AMUEEE

• Physical World and Measurement

  13 topics

  • Physics-scope and excitement
  • nature of physical laws
  • Physics, technology and society
  • Need for measurement
  • Units of measurement
  • systems of units
  • SI units, fundamental and derived units
  • Length, mass and time measurements
  • accuracy and precision of measuring instruments
  • errors in measurement
  • significant figures
  • Dimensions of physical quantities
  • dimensional analysis and its applications

• Kinematics

  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
  • relations for uniformly accelerated motion (graphical treatment)
  • Elementary concepts of differentiation and integration for describing motion
  • Scalar and vector quantities
  • Position and displacement vectors
  • general vectors and notation
  • equality of vectors
  • multiplication of vectors by a real number
  • addition and subtraction of vectors
  • Relative velocity
  • Unit vector
  • Resolution of a vector in a plane-rectangular components
  • Motion in a plane
  • Cases of uniform velocity and uniform acceleration
  • projectile motion
  • Uniform circular motion

• Laws of Motion

  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
  • Law of conservation of linear momentum and its applications
  • Equilibrium of concurrent forces
  • Static and kinetic friction, laws of friction, rolling friction
  • Lubrication
  • Dynamics of uniform circular motion
  • Centripetal force
  • examples of circular motion (vehicle on level circular road, vehicle on banked road)

• Work, Energy and Power

  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)
  • non-conservative forces: elastic and inelastic collisions in one and two dimensions

• Motion of System of Particles and Rigid Body

  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
  • moment of a force, torque, angular momentum
  • conservation of angular momentum with some examples
  • Equilibrium of rigid bodies
  • rigid body rotation and equations of rotational motion
  • Comparison of linear and rotational motions
  • moment of inertia, radius of gyration
  • Values of moments of inertia for simple geometrical objects (no derivation)
  • Statement of parallel and perpendicular axes theorems and their applications

• Gravitation

  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
  • Escape velocity
  • Orbital velocity of a satellite
  • Geo-stationary satellites

• Properties of Bulk Matter

  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)
  • Effect of gravity on fluid pressure
  • Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow
  • Bernoulli’s theorem and its applications
  • Surface energy and surface tension, angle of contact
  • application of surface tension ideas to drops, bubbles and capillary rise
  • Heat, temperature, thermal expansion
  • change of state-latent heat
  • Heat transfer-conduction, convection and radiation, thermal conductivity

• Thermodynamics

  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
  • Heat engines and refrigerators

• Behaviour of Perfect Gas and Kinetic Theory

  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
  • rms speed of gas molecules
  • degrees of freedom
  • law of equipartition of energy (statement only) and application to specific heats of gases
  • concept of mean free path
  • Avogadro’s number

• Oscillations and Waves

  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
  • simple pendulum-derivation of expression for its time period
  • free, forced and damped oscillations (qualitative ideas only), resonance
  • Wave motion
  • Longitudinal and transverse waves, speed of wave motion
  • Displacement relation for a progressive wave
  • Principle of superposition of waves
  • reflection of waves
  • standing waves in strings and organ pipes
  • fundamental mode and harmonics
  • Beats
  • Doppler effect

• Electrostatics

  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
  • Electric flux, statement of gauss’s theorem and its applications to find field due to infinitely long straight wire uniformly charges infinite plane sheet and uniformly charged thin spherical shell (field inside and outside)
  • Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charge
  • equipotential surfaces
  • electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field
  • Conductors and insulators, free charges and bound charges inside a conductor
  • Dielectrics and electric polarization
  • capacitors and capacitance, combination of capacitors in series and in parallel
  • capacitance of a parallel plate capacitor with and without dielectric medium between the plates
  • energy stored in a capacitor

• Current Electricity

  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
  • Carbon resistors colour code for carbon resistors
  • series and parallel combinations of resistors
  • temperature dependence of resistance
  • Internal resistance of a cell, potential difference and emf of a cell
  • combination of cells in series and in parallel
  • Kirchhoff’s laws and simple applications
  • Wheatstone bridge and metre bridge
  • Potentiometer – principle and its applications to measure potential difference and for comparing emf of two cells
  • measurement of internal resistance of a cell

• Magnetic Effects of Current and Magnetism

  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
  • Force on a current – carrying conductor in a uniform magnetic field
  • Force between two parallel current – carrying conductors – definition of ampere
  • Torque experienced by a current loop in uniform magnetic field
  • moving coil galvanometer – its current sensitivity and conversion to ammeter and voltmeter
  • Current loop as a magnetic dipole and its magnetic dipole moment
  • Magnetic dipole, moment of a revolving electron
  • magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis
  • Torque on magnetic dipole (bar magnet) in a uniform magnetic field
  • bar magnet as an equivalent solenoid magnetic field line
  • Earth’s magnetic field and magnetic elements
  • para – dia – and ferro – magnetic substances, with examples
  • Electromagnets and factors of affecting their strengths
  • Permanent magnets

• Electromagnetic Induction and Alternating Currents

  11 topics

  • Electromagnetic Induction
  • Faraday’s law
  • Induced emf and current
  • Lenz’s law
  • Eddy current self and mutual induction
  • Alternating currents, peak and rms value of alternating
  • current/voltage, reactance and impedance
  • LC oscillations (qualitative treatment only)
  • LCR series circuit, resonance
  • power in ac circuits wattles current
  • AC generator and transformer

• 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

  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
  • Refraction and dispersion of light through a prism
  • Scattering of light – blue colour of the sky and reddish appearance of the sun at sunrise and sunset
  • Optical instruments: Microscopes and astronomical Telescopes (reflecting and refraction) and their magnifying powers
  • Waves optics: Wave front and Huygens principle reflection and refraction of plane wave at a plane surface using wave fronts
  • Proof of laws of reflection and refraction using Huygen’s principle
  • Interference, Young’s double slit experiment and expression for fringe width
  • coherent sources and sustained interference of light
  • Diffraction due to a single slit, width of central maximum
  • Resolving power of microscopes and astronomical telescopes
  • Polarization, plane polarized light
  • Brewster’s law
  • Uses of plane polarized light and polaroids

• 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

  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
  • radioactive decay law
  • Mass-energy relation, mass defect
  • binding energy per nucleon and its variation with mass number
  • nuclear fission, nuclear fusion

• 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 all 214 topics in this subject.Show fewer topics

• Some Basic Concepts of Chemistry

  4 of 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

• Structure of Atom

  4 of 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

• Classification of Elements and Periodicity in Properties

  4 of 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

• Chemical Bonding and Molecular Structure

  4 of 9 topics

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

• States of Matter : Gases and Liquids

  4 of 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

• Chemical Thermodynamics

  4 of 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

• Equilibrium

  4 of 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

• 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

  4 of 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

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

  4 of 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

• Some p-Block Elements

  4 of 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

• Organic Chemistry – Some Basic Principles and Techniques

  4 of 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

• Hydrocarbons

  4 of 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

• Environmental Chemistry

  4 of 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

• Solid State

  4 of 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

• Solutions

  4 of 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

• Electrochemistry

  4 of 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)

• Chemical Kinetics

  4 of 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

• Surface Chemistry

  4 of 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

• 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

  4 of 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

• d and f-Block Elements

  4 of 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

• Coordination Compounds

  4 of 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)

• 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

  4 of 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

• 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

  4 of 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)

• Polymers

  4 of 6 topics

  • Classification – Natural and synthetic
  • methods of polymerization (addition and condensation)
  • copolymerization
  • Some important 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 114 of 213 topics in this subject.Show all 213 topics →

• SETS

  4 of 12 topics

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

• RELATIONS & FUNCTIONS

  4 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

• TRIGNOMETRIC FUCNTIONS

  4 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

• 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

  4 of 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

• 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

  4 of 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.

• STRAIGHT LINES

  4 of 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

• 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

  4 of 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

• Determinants

  4 of 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

• Continuity and Differentiability

  4 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

• 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

  3 of 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

• 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

  3 of 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

• Vectors

  3 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)

• Three – dimensional Geometry

  3 of 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

• Linear programming

  3 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

• Probability

  3 of 5 topics

  • Multiplication theorem on probability
  • Conditional probability, independent events, total probability
  • Baye’s theorem

Showing 92 of 132 topics in this subject.Show all 132 topics →