JEE Main Syllabus 2021: Subject-wise Syllabus for B.Tech, B.Arch and B.Plan Papers

Will NTA Reduce JEE Main 2021 Syllabus?

Lockdown situation due to the outbreak of COVID-19 has led to the delay in events of JEE Main 2020 session. This has created pressure among the JEE main 2021 session aspirants, hence they have demanded a reduction in the JEE Main 2021 syllabus.

• Yet there is no clarification by NTA regarding this. But a possibility of a reduction in JEE Main 2021 Syllabus is speculated. Director-General of NTA and Education Minister has hinted towards the reduction of JEE Main 2021 Syllabus.
• As preparation time has reduced for JEE Main 2021 aspirants, NTA might consider the point of reducing JEE Main 2021 Syllabus.
• JEE Main Syllabus is mostly prescribed from science subjects of class 11th & 12th. CBSE has already reduced class XI and XII syllabus by 30%. Therefore, the chances of reduction in JEE Main syllabus for 2021 has also increased.
• It is advisable that aspirants should keep preparing and not halt their preparation until the further update by NTA. Read JEE Main Preparation Tips.

• Matter and its nature

• Dalton’s Atomic Theory

• Concept of atom, molecule, element and compound

• Physical Quantities, SI Units, Atomic and molecular mass

• Laws of Chemical Combination, Chemical Equation and Stoichiometry

• Gaseous State – Measurable properties, Gas Laws, Kinetic theory of gases, Ideal Gas Equation, Van der Waals Equation and more

• Liquid State – Properties of liquids Vapor pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only)

• Solid State – Classification; Bragg’s Law; Unit cell and lattices; Electrical and Magnetic Properties

• Thomson and Rutherford Atomic Models

• Bohr Model of Hydrogen atom

• Dual Nature of Matter, De-Broglie Relationship, Heisenberg Uncertainty Principle

• Pauli’s Exclusion Principle and Hund’s Rule

• Shapes of s, p and d orbitals

• Kossel – Lewis Approach to Chemical Bond Formation

• Ionic Bonding

• Covalent Bonding

• Quantum Mechanical Approach to Covalent Bonding

• Molecular Orbital Theory

• Fundamentals of thermodynamics, System and surroundings, Extensive and Intensive Properties State Functions, Types of Processes

• 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, etc.

• Second Law of Thermodynamics – Spontaneity of Processes;
• ∆S of the universe and ∆G as the criteria for spontaneity

• Different methods for expressing concentration of solution – molality, molarity, mole fraction,
• Percentage by volume and mass both, vapour pressure of solutions and
• Raoult’s Law – ideal and no ideal solutions, vapor pressure

• Colligative properties of dilute solutions,
• Relative lowering of vapor pressure, depression of freezing point,
• Elevation of boiling of boiling point and osmotic pressure

• Determination of molecular mass using colligative properties,
• Abnormal value of molar mass,
• Van Hoff Factor and its significance

• Meaning of Equilibrium, Concept of dynamic equilibrium

• Equilibria involving Physical Processes – Law of Chemical Equilibrium,
• Equilibrium constants (Kp and Kc) and their significance,
• Significance of ∆G and ∆G° in chemical equilibria,
• Factors affecting equilibrium concentrations, pressure, temperature effect of catalyst;
• Le Chatelier’s principle.

• Equilibria involving Physical Processes – solid-liquid, liquid-gas and solid-gas equilibria,
• Henry’s Law, General characteristics of equilibrium involving physical processes.

• 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 multi stage ionization) and ionization constants,
• Ionization of water, pH scale, common ion effect,
• Hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products and buffer solutions.

• Electrical concepts of oxidation and reductions, 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,
• Koulrausch’s Law and its applications

• Electrochemical Cells – Electrolytic and Galvanic Cells, different types of electrodes, electrode potentials,
• Half-cell and cell reactions, emf of a galvanic cell and its measurement

• Nernst equation and its applications

• Rate of a chemical reaction, factors affecting the rate of reactions

• 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).

• Adsorption: Physisorption and chemisorption and their characteristics,
• Factors affecting the 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.

• Multimolecular, macromolecular and associated colloids (micelles), preparation and properties of colloids
• Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation, and flocculation.
• Emulsions and their characteristics.

• 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.

• Electrons gain enthalpy, valence, oxidation states and chemical reactivity.

• Steps involved in the extraction of metals
• Concentration, reduction (chemical and electrolytic methods) and refining
• Special reference to the extraction of Al, Cu, Zn, and Fe.

• Modes of occurrence of elements in nature, minerals, ores.

• Thermodynamic and electrochemical principles involved in the extraction of metals.

• The position of hydrogen in periodic table, isotopes, preparation, properties, and uses of hydrogen.

• Structure, preparation, reactions, and uses of hydrogen peroxide.

• Physical and chemical properties of water and heavy water.

• Hydrogen as a fuel

• Classification of hydrides: ionic, covalent and interstitial.

• Group 1 and Group 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, sodium chloride, sodium hydroxide and sodium hydrogen carbonate.

• Industrial uses of lime, limestone, Plaster of Paris and cement.

• The biological significance of Na, K, Mg and Ca.

• Group 13
• Preparations and properties of Boron and aluminium;
• Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride, alums.

• Group 14
• 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;
• Allotropic forms of Phosphorus;
• Preparation, properties, structure and uses of ammonia, nitric acid, phosphine halides, (PCLჳ, PCLཏ);
• Structures of oxides and oxoacids of nitrogen and phosphorus

• Group 16
• Preparation, properties, structures and uses of ozone;
• Allotropic forms of sulphur;
• Preparation, properties, structure 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;
• Structure of interhalogen compounds and oxides and oxoacids of halogens

• Group 18
• Occurrence and uses of noble gases;
• Structures of Fluorides and oxides of xenon

• 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: Lanthanides, Electronic configuration, oxidation states, chemical reactivity and lanthanide contraction, and
• Actinoids: Electronic configuration and oxidation states.

• Introduction to coordination compounds,
• Werner’s theory.

• ligands, coordination number, denticity, chelation.
• IUPAC nomenclature of mononuclear coordination compounds, isomerism.

• Bonding-Valence bond approach
• Basic ideas of Crystal field theory, colour and magnetic properties.

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

• Environmental pollution: Atmospheric, water, and soil.

• Atmospheric pollution: Tropospheric and stratospheric.

• Gaseous pollutants: Oxides of carbon, nitrogen, and sulfur, hydrocarbons;
• Their sources, harmful effects, and prevention.

• Greenhouse effect and Global warming, acid rain.

• Particulate pollutants: Smoke, dust, smog, fumes, mist;
• Their sources, harmful effects, and prevention.
• Stratospheric pollution: Formation and breakdown of ozone, depletion of ozone layer, its mechanism and effects.
• Water Pollution: Major pollutants such as pathogens, organic wastes, and chemical pollutants;
• Their harmful effects and prevention.

• Soil pollution: Major pollutants such as Pesticides (insecticides, herbicides and fungicides)
• Their harmful effects and prevention.
• Strategies to control environmental pollution.

• Purification – Crystallization, sublimation, distillation, differential extraction, and
• Chromatography principles and their applications.

• Qualitative Analysis – Detection of nitrogen, sulfur, phosphorus, and halogens.

• Quantitative Analysis (basic principles only) –
• Estimation of carbon, hydrogen, nitrogens, halogens, sulphur and phosphorus

• Calculations of Empirical and Molecular Formulae;
• Numerical Problems in organic quantitative analysis

• Tetravalency of Carbon, Shapes of simple molecules – hybridization (s and p)

• Classification of organic compounds based on functional groups: -C = C- and those containing halogens, oxygen, nitrogen, and sulfur;
• Homologous series.

• Isomerism – structural and stereoisomerism

• Nomenclature – 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 directions: Substitution, addition, elimination and rearrangement.

• 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 (Markownikoff’s and peroxide effect);
• Ozonolysis, oxidation, and polymerization.

• Alkynes – Acidic character;
• Addition of hydrogen, halogens, water and hydrogen halides;
• Polymerization.

• Aromatic Hydrocarbons – Nomenclature, Benzene Structure and Atomicity

• Mechanism of electrophilic substitution – halogenation, nitration,
• Friedel Crafts alkylation and acylation,
• Directive influence of the functional group in monosubstituted benzene.

• 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

• General methods of preparation, properties, reactions and uses

• Alcohol – Identification of primary, secondary and tertiary alcohols;
• Mechanism of dehydration.

• Phenols – Acidic nature, electrophilic substitution reactions
• Halogenation, nitration, and sulphonation,
• Reimer Tiemann reaction.

• Ethers – Structures

• 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 (Wolff Kishner and Clemmensen);
• The acidity of hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction.

• Chemical Tests to distinguish between aldehydes and ketones.

• Carboxylic Acid – Acidic strength and factors affecting it.

• 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.

• General Introduction and classification of polymers,
• General methods of polymerization, addition and condensation, co-polymerization

• Natural and synthetic rubber and vulcanization

• Some important polymers with emphasis on monomers and uses

• Polyethene, nylon, polyester, and bakelite.

• General Introduction and importance of biomolecules

• Carbohydrates – Classification: aldoses and ketoses;
• Monosaccharides (glucose and fructose), constituent monosaccharides or oligosaccharides (sucrose, lactose, maltose) and polysaccharides (starch, cellulose, glycogen).

• 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

• B Chemical Constitution of DNA and RNA, Biological Functions of Nuclei Acids

• Chemicals in medicines: Analgesics, tranquillizers, antiseptics, disinfectants, antimicrobials,
• Antifertility drugs, antibiotics, antacids, antihistamines, their meaning and common examples.

• Chemicals in food: Preservatives, artificial sweetening agents common examples.

• Cleansing Agents – Soaps and detergents, cleansing action

• Detection of extra elements (N, S, halogens) in organic compounds.

• Detection of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl and amino groups in organic compounds.

• The chemistry involved in the preparation of the following:
• Inorganic compounds
• Mohr’s salt, potash alum, and 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+, AI3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH4+, and
• Anions: CO32-, S2-, SO42-, NO2-, NO3-, CI-, Br, I. (Insoluble salts excluded).

• Chemical principles involved in the following experiments: Enthalpy of solution of CuSO4, Enthalpy of neutralization of strong acid and strong base,
• Preparation of lyophilic and lyophobic sols, and Kinetic study of the reaction of iodide ion with hydrogen peroxide at room temperature.

• Physics, Technology and society, S.I. units,

• Fundamental and derived units.

• Least count, accuracy and precision of measuring instruments, Errors in measurement,

• Dimensions of Physical quantities, dimensional analysis and its applications

• 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 graphs, 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

• 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,

• Work done by a constant force and a variable force; Kinetic and potential energies, Work-Energy theorem

• Power

• Potential energy of a spring, Conservation of mechanical energy, Conservative and nonconservative forces;

• Elastic and inelastic collisions in one and two dimensions.

• 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

• Moment of inertia, 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

• The Universal law of gravitation

• Acceleration due to gravity and its variation with altitude and depth
• Kepler’s laws of planetary motion

• Gravitational potential energy; gravitational potential.

• Escape velocity.

• Orbital velocity of a satellite. Geostationary satellites.

• Elastic behaviour, Stress-strain relationship,
• Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity.
• Pressure due to a fluid column

• Pascal’s law and its applications

• Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow,
• Reynolds number

• Bernoulli’s principle and its applications

• Surface energy and surface tension, angle of contact, 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, Newton’s law of cooling

• Thermal equilibrium, zeroth law of thermodynamics, concept of temperature

• Heat, work and internal energy

• First law of thermodynamics

• The second law of thermodynamics: reversible and irreversible processes

• Carnot engine and its efficiency

• Equation of state of a perfect gas, work done on compressing a gas.

• Kinetic theory of gases -assumptions, 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

• Periodic motion – 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

• Free, forced and damped oscillations,

• Resonance

• Wave motion

• Longitudinal and transverse waves, speed of a 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, Doppler effect in sound

• 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.

• Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field.

• Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel,
• Capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor.

• Electric current, Drift velocity, Ohm’s law, Electrical resistance,
• Resistances of different materials, V-I 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, combination of cells in series and in parallel

• Kirchhoff’s laws and their applications

• Wheatstone bridge, Metre bridge

• Potentiometer – principle and its applications.

• Biot – Savart law and its application to 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.

• Cyclotron

• Force on a current-carrying conductor in a uniform magnetic field.
• Force between two parallel current-carrying conductors-definition of ampere,
• Torque experienced by a current loop in uniform magnetic field

• Moving coil galvanometer, its current 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;
• Earth’s magnetic field and magnetic elements.

• Para-, dia-, and ferro- magnetic substances.

• Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.

• 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.

• 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.

• Reflection and refraction of light at plane and spherical surfaces, mirror formula,
• Total internal reflection and its applications,

• Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens,
• Combination of thin lenses in contact, 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.
• Resolving power of microscopes and astronomical telescopes,
• Polarisation, plane polarized light

• Brewster’s law, uses of plane polarized light and Polaroids.

• Dual nature of radiation

• Photoelectric effect,
• Hertz and Lenard’s observations

• Einstein’s photoelectric equation

• Particle nature of light

• Matter waves-wave nature of the particle, de Broglie relation.

• Davis son-Germer experiment.

• Alpha-particle scattering experiment

• Rutherford’s model of the atom

• Bohr model, energy levels, hydrogen spectrum

• Composition and size of the nucleus, atomic masses, isotopes, isobars, and 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.

• Semiconductors

• Semiconductor diode: I-V characteristics in forward and reverse bias

• Diode as a rectifier

• 1-V characteristics of LED, 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

• Propagation of electromagnetic waves in the atmosphere

• Sky and space wave propagation, Need for modulation,
• Amplitude and Frequency Modulation, Bandwidth of signals,
• Bandwidth of Transmission medium,

• Basic Elements of a Communication System (Block Diagram only).

• Sets and their representation

• Union, intersection and complement of sets and their algebraic properties

• Power set

• Relation, Types of relations, equivalence relations, functions

• One-one, into and onto functions, composition of functions

• 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, square root of a complex number.

• Triangle inequality.

• Quadratic equations in real and complex number systems and their solutions.

• The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

• Algebra of matrices, types of matrices, and matrices of order two and three.

• Properties of determinants, evaluation of determinants, the 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

• The fundamental principle of counting.

• Permutation as an arrangement and combination as a selection.

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

• The principle of Mathematical Induction and its simple applications.

• Binomial theorem for a positive integral index.

• General term and middle term.

• Properties of Binomial coefficients and simple applications.

• Arithmetic and Geometric progressions, insertion of arithmetic.

• Geometric means between two given numbers.

• The relation between A.M. and G.M.

• Sum up to n terms of special series: Sn, Sn2, Sn3

• Arithmetic – Geometric progression.

• Real-valued functions, algebra of functions, polynomials, 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 up to two.

• Rolle’s and Lagrange’s Mean Value Theorems.

• Rate of change of quantities, monotonic – increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normals

• Integral as an antiderivative.

• Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.

• Integration by substitution, by parts, and by partial fractions.

• Integration using trigonometric identities.

• Integral as limit of a sum.

• Simple Integrals, Fundamental Theorem of Calculus.
• Properties of definite integrals, evaluation of definite integrals,
• Determining areas of the regions bounded by simple curves in standard form

• Ordinary differential equations, their order, and degree.

• Formation of differential equations.

• The solution of differential equations by the method of separation of variables.

• The solution of homogeneous and linear differential equations of the type.

• Cartesian system of rectangular coordinates in a plane, distance formula, section formula,
• Locus and its equation, translation of axes, the slope of a line,
• Parallel and perpendicular lines, intercepts of a line on the coordinate axes.

• Straight lines

• The distance of a point from a line, equations of internal and external bisectors of angles between two lines,
• Coordinates of the centroid, orthocentre, and circumcentre of a triangle,
• Equation of the family of lines passing through the point of intersection of two lines.

• Circles, conic sections: Standard form of equation of a circle, a 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
• Circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent.

• Sections of cones, 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.

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

• Section formula, direction 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.

• Vectors and scalar

• Components of a vector in two dimensions and three-dimensional space.

• Scalar and vector products

• 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,
• Bayes theorem, probability distribution of a random variate,
• Bernoulli trials and Binomial distribution.

• Trigonometric identities and equations.

• Trigonometric functions.

• Inverse trigonometric functions and their properties.

• Heights and Distances

• Statements, logical operations and, or, implies, implied by, if and only if.

• Understanding of tautology, contradiction, converse, and contrapositive

• Awareness of Places, Persons, Building and Materials Texture and Objects related to Architecture
• 3D- Perception and Appreciation of scale and proportion of Objects

• Visualizing 3D Objects from 2D drawings

• Visualizing different sides of 3D objects

• Mental Ability

• Analytical reasoning and Colour texture