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
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
Human Reproduction
Overview summary
Overall Guide
Types of Solids
Packing in Solids
Defects in Crystals
Types of Solutions
Concentration Terms (Molality, Molarity, etc.)
Raoult’s Law & Colligative Properties
Galvanic Cells (Voltaic Cells)
Nernst Equation
Electrolysis
Rate of Reaction
Order and Molecularity of a Reaction
Arrhenius Equation
Adsorption
Colloids and Emulsions
Catalysis
Metallurgy
Extraction and Refining Methods
p-Block Elements – Groups 15 to 18
Important Compounds – NH₃, HNO₃, H₂SO₄
Transition Elements
Lanthanides and Actinides
The d- and f-Block Elements – Properties and Uses
Ligands & Coordination Number
IUPAC Naming of Organic Compounds
Bonding Theories
SN1 and SN2 mechanisms
Properties and Uses
Structure & Preparation
Reactions and Uses
Nomenclature
Nucleophilic Addition Reactions
Amines, Cyanides & Isocyanides
Diazonium Salts
Carbohydrates, Proteins, Vitamins & Nucleic Acids
Types & Classification
Natural and Synthetic Polymers
Drugs & Medicines
Soaps and Detergents
Food additives
Mole Concept
Stoichiometry
Empirical and Molecular Formula
Limiting Reagent
Bohr’s Model of the Atom
Quantum Mechanical Model of the Atom
Electronic Configuration
Quantum Numbers
Modern Periodic Table
Periodic Trends in the Periodic Table
Ionic and Covalent Bonding
VSEPR Theory
Hybridization and Molecular Orbital Theory
test
Ideal Gas Equation
Kinetic Molecular Theory (KMT)
Real Gases and van der Waals Equation
First Law of Thermodynamics
Enthalpy, Entropy, and Spontaneity
Hess’s Law of Constant Heat Summation
Chemical and Ionic Equilibrium
Le Chatelier’s Principle
pH, Ka, Kb, Kw, and Solubility Product
Oxidation Number
Balancing Redox Equations
Electrochemical Series
Hydrogen – Properties and Uses
Hydrogen Peroxide (H₂O₂)
Isotopes of Hydrogen
The s-Block Element – General Properties
Biological Importance
Compounds like NaCl, CaO, CaCO₃
Group 13 and Group 14 Elements
Boron, Carbon and Silicon Compounds
IUPAC Nomenclature
Isomerism
Reaction Intermediates
Purification Methods
Alkanes, Alkenes, and Alkynes
Aromatic Hydrocarbons
Reactions and Mechanisms
Pollution (Air, Water, Soil)
Green Chemistry
Ozone Depletion and Greenhouse Effect
Introduction to Electrostatics
Properties of Electric Charge
Conductors and Insulators
Methods of Charging
Coulomb’s Law
Principle of Superposition in Electrostatics
Electric Field
Electric Field Lines
Electric Field Due to a System of Charges
Electric Dipole
Torque on a Dipole in Uniform Electric Field
Potential Energy of a Dipole in a Uniform Electric Field
Continuous Charge Distributions
Electric Field Due to a Line Charge
Electric Field Due to a Ring of Charge (on Axis)
Gauss’s Law
Applications of Gauss’s Law
Electric Flux
Electrostatic Potential
Electrostatic Potential Energy
Capacitance
Combination of Capacitors
Energy Stored in a Capacitor
Van de Graaff Generator
Electric Current Basics
Ohm’s Law and Resistivity
Electrical Energy and Power
Combination of Resistors
EMF and Internal Resistance
Kirchhoff’s Laws (KCL & KVL)
Wheatstone Bridge and Meter Bridge
Potentiometer
Magnetic Force and Motion
Magnetic Force on Current-Carrying Conductors
Magnetic Field Due to Currents
Ampere’s Circuital Law
Magnetic Dipole and Torque
Moving Coil Galvanometer
Magnetic Properties of Materials
Magnetization and Magnetic Field Intensity
Magnetic Susceptibility and Permeability
Hysteresis and Hysteresis Loop
Curie’s Law and Curie Temperature
Faraday’s Laws of Electromagnetic Induction (EMI)
Lenz’s Law
Motional Electromotive Force (EMF)
Self-Induction and Mutual Induction
Energy Stored in an Inductor
AC Voltage and Current
RMS and Average Values of Alternating Current and Voltage
Reactance and Impedance
Phase Relationships in R, L, and C Circuits
Power in AC Circuits
Nature and Production of Electromagnetic Waves
Maxwell’s Equations and Electromagnetic Wave Equation
Properties of Electromagnetic Waves
Electromagnetic Spectrum
Energy and Momentum in Electromagnetic Waves
Reflection and Refraction of Light
Total Internal Reflection (TIR)
Lenses and Image Formation
Prism and Dispersion of Light
Optical Instruments
Huygens’ Principle and Wavefronts
Interference of Light
Diffraction of Light
Polarization of Light
Coherent and Incoherent Sources
Photoelectric Effect
Characteristics of Photoelectric Effect
Wave-Particle Duality
de Broglie Wavelength
Experimental Verification of de Broglie Waves
Atomic Models
Bohr’s Model of Hydrogen Atom
Energy Levels and Spectra
Limitations of Bohr’s Model
Atomic Spectra and Line Spectra
Composition and Properties of the Nucleus
Isotopes, Isobars, and Isotones
Radioactivity and Types of Radioactive Decay
Law of Radioactive Decay
Nuclear Binding Energy and Mass Defect
Semiconductors and Their Types
P-N Junction and Its Characteristics
Semiconductor Diode and Its Applications
Logic Gates and Boolean Algebra
Transistors and Their Applications
What is Physics?
Fundamental Forces in Nature
Nature of Physical Laws
Unification and Reductionism
Scope and Excitement of Physics
Test
Fundamental and Derived Units
Measurement of Length, Mass, and Time
Errors in Measurement
Significant Figures
Dimensions and Dimensional Analysis
Basic Concepts of Motion
Uniform and Non-Uniform Motion
Equations of Motion for Uniform Acceleration
Graphical Representation of Motion
Relative Velocity
Scalars and Vectors
Projectile Motion
Uniform Circular Motion
Relative Motion in Two Dimensions
Vector Resolution and Components
Newton’s Laws of Motion
Inertia and Mass
Free Body Diagrams (FBD)
Friction
Circular Motion and Banking of Roads
Work Done by a Force
Kinetic and Potential Energy
Work-Energy Theorem
Law of Conservation of Energy
Power and Its Measurement
Centre of Mass (COM)
Linear Momentum and Its Conservation
Rotational Motion of Rigid Bodies
Moment of Inertia (MI)
Torque, Angular Momentum, and Equilibrium
Universal Law of Gravitation
Acceleration Due to Gravity (g)
Gravitational Potential and Potential Energy
Motion of Satellites
Escape Speed and Energy
Stress and Strain
Hooke’s Law and Elastic Limit
Elastic Moduli – Stress, Strain, and the Moduli of Elasticity
Stress-Strain Curve
Applications of Elastic Behavior
Pressure in a Fluid
Pascal’s Law
Buoyancy and Archimedes’ Principle
Bernoulli’s Principle
Viscosity and Surface Tension
Heat and Temperature
Specific Heat Capacity
Change of State and Latent Heat
Thermal Expansion
Heat Transfer Mechanisms
Thermodynamic System and Surroundings
Work and Heat in Thermodynamics
Thermodynamic Processes
Specific Heat Capacities and Mayer’s Relation
Molecular Nature of Matter
Kinetic Interpretation of Temperature
Degrees of Freedom and Equipartition of Energy
Mean Free Path and Distribution of Molecular Speeds
Simple Harmonic Motion (SHM)
Restoring Force and Acceleration in Simple Harmonic Motion (SHM)
Energy in Simple Harmonic Motion (SHM)
Damped Oscillations
Forced Oscillations and Resonance
Types of Waves
Wave Parameters and Equation of a Progressive Wave
Speed of Sound in Different Media
Principle of Superposition and Interference
Standing Waves and Resonance