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Some Basic Concepts of Chemistry
Structure of Atom
Classification of Elements and Periodicity in Properties
Chemical Bonding and Molecular Structure
States of Matter: Gases and Liquids
Thermodynamics
Redox Reactions
The Hydrogen
The s-Block Element
Some p-Block Elements
Organic Chemistry - Principles and techniques
Hydrocarbons
Environmental Chemistry
Solid State
Solutions
Electrochemistry
Chemical Kinetics
Surface Chemistry
p-Block Elements (Group 15, 16, 17, 18)
The d-Block and f-Block Elements
Coordination Compounds
Haloalkanes and Haloarenes
Alcohols, Phenols, and Ethers
Aldehydes, Ketones and Carboxylic Acids
Organic Compounds Containing Nitrogen
Biomolecules
Polymers
Chemistry in Everyday Life
Physical World
Units and Measurements
Kinematics: Motion in a Straight Line
Kinematics: Motion in a Plane
Laws of Motion
Work, Energy and Power
System of Particles and Rotational Motion
Gravitation
Mechanical Properties of solids
Mechanical Properties of Fluids
Thermal Properties of Matter
Behaviour of Perfect Gas and Kinetic Theory
Oscillations and Waves
Electrostatics
Current Electricity
Moving Charges and Magnetism
Magnetism and Matter
Electromagnetic Induction and Alternating Currents
Electromagnetic Waves
Ray Optics
Optical Instruments
Wave Optics
Atoms and Nuclei
Electronic Devices
Dual Nature of Matter and Radiation
Introduction
Types of relations: reflexive, symmetric, transitive, and equivalence relations
Types of functions: one-one, onto, composite functions, inverse of a function
Binary operations
Questions and Answers
Important Formulas
Examples
Test
Concept, notation, order, equality, types of matrices, zero and identity matrix
Operations: Addition, multiplication, scalar multiplication
Transpose, symmetric and skew symmetric matrices
Properties of matrix operations
Determinants of order up to 3
Cofactors, adjoint, and inverse of a matrix
Solution of system of linear equations using matrices and determinants (Cramer’s Rule)
Properties of determinants
Minors, cofactors
Applications in solving linear equations (2x2 and 3x3 systems)
Limits and Continuity
Differentiability
Rules of Differentiation
Applications of Derivatives
Differential Coefficients of Parametric and Implicit Functions
Logarithmic Differentiation
Exponential Growth and Decay
Indefinite integrals: Integration as inverse of differentiation
Methods: Substitution, partial fractions, by parts
Definite integrals: Fundamental theorem of calculus
Properties of definite integrals
Vectors and scalars
Types of vectors
Addition, scalar multiplication
Dot product and cross product
Applications in geometry
Definition & Overview
Direction cosines and ratios
Equation of a line in space
Equation of a plane
Angle between two lines, two planes, line and plane
Distance between point and plane, two lines, etc
Introduction to linear programming problems
Graphical method of solution (two variables only)
Feasible and infeasible regions
Optimal solution
Definition of Probability
Conditional Probability
Independent events
Bayes’ theorem
Random variables and probability distributions (binomial)
Mean and variance of random variables
Definition, order, degree
General and particular solutions
Formation of differential equations
Solutions of first-order linear differential equations
Definition
Area under curves (lines, parabolas)
Area between two curves
Basic concepts, principal value branch
Graphs of inverse trigonometric functions
Elementary properties
Sets and their representations
Types of sets, Venn diagrams
Operations on sets
Relations and functions
Types of relations and functions
Complex numbers in the form a+ib
Argand plane and polar representation
Quadratic equations with real coefficients
Overview
Arithmetic Progression (AP)
Geometric Progression (GP)
Sum of n terms of special series
Arithmetic-Geometric progression
Concept of limit
Continuity of functions
Differentiability and derivatives
Application of derivatives
Mathematical Reasoning
Measures of central tendency and dispersion
Probability concepts
Conditional probability and Bayes’ theorem
Circles and conic sections (parabola, ellipse, hyperbola)
Fundamental principle of counting
Permutations, Combinations and Applications