Syllabus and Practice Questions from Maths for Engineering Entrance Exams

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

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

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

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

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

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

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

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

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

Linear Inequations

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

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

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

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

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