AMUEEE

• Physical World and Measurement

  5 of 13 topics

  • Physics-scope and excitement
  • nature of physical laws
  • Physics, technology and society
  • Need for measurement
  • Units of measurement

• Kinematics

  5 of 20 topics

  • Frame of reference
  • Motion in a straight line
  • Position-time graph, speed and velocity
  • Uniform and non-uniform motion, average speed and instantaneous velocity
  • Uniformly accelerated motion, velocity-time, position-time graphs

• Laws of Motion

  5 of 12 topics

  • Intuitive concepts of force
  • Inertia, Newton’s first law of motion
  • momentum and Newton’s second law of motion
  • impulse
  • Newton’s third law of motion

• Work, Energy and Power

  5 of 6 topics

  • Scalar product of vectors
  • Work done by a constant force and a variable force
  • kinetic energy, work-energy theorem, power
  • Notion of potential energy, potential energy of a spring
  • conservative forces: conservation of mechanical energy (kinetic and potential energies)

• Motion of System of Particles and Rigid Body

  5 of 13 topics

  • Centre of mass of a two-particle system
  • momentum conversation and centre of mass motion
  • Centre of mass of a rigid body
  • centre of mass of uniform rod
  • Vector product of vectors

• Gravitation

  5 of 8 topics

  • Keplar’s laws of planetary motion
  • The universal law of gravitation
  • Acceleration due to gravity and its variation with altitude and depth
  • Gravitational potential energy
  • gravitational potential

• Properties of Bulk Matter

  5 of 13 topics

  • Elastic behaviour
  • Stress-strain relationship
  • Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity
  • Pressure due to a fluid column
  • Pascal’s law and its applications (hydraulic lift and hydraulic brakes)

• Thermodynamics

  5 of 6 topics

  • Thermal equilibrium and definition of temperature (zeroth law of thermodynamics)
  • Heat, work and internal energy
  • First law of thermodynamics
  • Isothermal & adiabatic process
  • Second law of thermodynamics: reversible and irreversible processes

• Behaviour of Perfect Gas and Kinetic Theory

  5 of 10 topics

  • Equation of state of perfect gas
  • work done on compressing a gas
  • Kinetic theory of gases-assumptions
  • concept of pressure
  • Kinetic Interpretation of temperature

• Oscillations and Waves

  5 of 16 topics

  • Periodic motion-period, frequency, displacement as a function of time
  • Periodic functions
  • Simple harmonic motion (S.H.M) and its equation
  • oscillations of a spring-restoring force and force constant
  • energy in S.H.M.-kinetic and potential energies

• Electrostatics

  5 of 14 topics

  • Electric charges, Conservation of charge
  • Coulomb’s low-force between two point charges
  • forces between multiple charges, superposition principle and continuous charge distribution
  • Electric field, electric field due to a point charge, electric field lines
  • electric dipole electric field due to a dipole torque on a dipole in uniform electric field

• Current Electricity

  5 of 14 topics

  • Electric current flow of electric chargers in a metallic conductor drift velocity, mobility and their relation with electric current
  • Ohm’s Law electrical resistance
  • V-I characteristics (linear and non-linear)
  • electrical energy and power
  • electrical resistivity and conductivity

• Magnetic Effects of Current and Magnetism

  5 of 18 topics

  • Concept of magnetic field, Oersted’s experiment
  • Biot-Savart law and its application to current carrying circular loop
  • Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids
  • Force on a moving charge in uniform magnetic and electric fields
  • Cyclotron

• Electromagnetic Induction and Alternating Currents

  5 of 11 topics

  • Electromagnetic Induction
  • Faraday’s law
  • Induced emf and current
  • Lenz’s law
  • Eddy current self and mutual induction

• Electromagnetic Waves

  4 topics

  • Displacement current
  • Electromagnetic wave and their characteristics (qualitative ideas only)
  • Transverse nature of electromagnetic waves
  • Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses

• Optics

  5 of 17 topics

  • Reflection of light spherical mirrors, mirror formula
  • refraction of light, total internal reflection and its applications
  • optical fibres refraction at spherical surfaces
  • lenses thin lens formula lens maker’s Formula
  • Magnification power of a lens, combination of thin lenses in contract

• Dual Nature of Matter and Radiation

  5 topics

  • Dual nature of Radiation
  • Photoelectric, Hertz and Lenard’s observations
  • Einstein’s Photoelectric equation – particle nature of light
  • Matter waves-wave nature of particles, de Broglie relation
  • Davission – Germer experiment

• Atoms & Nuclei

  5 of 9 topics

  • Alpha-particle scattering experiment
  • Rutherford’s model of atom
  • Bohr model, energy levels hydrogen spectrum
  • Composition and size of nucleus
  • Radioactivity – alpha, beta and gamma particles/rays and their properties

• Electronic Devices

  5 topics

  • Semiconductors
  • semiconductor diode – I – V. characteristics in forward and reverse bias
  • diode as a rectifier
  • I – V characteristics of LED, photodiode, solar cell and Zener diode
  • Zener diode as a voltage regulator

Showing 94 of 214 topics in this subject.Show all 214 topics →

• Some Basic Concepts of Chemistry

  8 topics

  • 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

• Structure of Atom

  14 topics

  • 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

• Classification of Elements and Periodicity in Properties

  5 topics

  • 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, electron gain enthalpy, electronegativity, valence
  • Nomenclature of elements with atomic number greater than 100

• Chemical Bonding and Molecular Structure

  9 topics

  • Valence electrons, ionic bond, covalent bond, bond parameters
  • Lewis structure
  • polar character of 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

• States of Matter : Gases and Liquids

  7 topics

  • 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)

• Chemical Thermodynamics

  10 topics

  • 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, 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

• Equilibrium

  12 topics

  • 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)
  • buffer solutions, Henderson equation
  • solubility product
  • common ion effect (with illustrative examples)

• Redox Reactions

  4 topics

  • 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

• Hydrogen

  5 topics

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

• s-Block Elements (Alkali and Alkaline earth metals)

  9 topics

  • Group 1 and Group 2 elements
  • General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship
  • trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii)
  • trends in chemical reactivity with oxygen, water, hydrogen and halogens
  • Preparation and Properties of some Important Compounds
  • Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogencarbonate
  • biological importance of sodium and potassium
  • CaO CaCO3, and industrial use of lime and limestone
  • biological importance of Mg and Ca

• Some p-Block Elements

  9 topics

  • 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, 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, physical and chemical properties
  • uses of some important compounds: oxides
  • Important compounds of silicon and a few uses : silicon tetrachloride, silicones, silicates and zeolites, their uses

• Organic Chemistry – Some Basic Principles and Techniques

  6 topics

  • 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

• Hydrocarbons

  11 topics

  • Classification of Hydrocarbons
  • Aliphatic hydrocarbons
  • Alkanes – Nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis
  • Alkenes – Nomenclature, structure of double bond (ethane), geometrical isomerism, physical properties, methods of preparation
  • chemical reactions: addition of hydrogen, halogen, water, hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition
  • 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
  • directive influence of functional group in mon-substituted benzene
  • carcinogenicity and toxicity

• Environmental Chemistry

  6 topics

  • 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

• Solid State

  8 topics

  • 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

• Solutions

  6 topics

  • 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

• Electrochemistry

  10 topics

  • Redox reactions
  • conductance in electrolytic 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

• Chemical Kinetics

  7 topics

  • 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

• Surface Chemistry

  8 topics

  • 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

• General Principles and Processes of Isolation of Elements

  2 topics

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

• p-Block Elements

  18 topics

  • Group 15 elements : General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties
  • nitrogen – preparation, properties and uses
  • compounds of nitrogen : preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only)
  • Phosophorous – allotropic forms
  • compounds of phosphorous : preparation and properties of phosphine, halides (PCI3, PCI5) 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
  • 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, 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

• d and f-Block Elements

  5 topics

  • 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, catalytic property, magnetic properties, interstitial compounds, alloy formation
  • Preparation and properties of K2Cr2O7 and KMnO4
  • Lanthanoids – electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences
  • Actinoids – Electronic configuration, oxidation states and comparison with lanthenoids

• Coordination Compounds

  5 topics

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

• Haloalkanes and Haloarenes

  4 topics

  • 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

• Alcohols, Phenols and Ethers

  5 topics

  • 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

• Aldehydes, Ketones and Carboxylic Acids

  2 topics

  • 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
  • Carboxylic Acids : Nomenclature, acidic nature, methods of preparation, physical and chemical properties

• Organic Compounds Containing Nitrogen

  3 topics

  • 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

• Biomolecules

  6 topics

  • Carbohydrates – Classification (aldoses and ketoses), monosaccharide (glucose and fructose), D-L configuration, oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen)
  • 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

• Polymers

  6 topics

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

• Chemistry in Every Day Life

  3 topics

  • 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

Showing all 213 topics in this subject.Show fewer topics

• SETS

  5 of 12 topics

  • Sets and their representations
  • Empty set
  • Finite & Infinite sets
  • Equal sets
  • Subsets

• RELATIONS & FUNCTIONS

  5 of 8 topics

  • 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, codomain and range of a relation
  • Function as a special kind of relation from one set to another

• TRIGNOMETRIC FUCNTIONS

  5 of 8 topics

  • 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
  • Truth of the identity sin2 x + cos2 x = 1 for all x
  • Signs of trigonometric functions and sketch of their graphs

• PRINCIPLE OF MATHEMATICAL INDUCTION

  2 topics

  • 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

  5 topics

  • Need for complex numbers
  • Brief description of algebraic properties of complex numbers
  • Argand plane and polar representation of complex numbers
  • Statement of Fundamental Theorem of Algebra
  • Solution of quadratic equations in the complex number system

• LINEAR INEQUALITIES

  4 topics

  • 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
  • Solution of system mof linear inequalities in two variables graphically

• PERMUTATIONS AND COMBINATIONS

  3 topics

  • Fundamental principle of counting
  • Factorial n (n1)
  • Permutations and combinations, derivation of formulae and their connections, simple applications

• BINOMIAL THEOREM

  3 topics

  • 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

  5 topics

  • Sequence and Series
  • Arithmetic progression (AP), arithmetic mean (A.M.)
  • Geometric progression (GP, General term of a GP, sum of n terms of a G.P., Geometric mean (GM)
  • relation between A.M. and G.M.
  • Sum to n terms of the special series

• STRAIGHT LINES

  5 topics

  • Brief recall of 2 D 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
  • General equation of a line
  • Distance of a point from a line

• CONIC SECTION

  3 topics

  • 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
  • Standard equation of a circle

• INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

  3 topics

  • Coordinate axes and coordinate planes in three dimensions
  • Coordinatoes of a point
  • Distance between two points and section formula

• LIMITS AND DERIVATIVES

  4 topics

  • 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, product and quotient of functions
  • Derivatives of polynomial and trigonometric functions

• MATHEMATICAL REASONING

  3 topics

  • 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”, “there exists” and their use through variety of examples related to real life and mathematics
  • Validating the statements involving the connecting words – difference between contradiction, converse and contrapositive

• PROBABILITY

  4 topics

  • 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, connections with the theories of earlier classes
  • Probability of an event, Probability of `not’, `and’ and `or’ events

• Relations and Functions

  2 topics

  • Types of relations : reflexive, symmetric, transitive and equivalence relations
  • One to one and onto functions, composite functions, inverse of a function

• Inverse Trigonometric Functions

  3 topics

  • Definition, range, domain, principal value branches
  • Graphs of inverse trigonometric functions
  • Elementary properties of inverse trigonometric functions

• Matrices

  5 topics

  • 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, 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)
  • Concept of elementary row and column operations
  • Invertible matrices and proof of the uniqueness of inverse, if it exists

• Determinants

  5 topics

  • 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
  • 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

• Continuity and Differentiability

  5 of 7 topics

  • Continuity and Differentiability, derivative of composite functions, chain rule
  • derivative of inverse trigonometric functions, derivative of implicit function
  • Concept of exponential and logarithmic functions and their derivative
  • Logarithmic differentiation
  • Derivative of functions expressed in parametric forms

• Applications of Derivatives

  2 topics

  • Applications of derivatives : rate of change, increasing / decreasing functions, tangents and normal, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
  • Simple problems (that illustrate basic principles and understanding of the subject as well as real life situations)

• Integrals

  5 topics

  • Integration as inverse process of differentiation
  • Integration of a variety of functions by substitution, by partial fractions and by parts
  • 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

  2 topics

  • 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

  5 topics

  • 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
  • homogeneous differential equations of first order and first degree
  • Solutions of linear differential equations

• Vectors

  5 of 8 topics

  • 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
  • addition of vectors, multiplication of a vector by a scalar

• Three – dimensional Geometry

  5 topics

  • 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
  • Angle between (1) two lines, (ii) two planes, (iii) a line and plane
  • Distance of a point from a plane

• Linear programming

  5 of 6 topics

  • Introduction, definition of related terminology such as constraints, objective function, optimization
  • different types of linear programming (LP) problems
  • mathematical formulation of LP, problems
  • graphical method of solution for problems in two variables
  • feasible and infeasible regions, feasible and infeasible solutions

• Probability

  5 topics

  • 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
  • Repeated independent (Bernoulli) trials and Binomial distribution

Showing 113 of 132 topics in this subject.Show all 132 topics →