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IIT-JEE Class Mathematic - Preview

  • Sets
    HD Video Lectures - 21, Questions- 25
    • Introduction to Set Theory
    • Representation of Sets
    • Practice Questions (Set 1)
    • Finite Sets and Infinite Sets
    • Equal Sets
    • What Are Subsets?
    • More About Subsets
    • Power Set and Universal Set
    • Intervals as Subsets of Real Numbers
    • Venn Diagrams
    • Union of Sets
    • Intersection of Sets
    • Difference of Sets
    • Complement of a Set
    • Some Laws on Complement of a Set
    • More About Union and Intersection of Sets
    • Practice Questions (Set 2)
    • Important Results on Cardinality of Two Sets
    • Practical Problems on Operations of Sets
    • Important Results on Cardinality of Three Sets
    • Practice Questions (Set 3)
    Relations
    HD Video Lectures - 12, Questions- 25
    • Understanding Cartesian Product of Sets
    • Problems on Cartesian Product of Sets
    • Understanding Relations
    • Problems on Relations
    • Terms Related to Relations
    • Introduction to Types of Relations
    • Types of Relations
    • Equivalence Relation and Its Examples
    • Problems on Types of Relations
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    Functions
    HD Video Lectures - 66, Questions- 25
    • Introduction to Functions
    • Function: A Special Relation
    • Terms Related to Functions
    • Domain and Range of a Function
    • Even Functions and Odd Functions
    • Identity Function and Constant Function
    • Understanding Polynomial Functions
    • Quadratic Polynomial Function
    • Problems Related to Quadratic Functions
    • Rational Functions
    • Understanding the Modulus Function
    • Properties of Modulus Function
    • Problems on the Modulus Function
    • Understanding the Signum Function
    • The Greatest Integer Function
    • Problems on the Step Function
    • Fractional Part Function
    • e: A Special Number
    • The Exponential Function
    • The Logarithm Function
    • Properties of Logarithms – 1
    • Properties of Logarithms – 2
    • Problems on the Domain and Range of Logarithms
    • Graph of Logarithmic Functions
    • Problems Related to Logarithmic Functions
    • What Is an Angle?
    • Introduction to Trigonometric Functions
    • Definitions of Trigonometric Functions
    • Observations on the Definition
    • Domain, Range and Graph of the Sine Function
    • Domain, Range and Graph of the Cosine Function
    • Comparing Sine and Cosine Functions
    • Domain, Range and Graph of the Cosecant and Secant Functions
    • Domain, Range and Graph of the Tangent and Cotangent Functions
    • Problems on Trigonometric Functions – 1
    • Problems on Trigonometric Functions – 2
    • Finding the Trigonometric Values of Some Specific Angles
    • Problems on Finding the Values of Trigonometric Functions
    • Introduction to One-to-One and Onto Functions
    • Properties of One-to-One Functions
    • Methods to Find One-to-One Functions
    • Problems on One-to-One and Onto Functions
    • Understanding Composition of Functions
    • Properties of Composite Functions
    • Defining the Inverse of a Function
    • Properties of Inverse Functions
    • Problems on Composite and Inverse Functions
    • Introduction to Inverse Trigonometric Functions
    • Sine and Cosine Inverse Functions
    • Tangent and Cotangent Inverse Functions
    • Cosecant and Secant Inverse Functions
    • Problems on Inverse Trigonometric Functions
    • Transformations of Graphs – 1
    • Transformations of Graphs – 2
    • Problems on Transformations of Graphs – 1
    • Problems on Transformations of Graphs – 2
    • Periodic Functions
    • Properties of Periodic Functions
    • Functional Equations
    • Solving Non-standard Functional Equations
    • Finding the Number of Functions
    • Problems on Finding the Number of Functions
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    • Practice Questions (Set 4)
    Mathematical Induction
    HD Video Lectures - 4, Questions- 25
    • Introduction to the Principle of Mathematical Induction
    • The Method of the Principle of Mathematical Induction
    • Divisibility and Inequality Problems on the Principle of Mathematical Induction
    • Practice Questions
    Complex Numbers
    HD Video Lectures - 20, Questions- 25
    • What Are Imaginary Numbers?
    • Complex Numbers and Their Representation
    • Algebra of Complex Numbers
    • Square Root of a Complex Number
    • Modulus of a Complex Number
    • Argument of a Complex Number
    • Conjugate of a Complex Number
    • How to Find the Principal Argument
    • Polar Coordinates and the Euler Form
    • Cube Roots of Unity
    • Quadratic Equations and Complex Roots
    • De Moivre's Theorem
    • nth Roots of Unity
    • Practice Questions (Set 1)
    • Vector Representation of Complex Numbers and Its Applications
    • Important Results Based on Modulus and Argument
    • Geometry and Locus in Complex Numbers
    • Triangle Inequality
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    Linear Inequalities
    HD Video Lectures - 4, Questions- 25
    • Introduction to Linear Inequalities
    • Algebraic Solutions of Linear Inequalities in One Variable
    • Solutions of Linear Inequalities in Two Variables – Part 1
    • Solutions of Linear Inequalities in Two Variables – Part 2
    Permutations and Combinations
    HD Video Lectures - 22, Questions- 25
    • Introduction to Permutations and Combinations
    • The Fundamental Principle of Counting
    • Examples on the Fundamental Principle of Counting
    • The Meaning of n!
    • Number of Arrangements – Permutations
    • Properties of nPr and Examples
    • Number of Selections – Combinations
    • Properties of nCr and Examples
    • Examples of Permutations and Combinations
    • Permutations of Alike Objects
    • The Classical Problem of Seating Arrangements
    • Game of Words: Lexicography and Dictionary
    • Game of Digits and Divisibility Concept
    • Permutations and Combinations of Playing Cards
    • Circular Permutation
    • Distribution of Identical Objects Into Groups – Part 1
    • Distribution of Identical Objects Into Groups – Part 2
    • Distribution of Distinct Objects Into Groups
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    • Practice Questions (Set 4)
    Binomial Theorem and Its Applications
    HD Video Lectures - 0, Questions- 25
    Sequence and Series
    HD Video Lectures - 0, Questions- 25
    Mathematical Reasoning
    HD Video Lectures - 8, Questions- 25
    • Introduction to Mathematical Reasoning
    • Compound Statements, Truth Value, Truth Table and Connectives
    • What Are Quantifiers?
    • Implications or Conditional
    • Converse, Inverse and Contrapositive
    • Bi-Conditional Statements or Equivalence
    • Logical Equivalence, Fallacy and Tautology
    • Practice Questions
    Matrices and Determinants
    HD Video Lectures - 36, Questions- 25
    • What Is a Matrix?
    • Order of a Matrix
    • Types of Matrices
    • Matrix Algebra
    • How to Multiply Two Matrices
    • Properties of Matrix Multiplication
    • Problems on Algebra of Matrices
    • What Is Determinant of a Matrix?
    • Algebraic Properties of Determinants
    • Transpose of a Matrix
    • Properties of Symmetric Matrices and Skew-Symmetric Matrices
    • What Is Inverse of a Matrix?
    • Elementary Operations
    • Finding the Inverse of a Matrix Using Elementary Operations
    • What Is a Determinant?
    • Finding the Determinant of a Matrix
    • Problems on Finding the Determinant of Matrices
    • Properties of Determinants – 1
    • Properties of Determinants – 2
    • Properties of Determinants – 3
    • Properties of Determinants – 4
    • Problems on Properties of Determinants (Set 1)
    • Problems on Properties of Determinants (Set 2)
    • Finding the Area of a Triangle Using Determinants
    • Understanding Minor and Cofactor of an Element
    • What Is Adjoint of a Matrix?
    • Finding the Inverse of a Matrix Using Adjoint
    • Properties of Adjoint and Inverse of Matrices
    • Problems on Properties of Adjoint and Inverse of Matrices
    • Solving a System of Linear Equations Using Matrices
    • Problems on Solving System of Linear Equations
    • Solving a System of Linear Equations Using Cramer's Rule
    • Problems on Cramer's Rule
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    Trigonometric Functions, Identities and Equations
    HD Video Lectures - 27, Questions- 25
    • Introduction to Trigonometric Functions
    • What Is an Angle?
    • Problems on the Measure of an Angle
    • Defining Trigonometric Functions
    • Problems on Trigonometric Identities
    • Observations on the Definition
    • Domain, Range and Graph of the Sine Function
    • Domain, Range and Graph of the Cosine Function
    • Domain, Range and Graph of the Cosecant and Secant Functions
    • Domain, Range and Graph of the Tangent and Cotangent Functions
    • Problems on Trigonometric Functions
    • Finding the Trigonometric Values of Some Specific Angles
    • Problems on Finding the Values of Trigonometric Functions
    • Trigonometric Functions of the Sum and Difference of Two Angles – 1
    • Trigonometric Functions of the Sum and Difference of Two Angles – 2
    • Problems on Trigonometric Functions of the Sum and Difference of Two Angles
    • Multiple-Angle Identities
    • Problems on Multiple-Angle Identities – 1
    • Problems on Multiple-Angle Identities – 2
    • Problems on Multiple-Angle Identities – 3
    • Finding the Range of Trigonometric Functions – 1
    • Finding the Range of Trigonometric Functions – 2
    • Trigonometric Equations – 1
    • Trigonometric Equations – 2
    • Problems on Trigonometric Equations
    • Solving Trigonometric Equations Using Identities – 1
    • Solving Trigonometric Equations Using Identities – 2
    Inverse Trigonometric Functions
    HD Video Lectures - 16, Questions- 25
    • Introduction to Inverse Trigonometric Functions
    • Sine and Cosine Inverse Functions
    • Tangent and Cotangent Inverse Functions
    • Cosecant and Secant Inverse Functions
    • Solving Inverse Trigonometry Problems – 1
    • Inverse Trigonometric Identities – 1
    • Inverse Trigonometric Identities – 2
    • Solving Inverse Trigonometry Problems – 2
    • Solving Inverse Trigonometry Problems – 3
    • Solving Inverse Trigonometry Problems – 4
    • Inverse Trigonometric Identities – 3
    • Problems on Inverse Trigonometric Identities
    • Solving Inverse Trigonometry Problems by Substitution
    • Solving Summation Problems
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    Properties of Triangles
    HD Video Lectures - 9, Questions- 25
    • Revisiting Terms Related to Triangles
    • Understanding the Sine Rule
    • Problems on the Sine Rule
    • Understanding the Cosine Rule
    • Problems on the Cosine Rule
    • Understanding the Projection Rule and Napier's Analogy
    • Understanding the Different Relations of Area of a Triangle
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    Straight Lines
    HD Video Lectures - 19, Questions- 25
    • Revisiting the Cartesian Plane
    • Slope of a Straight Line
    • Importance of Slope and Its Uses
    • Equation of a Line – Part 1
    • Equation of a Line – Part 2
    • Equation of a Line – Normal Form
    • Interpreting the General Equation of a Line
    • Distance of a Point From a Line
    • Equations of the Angle Bisectors of Two Lines
    • Concurrency of Straight Lines
    • Family of Straight Lines – Part 1
    • Family of Straight Lines – Part 2
    • Family of Straight Lines – Part 3
    • Straight Lines and Triangles – Part 1
    • Straight Lines and Triangles – Part 2
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    • Practice Questions (Set 4)
    Locus and Translation of Axes
    HD Video Lectures - 6, Questions- 25
    • Introduction to Locus and Its Equation
    • Examples on Locus Equation – 1
    • Examples on Locus Equation – 2
    • Translation of Axes – Part 1
    • Translation of Axes – Part 2
    • Example Questions on Translation of Axes
    Circles
    HD Video Lectures - 14, Questions- 25
    • Equation of a Circle in the Standard Form
    • Other Forms of Equation of Circle
    • Different Approaches for Writing the Equation of a Circle
    • Points of Intersection of a Line and a Circle
    • Condition for a Line to Be Tangent to a Circle
    • Equation of Tangent to a Circle at a Point
    • Equation of Tangent to a Circle From an External Point
    • System of Two Circles
    • Practice Questions on System of Two Circles
    • Points of Intersection of Two Circles and Common Chord
    • Parametric Form of a Circle
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    Conic Sections
    HD Video Lectures - 38, Questions- 25
    • Introduction to Conic Sections
    • Parabola and Its Geometry
    • Parabola Equation and Latus Rectum
    • Equations of Translated Parabolas
    • Parametric Form of a Parabola
    • Condition for a Line to Be a Tangent to a Parabola
    • Equation of Tangents to a Parabola
    • Normal to a Parabola
    • Properties of Tangents and Normals to a Parabola
    • Connecting the Four Basic Parabolas
    • Practice Questions on Parabola (Set 1)
    • Practice Questions on Parabola (Set 2)
    • Ellipse and Its Geometry – Part 1
    • Ellipse and Its Geometry – Part 2
    • Equation of an Ellipse
    • Latus Rectum of an Ellipse
    • Directrix of an Ellipse
    • Practice Questions on Ellipse (Set 1)
    • Practice Questions on Ellipse (Set 2)
    • Condition for a Line to Be a Tangent to an Ellipse
    • Equation of a Tangent to a Parabola
    • Normal to an Ellipse
    • Equation of Ellipse Not Centred at the Origin
    • Parametric Form of an Ellipse
    • Practice Questions on Ellipse (Set 3)
    • Practice Questions on Ellipse (Set 4)
    • Hyperbola and Its Geometry
    • Equation of a Hyperbola
    • Eccentricity and Latus Rectum of a Hyperbola
    • Directrix of a Hyperbola
    • Practice Questions on Hyperbola (Set 1)
    • Intersection of a Line and a Hyperbola
    • Tangents to a Hyperbola
    • Normals to a Hyperbola
    • Equations of Hyperbolas Not Centred at the Origin
    • Parametric Form of a Hyperbola
    • Practice Questions on Hyperbola (Set 2)
    • Shortest Distance Between Two Curves
    Limits, Continuity and Differentiability
    HD Video Lectures - 44, Questions- 25
    • Introduction to Differential Calculus
    • Limits and Its Existence
    • Algebra of Limits
    • Some Useful Insights in Limits
    • Indeterminate Forms
    • Limits of Rational Functions
    • Sandwich Theorem and Limits of Trigonometric Functions
    • Problems on Sandwich Theorem
    • Limit by Expansion
    • Limits of the Form 0/0, ∞/ ∞ and ∞ – ∞
    • Solving Limits of the Form 0⁰ and ∞⁰
    • Solving Limits of the Form 1^∞
    • Common Mistakes in Limit Evaluation
    • Limit Evaluation by Graphs
    • Introduction to Derivatives
    • Derivatives of Some Elementary Trigonometric Functions
    • Algebra of Derivatives
    • Quotient Rule
    • Practice Questions on Derivatives (Set 1)
    • Understanding Continuity
    • Algebra of Continuity
    • Intermediate Value Theorem
    • Practice Questions on Continuity
    • Understanding Differentiability
    • Continuity and Differentiability by Tracing the Graph
    • Chain Rule
    • Derivative of Implicit Functions
    • Differentiation of Inverse Trigonometric Functions
    • Differentiation of Exponential and Logarithmic Functions
    • Practice Questions on Derivatives (Set 2)
    • Differentiation of Parametric Forms
    • Higher-Order Derivatives
    • Practice Questions on Derivatives (Set 3)
    • L’Hôpital’s Rule
    • Derivative of Determinants
    • Mean Value Theorems
    • Practice Questions on Mean Value Theorems
    • Some Important Points in Derivatives
    • Comparison of Graphs
    • Practice Questions on Limits (Set 1)
    • Practice Questions on Limits (Set 2)
    • Practice Questions on Continuity and Differentiability (Set 1)
    • Practice Questions on Continuity and Differentiability (Set 2)
    • Practice Questions on Differentiation
    Application of Derivatives
    HD Video Lectures - 0, Questions- 25
    Indefinite Integration
    HD Video Lectures - 29, Questions- 25
    • Introduction to Integral Calculus
    • Geometrical Meaning of Integration
    • Integration by Method of Inspection
    • Properties of Indefinite Integrals
    • Similarities and Differences Between Differentiation and Integration
    • Practice Questions (Set 1)
    • Integration by Method of Substitution
    • Some Standard Results by the Substitution Method and Some Standard Substitutions
    • Integration With the Help of Trigonometric Identities
    • Practice Questions (Set 2)
    • Integrals of Some Standard Integrands: Part 1
    • Integrals of Some Standard Integrands: Part 2
    • Practice Questions (Set 3)
    • Integration by the Method of Partial Fractions: Part 1
    • Integration by the Method of Partial Fractions: Part 2
    • Practice Questions (Set 4)
    • Problems on the Combined Concept of Substitution and Partial Fractions
    • Integration by Changing the Variable of Integration
    • Integration by Parts
    • Some Special Integrands: Part 1
    • Some Special Integrands: Part 2
    • Practice Questions (Set 5)
    • Integration of Trigonometric Functions
    • Practice Questions (Set 6)
    • Practice Questions (Set 7)
    • Practice Questions (Set 8)
    • Practice Questions (Set 9)
    • Miscellaneous Practice Questions (Set 1)
    • Miscellaneous Practice Questions (Set 2)
    Definite Integration
    HD Video Lectures - 19, Questions- 25
    • Introduction to Definite Integration
    • The Fundamental Theorem of Integral Calculus
    • Definite Integral as the Limit of a Sum: Part 1
    • Definite Integral as the Limit of a Sum: Part 2
    • Practice Questions (Set 1)
    • Definite Integration by Substitution
    • Properties of Definite Integrals: Part 1
    • Properties of Definite Integrals: Part 2
    • Properties of Definite Integrals: Part 3
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    • Definite Integration by Graphs of the Functions
    • Leibniz Rule
    • Reduction Method
    • Some Useful Insights and General Inequalities
    • Practice Questions (Set 4)
    • Practice Questions (Set 5)
    • Practice Questions (Set 6)
    • Practice Questions (Set 7)
    Application of Integrals
    HD Video Lectures - 6, Questions- 25
    • Introduction to Application of Integrals
    • Area Between a Line and a Curve
    • Finding the Area Between Two Curves
    • Calculating the Bounded Area by Changing the Axis
    • Finding the Area by Tracing the Graph of a Curve
    • Practice Questions
    Differential Equations
    HD Video Lectures - 0, Questions- 25
    Vector Algebra
    HD Video Lectures - 0, Questions- 25
    3D Geometry
    HD Video Lectures - 0, Questions- 25
    Statistics
    HD Video Lectures - 8, Questions- 25
    • Introduction to Statistics
    • Ungrouped Data and Grouped Data – Part 1
    • Ungrouped Data and Grouped Data – Part 2
    • Mean Deviation of Data
    • Standard Deviation of Data
    • Coefficient of Variation
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    Probability
    HD Video Lectures - 22, Questions- 25
    • Probability: A Chance of an Event
    • Random Experiments and Their Sample Space
    • Events and Its Algebra
    • Axiomatic Approach to Probability – Part 1
    • Axiomatic Approach to Probability – Part 2
    • Axiomatic Approach to Probability With Venn Diagrams
    • Introduction to Conditional Probability
    • Properties and Examples of Conditional Probability
    • Practice Questions on Conditional Probability
    • Multiplication Theorem of Probability and Independent Events
    • Total Probability and Bayes' Theorem
    • Practice Questions on Bayes' Theorem
    • Random Variables and Its Probability Distributions
    • Mean of a Random Variable
    • Variance of a Random Variable
    • Bernoulli Trials and Binomial Distribution
    • Practice Questions on Bernoulli Trials and Binomial Distribution
    • Practice Questions (Set 1)
    • Practice Questions (Set 2)
    • Practice Questions (Set 3)
    • Practice Questions (Set 4)
    • Practice Questions (Set 5)
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