ECAT Subject

Mathematics Chapter-wise

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01
Number System
5 topics · 100 MCQs
  • Real Numbers
  • Complex Numbers
  • Properties of Real Numbers
  • Inequalities
  • Absolute Values
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02
Sets, Functions and Groups
5 topics · 100 MCQs
  • Set Operations
  • Venn Diagrams
  • Types of Functions
  • Composition of Functions
  • Groups
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03
Matrices and Determinants
5 topics · 100 MCQs
  • Matrix Operations
  • Determinants
  • Inverse of Matrix
  • Cramer's Rule
  • System of Linear Equations
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04
Quadratic Equations
5 topics · 100 MCQs
  • Discriminant
  • Nature of Roots
  • Sum & Product of Roots
  • Quadratic Formula
  • Equations Reducible to Quadratic
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05
Partial Fractions
5 topics · 100 MCQs
  • Proper Fractions
  • Repeated Linear Factors
  • Irreducible Quadratic Factors
  • Improper Fractions
  • Partial Fraction Decomposition
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06
Sequences and Series
5 topics · 100 MCQs
  • Arithmetic Progression
  • Geometric Progression
  • Harmonic Progression
  • Arithmetic Mean
  • Geometric Mean
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07
Permutation, Combination & Probability
5 topics · 100 MCQs
  • Counting Principle
  • Permutations
  • Combinations
  • Probability Rules
  • Conditional Probability
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08
Mathematical Induction & Binomial Theorem
5 topics · 100 MCQs
  • Principle of Mathematical Induction
  • Binomial Theorem
  • Pascal's Triangle
  • General Term
  • Middle Term
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09
Fundamentals of Trigonometry
5 topics · 100 MCQs
  • Angle Measurement
  • Trigonometric Ratios
  • Circular System
  • Signs of Trig Functions
  • Pythagorean Identities
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10
Trigonometric Identities
5 topics · 100 MCQs
  • Sum & Difference Formulas
  • Double Angle Formulas
  • Half Angle Formulas
  • Product-to-Sum
  • Sum-to-Product
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11
Trigonometric Functions and Graphs
5 topics · 100 MCQs
  • Graphs of sin, cos, tan
  • Amplitude & Period
  • Phase Shift
  • Domain & Range
  • Periodicity
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12
Application of Trigonometry
5 topics · 100 MCQs
  • Law of Sines
  • Law of Cosines
  • Area of Triangle
  • Angle of Elevation
  • Angle of Depression
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13
Inverse Trigonometric Functions
5 topics · 100 MCQs
  • Inverse Sine
  • Inverse Cosine
  • Inverse Tangent
  • Domain & Range
  • Identities
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14
Solutions of Trigonometric Equations
5 topics · 100 MCQs
  • General Solution
  • Specific Solutions
  • Equations with Multiple Angles
  • sin θ = k
  • cos θ = k
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15
Functions and Limits
5 topics · 100 MCQs
  • Types of Functions
  • Algebraic Limits
  • Limits at Infinity
  • Continuity
  • L'Hopital's Rule
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16
Differentiation
5 topics · 100 MCQs
  • Derivative Definition
  • Product & Quotient Rule
  • Chain Rule
  • Implicit Differentiation
  • Higher Derivatives
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17
Integration
5 topics · 100 MCQs
  • Indefinite Integrals
  • Definite Integrals
  • Integration by Substitution
  • Integration by Parts
  • Area Under Curve
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18
Analytic Geometry
5 topics · 100 MCQs
  • Distance Formula
  • Section Formula
  • Slope of Line
  • Equation of Line
  • Circle Equations
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19
Linear Inequalities & Linear Programming
5 topics · 100 MCQs
  • Graphing Inequalities
  • Feasible Region
  • Objective Function
  • Corner Point Method
  • Optimization
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20
Conic Section
5 topics · 100 MCQs
  • Circle
  • Parabola
  • Ellipse
  • Hyperbola
  • General Equation
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21
Vectors
5 topics · 100 MCQs
  • Vector Operations
  • Dot Product
  • Cross Product
  • Unit Vector
  • Vector in 3D
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