دانلود کتاب IIT JEE Super Course in Mathematics: Algebra II

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Cover
Contents
Preface
Chapter 1: Complex Numbers
Study Material
Complex Numbers—Introduction
Algebra of complex numbers
Concept Strand
Algebra of Complex Numbers
Concept Strands
Modulus Amplitude Form Representation of a Complex Number (or Polar Form Representation of a Complex Number)
Observations
Concept Strands
Geometrical Representation of Complex Numbers-Argand Diagram
Geometrical Representations of the Sum and Difference of Two Complex Numbers
De Moivre’s Theorem
Euler’s Formula
Concept Strands
nth Roots of Unity
Logarithm of a Complex Number
Concept Connectors
Topic Grip
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
IIT Assignment Exercise
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
Additional Practice Exercise
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Questions
Solutions
Answer Keys
Hints and Explanations
Chapter 2: Matrices and Determinants
Study Material
Introduction
Definition of a Matrix
Special types of matrices
Algebra of Matrices
Concept Strands
Concept Strands
Observations
Concept Strands
Observations
Transpose of a Matrix
Conjugation Operation
Concept Strand
Observations
Observations
Concept Strands
Observations
Concept of a Determinant
Properties of Determinants
Concept Strands
Solution of Linear System of Equations
Concept Strands
Concept Strands
Homogeneous Linear System of Equations
Concept Strands
Product of two Determinants
Concept Strands
Solution of a Non-Homogenous Linear System of Equations Using Matrices
Concept Strand
Derivative of a Determinant
Concept Strand
Concept Connectors
Topic Grip
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
IIT Assignment Exercise
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
Additional Practice Exercise
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Questions
Solutions
Answer Keys
Hints and Explanations
Chapter 3: Permutations, Combinations and Binomial Theorem
Study Material
Introduction
Formula for nPr
Results
Concept Strands
Permutations—When Some of the Objects (or Things)
are not Distinct (I.E., Some Objects are Alike)
Result
Concept Strand
Circular Permutations
Concept Strand
Formula for nCr or (nr)
Concept Strands
Concept Strands
Method of Induction
Concept Strands
Binomial Theorem
Concept Strands
Expansion of (1 + x)n Where,
n is a Positive Integer
Concept Strand
Binomial Series
Concept Strands
Concept Connectors
Topic Grip
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
IIT Assignment Exercise
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
Additional Practice Exercise
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Questions
Solutions
Answer Keys
Hints and Explanations
Chapter 4: Theory of Probability
Study Material
Introduction
Events or Outcomes
Definition of Probability
Concept Strands
Probability–Axiomatic Approach
Observations
Concept Strands
Conditional Probability
Concept Strands
Independent Events
Concept Strands
Bayes’ Theorem or Bayes’ Formula
Statement of Bayes’ theorem
Concept Strands
Binomial Distribution [or Binomial Model]
Concept Strands
Geometric Probability or Probability in Continuum
Concept Strands
Concept Connectors
Topic Grip
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
IIT Assignment Exercise
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
Additional Practice Exercise
Subjective Questions
Straight Objective Type Questions
Assertion–Reason Type Questions
Linked Comprehension Type Questions
Multiple Correct Objective Type Questions
Matrix-Match Type Question
Solutions
Answer Keys
Hints and Explanations