variable.

UNIT 9: INTEGRAL CALCULAS:
Integral as an anti-derivative, Fundamental Integrals involving algebraic, trigonometric, exponential, and logarithms functions. Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities. Integral as limit of a sum. The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

UNIT 10: DIFFRENTIAL EQUATIONS
Ordinary differential equations, their order, and degree, the formation of differential equations, solution of differential equation by the method of separation of variables, solution of a homogeneous and linear differential equation of the type

dy/dx+𝑝(𝑥)𝑦 = 𝑞(𝑥)

UNIT11: CO-ORDINATE GEOMETRY
Cartesian system of rectangular coordinates 10 in a plane, distance formula, sections formula, locus, and its equation, translation of axis, slop of a line, parallel and perpendicular lines, intercept of a line on the co-ordinate axes.
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, equations of internal and external by sectors of angles between two lines co-ordinate of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.
Circle, conic sections
A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, 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 condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for Y = mx + c to be a tangent and point (s) of tangency.

UNIT12: THREE DIMENSIONAL GEOMETRY
Coordinates of a point in space, the distance between two points, section formula, directions ratios, direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them, and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

UNIT 13: VECTOR ALGEBRA
Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product.

UNIT 14: STATISTICS AND PROBABILITY
Measures of discretion; 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 variate, Bernoulli trials, and binomial distribution.

UNIT 15: TRIGONOMETRY
Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions, and their properties, heights, and distance.

UNIT 16: MATHEMATICAL REASONING
Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse, and contrapositive.

Part –II APTITUDE TEST

UNIT – 1 Awareness of persons. Buildings, Materials
Objects, Texture related to Architecture and Build-envirounmentVisusalising threedimensional objects from two-dimensional drawings. Visualizing. Different sides of threedimensional 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) 2023 Paper-2B Exam (B.Planning) – Mathematics:

UNIT1: SETS, RELATIONS, AND FUNCTIONS:
Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.

UNIT2: 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 number, modulus and argument (or amplitude) of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions Relations between roots and co-efficient, nature of roots, the formation of quadratic equations with given roots.

UNIT 3: MATRICES AND DETERMINANTS:
Matrices, algebra of matrices, type of matrices, determinants, and matrices of order two and three, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint, and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

UNIT4: PERMUTATIONS AND COMBINATIONS:
The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications.

UNIT 5: MATHEMATICAL INDUCTIONS:
Principle of Mathematical Induction and its simple applications.

UNIT 6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients, and simple applications.

UNIT 7: SEQUENCE AND SERIES:
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression.

UNIT 8: LIMIT, CONTINUITY, AND DIFFERENTIABILITY:
Inverse functions, polynomials, rational, trigonometric, logarithmic, exponential, and real-valued functions are all included in the algebra of functions. Simple function graphs. Differentiability, continuity, and limits. differentiation of two functions’ product, quotient, difference, and sum. Differentiation of logarithmic, exponential, composite, implicit, inverse, and trigonometric functions; derivatives up to order two; Rolle’s and Lagrange’s Average amount Theorems and Derivative Applications: Rate of monotonic quantity change Functions that increase and decrease, maxima and minima of tangents, normal, and functions of a single variable.

UNIT 9: INTEGRAL CALCULAS:
Integral as an anti-derivative, Fundamental Integrals involving algebraic, trigonometric, exponential, and logarithms functions. Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities. Integral as limit of a sum. The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

UNIT 10: DIFFRENTIAL EQUATIONS
Ordinary differential equations, their order, and degree, the formation of differential equations, solution of differential equation by the method of separation of variables, solution of a homogeneous and linear differential equation of the type

dy/dx+𝑝(𝑥)𝑦 = 𝑞(𝑥)

UNIT 11: CO-ORDINATE GEOMETRY
Cartesian system of rectangular coordinates 10 in a plane, distance formula, sections formula, locus, and its equation, translation of axis, slop of a line, parallel and perpendicular lines, intercept of a line on the co-ordinate axes.
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, equations of internal and external by sectors of angles between two lines co-ordinate of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.
Circle, conic sections
A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, 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 condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency.

UNIT 12:THREE DIMENSIONAL GEOMETRY
Coordinates of a point in space, the distance between two points, section formula, directions ratios, direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them, and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, and coplanar lines.

UNIT 13: VECTOR ALGEBRA
Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products, scalar and vector triple product.

UNIT 14: STATISTICS AND PROBABILITY
Measures of discretion; 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 variate, Bernoulli trials, and binomial distribution.

UNIT 15: TRIGONOMETRY
Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions, and their properties, heights, and distance.

UNIT 16: MATHEMATICAL REASONING
Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse, and contrapositive.

APTITUDE TEST:

UNIT-1 Awareness of persons. Buildings, Materials.
Objects, Texture related to Architecture and Build-envirounmentVisusalising threedimensional objects from two-dimensional drawings. Visualizing. Different sides of threedimensional 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 Plan, elevations and 3D views of objects, Creating two-dimensional and three-dimensional compositions using given shapes and forms.

PLANNING:

UNIT-1 GENERAL AWARENESS
General knowledge questions and knowledge about prominent cities, development issues, government programs, etc.

UNIT-2 SOCIAL SCIENCES
The idea of nationalism, nationalism in India, pre-modern world, 19th-century global economy, colonialism, and colonial cities, industrialization, resources, and development, types of resources, agriculture, water, mineral resources, industries, national economy; Human Settlements
Power-sharing, federalism, political parties, democracy, the constitution of India
Economic development- economic sectors, globalization, the concept of development, poverty; Population structure, social exclusion, and inequality, urbanization, rural development, colonial cities,

UNIT-3 THINKING SKILLS
Comprehension (unseen passage); map reading skills, scale, distance, direction, area, etc.; critical reasoning; understanding of charts, graphs, and tables; basic concepts of statistics and quantitative reasoning

 

Click here for JEE (Main) Exam 2023 Complete Syllabus