AMU Entrance Exam 2026: Answer Key (Out), Result, Admission Process

Chemistry-Class-XI: Unit 01

• General introduction: Importance and scope of chemistry
• Historical approach to particulate nature of matter, laws of chemical combination, Dalton’s atomic theory: Concept of elements, atoms and molecules
• Atomic and molecular masses
• Mole concept and molar mass; percentage composition and empirical and molecular formula; chemical reactions, stoichiometry and calculations based on stoichiometry

Chemistry-Class-XI: Unit 02

• Discovery of electron, proton and neutron; atomic number, isotopes and isobars
• Thompson’s model and its limitations, Rutherford’s model and its limitations, Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, De Broglie’s relationship, Heisenberg uncertainty principle
• Concept of orbitals, quantum numbers, shapes of s, p, and d orbitals, rules for filling electrons in orbitals Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms
• Stability of half filled and completely filled orbitals

Chemistry-Class-XI: Unit 03

• Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements-atomic radii, ionic radii, inert gas radii, ionization enthalpy
• Periodic trends in properties of elements-electron gain enthalpy, electronegativity, valence, nomenclature of elements with atomic number greater than 100

Chemistry-Class-XI: Unit 04

• Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory
• Concept of hybridization involving s, p, and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules (qualitative idea only)
• Hydrogen bond

Chemistry-Class-XI: Unit 05

• Three states of matter, intermolecular interactions, types of bonding, melting and boiling points, role of gas laws in elucidating the concept of the molecule, Boyle’s law, Charle’s law, Gay Lussac’s law, Avogadro’s law, ideal behaviour
• Empirical derivation of gas equation, Avogadro number, ideal gas equation
• Deviation from ideal behaviour, liquefaction of gases, critical temperature, kinetic energy and molecular speeds (elementary idea)
• Liquid state-vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations)

Chemistry-Class-XI: Unit 06

• Concepts of system, types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions
• First law of thermodynamics-internal energy and enthalpy, heat capacity and specific heat, measurement of ∆U and ∆H, Hess’s law of constant heat summation, enthalpy of: Bond dissociation, combustion, formation, atomization, sublimation
• Enthalpy of: Phase transition, ionization, solution and dilution
• Introduction of entropy as a state function, second law of thermodynamics, Gibbs energy change for spontaneous and non-spontaneous process, criteria for equilibrium

Chemistry-Class-XI: Unit 07

• Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium-Le Chatelier’s principle; ionic equilibrium-ionization of acids and bases, strong and weak electrolytes
• Degree of ionization, ionization of polybasic acids, acid strength, concept of pH, hydrolysis of salts (elementary idea), 4 buffer solutions, Henderson equation, solubility product, common ion effect (with illustrative examples)
• Redox reactions: Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions in terms of loss and gain of electron and change in oxidation numbers, applications of redox reactions

Chemistry-Class-XI: Unit 08

• Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides-ionic, covalent and interstitial; physical and chemical properties of water, heavy water, hydrogen peroxide-preparation, reactions
• Hydrogen peroxide-use and structure; hydrogen as a fuel

Chemistry-Class-XI: Unit 09

• Group 1 and group 2 elements: General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship
• Group 1 and group 2 elements: Trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses
• Preparation and properties of some important compounds: Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogencarbonate, biological importance of sodium and potassium
• CaO, CaCO, and industrial use of lime and limestone, biological importance of Mg and Ca

Chemistry-Class-XI: Unit 10

• General Introduction to p-block elements
• Group 13 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; boron-physical and chemical properties
• Group 13 elements: Boron-some important compounds; borax, boric acids, boron hydrides. Aluminium: uses, reactions with acids and alkalies.
• Group 14 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous beheaviour of first element. Carbon-catenation, allotropic forms
• Group 14 elements: Carbon-physical and chemical properties; uses of some important compounds: oxides

Chemistry-Class-XI: Unit 11

• General introduction, methods of purification, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds
• Electronic displacements in a covalent bond: Inductive effect, electrometric effect, resonance and hyper conjugation
• Homolytic and heterolytic fission of a covalent bond: Free radicals, carbocations, carbonions; electrophiles and nucleophiles, types of organic reactions

Chemistry-Class-XI: Unit 12

• Classification of Hydrocarbons
• Aliphatic hydrocarbons: Alkanes-nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis
• Aliphatic hydrocarbons: Alkenes-nomenclature, structure of double bond (ethane), geometrical isomerism, physical properties, methods of preparation; chemical reactions: Addition of hydrogen, halogen, water
• Aliphatic hydrocarbons: Alkenes-chemical reactions: Hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition
• Aliphatic hydrocarbons: Alkynes-nomenclature, structure of triple bond (ethyne), physical properties, methods of preparation, chemical reactions: Acidic character of alkynes, addition reaction of-hydrogen, halogens, hydrogen halides and water
• Aromatic hydrocarbons: Introduction, IUPAC nomenclature; benzene: Resonance, aromaticity; chemical properties: Mechanism of electrophilic substitution-nitration sulphonation, halogenation, Friedel Craft’s alkylation and acylation
• Aromatic hydrocarbons: Directive influence of functional group in mon-substituted benzene; carcinogenicity and toxicity

Chemistry-Class-XI: Unit 13

• Environmental pollution-air, water and soil pollution, chemical reactions in atmosphere, smogs, major atmospheric pollutants; acid rain, ozone and its reactions, effects of depletion of ozone layer
• Greenhouse effect and global warming-pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution

Chemistry-Class-XII: Unit 01

• Classificatioin of solids based on different binding forces molecular, ionic covalent and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices
• Calculations of density of unit cell, packing in solids, packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects electrical and magnetic properties, band theory of metals, conductors
• Semiconductors and insulators and n and p type semiconductors

Chemistry-Class-XII: Unit 02

• Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties-relative lowering of vapour pressure, Raoult’s law, elevation of B.P., depression of freezing point
• Osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, Vant Hoff factor

Chemistry-Class-XII: Unit 03

• Redox reactions; conductance in electrylytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea)
• Dry cell electrolytic cells and galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells. Relation between Gibbs energy change and EMF of a cell, fuel cells; corrosion

Chemistry-Class-XII: Unit 04

• Rate of a reaction (average and instantaneous), factors affecting rates of reaction: Concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant
• Integrated rate equations and half life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment)
• Activation energy, Arrhenious equation

Chemistry-Class-XII: Unit 05

• Adsorption-physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis thomogenous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: distinction between true solutions, colloids and suspensions
• Lyophillic, lyophobic multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsions – types of emulsions

Chemistry-Class-XII: Unit 06

• Principles and methods of extraction-concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron

Chemistry-Class-XII: Unit 07

• Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen-preparation, properties and uses
• Group 15 elements: Compounds of nitrogen-preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); phosophorous-allotropic forms
• Group 15 elements: Compounds of phosphorous-preparation and properties of phosphine, halides (PCI, PCI) and oxoacids (elementary idea only)
• Group 16 elements: General introduction, electronic configuration, oxidationi states, occurrence, trends in physical and chemical properties; dioxygen: Preparation, properties and uses; classification of oxides; ozone. Sulphur-allotropic forms
• Group 16 elements: Sulphur-compounds of sulphur: Preparation, properties and uses of sulphur dioxide; sulphuric acid: Industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only)
• Group 17 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: Preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds
• Group 17 elements: Compounds of halogens-oxoacids of halogens (structures only)
• Group 18 elements: General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses, compounds of xenon and their structure

Chemistry-Class-XII: Unit 08

• General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals-metallic character, ionization enthalpy, oxidation states, ionic radii, colour
• General trends in properties of the first row transition metals-catalytic property, magnetic properties, interstitial compounds, alloy formation
• Preparation and properties of KCrO and KMnO
• Lanthanoids-electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences
• Actinoids-electronic configuration, oxidation states and comparison with lanthenoids

Chemistry-Class-XII: Unit 09

• Coordination compounds: Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, bonding, Werner’s theory VBT, CFT
• Coordination compounds: Isomerism (structural and stereo) importance of coordination compounds (in qualitative inclusion, extraction of metals and biological systems)

Chemistry-Class-XII: Unit 10

• Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions. Optical rotation
• Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only)
• Uses and environmental effects of-dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT

Chemistry-Class-XII: Unit 11

• Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses, with special reference to methanol and ethanol
• Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reaction, uses of phenols
• Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses

Chemistry-Class-XII: Unit 12

• Aldehydes and ketones: Nomenclature, nature of carbonyl group, method of preparation, physical and chemical properties, and mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses
• Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses

Chemistry-Class-XII: Unit 13

• Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary secondary and tertiary amines
• Cyanides and isocyanides: Will be mentioned at relevant places in context
• Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry

Chemistry-Class-XII: Unit 14

• Carbohydrates: Classification (aldoses and ketoses), monosaccharide (glucose and fructose), D-L configuration, oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); importance
• Proteins: Elementary idea of-amino acids, peptide bond, polypeptides, proteins, primary structure, secondary structure, tertiary structure and quaternary structure (qualitative idea only), denaturation of proteins; enzymes
• Hormones: Elementary idea (excluding structure)
• Vitamins: Classification and functions
• Nucleic acids: DNA and RNA

Chemistry-Class-XII: Unit 15

• Classification: Natural and synthetic, methods of polymerization (addition and condensation), copolymerization, some important polymers; natural and synthetic like polythene, nylon, polyesters, bakelite, rubber
• Classification: Biodegradable and non-biodegradable polymers

Chemistry-Class-XII: Unit 16

• Chemicals in medicines: Analgesics, tranqualizers, antiseptic, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antithistamines
• Chemicals in food: Preservatives, artificial sweetening agents, elementary idea of antioxidants
• Cleansing agents: Soaps and detergents, cleansing action

Mathematics-Class-XI: Unit 01

• Sets: Sets and their representations. Empty set. Finite and infinite sets. Equal sets. Subsets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets
• Sets: Difference of sets. Complement of a set
• Relations and functions: Orders pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain
• Relations and functions: Codomain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable
• Relations and functions: Domain and range of these functions, constant, identity, polynomial, rational modulus, signum and greatest integer functions with their graphs, sum, difference, product and quotients of functions
• Trignometric functions: Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle
• Trignometric functions: Truth of the identity sin2 x + cos2 x = 1 for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x+y) in terms of sin x, sin y, cos x and cos y
• Trignometric functions: Deducing the identities like the following-tan (x ± y) = tan x ± tan y/ 1 ± tan x tan y, cot (x ± y) = cot x cot y ± 1/ cot y cot x
• Trignometric functions: Deducing the identities like the following-Sin x + Sin y = 2 Sin (x + y/ 2) cos (x - y)/ 2 Cos (x- y)/ 2 Cos x + Cos y = 2 Cos (x + y)/ 2 Cos (x – y)/ 2
• Trignometric functions: Deducing the identities like the following-Sin x - Sin y = 2 Cos (x + y/ 2) Sin (x - y)/ 2 Cos x – Cos y = 2 Sin (x + y/ 2) sin (x – y/ 2)
• Trignometric functions: Identities related to sin 2 x, cos 2 x, tan 2 x, sin 3 x, cos 3 x and tan 3 x. General solution of trigonometric equiations of the type sin θ = sin alpha

Mathematics-Class-XI: Unit 02

• Principle of mathematical induction: Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications
• Complex numbers and quadratic equations: Need for complex numbers, especially √ -1 , to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers
• Complex numbers and quadratic equations: Argand plane and polar representation of complex numbers. Statement of fundamental theorem of algebra, solution of quadratic equations in the complex number system
• Linear inequalites: Linear inequalities, algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables
• Linear inequalites: Solution of system of linear inequalities in two variables graphically
• Permutations and combinations: Fundamental principle of counting. Factorial n (n1) permutations and combinations, derivation of formulae and their connections, simple applications
• Binomial theorem: History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications
• Sequence and series: Sequence and series, arithmetic progression (A.P.), arithmetic mean (A.M.) geometric progression (G.P., general term of a G.P., sum of n terms of a G.P., geometric mean (G.M.), relation between A.M. and G.M
• Sequence and series: Sum to n terms of the special series ∑n , ∑n and ∑n .

Mathematics-Class-XI: Unit 03

• Straight lines: Brief recall of 2D from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: Parallel to axes, point-slope form, slope intercept form, two point form, intercepts form and normal form
• Straight lines: General equation of a line. Distance of a point from a line
• Conic section: Sections of a cone-circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of conic section. Standard equations and simple properties of parabola, ellipse and hyperbola
• Conic section: Standard equation of a circle
• Introduction to three dimensional geometry: Coordinate axes and coordinate planes in three dimensions. Coordinatoes of a point. Distance between two points and section formula

Mathematics-Class-XI: Unit 04

• Limits and derivatives: Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference
• Limits and derivatives: Product and quotient of functions. Derivatives of polynomial and trigonometric functions

Mathematics-Class-XI: Unit 05

• Mathematical reasoning: Mathematically acceptable statements. Connecting words/ phrases-consolidating the understanding of “if and only if (necessary and sufficient) condition”, implies”, and/ or”, implied by, “and”, “or”
• Mathematical reasoning: Connecting words/ phrases-consolidating the understanding of “there exists” and their use through variety of examples related to real life and mathematics
• Mathematical reasoning: Validating the statements involving the connecting words-difference between contradiction, converse and contrapositive
• Probability: Random experiments-outcomes, sample, spaces (set representation). Events: Occurrence of events, `not’, `and’ and `or’ events, exhaustive events, mutually exclusive events, axiomatic (set theoretic) probability
• Probability: Connections with the theories of earlier classes. Probability of an event, Probability of `not’, `and’ and `or’ events

Mathematics-Class-XII: Unit 01

• Relations and functions: Types of relations-reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations
• Inverse trigonometric functions: Definition, range, domain, principal value branches, graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions

Mathematics-Class-XII: Unit 02

• Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and kew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition
• Matrices: Multiplication and scalar multiplication. Non commutativity of multiplication of matrices and existence of non zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
• Matrices: Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists (here all matrices will have real entries)
• Determinants: Determinant of a square matrix (upto 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. A joint and inverse of a square matrix
• Determinants: Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix
• Applications of derivatives: Maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
• Applications of derivatives: Simple problems (that illustrate basic principles and understanding of the subject as well as real life situations)
• Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type: ∫ dx/ x ± a, ∫ dx/ x ± a, ∫ dx/ √ a - x, ∫ dx/ ax + bx + c
• Integrals: Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type: ∫ dx/ √ ax + bx + c, ∫ (px + q)/ ax + bx + c dx, ∫ (px + q)/ √ ax + bx + c dx, ∫ √ a ± xdx
• Integrals: Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type: ∫ √ x - adx to be evaluated
• Integrals: Define integrals as a limit of sum, Fundamental theorem of calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals
• Applications of the integrals: Applications in findings the area under simple curves, especially lines, areas of circles/ parabolas/ ellipse (in standard form only), area between the two above said curves (the region should be clearly identifiable)
• Differential equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables
• Differential equations: Homogeneous differential equations of first order and first degree. Solutions of linear differential equations of the type: dx/ dy + py = q, where p and q are functions of x

Mathematics-Class-XII: Unit 03

• Continuity and differentiability: Continuity and Differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit function
• Continuity and differentiability: Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives
• Continuity and differentiability: Rolle’s and Lagrange’s mean value theorems (without proof) and their geometric interoperations
• Applications of derivatives: Applications of derivatives-rate of change, increasing/ decreasing functions, tangents and normal, approximation

Mathematics-Class-XII: Unit 04

• Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector
• Vectors: Addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors
• Three-dimensional geometry: Direction cosines/ ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane
• Three-dimensional geometry: Angle between-(i) two lines, (ii) two planes, (iii) a line and plane. Distance of a point from a plane

Mathematics-Class-XII: Unit 05

• Linear programming: Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (LP) problems, mathematical formulation of LP, problems
• Linear programming: Graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optional feasible solutions (upto three non trivial constraints)

Mathematics-Class-XII: Unit 06

• Probability: Multiplication theorem on probability, conditional probability, independent events, total probability, Baye’s theorem, random Variable and its probability distribution, mean and variance of random variable
• Probability: Repeated independent (Bernoulli) trials and binomial distribution

General awareness and current affairs: Unit 01

General awareness and current affairs: Unit 02

General awareness and current affairs: Unit 03

General awareness and current affairs: Unit 04

General awareness and current affairs: Unit 05

General awareness and current affairs: Unit 06

General awareness and current affairs: Unit 07

General awareness and current affairs: Unit 08

General awareness and current affairs: Unit 09

General awareness and current affairs: Unit 10

General awareness and current affairs: Unit 11

• Introductory physical geography; Indian physical environment

General awareness and current affairs: Unit 12

General awareness and current affairs: Unit 13

General awareness and current affairs: Unit 14

General awareness and current affairs: Unit 15

General awareness and current affairs: Unit 16

General awareness and current affairs: Unit 17

General awareness and current affairs: Unit 18

Reasoning and intelligence: Unit 01

Reasoning and intelligence: Unit 02

Reasoning and intelligence: Unit 03

Reasoning and intelligence: Unit 04

Reasoning and intelligence: Unit 05

Indo-islamic, culture theology, aligarh movement: Unit 01

Indo-islamic, culture theology, aligarh movement: Unit 02

Indo-islamic, culture theology, aligarh movement: Unit 03

• Akbar: Major medieval monuments

Indo-islamic, culture theology, aligarh movement: Unit 04

• Sir Syed Ahmad Khan and his companions, Aligarh movement

Accountancy: Unit 01

Accountancy: Unit 02

• Goodwill, admission, retirement and death of partner and dissolution of partnership firms

Accountancy: Unit 03

• Issue of shares and debentures, forfeiture and reissue, redemption of shares and debentures, final accounts of companies

Accountancy: Unit 04

• Ratio analysis-profitability, liquidity, solvency and activity ratios, cash and (as per revised standard issued by ICAI)

Accountancy: Unit 05

• Concepts, features and structures

Business studies: Unit 01

Business studies: Unit 02

• Financial management, financial plans, money market, stock exchange and SEBI

Business studies: Unit 03

• Concept, functions and marketing mix

Business studies: Unit 04

• Consumer rights, consumer awareness and redressal system

Economics: Unit 01

Economics: Unit 02

Economics: Unit 03

Economics: Unit 04

Economics: Unit 05

Economics: Unit 06

Economics: Unit 07

Elementary mathematics and statistics: Unit 01

• Collection, organization and presentation of data; measures of central tendency-mean (simple and weighted), median and mode; measures of dispersion-absolute dispersion (range, quartile deviation, mean deviation, standard deviation)
• Relative dispersion (coefficient of quartile deviation, coefficient of mean deviation, coefficient of variation); correlation-measures of correlation; introduction to index numbers; probability

Reasoning and numerical ability: Unit 01

Reasoning and numerical ability: Unit 02

Reasoning and numerical ability: Unit 03

Reasoning and numerical ability: Unit 04

Reasoning and numerical ability: Unit 05

General awareness: Unit 01

General awareness: Unit 02

General awareness: Unit 03

General awareness: Unit 04

General awareness: Unit 05

General awareness: Unit 06

Physics: Unit 01

Physics: Unit 02

Physics: Unit 03

Physics: Unit 04

Physics: Unit 05

Physics: Unit 06

Physics: Unit 07

Physics: Unit 08

Physics: Unit 09

Physics: Unit 10

Physics: Unit 11

Physics: Unit 12

Physics: Unit 13

Physics: Unit 14

Physics: Unit 15

Physics: Unit 16

Physics: Unit 17

Physics: Unit 18

Physics: Unit 19

Physics: Unit 20

Mathematics: Unit 01

Mathematics: Unit 02

Mathematics: Unit 03

Mathematics: Unit 04

Mathematics: Unit 05

Mathematics: Unit 06

Mathematics: Unit 07

Mathematics: Unit 08

Mathematics: Unit 09

Mathematics: Unit 10

Mathematics: Unit 11

Mathematics: Unit 12

Mathematics: Unit 13

Mathematics: Unit 14

Mathematics: Unit 15

Mathematics: Unit 16

Mathematics: Unit 17

Mathematics: Unit 18

Mathematics: Unit 19

Mathematics: Unit 20

Mathematics: Unit 21

Mathematics: Unit 22

Mathematics: Unit 23

Mathematics: Unit 24

Mathematics: Unit 25

Mathematics: Unit 26

Mathematics: Unit 27

Mathematics: Unit 28

Chemistry-Class-XI: Unit 01

• General introduction: Importance and scope of chemistry
• Historical approach to particulate nature of matter, laws of chemical combination, Dalton’s atomic theory: Concept of elements, atoms and molecules
• Atomic and molecular masses
• Mole concept and molar mass; percentage composition and empirical and molecular formula; chemical reactions, stoichiometry and calculations based on stoichiometry

Chemistry-Class-XI: Unit 02

• Discovery of electron, proton and neutron; atomic number, isotopes and isobars
• Thompson’s model and its limitations, Rutherford’s model and its limitations, Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, De Broglie’s relationship, Heisenberg uncertainty principle
• Concept of orbitals, quantum numbers, shapes of s, p, and d orbitals, rules for filling electrons in orbitals Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms
• Stability of half filled and completely filled orbitals

Chemistry-Class-XI: Unit 03

• Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements-atomic radii, ionic radii, inert gas radii, ionization enthalpy
• Periodic trends in properties of elements-electron gain enthalpy, electronegativity, valence, nomenclature of elements with atomic number greater than 100

Chemistry-Class-XI: Unit 04

• Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory
• Concept of hybridization involving s, p, and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules (qualitative idea only)
• Hydrogen bond

Chemistry-Class-XI: Unit 05

• Three states of matter, intermolecular interactions, types of bonding, melting and boiling points, role of gas laws in elucidating the concept of the molecule, Boyle’s law, Charle’s law, Gay Lussac’s law, Avogadro’s law, ideal behaviour
• Empirical derivation of gas equation, Avogadro number, ideal gas equation
• Deviation from ideal behaviour, liquefaction of gases, critical temperature, kinetic energy and molecular speeds (elementary idea)
• Liquid state-vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations)

Chemistry-Class-XI: Unit 06

• Concepts of system, types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions
• First law of thermodynamics-internal energy and enthalpy, heat capacity and specific heat, measurement of ∆U and ∆H, Hess’s law of constant heat summation, enthalpy of: Bond dissociation, combustion, formation, atomization, sublimation
• Enthalpy of: Phase transition, ionization, solution and dilution
• Introduction of entropy as a state function, second law of thermodynamics, Gibbs energy change for spontaneous and non-spontaneous process, criteria for equilibrium

Chemistry-Class-XI: Unit 07

• Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium-Le Chatelier’s principle; ionic equilibrium-ionization of acids and bases, strong and weak electrolytes
• Degree of ionization, ionization of polybasic acids, acid strength, concept of pH, hydrolysis of salts (elementary idea), 4 buffer solutions, Henderson equation, solubility product, common ion effect (with illustrative examples)
• Redox reactions: Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions in terms of loss and gain of electron and change in oxidation numbers, applications of redox reactions

Chemistry-Class-XI: Unit 08

• Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides-ionic, covalent and interstitial; physical and chemical properties of water, heavy water, hydrogen peroxide-preparation, reactions
• Hydrogen peroxide-use and structure; hydrogen as a fuel

Chemistry-Class-XI: Unit 09

• Group 1 and group 2 elements: General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship
• Group 1 and group 2 elements: Trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses
• Preparation and properties of some important compounds: Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogencarbonate, biological importance of sodium and potassium
• CaO, CaCO, and industrial use of lime and limestone, biological importance of Mg and Ca

Chemistry-Class-XI: Unit 10

• General Introduction to p-block elements
• Group 13 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; boron-physical and chemical properties
• Group 13 elements: Boron-some important compounds; borax, boric acids, boron hydrides. Aluminium: uses, reactions with acids and alkalies.
• Group 14 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous beheaviour of first element. Carbon-catenation, allotropic forms
• Group 14 elements: Carbon-physical and chemical properties; uses of some important compounds: oxides

Chemistry-Class-XI: Unit 11

• General introduction, methods of purification, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds
• Electronic displacements in a covalent bond: Inductive effect, electrometric effect, resonance and hyper conjugation
• Homolytic and heterolytic fission of a covalent bond: Free radicals, carbocations, carbonions; electrophiles and nucleophiles, types of organic reactions

Chemistry-Class-XI: Unit 12

• Classification of Hydrocarbons
• Aliphatic hydrocarbons: Alkanes-nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis
• Aliphatic hydrocarbons: Alkenes-nomenclature, structure of double bond (ethane), geometrical isomerism, physical properties, methods of preparation; chemical reactions: Addition of hydrogen, halogen, water
• Aliphatic hydrocarbons: Alkenes-chemical reactions: Hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition
• Aliphatic hydrocarbons: Alkynes-nomenclature, structure of triple bond (ethyne), physical properties, methods of preparation, chemical reactions: Acidic character of alkynes, addition reaction of-hydrogen, halogens, hydrogen halides and water
• Aromatic hydrocarbons: Introduction, IUPAC nomenclature; benzene: Resonance, aromaticity; chemical properties: Mechanism of electrophilic substitution-nitration sulphonation, halogenation, Friedel Craft’s alkylation and acylation
• Aromatic hydrocarbons: Directive influence of functional group in mon-substituted benzene; carcinogenicity and toxicity

Chemistry-Class-XI: Unit 13

• Environmental pollution-air, water and soil pollution, chemical reactions in atmosphere, smogs, major atmospheric pollutants; acid rain, ozone and its reactions, effects of depletion of ozone layer
• Greenhouse effect and global warming-pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution

Chemistry-Class-XII: Unit 01

• Classificatioin of solids based on different binding forces molecular, ionic covalent and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices
• Calculations of density of unit cell, packing in solids, packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects electrical and magnetic properties, band theory of metals, conductors
• Semiconductors and insulators and n and p type semiconductors

Chemistry-Class-XII: Unit 02

• Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties-relative lowering of vapour pressure, Raoult’s law, elevation of B.P., depression of freezing point
• Osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, Vant Hoff factor

Chemistry-Class-XII: Unit 03

• Redox reactions; conductance in electrylytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea)
• Dry cell electrolytic cells and galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells. Relation between Gibbs energy change and EMF of a cell, fuel cells; corrosion

Chemistry-Class-XII: Unit 04

• Rate of a reaction (average and instantaneous), factors affecting rates of reaction: Concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant
• Integrated rate equations and half life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment)
• Activation energy, Arrhenious equation

Chemistry-Class-XII: Unit 05

• Adsorption-physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis thomogenous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: distinction between true solutions, colloids and suspensions
• Lyophillic, lyophobic multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsions – types of emulsions

Chemistry-Class-XII: Unit 06

• Principles and methods of extraction-concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron

Chemistry-Class-XII: Unit 07

• Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen-preparation, properties and uses
• Group 15 elements: Compounds of nitrogen-preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); phosophorous-allotropic forms
• Group 15 elements: Compounds of phosphorous-preparation and properties of phosphine, halides (PCI, PCI) and oxoacids (elementary idea only)
• Group 16 elements: General introduction, electronic configuration, oxidationi states, occurrence, trends in physical and chemical properties; dioxygen: Preparation, properties and uses; classification of oxides; ozone. Sulphur-allotropic forms
• Group 16 elements: Sulphur-compounds of sulphur: Preparation, properties and uses of sulphur dioxide; sulphuric acid: Industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only)
• Group 17 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: Preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds
• Group 17 elements: Compounds of halogens-oxoacids of halogens (structures only)
• Group 18 elements: General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses, compounds of xenon and their structure

Chemistry-Class-XII: Unit 08

• General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals-metallic character, ionization enthalpy, oxidation states, ionic radii, colour
• General trends in properties of the first row transition metals-catalytic property, magnetic properties, interstitial compounds, alloy formation
• Preparation and properties of KCrO and KMnO
• Lanthanoids-electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences
• Actinoids-electronic configuration, oxidation states and comparison with lanthenoids

Chemistry-Class-XII: Unit 09

• Coordination compounds: Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, bonding, Werner’s theory VBT, CFT
• Coordination compounds: Isomerism (structural and stereo) importance of coordination compounds (in qualitative inclusion, extraction of metals and biological systems)

Chemistry-Class-XII: Unit 10

• Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions. Optical rotation
• Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only)
• Uses and environmental effects of-dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT

Chemistry-Class-XII: Unit 11

• Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses, with special reference to methanol and ethanol
• Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reaction, uses of phenols
• Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses

Chemistry-Class-XII: Unit 12

• Aldehydes and ketones: Nomenclature, nature of carbonyl group, method of preparation, physical and chemical properties, and mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses
• Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses

Chemistry-Class-XII: Unit 13

• Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary secondary and tertiary amines
• Cyanides and isocyanides: Will be mentioned at relevant places in context
• Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry

Chemistry-Class-XII: Unit 14

• Carbohydrates: Classification (aldoses and ketoses), monosaccharide (glucose and fructose), D-L configuration, oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); importance
• Proteins: Elementary idea of-amino acids, peptide bond, polypeptides, proteins, primary structure, secondary structure, tertiary structure and quaternary structure (qualitative idea only), denaturation of proteins; enzymes
• Hormones: Elementary idea (excluding structure)
• Vitamins: Classification and functions
• Nucleic acids: DNA and RNA

Chemistry-Class-XII: Unit 15

• Classification: Natural and synthetic, methods of polymerization (addition and condensation), copolymerization, some important polymers; natural and synthetic like polythene, nylon, polyesters, bakelite, rubber
• Classification: Biodegradable and non-biodegradable polymers

Chemistry-Class-XII: Unit 16

• Chemicals in medicines: Analgesics, tranqualizers, antiseptic, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antithistamines
• Chemicals in food: Preservatives, artificial sweetening agents, elementary idea of antioxidants
• Cleansing agents: Soaps and detergents, cleansing action

Biology-Class-XI (Botany): Unit 01

• The living world: What is living?, biodiversity; need for classification; three domains of life; taxonomy and systematics; concept of species and taxonomical hierarchy; binomial nomenclature; tools for study of taxonomy-museums, zoological parks, herbaria
• The living world: Tools for study of taxonomy-botanical gardens
• Biological classification five kingdom: Classification; salient features and classification of monera, protista and fungi into major groups: Lichens, viruses and viroids
• Plant kingdom: Salient features and classification of plants into major groups-algae, bryophyta, pteridophyta, gymnospermae and angiospermae (three to five salient and distinguishing features and at least two examples of each category)
• Plant kingdom: Angiosperms-classification upto class, characteristic features and examples
• Animal kingdom: Salient features and classification of animals non-chordates up to phyla level and chordates up to class level (three to five salient features and at least two examples of each category) (no live animals or specimen should be displayed)

Biology-Class-XI (Botany): Unit 02

• Morphology of flowering plants: Morphology and modifications-inflorescence, flower, fruit and seed
• Anatomy of flowering plants: Anatomy and functions of different parts of flowering plants-root, stem, leaf, tissue (to be dealt along with the relevant experiment of the practical syllabus)
• Structural organisation in animals: Animal tissues-morphology, anatomy and functions of different systems (digestive, circulatory, respiratory, nervous and reproductive) of an insect (cockroach) (a brief account only)

Biology-Class-XI (Botany): Unit 03

• Cell-the unit of life: Cell theory and cell as the basic unit of life-structure of prokaryotic and eukaryotic cells; plant cell and animal cell; cell envelope; cell membrane, cell wall; cell organelles-structure and function; endomembrane system
• Cell-the unit of life: Endoplasmic reticulum, golgi bodies, lysosomes, vacuoles; mitochondria, ribosomes, plastids, microbodies; cytoskeleton, cilia, flagella, centrioles (ultrastructure and function); nucleus, nuclear membrane, chromatin, nucleolus
• Biomolecules: Chemical constituents of living cells-biomolecules, structure and function of proteins, carbohydrates, lipids, nucleic acids, enzymes, types, properties, enzyme action
• Cell cycle and cell division: Cell cycle, mitosis, meiosis and their significance

Biology-Class-XI (Botany): Unit 04

• Transport in plants: Movement of water, gases and nutrients; cell to cell transport, diffusion, facilitated diffusion, active transport; plant-water relations, imbibition, water potential, osmosis, plasmolysis; long distance transport of water-absorption
• Transport in plants: Long distance transport of water-apoplast, symplast, transpiration pull, root pressure and guttation; transpiration, opening and closing of stomata; uptake and translocation of mineral nutrients-transport of food, phloem transport
• Transport in plants: Uptake and translocation of mineral nutrients-massflow hypothesis; diffusion of gases
• Mineral nutrition: Essential minerals, macro- and micronutrients and their role; deficiency symptoms; mineral toxicity; elementary idea of hydroponics as a method to study mineral nutrition; nitrogen metabolism, nitrogen cycle
• Mineral nutrition: Biological nitrogen fixation
• Photosynthesis in higher plants: Photosynthesis as a mean of autotrophic nutrition; site of photosynthesis, pigments involved in photosynthesis (elementary idea); photochemical and biosynthetic phases of photosynthesis
• Photosynthesis in higher plants: Cyclic and non cyclic photophosphorylation; chemiosmotic hypothesis; photorespiration; C and C pathways; factors affecting photosynthesis.
• Respiration in plants: Exchange of gases; cellular respiration-glycolysis, fermentation (anaerobic), TCA cycle and electron transport system (aerobic); energy relations-number of ATP molecules generated; amphibolic pathways; respiratory quotient
• Plant-growth and development: Seed germination; phases of plant growth and plant growth rate; conditions of growth; differentiation, dedifferentiation and redifferentiation; sequence of developmental processes in a plant cell
• Plant-growth and development: Growth regulators-auxin, gibberellin, cytokinin, ethylene, ABA; seed dormancy; vernalisation; photoperiodism

Biology-Class-XI (Botany): Unit 05

• Digestion and absorption: Alimentary canal and digestive glands, role of digestive enzymes and gastrointestinal hormones; peristalsis, digestion, absorption and assimilation of proteins, carbohydrates and fats; calorific values of proteins
• Digestion and absorption: Carbohydrates and fats; egestion; nutritional and digestive disorders-PEM, indigestion, constipation, vomiting, jaundice, diarrhoea
• Breating and exchange of gases: Respiratory organs in animals (recall only); respiratory system in humans; mechanism of breathing and its regulation in humans-exchange of gases, transport of gases and regulation of respiration, respiratory volume
• Breating and exchange of gases: Disorders related to respiration-asthma, emphysema, occupational respiratory disorders
• Body fluids and circulation: Composition of blood, blood groups, coagulation of blood; composition of lymph and its function; human circulatory system-structure of human heart and blood vessels; cardiac cycle, cardiac output, ECG; double circulation
• Body fluids and circulation: Regulation of cardiac activity; disorders of circulatory system-hypertension, coronary artery disease, angina pectoris, heart failure.
• Excretory products and their elimination: Modes of excretion-ammonotelism, ureotelism, uricotelism; human excretory system-structure and function; urine formation, osmoregulation; regulation of kidney function-renin, angiotensin, atrial natriuretic factor
• Excretory products and their elimination: Regulation of kidney function-ADH and diabetes insipidus; role of other organs in excretion; disorders-uraemia, renal failure, renal calculi, nephritis; dialysis and artificial kidney
• Locomotion and movement: Types of movement-ciliary, flagellar, muscular; skeletal muscle-contractile proteins and muscle contraction; skeletal system and its functions; joints; disorders of muscular and skeletal system-myasthenia gravis, tetany
• Locomotion and movement: Disorders of muscular and skeletal system-muscular dystrophy, arthritis, osteoporosis, gout
• Neural control and coordination: Neuron and nerves; nervous system in humans-central nervous system; peripheral nervous system and visceral nervous system; generation and conduction of nerve impulse; reflex action; sensory perception; sense organs
• Neural control and coordination: Elementary structure and functions of eye and ear
• Chemical coordination and integration: Endocrine glands and hormones; human endocrine system-hypothalamus, pituitary, pineal, thyroid, parathyroid, adrenal, pancreas, gonads; mechanism of hormone action (elementary idea)
• Chemical coordination and integration: Role of hormones as messengers and regulators, hypo- and hyperactivity and related disorders; dwarfism, acromegaly, cretinism, goiter, exophthalmic goiter, diabetes, Addison's disease

Biology-Class-XII (Botany): Unit 01

• Reproduction in organisms: Reproduction, a characteristic feature of all organisms for continuation of species; modes of reproduction-asexual and sexual reproduction; asexual reproduction-binary fission, sporulation, budding, gemmule formation
• Reproduction in organisms: Asexual reproduction-fragmentation; vegetative propagation in plants
• Sexual reproduction in flowering plants: Flower structure; development of male and female gametophytes; pollination-types, agencies and examples; outbreeding devices; pollen-pistil interaction; double fertilization
• Sexual reproduction in flowering plants: Post fertilization events-development of endosperm and embryo, development of seed and formation of fruit; special modesapomixis, parthenocarpy, polyembryony; significance of seed dispersal and fruit formation
• Human reproduction: Male and female reproductive systems; microscopic anatomy of testis and ovary; gametogenesis-spermatogenesis and oogenesis; menstrual cycle; fertilisation, embryo development upto blastocyst formation, implantation
• Human reproduction: Pregnancy and placenta formation (elementary idea); parturition (elementary idea); lactation (elementary idea)
• Reproductive health: Need for reproductive health and prevention of sexually transmitted diseases (STDS); birth control-need and methods, contraception and medical termination of pregnancy (MTP); amniocentesis
• Reproductive health: Infertility and assisted reproductive technologies-IVF, ZIFT, GIFT (elementary idea for general awareness)

Biology-Class-XII (Botany): Unit 02

• Principles of inheritance and variation-heredity and variation: Mendelian inheritance; deviations from Mendelism-incomplete dominance, codominance, multiple alleles and inheritance of blood groups, chromosome theory of inheritance; chromosomes and genes
• Principles of inheritance and variation-heredity and variation: Sex determination-in humans, birds and honey bee; linkage and crossing over; sex linked inheritance-haemophilia, colour blindness; Mendelian disorders in humans-thalassemia
• Principles of inheritance and variation-heredity and variation: Chromosomal disorders in humans; Down's syndrome, Turner's and Klinefelter's syndromes
• Molecular basis of inheritance: Search for genetic material and DNA as genetic material; structure of DNA and RNA; DNA packaging; DNA replication; central dogma; transcription, genetic code, translation; gene expression and regulation-lac operon
• Molecular basis of inheritance: Genome and human and rice genome projects; DNA fingerprinting
• Evolution: Origin of life; biological evolution and evidences for biological evolution (paleontology, comparative anatomy, embryology and molecular evidences); Darwin's contribution, modern synthetic theory of evolution
• Evolution: Mechanism of evolution-variation (mutation and recombination) and natural selection with examples, types of natural selection; gene flow and genetic drift; Hardy-Weinberg's principle; adaptive radiation; human evolution

Biology-Class-XII (Botany): Unit 03

• Human health and diseases: Pathogens; parasites causing human diseases (malaria, dengue, chickengunia, filariasis, ascariasis, typhoid, pneumonia, common cold, amoebiasis, ring worm) and their control; basic concepts of immunology-vaccines; cancer
• Human health and diseases: Basic concepts of immunology-HIV and AIDS; adolescence-drug and alcohol abuse
• Strategies for enhancement in food production: Improvement in food production-plant breeding, tissue culture, single cell protein, biofortification, apiculture and animal husbandry
• Microbes in human welfare: In household food processing, industrial production, sewage treatment, energy generation and microbes as biocontrol agents and biofertilizers. Antibiotics; production and judicious use

Biology-Class-XII (Botany): Unit 04

• Biotechnology-principles and processes: Genetic engineering (recombinant DNA technology)
• Biotechnology and its application: Application of biotechnology in health and agriculture- human insulin and vaccine production, stem cell technology, gene therapy; genetically modified organisms-Bt crops; transgenic animals; biosafety issues
• Biotechnology and its application: Biopiracy and patents

Biology-Class-XII (Botany): Unit 05

• Organisms and populations: Organisms and environment-habitat and niche, population and ecological adaptations; population interactions-mutualism, competition, predation, parasitism; population attributes-growth, birth rate and death rate, age distribution
• Ecosystem: Ecosystems-patterns, components; productivity and decomposition; energy flow; pyramids of number, biomass, energy; nutrient cycles (carbon and phosphorous); ecological succession; ecosystem services-carbon fixation, pollination, seed dispersal
• Ecosystem: Oxygen release (in brief)
• Biodiversity and its conservation: Concept of biodiversity; patterns of biodiversity; importance of biodiversity; loss of biodiversity; biodiversity conservation; hotspots, endangered organisms, extinction, red data book, biosphere reserves
• Biodiversity and its conservation: National parks, sanctuaries and Ramsar sites
• Environmental issues: Air pollution and its control; water pollution and its control; agrochemicals and their effects; solid waste management; radioactive waste management; greenhouse effect and climate change; ozone layer depletion; deforestation
• Environmental issues: Any one case study as success story addressing environmental issue (s)

Biology-Zoology: Unit 01

Biology-Zoology: Unit 02

Biology-Zoology: Unit 03

Biology-Zoology: Unit 04

• Types and structure

Biology-Zoology: Unit 05

Biology-Zoology: Unit 06

Biology-Zoology: Unit 07

Biology-Zoology: Unit 08

Biology-Zoology: Unit 09

Biology-Zoology: Unit 10

Biology-Zoology: Unit 11

Biology-Zoology: Unit 12

Biology-Zoology: Unit 13

Biology-Zoology: Unit 14

Biology-Zoology: Unit 15

Biology-Zoology: Unit 16

Biology-Zoology: Unit 17

Biology-Zoology: Unit 18

Biology-Zoology: Unit 19

Biology-Zoology: Unit 20

Biology-Zoology: Unit 21

Biology-Zoology: Unit 22

Biology-Zoology: Unit 23

Home science: Unit 01

Home science: Unit 02

Home science: Unit 03

• Protection from preventable diseases, characteristics and needs of differently abled children, substitute care at home and outside

Home science: Unit 04

• Nutrients and their sources, nutrition for self and family, basics of therapeutic nutrition, selection and storage of food, food adulteration

Home science: Unit 05

• Elements and principles of design in house planning, furnishing, money management, role of consumers in the economy, work simplication

Home science: Unit 06

• Fiber science, basic finishes, statin removal, fabric construction, clothing and its relation to personality

Chemistry-Class-XI: Unit 01

• General introduction: Importance and scope of chemistry
• Historical approach to particulate nature of matter, laws of chemical combination, Dalton’s atomic theory: Concept of elements, atoms and molecules
• Atomic and molecular masses
• Mole concept and molar mass; percentage composition and empirical and molecular formula; chemical reactions, stoichiometry and calculations based on stoichiometry

Chemistry-Class-XI: Unit 02

• Discovery of electron, proton and neutron; atomic number, isotopes and isobars
• Thompson’s model and its limitations, Rutherford’s model and its limitations, Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, De Broglie’s relationship, Heisenberg uncertainty principle
• Concept of orbitals, quantum numbers, shapes of s, p, and d orbitals, rules for filling electrons in orbitals Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms
• Stability of half filled and completely filled orbitals

Chemistry-Class-XI: Unit 03

• Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements-atomic radii, ionic radii, inert gas radii, ionization enthalpy
• Periodic trends in properties of elements-electron gain enthalpy, electronegativity, valence, nomenclature of elements with atomic number greater than 100

Chemistry-Class-XI: Unit 04

• Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory
• Concept of hybridization involving s, p, and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules (qualitative idea only)
• Hydrogen bond

Chemistry-Class-XI: Unit 05

• Three states of matter, intermolecular interactions, types of bonding, melting and boiling points, role of gas laws in elucidating the concept of the molecule, Boyle’s law, Charle’s law, Gay Lussac’s law, Avogadro’s law, ideal behaviour
• Empirical derivation of gas equation, Avogadro number, ideal gas equation
• Deviation from ideal behaviour, liquefaction of gases, critical temperature, kinetic energy and molecular speeds (elementary idea)
• Liquid state-vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations)

Chemistry-Class-XI: Unit 06

• Concepts of system, types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions
• First law of thermodynamics-internal energy and enthalpy, heat capacity and specific heat, measurement of ∆U and ∆H, Hess’s law of constant heat summation, enthalpy of: Bond dissociation, combustion, formation, atomization, sublimation
• Enthalpy of: Phase transition, ionization, solution and dilution
• Introduction of entropy as a state function, second law of thermodynamics, Gibbs energy change for spontaneous and non-spontaneous process, criteria for equilibrium

Chemistry-Class-XI: Unit 07

• Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium-Le Chatelier’s principle; ionic equilibrium-ionization of acids and bases, strong and weak electrolytes
• Degree of ionization, ionization of polybasic acids, acid strength, concept of pH, hydrolysis of salts (elementary idea), 4 buffer solutions, Henderson equation, solubility product, common ion effect (with illustrative examples)
• Redox reactions: Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions in terms of loss and gain of electron and change in oxidation numbers, applications of redox reactions

Chemistry-Class-XI: Unit 08

• Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides-ionic, covalent and interstitial; physical and chemical properties of water, heavy water, hydrogen peroxide-preparation, reactions
• Hydrogen peroxide-use and structure; hydrogen as a fuel

Chemistry-Class-XI: Unit 09

• Group 1 and group 2 elements: General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship
• Group 1 and group 2 elements: Trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses
• Preparation and properties of some important compounds: Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogencarbonate, biological importance of sodium and potassium
• CaO, CaCO, and industrial use of lime and limestone, biological importance of Mg and Ca

Chemistry-Class-XI: Unit 10

• General Introduction to p-block elements
• Group 13 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; boron-physical and chemical properties
• Group 13 elements: Boron-some important compounds; borax, boric acids, boron hydrides. Aluminium: uses, reactions with acids and alkalies.
• Group 14 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous beheaviour of first element. Carbon-catenation, allotropic forms
• Group 14 elements: Carbon-physical and chemical properties; uses of some important compounds: oxides

Chemistry-Class-XI: Unit 11

• General introduction, methods of purification, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds
• Electronic displacements in a covalent bond: Inductive effect, electrometric effect, resonance and hyper conjugation
• Homolytic and heterolytic fission of a covalent bond: Free radicals, carbocations, carbonions; electrophiles and nucleophiles, types of organic reactions

Chemistry-Class-XI: Unit 12

• Classification of Hydrocarbons
• Aliphatic hydrocarbons: Alkanes-nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis
• Aliphatic hydrocarbons: Alkenes-nomenclature, structure of double bond (ethane), geometrical isomerism, physical properties, methods of preparation; chemical reactions: Addition of hydrogen, halogen, water
• Aliphatic hydrocarbons: Alkenes-chemical reactions: Hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition
• Aliphatic hydrocarbons: Alkynes-nomenclature, structure of triple bond (ethyne), physical properties, methods of preparation, chemical reactions: Acidic character of alkynes, addition reaction of-hydrogen, halogens, hydrogen halides and water
• Aromatic hydrocarbons: Introduction, IUPAC nomenclature; benzene: Resonance, aromaticity; chemical properties: Mechanism of electrophilic substitution-nitration sulphonation, halogenation, Friedel Craft’s alkylation and acylation
• Aromatic hydrocarbons: Directive influence of functional group in mon-substituted benzene; carcinogenicity and toxicity

Chemistry-Class-XI: Unit 13

• Environmental pollution-air, water and soil pollution, chemical reactions in atmosphere, smogs, major atmospheric pollutants; acid rain, ozone and its reactions, effects of depletion of ozone layer
• Greenhouse effect and global warming-pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution

Chemistry-Class-XII: Unit 01

• Classificatioin of solids based on different binding forces molecular, ionic covalent and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices
• Calculations of density of unit cell, packing in solids, packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects electrical and magnetic properties, band theory of metals, conductors
• Semiconductors and insulators and n and p type semiconductors

Chemistry-Class-XII: Unit 02

• Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties-relative lowering of vapour pressure, Raoult’s law, elevation of B.P., depression of freezing point
• Osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, Vant Hoff factor

Chemistry-Class-XII: Unit 03

• Redox reactions; conductance in electrylytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea)
• Dry cell electrolytic cells and galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells. Relation between Gibbs energy change and EMF of a cell, fuel cells; corrosion

Chemistry-Class-XII: Unit 04

• Rate of a reaction (average and instantaneous), factors affecting rates of reaction: Concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant
• Integrated rate equations and half life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment)
• Activation energy, Arrhenious equation

Chemistry-Class-XII: Unit 05

• Adsorption-physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis thomogenous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: distinction between true solutions, colloids and suspensions
• Lyophillic, lyophobic multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsions – types of emulsions

Chemistry-Class-XII: Unit 06

• Principles and methods of extraction-concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron

Chemistry-Class-XII: Unit 07

• Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen-preparation, properties and uses
• Group 15 elements: Compounds of nitrogen-preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); phosophorous-allotropic forms
• Group 15 elements: Compounds of phosphorous-preparation and properties of phosphine, halides (PCI, PCI) and oxoacids (elementary idea only)
• Group 16 elements: General introduction, electronic configuration, oxidationi states, occurrence, trends in physical and chemical properties; dioxygen: Preparation, properties and uses; classification of oxides; ozone. Sulphur-allotropic forms
• Group 16 elements: Sulphur-compounds of sulphur: Preparation, properties and uses of sulphur dioxide; sulphuric acid: Industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only)
• Group 17 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: Preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds
• Group 17 elements: Compounds of halogens-oxoacids of halogens (structures only)
• Group 18 elements: General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses, compounds of xenon and their structure

Chemistry-Class-XII: Unit 08

• General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals-metallic character, ionization enthalpy, oxidation states, ionic radii, colour
• General trends in properties of the first row transition metals-catalytic property, magnetic properties, interstitial compounds, alloy formation
• Preparation and properties of KCrO and KMnO
• Lanthanoids-electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences
• Actinoids-electronic configuration, oxidation states and comparison with lanthenoids

Chemistry-Class-XII: Unit 09

• Coordination compounds: Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, bonding, Werner’s theory VBT, CFT
• Coordination compounds: Isomerism (structural and stereo) importance of coordination compounds (in qualitative inclusion, extraction of metals and biological systems)

Chemistry-Class-XII: Unit 10

• Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions. Optical rotation
• Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only)
• Uses and environmental effects of-dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT

Chemistry-Class-XII: Unit 11

• Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses, with special reference to methanol and ethanol
• Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reaction, uses of phenols
• Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses

Chemistry-Class-XII: Unit 12

• Aldehydes and ketones: Nomenclature, nature of carbonyl group, method of preparation, physical and chemical properties, and mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses
• Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses

Chemistry-Class-XII: Unit 13

• Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary secondary and tertiary amines
• Cyanides and isocyanides: Will be mentioned at relevant places in context
• Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry

Chemistry-Class-XII: Unit 14

• Carbohydrates: Classification (aldoses and ketoses), monosaccharide (glucose and fructose), D-L configuration, oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); importance
• Proteins: Elementary idea of-amino acids, peptide bond, polypeptides, proteins, primary structure, secondary structure, tertiary structure and quaternary structure (qualitative idea only), denaturation of proteins; enzymes
• Hormones: Elementary idea (excluding structure)
• Vitamins: Classification and functions
• Nucleic acids: DNA and RNA

Chemistry-Class-XII: Unit 15

• Classification: Natural and synthetic, methods of polymerization (addition and condensation), copolymerization, some important polymers; natural and synthetic like polythene, nylon, polyesters, bakelite, rubber
• Classification: Biodegradable and non-biodegradable polymers

Chemistry-Class-XII: Unit 16

• Chemicals in medicines: Analgesics, tranqualizers, antiseptic, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antithistamines
• Chemicals in food: Preservatives, artificial sweetening agents, elementary idea of antioxidants
• Cleansing agents: Soaps and detergents, cleansing action

Mathematics-Class-XI: Unit 01

• Sets: Sets and their representations. Empty set. Finite and infinite sets. Equal sets. Subsets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets
• Sets: Difference of sets. Complement of a set
• Relations and functions: Orders pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain
• Relations and functions: Codomain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable
• Relations and functions: Domain and range of these functions, constant, identity, polynomial, rational modulus, signum and greatest integer functions with their graphs, sum, difference, product and quotients of functions
• Trignometric functions: Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle
• Trignometric functions: Truth of the identity sin2 x + cos2 x = 1 for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x+y) in terms of sin x, sin y, cos x and cos y
• Trignometric functions: Deducing the identities like the following-tan (x ± y) = tan x ± tan y/ 1 ± tan x tan y, cot (x ± y) = cot x cot y ± 1/ cot y cot x
• Trignometric functions: Deducing the identities like the following-Sin x + Sin y = 2 Sin (x + y/ 2) cos (x - y)/ 2 Cos (x- y)/ 2 Cos x + Cos y = 2 Cos (x + y)/ 2 Cos (x – y)/ 2
• Trignometric functions: Deducing the identities like the following-Sin x - Sin y = 2 Cos (x + y/ 2) Sin (x - y)/ 2 Cos x – Cos y = 2 Sin (x + y/ 2) sin (x – y/ 2)
• Trignometric functions: Identities related to sin 2 x, cos 2 x, tan 2 x, sin 3 x, cos 3 x and tan 3 x. General solution of trigonometric equiations of the type sin θ = sin alpha

Mathematics-Class-XI: Unit 02

• Principle of mathematical induction: Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications
• Complex numbers and quadratic equations: Need for complex numbers, especially √ -1 , to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers
• Complex numbers and quadratic equations: Argand plane and polar representation of complex numbers. Statement of fundamental theorem of algebra, solution of quadratic equations in the complex number system
• Linear inequalites: Linear inequalities, algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables
• Linear inequalites: Solution of system of linear inequalities in two variables graphically
• Permutations and combinations: Fundamental principle of counting. Factorial n (n1) permutations and combinations, derivation of formulae and their connections, simple applications
• Binomial theorem: History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications
• Sequence and series: Sequence and series, arithmetic progression (A.P.), arithmetic mean (A.M.) geometric progression (G.P., general term of a G.P., sum of n terms of a G.P., geometric mean (G.M.), relation between A.M. and G.M
• Sequence and series: Sum to n terms of the special series ∑n , ∑n and ∑n .

Mathematics-Class-XI: Unit 03

• Straight lines: Brief recall of 2D from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: Parallel to axes, point-slope form, slope intercept form, two point form, intercepts form and normal form
• Straight lines: General equation of a line. Distance of a point from a line
• Conic section: Sections of a cone-circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of conic section. Standard equations and simple properties of parabola, ellipse and hyperbola
• Conic section: Standard equation of a circle
• Introduction to three dimensional geometry: Coordinate axes and coordinate planes in three dimensions. Coordinatoes of a point. Distance between two points and section formula

Mathematics-Class-XI: Unit 04

• Limits and derivatives: Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference
• Limits and derivatives: Product and quotient of functions. Derivatives of polynomial and trigonometric functions

Mathematics-Class-XI: Unit 05

• Mathematical reasoning: Mathematically acceptable statements. Connecting words/ phrases-consolidating the understanding of “if and only if (necessary and sufficient) condition”, implies”, and/ or”, implied by, “and”, “or”
• Mathematical reasoning: Connecting words/ phrases-consolidating the understanding of “there exists” and their use through variety of examples related to real life and mathematics
• Mathematical reasoning: Validating the statements involving the connecting words-difference between contradiction, converse and contrapositive
• Probability: Random experiments-outcomes, sample, spaces (set representation). Events: Occurrence of events, `not’, `and’ and `or’ events, exhaustive events, mutually exclusive events, axiomatic (set theoretic) probability
• Probability: Connections with the theories of earlier classes. Probability of an event, Probability of `not’, `and’ and `or’ events

Mathematics-Class-XII: Unit 01

• Relations and functions: Types of relations-reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations
• Inverse trigonometric functions: Definition, range, domain, principal value branches, graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions

Mathematics-Class-XII: Unit 02

• Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and kew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition
• Matrices: Multiplication and scalar multiplication. Non commutativity of multiplication of matrices and existence of non zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
• Matrices: Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists (here all matrices will have real entries)
• Determinants: Determinant of a square matrix (upto 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. A joint and inverse of a square matrix
• Determinants: Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix
• Applications of derivatives: Maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
• Applications of derivatives: Simple problems (that illustrate basic principles and understanding of the subject as well as real life situations)
• Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type: ∫ dx/ x ± a, ∫ dx/ x ± a, ∫ dx/ √ a - x, ∫ dx/ ax + bx + c
• Integrals: Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type: ∫ dx/ √ ax + bx + c, ∫ (px + q)/ ax + bx + c dx, ∫ (px + q)/ √ ax + bx + c dx, ∫ √ a ± xdx
• Integrals: Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type: ∫ √ x - adx to be evaluated
• Integrals: Define integrals as a limit of sum, Fundamental theorem of calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals
• Applications of the integrals: Applications in findings the area under simple curves, especially lines, areas of circles/ parabolas/ ellipse (in standard form only), area between the two above said curves (the region should be clearly identifiable)
• Differential equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables
• Differential equations: Homogeneous differential equations of first order and first degree. Solutions of linear differential equations of the type: dx/ dy + py = q, where p and q are functions of x

Mathematics-Class-XII: Unit 03

• Continuity and differentiability: Continuity and Differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit function
• Continuity and differentiability: Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives
• Continuity and differentiability: Rolle’s and Lagrange’s mean value theorems (without proof) and their geometric interoperations
• Applications of derivatives: Applications of derivatives-rate of change, increasing/ decreasing functions, tangents and normal, approximation

Mathematics-Class-XII: Unit 04

• Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector
• Vectors: Addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors
• Three-dimensional geometry: Direction cosines/ ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane
• Three-dimensional geometry: Angle between-(i) two lines, (ii) two planes, (iii) a line and plane. Distance of a point from a plane

Mathematics-Class-XII: Unit 05

• Linear programming: Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (LP) problems, mathematical formulation of LP, problems
• Linear programming: Graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optional feasible solutions (upto three non trivial constraints)

Mathematics-Class-XII: Unit 06

• Probability: Multiplication theorem on probability, conditional probability, independent events, total probability, Baye’s theorem, random Variable and its probability distribution, mean and variance of random variable
• Probability: Repeated independent (Bernoulli) trials and binomial distribution

Architecture aptitude test: Unit 01

• Simple drawing depicting the total object in its right form and proportion, surface texture, relative location and details of its component parts in appropriate scale
• Common domestic or day-to-day life usable objects like furniture, equipment, etc from memory

Architecture aptitude test: Unit 02

• Exercises in geometrical drawing containing lines, angles, triangles, quadrilaterals, polygons, circles, etc
• Study of plan (top view), elevation (front or side views) of simple solid objects like prisms, cones, cylinders, cubes, splayed surface holders, etc

Architecture aptitude test: Unit 03

• Understanding and appreciation of three-dimensional forms with building elements, color, volume and orientation
• Visualization through structuring objects in memory

Architecture aptitude test: Unit 04

• Composition exercise with given elements, context mapping, creativity check through innovative uncommon test with familiar objects
• Sense of color grouping or application

Architecture aptitude test: Unit 05

• General interest and awareness of famous architectural creations-both national and international, places and personalities (architects, designers, etc) in the related domain

Mathematics: Unit 01

• Successive differentiation: Derivatives of higher order, nth derivative of well-known functions, Leibnitz’s theorem (without proof). Expansion of functions, Maclaurin’s theorem and Taylor’s theorem (without proof)
• Successive differentiation: Indeterminate forms: 0/0, ∞/∞, 0 x ∞, ∞ - ∞ and 0⁰, 1∞, 0∞. Asymptotes of the algebraic curves, parallel asymptotes, Asymptotes parallel to x-axis and y-axis
• Curvature: Angle between radius vector and tangent, derivative of arc length in cartesian, parametric and polar form, calculation of curvature in cartesian, parametric and polar form. Radius of curvature in the three forms, multiple points
• Curvature: Convexity and concavity of a curve, points of inflexion, tracing of cartesian curves, idea of some well known polar curves, functions of two or more variables, partial differential coefficients, homogeneous functions
• Curvature: Euler’s theorem on homogeneous functions
• Gamma functions, Integration of the type , length of curves for cartesian, parametric and polar equations, intrinsic equation from cartesian, parametric and polar equations, volume and surfaces of solids of revolution of cartesian
• Parametric and polar curves

Mathematics: Unit 02

• General equations, pair of straight line through origin, lines joining the origin to the intersection of a curve and a line
• The conic section, equation to a conic section
• Intersection of a straight line and a conic
• Equation of a tangent to a conic, condition of tangency
• Pair of tangents from a point
• Chord of contact of a pair of tangents to a conic
• Pole and polar, conjugate points
• Conjugate lines
• The condition of conjugacy
• Chord with a given middle point
• Centre of a conic and diameter
• Equation of the conic when the origin is transferred to the centre
• Conjugate diameters
• Change of rectangular axes without change of origin
• Removal of xy-term
• Invariants
• Nature of conic, summary
• Tracing of parabola, the asymptotes of hyperbola
• Conjugate hyperbola
• Asymptotes
• The length and position of axes
• Coordinate of foci
• Polar equation of a conic when focus is at the pole
• Directrices, tracing of the conic
• Equation of the chord when the vectorial angles of the extremities are given
• Equation of the tangent at the point whose vectorial angle is α
• Normal, polar
• Direction cosines of a line
• Projection of a segment
• Angles between two lines
• Distance of a point from a line
• Equation of a plane
• Length of perpendicular from a point to a plane
• Cylinder and its equation
• Right circular cylinder
• Equation of a right circular cylinder
• Equation of a cone
• Equation of a cone when the vertex is at the origin
• Condition for general equation of second degree to represent a cone
• Tangent plane to a cone, a property of the tangent plane to a cone
• Condition of tangency
• Reciprocal cone
• Cone with three mutually perpendicular generators, number of mutually perpendicular generators
• The standard equation of central conicoids
• The tangent plane
• Condition of tangency of a plane
• Section with a given centre
• Locus of the mid-points of a system of parallel chords
• The polar plane, polar lines
• Enveloping cone
• Classification of central conicoids
• The normal
• Normals from given point
• Conjugate diametral plane and diameters of ellipsoid
• Paraboloid (elliptic and hyperbolic)
• Tangent plane to a paraboloid

Mathematics: Unit 03

• Absolute, relative and percentage errors, general error formula, error in series approximation, solution of algebraic and transcendental equations, the bisection and Regulafalsi method, iteration methods namely, Newton-Raphson method
• Generalized Newton’s method, solution of system of linear equations using direct methods such as matrix inversion, Gauss elimination and LU decomposition including some iteration methods namely, Jacobi and Gauss-Siedel methods
• The algebraic eigen value problems using iterative and householder methods
• Symbols of Δ,, E, E-1 , D,  and and their relations, Newton-Gregory forward and backward difference formulae, Gauss’s, Stirling’s and Bessel’s formulae, Lagrange’s formula, divided differences and their properties
• Newton’s general interpolation formula, inverse interpolation formula and interpolation with cubic splines
• Numerical differentiation and integration, numerical differentiation of tabular and nontabular functions including error estimations, numerical integration using Gauss quadrature formulae, trapezoidal, Simpson’s 1/3- and 3/8-Rule
• Weddle’s Rule and Newton-Cotes formula including error estimation, curve fitting and approximations, least squares curve fitting procedures, different types of approximations, least squares polynomial approximation
• Chebyshev polynomials and its application in various approximations
• Ordinary differential equations, Euler’s and modified Euler’s methods, Picard’s method, Taylor series method, Runge-Kutta methods of 2nd and 4th order, multi-step methods, Milne-Simpson method, Adam Bashforth-Moulton method
• Boundary value problems using finite difference method

Mathematics: Unit 04

• Exact differential equations
• Integrating factors
• Total differential equations
• Differential equations of first order but not of first degree
• Equations solvable for p, y and x
• Clairaut’s equations
• Linear differential equations of order n
• Homogeneous and non-homogeneous differential equations of order n with constant coefficients
• Complementary functions
• Different forms of particular integrals
• Linear differential equations with non-constant coefficients
• Reduction of order method
• The Cauchy-Euler’s equation of order n
• The Legendre’s linear equation
• Methods of undetermined coefficients and variation of parameters
• Series solution of differential equations
• Frobenius method
• Different cases
• Bessel, Legendre and hypergeometric differential equations and their solutions
• Simultaneous total different equations
• Equations of the form dx/P=dy/Q=dz/R
• Methods of grouping and multipliers
• Solution of a system of linear differential equation with constant coefficients
• An equivalent triangular system
• Degenerate case
• Laplace transforms
• Linearity of Laplace transforms
• First shifting property
• Table of Laplace transforms
• Inverse Laplace transforms
• Laplace transform of derivative and integrals
• Unit step function and its Laplace transform
• Second shifting property
• Unit impulsive function and its Laplace transform
• Convolution and periodic function theorems
• Solution of linear differential equations with constant coefficients using Laplace transform methods
• Formation and solution of a partial differential equations
• Equations easily integrable
• Linear partial differential equations of first order
• Non-linear partial differential equation of first order and their different forms
• Charpit’s method
• Homogeneous linear partial differential equations with constant coefficients
• Different cases for complimentary functions and particular integrals
• Non-homogeneous partial differential equations with constant coefficients
• Classification of second order linear partial differential equations
• Method of separation of variables
• Fourier series
• Even and odd functions and their fourier series
• Change of interval
• Vibration of stretched string
• One and two dimensional heat flow
• Solution of Laplace equation in Cartesian and polar co-ordinates
• Variation of a functional
• Variational problems
• Euler’s equations and its various cases
• Externals
• Functional depending on unknown functions, functionals depending on higher derivatives
• Variational problems in parametric form
• Isoperimetric problem
• Canonical form of Euler’s equation
• Functionals depending on functions of several independent variables
• Ostrogradsky’s equation

Mathematics: Unit 05

• Functions of several variables, contour lines, level curves and level surfaces, limits and continuity for functions of two and more variables, partial derivatives, partial derivatives and continuity, differentiability
• The chain rule for functions of two and three variables
• Directional derivatives, gradient vectors, tangent planes, linearization and differentials, extreme values and saddle points, local and absolute maxima/ minima, the method of Lagrange multipliers (with one constraint only)
• Taylor’s series for function of two variables, partial derivatives with constrained variables
• Double integral over a rectangle region, double integral as volume, double integral over non rectangular regions, Fubini’s theorem, area of a region in a plane, transformation of double integral from Cartesian to polar coordinates and vice-versa
• Spherical and cylindrical coordinates, triple integral in Cartesian, cylindrical and spherical coordinates. line integral, gradient field, Green’s theorem in a plane, evaluation of line integral using Green’s theorem, surface area, surface integral
• Strokes theorem

Mathematics: Unit 06

• Binary operations, definitions of group, ring and field with examples, vector spaces, subspaces, span of a set, sum of subspaces, linear dependence and independence, dimension and basis, coordinates of a vector relative to the ordered basis
• Dimension theorem
• Linear transformation and its properties, range and kernel of a linear transformation, rank and nullity of linear transformation, rank-nullity theorem, inverse of linear transformation
• The vector space L(U,V) and its dimension, composition of linear transformations, matrix associated with a linear transformation, linear transformation associated with a matrix, matrix as a linear transformation and its rank and nullity
• Elementary row operations and row-reduced echelon form, inverse of a matrix through elementary row operation, solution of a system of linear equations, eigen-values, eigen vectors

Statistics: Unit 01

• Measures of central tendency, dispersion, Skewnes and Kurtosis, scatter diagram, correlation coefficient, rank correlation, Spearman’s and Kendall’s measures, multiple correlations in three variables, partial correlation in three variables
• Regression lines, regression coefficient and principal of least squares and curve fitting

Statistics: Unit 02

• Definition of probability, discrete and continuous sample space, events, independent and mutually exclusive events, random experiment, conditional probability, Baye’s theorem and its application, random variables, mathematical expectation
• Chesbyshev’s inequality

Statistics: Unit 03

• Uniform, binomial, Poisson, geometric, hypergeometric, normal exponential gamma and beta distribution, their means, variances and other properties

Statistics: Unit 04

• Concept of population and sampling, census and sample survey, random sample, sample size, non-sampling errors, concept of bias and standard error of an estimate, sampling distributions, tests of significance based on t, chi-square and F tests

Statistics: Unit 05

• Requirements of a good estimator, methods of estimation (MLE and method of moments), interval estimation
• Testing of hypothesis, simple and composite hypothesis, errors of first and second type and critical region

Statistics: Unit 06

• ANOVA for one way and two way classifications, principles of design of experiments, CRD, RBD and LSD, General LPP, graphical and simplex method of solving LPP

Computer science: Unit 01

Computer science: Unit 02

Computer science: Unit 03

Computer science: Unit 04