mathematics

This subject covers units such as trigonometry, algebra, coordinate geometry, differential calculus, integral calculus, statistics and probability, statics and dynamics and, vectors and 3d geometry

Algebra covers chapters such as Permutation and Combination, Complex Numbers, Binomial Theorem, Sequence and Series, Matrices and Determinants, Theory of Equation, Fundamentals of Mathematics and, Set Theory and Relations

Algebra

Trigonometry covers chapters such as Inverse Trigonometric Functions, Properties of Triangle, Heights and Distances, Trigonometric Ratios and Identities and, Trigonometric Equations and Inequations

Trigonometry

Coordinate Geometry covers chapters such as Circle, Ellipse, Parabola, Hyperbola and, Straight Line

Coordinate Geometry

Differential Calculus covers chapters such as Functions, Limits, Application of Derivatives, Continuity and Differentiability and, Differential Coefficient

Differential Calculus

Integral Calculus covers chapters such as Differential Equation, Definite Integration, Indefinite Integration and, Area under Curves

Integral Calculus

Vectors and 3D Geometry covers chapters such as Vector Algebra and Three Dimensional Geometry

Vectors and 3D Geometry

Statistics and Probability covers chapters such as Probability and Statistics

Statistics and Probability

Statics and Dynamics covers chapters such as Dynamics and Statics

Statics and Dynamics

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics

Mathematics Crash Course NDA & NA EE

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS

Tangent to the Ellipse at a Given Point

Variance and Standard Deviation for Ungrouped Distribution

Formation of Differential Equations

Finding Inverse by Elementary Transformations

Mean Deviation About Mean and Median for Ungrouped Data

Discrete Frequency Stats: Mean, Variance, SD

Mean Deviation, Its Merits, and Demerits

Quartile Deviation

Relations

Coefficient of Variation

Measures of Dispersion

Mean Deviation of Ungrouped Data

Variance - Properties, Merits and Demerits

Standard Deviation - Properties, Merits and Demerits

Variance and SD for Grouped Frequency Distribution

Binary Operations and Operation Tables

Intervals and Subsets of Real Numbers

Variance and SD of Continuous Distribution

Mean Deviation of Grouped Data

Mean of Grouped Data: Example

Value of Determinant (Cofactor Expansion)

Minor and Cofactor of Elements of a Determinant

Equilibrium of Rigid Body

Base of Logarithm

Exponents & Logarithms

Examples of Area of Triangles

Examples of Properties of Triangles

Napier's Analogy

The Projection Formula

Cosine Rule

Sine Rule

Properties of Triangles

Examples on Logarithms

Working Rules for Logarithms

Logarithm: Characteristic and Mantissa

Properties of Determinants (Part 3)

Properties of Determinants (Part 2)

Properties of Determinants (Part 1)

n- Geometric Means Between Two Numbers

Illustration on Properties of Determinant

Properties of Determinant (Part 4)

Special Types of Matrices

Properties of ITF: Illustration-3

Properties of ITF: Illustration-2

Properties of ITF: Illustration-1

Properties of Inverse Trigonometric Functions

The Inverse of Cot Function

Graph of sin⁻¹ x

The Inverse of Sine Function

Inverse Function: Theorem

Inverse Function

One-one and Onto of Composition of Functions

Composite Functions: Illustration

Composition of Functions: Theorem

Composition of Functions

Types of Functions

Definition and Equation of a Circle

Angle Between Two Lines

Conditions for Two Lines to Be Parallel

Finding N Arithmetic Means Between Two Numbers

Arithmetic Mean

Roots of Quadratic Equation: Illustration

Convert Degree Into Radian & Radian Into Degree

Relation Between Radian and Degree

Systems for Measurement of Angles

Modulus Function

Graphs of Linear Real-Valued Functions

Real-Valued Functions

Range of a Function: Illustration

Domain, Co-Domain and Range of a Function

Concept of a Function

Properties of Cartesian Product : Example

Example on Cartesian Product of Sets

Cartesian Product of Sets: Example

Cartesian Product of Two Sets: Illustration

Cartesian Product of Sets

Equality of Ordered Pairs

Ordered Pairs

Verification: n(A∪B)=n(A)+n(B)-n(A∩B)

Complement of Set

Symmetric Difference of Sets

Difference of Sets

Distributive Law of Sets

Examples of De Morgan’s Law and Distributive Law

The Intersection in Set Operations

The Union in Set Operations

Venn Diagrams

Subsets and Equal Sets

Universal Set and Subsets

Power Set of a Set

Equivalent Sets

Finite and Infinite Sets

Empty Set

Cardinality and Types of Sets

Notations for a Set

Tangent at a Point on Circle: Theorem

Nature of the Roots: Illustration 1

Perfect Square Method to Solve Quadratic Equation

Exponents and Surds

Forces and Motion

This chapter covers topics such as Basics of Vectors, Linearly Dependent and Independent Vectors, Scalar and Vector Triple Products, Geometrical Application of Vectors, Dot Product of Two Vectors, and Addition of Vectors.

Vector Algebra

This chapter covers topics such as Equation of Plane, Equation of a Line in 3D, Family of Planes, Interaction between a Line and a Plane, Line and a Point, Interaction between Two Planes, Basics of 3D Geometry, and Plane and a Point.

Three Dimensional Geometry

This chapter covers topics such as Conditional Identities, Trigonometric Series, Basics of Trigonometry, Trigonometric Identities, Trigonometric Functions and Properties, and Range of Trigonometric Expressions.

Trigonometric Ratios and Identities

This chapter covers topics such as Trigonometric Inequations and Trigonometric Equations.

Trigonometric Equations and Inequations

This chapter covers topics such as Excentral Triangle and Pedal Triangle, Inradius, Exradii and Circumradius, Distance between Various Centre Points of a Triangle, and Half-Angle Formula and the Area of a Triangle.

Properties of Triangle

This chapter covers topics such as Properties of Inverse Trigonometric Functions, Identities of Inverse Trigonometric Functions, Basics of Inverse Trigonometric Functions, and Inverse Trigonometric Equations and Inequalities.

Inverse Trigonometric Functions

This chapter covers the topic of Heights and Distances.

Heights and Distances

This chapter covers topics such as Measures of Dispersion, Measures of Central Tendency, Basics of Statistics, Correlation and Covariance, and Regression.

Statistics

This chapter covers topics such as Bernoulli Trials and Binomial Distribution, Algebra of Probability, Total Probability and Bayes' Theorem, Basics of Probability, Conditional Probability, and Probability Distribution of a Random Variate.

Probability

This chapter covers topics such as Integration Using Trigonometric Identities, Methods of Integration, Integration of Rational Functions, Integration of Irrational Functions, and Reduction Formulae for Indefinite Integration.

Indefinite Integration

This chapter covers topics such as Exact Differential Equations, Variable Separable Form, Linear Differential Equations, Homogeneous Differential Equations, Application of Differential Equations, and Basics of Differential Equations.

Differential Equation

This chapter covers topics such as Reduction Formulae for Definite Integration, Definite Integral as Limit of a Sum, Newton Leibnitz's Theorem, Properties of Definite Integral, Basics of Definite Integral, and Estimation of Definite Integral.

Definite Integration

This chapter covers topics such as Area Bounded between Two Curves, Curve Tracing, and Area Under the Curve.

Area under Curves

This chapter covers topics such as Methods of Evaluation of Limits and Basics of Limits.

Limits

This chapter covers topics such as Transformation of Graphs, Composite Functions, Even and Odd Functions, Types of Functions, Inverse Functions, Basics of Functions, and Periodic Functions.

Functions

This chapter covers topics such as Basics of Differentiation, Higher Order Derivatives, and Methods of Differentiation.

Differential Coefficient

This chapter covers topics such as Differentiability of a Function, Properties of Continuous Functions, Properties of Differentiable Functions, and Continuity of a Function.

Continuity and Differentiability

This chapter covers topics such as Derivative as Rate of Change, Maxima and Minima, Mean Value Theorems, Monotonicity, Interaction between Two Curves, and Tangent and Normal.

Application of Derivatives

This chapter covers topics such as Pair of Straight Lines, Straight Line and a Point, Angle Bisectors, Special Points in a Triangle, Family of Straight Lines, Interaction between Two Straight Lines, and Transformation of Axes.

Straight Line

This chapter covers topics such as Interaction between Two Conics, Properties of Parabola, Pair of Tangents, Chord of Contact and Chord with Midpoint of a Parabola, Tangent and Normal to a Parabola, Basics of Parabola, etc.

Parabola

This chapter covers topics such as Rectangular Hyperbola Having Coordinate Axes as Asymptotes, Asymptotes of Hyperbola, Pair of Tangents, Chord of Contact and Chord with Midpoint of a Hyperbola, Tangent and Normal to a Hyperbola, etc.

Hyperbola

This chapter covers topics such as Pair of Tangents, Chord of Contact and Chord with Midpoint of an Ellipse, Basics of Ellipse, Tangent and Normal to an Ellipse, Properties of Ellipse, Interaction between Two Conics, etc.

Ellipse

This chapter covers topics such as Interaction between Circle and a Line, Circle and a Point, Pair of Tangents, Chord of Contact and Chord with Midpoint of a Circle, Interaction between Two Circles, Basics of Circle, Family of Circles, etc.

Circle

This chapter covers topics such as Algebraic Equations of Higher Degree, Range and Graph of Quadratic Expressions, Quadratic Equation and Its Solutions, Common Roots, Algebraic Expressions, Equations and Identities, Location of Roots, etc.

Theory of Equation

This chapter covers topics such as Types of Sets, Basics of Sets, Subsets and Power Set, Algebra of Sets, Types of Relations, Basics of Relations, and Binary Operations.

Set Theory and Relations

This chapter covers topics such as Geometric Progression, Basics of Sequence and Series, Harmonic Progression, A.M., G.M., H.M. and their Relations, Arithmetico-Geometric Progression, Arithmetic Progression and Miscellaneous Series.

Sequence and Series

This chapter covers topics such as Combination, Permutation, Division and Distribution of Objects, Inclusion-Exclusion Principle, Circular Permutation, and Fundamental Principles of Counting.

Permutation and Combination

This chapter covers topics such as Special Types of Matrices, Algebra of Matrices, Basics of Matrices, Symmetric and Skew-Symmetric Matrices, Inverse of a Matrix, System of Linear Equations, Properties of Determinants, etc.

Matrices and Determinants

This chapter covers topics such as Logarithmic Equations and Inequalities, Properties of Logarithms, and Basics of Logarithm.

Logarithm and its Applications

This chapter covers topics such as Logarithmic Series, Surds and Indices, Partial Fractions, Exponential Series, Number System, Variation, Algebraic Inequalities, and Ratio and Proportion.

Fundamentals of Mathematics

This chapter covers topics such as Basics of Complex Numbers, De Moivre's Theorem, Algebra of Complex Numbers, Properties of Conjugate, Modulus and Argument of Complex Numbers, Roots of Unity, and Geometry of Complex Numbers.

Complex Numbers

This chapter covers topics such as Binomial Theorem for Positive Integral Index, Properties of Binomial Coefficients, Multinomial Theorem, Binomial Theorem for any Index, Series Involving Binomial Coefficients, General Term, etc.

Binomial Theorem

This chapter covers topics such as Uniform Motion and its Equation and Basics of Dynamics.

Dynamics

This chapter covers topics such as Equilibrium and Basics of Statics.

Statics

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