# Syllabus and Practice Questions from Maths for Engineering Entrance Exams

Mathematics is one of the main subjects under Engineering Entrance Exams.
On this page, youâ€™ll find the detailed list of topics covered under Mathematics.
Each topic leads to a page containing practice questions with detailed solutions from that topic.

##### Mathematics Syllabus

##### Complex Numbers

Lines and Distances
Basics of Complex Numbers
Operations on Complex Numbers
Modulus of Complex Numbers
Basic Geometry in Argand Plane
Conjugate and its Properties
Euler Form of Complex Number
Cube Roots of Unity and their Properties
Higher Roots of Unity

##### Sequence and Series

Special Series
General Series
Introduction to Sequences and Series
Arithmetic Progression
Geometric Progression
Harmonic Progression
Arithmetico Geometric Progression
Means
Exponential and Logarithmic Series

##### Integral Calculus

Introduction to Indefinite Integrals
Fundamental Integrals
Properties of Indefinite Integrals
Integration by Substitution
Integration using Partial Fractions
Integration by Parts
Special Integrals (Trigonometric Functions)
Special Integrals (Exponential Functions)
Special Integrals (Algebraic Functions)
Special Integrals (Irrational Functions)
Integrals of Special Functions
Complex Integrations
Definite Integrals
Changing Variable
Properties of Definite Integral
Definite Integrals of Special Functions
Integration using Leibnitz Rule
Using Inequalities to Solve Definite Integral
Definite Integral as a Limit of Sum
Mean Value theorem
Application of Definite integrals
Curve Sketching
Sketching Simple Curves
Area of Bounded Regions
+14 more topics

##### Coordinate Geometry

Cartesian Coordinate System
Polar Coordinate System
Distance Between Two Points in 2D
Section Formulae
Triangles and Quadrilateral
Locus and Its Equation
Transformation of Axes
Basics of Straight Lines
Various Forms of Equation of Line
Position of Points Relative to a Line
Distance of Point from a Line
Concurrent and Family of Lines
Angular Bisectors of Intersecting Lines
Foot of the Perpendicular
Image of a Point about a Line Mirror
Equation of Line in Parametric Form
Real Life Applications
Pair of Straight Lines Through Origin
General Equation of Pair of Straight Lines
Equation of Circles in Different Forms
Tangent of Ellipse
Normal of Ellipse
Chords of Ellipse
Concyclic Points of Ellipse
Reflection Property of Ellipse
Position of a Point/Line w.r.t Circle
Tangent and Secant of Circle
Normal to the Circle
Chords of Circle
Non-intersecting, Intersecting, Touching circles
Cyclic Polygons
Family of Circles
Conic Sections
Equation of Parabola
Position of Point w.r.t Parabola
Tangent of Parabola
Normal of Parabola
Chords of Parabola
Reflection Property of Parabola
Parabola of Form (ax+by)^2+2gx+2fy+c=0
Equations of Ellipse
Position of a Point w.r.t Ellipse
Equation of Ellipse in General Form
Equation of Hyperbola
Position of a Point w.r.t Hyperbola
Tangent of Hyperbola
Normal of Hyperbola
Chords of Hyperbola
Concyclic Points of Hyperbola
Asymptotes of Hyperbola
Rectangular Hyperbola
Reflection Property of Hyperbola
Equation of Hyperbola in General Form
+43 more topics

##### Statistics

Mean
Median
Mode
Measure of Central Tendency
Range and Mean Deviation
Variance and Standard Deviation
Measures of Dispersion
Analysis of Frequency Distribution

##### Probability

Conditional Probability
Bayes' Theorem
Probability on Multinomial Theorem
Events and its Algebra
Diagrammatic Representation of Outcomes
Probability
Basic Theorems of Probability
Multiplication Theorem
Poisson's Distribution
Probability on Uncountable Uniform Spaces
Probability Distribution
Binomial Distribution
+2 more topics

##### Mathematical Induction

Mathematical Statement
Algebra of Statements
Truth Tables
Statement Pattern and Logical Equivalence
Principle of Mathematical Induction
Mathematical Modelling

##### Theory of Equations

Exponential Notation
Logarithmic Notation
Laws of Logarithm
Value of a Logarithm
Anti Logarithms
Applications of Logarithms
Quadratic Equations
Solving Quadratic Equation
Nature of Roots of Quadratic Equations
Roots and Coefficients of Quadratic Equations
Common Roots
Quadratic Functions and Graphs
Quadratic Fractions
Quadratic Inequalities
Indeterminate Functions
Fundamental Theorem of Algebra
General Theorems
Roots and Coefficients of Equations
Nature of Roots of Equations
Transformation of Equation
Cubic Equations
Biquadratic and Quartic Equations
Inequalities
Partial Fractions
+14 more topics

##### Matrices and Determinants

Types of Matrices
Operations on Matrices
Properties of Matrices
Transpose of a Matrix
Symmetric and Skew Symmetric Matrix
Transformation of a Matrix
Inverse of a Matrix
Determinants
Properties of Determinants
Minor and Cofactor
Adjoint and Inverse of a Matrix
Properties of Inverse Matrix
Application of Matrices and Determinants
+3 more topics

##### Permutations and Combinations

Problems on Divisors
Problems on Integral Solutions
Problems on Geometric Figures
Combinations of Similar Things
Groups
Divisibility, Factorial Test and Summations
Fundamental Principles of Counting
Permutations
Permutation Involving Restrictions
Circular Permutations
Circular Permutations with Restrictions/Groupings
Combination
Combinations of Dissimilar Things
Arrangement in Groups
+4 more topics

##### Binomial Theorem

Binomial Expansion for Positive Integral Index
General and Middle Term
Binomial Theorem for Negative Integer or Fractional Index
Binomial Coefficients
Application of Binomial Expansion

##### Linear Programming

##### Sets and Relations

Sets
Types of Sets
Subsets and Supersets
Operations on Sets
Venn Diagrams
Cartesian Product
Relations
Types of Relations
Functions
Representation of Functions
Binary Operations
Types of Functions
Even/Odd and Periodic Functions
Special Functions
Algebra of Real Functions
Composite and Inverse Functions
Transformation of Graphs
+7 more topics

##### Differential Equations

Introduction to Differential Equations
Types of Solution of Differential Equation
Formation of Differential Equation
Variable Separable Differential Equation
Homogeneous Differential Equation
Linear Differential Equation
Orthogonal Trajectory

##### Vectors and 3D Geometry

Introduction to Vector Algebra
Types of Vectors
Operations on Vector
Vector Component Form
Section Formula
Linear Combination of Vectors
Dot Product
Applications of Dot Product
Vector Product
Applications of Vector Product
Applications of Dot and Cross Product in Real Life
Lines in Vector Form
Plane in Vector Form
Scalar Triple Product
Vector Triple Product
Applications of Vectors to Geometry
Reciprocal System of Vectors
Vector Equations
Introduction to 3D Geometry
Distance Between Two Points in 3D
Section Formula in 3D
Direction Cosines and Direction Ratios
Lines in 3D
Plane in 3D
Sphere in 3D
Translation of Axes and Locus
+16 more topics

##### Differential Calculus

Direct Method
Standard Simplifications
Sandwich Theorem and Trigonometric Functions
Limits
L'Hospital's Rule
Limit of Exponential and Logarithmic Function
Limits of Special Functions
Discontinuity of a Function
Algebra of Continuous Functions
Derivatives
First Principle of Differentiation
Logarithmic Differentiation
Differentiation of Implicit Functions
Differentiation by Substitution
Differentiation of an Infinite Expression
Higher Order Derivatives
Differentiation of Determinants
Rolle's Theorem and Intermediate Value Theorem
Lagrange's Mean Value Theorem
Taylor's and Maclaurin's Series
Rate Measurement
Approximations and Differentials
Nature of the Function
Maxima and Minima
Applications on Geometrical Figures
Continuity of a Function
Continuity and Differentiability
Algebra of Derivative of Functions
Chain and Reciprocal Rule
Differentiation of Functions in Parametric Form
Nature of Roots of Polynomial Function
+21 more topics

##### Trigonometry

Domain and Range of Trigonometric functions
Trigonometric Ratios of Any Angle
Measurement of Angles
Trigonometric Functions
Periodicity of Trigonometric Functions
Compound Angles
Multiple and Submultiple Angles
Trigonometric Equations
Trigonometric Inequations
Graphs of Trigonometric Ratios
Extrema of Trigonometric Functions
Heights and Distances
Basic Relation Between Sides and Angles
Inverse Trigonometric Functions
Graphs of Inverse Trigonometric Functions
Properties of Inverse Trigonometric Functions
Inverse Trigonometric Inequalities
+7 more topics