SYLLABUS
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING
AND STATISTICS
(One paper – Three hours – 100 Marks)
Objectives:
(a) To develop an understanding of the basic mathematical and statistical tools and their application
in Business, Finance and Economics.
(b) To develop logical reasoning skills and apply the same in simple problem solving.
Contents:
PART – A. BUSINESS MATHEMATICS (40 MARKS)
1. Ratio and Proportion, Indices and Logarithms
Ratio and Proportion (Business Applications related to Ration and Proportion) Laws of Indices,
Exponents and Logarithms and Anti Logarithms.
2. Equations and Matrices
(i) Equations: Simultaneous linear equations up to three variables, Quadratic and Cubic
equations in one variable.
(ii) Matrices: Algebra of Matrices, Inverse of a Matrix and determinants, solving system of
equations by Cramer’s Rule (involving not more than three variables).
3. Linear Inequalities with Objective Functions and Optimization w.r.t. objective function.
4. Time value of Money
(i) Simple Interest
(ii) Compound interest
(iii) Depreciation
(iv) Effective Rate of Interest
(v) Present Value
(vi) Net Present Value
(vii) Future Value
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(viii) Perpetuity
(ix) Annuities
(x) Sinking Funds
(xi) Valuation of Bonds
(xii) Calculating of EMI
(xiii) Calculations of Returns:
a)
Nominal Rate of Return
b)
Effective Rate of Return
c)
Compound Annual Growth Rate (CAGR)
5. Permutations and Combinations
Basic concepts of Permutations and Combinations: Introduction, the Factorial, Permutations,
results, Circular Permutations, Permutations with restrictions, Combinations with standard
results.
6. Sequence and Series
Introduction Sequences, Series, Arithmetic and Geometric progression, Relationship between
AM and GM and Sum of n terms of special series
7. Sets, Relations and Functions
8. Basic applications of Differential and Integral calculus (Excluding the trigonometric
applications), Applications of Marginal Cost and Marginal Revenue etc.,
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PART – B: LOGICAL REASONING (20 MARKS)
1. Number series, Coding and Decoding and odd man out.
2. Direction Tests
3. Seating Arrangements
4. Blood Relations
5. Syllogism
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PART – C: STATISTICS (40 MARKS)
1. Statistical description of Data
Statistical Representation of Data, Diagrammatic representation of data, Frequency distribution,
Graphical representation of Frequency Distribution – Histogram, Frequency Polygon, Ogive, Pie-
chart.
2. Measures of Central tendency and Dispersion
Measures of Central Tendency and Dispersion: Mean Median, Mode, Mean Deviation, Quartiles
and Quartile Deviation, Standard Deviation, Co-efficient of Variation, Coefficient of Quartile
Deviation.
3. Probability
Probability:Independent and dependent events; mutually exclusive events. Total and Compound
Probability and Mathematical Expectation.
4. Theoretical Distributions
Theoretical Distributions: Binomial Distribution, Poisson distribution – Basic application and
Normal Distribution – Basic applications.
5. Correlation and Regression
Correlation and Regression: Scatter diagram, Karl Pearson’s Coefficient of Correlation Rank
Correlation, Probable Error and Probable limits. Regression lines, Regression equations,
Regression coefficients.
6. Index Numbers and Time Series
(i) Index Numbers: Uses of Index Numbers, Problems involved in construction of Index
Numbers, Methods of construction of Index Numbers.
(ii) Time Series Analysis : Components of Time Series and Calculation of Trend by Moving
Average Method.
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CONTENTS
PART – A : BUSINESS MATHEMATICS
Chapter – 1: Ratio And Proportion, Indices, Logarithms
1.1 Unit 1 - Ratio .....................................................................................................................................1.1
1.2 Unit 2 - Proportion ..........................................................................................................................1.8
1.3 Unit 3 - Indices ...............................................................................................................................1.15
1.4 Unit 4 - Logarithm ........................................................................................................................1.23
Additional Question Bank ............................................................................................................1.35
Chapter – 2: Equations and Matrices
Unit I: Equations
2.1.1 Introduction ......................................................................................................................................2.2
2.1.2 Simple Equation ...............................................................................................................................2.2
2.1.3 Simultaneous Linear Equations in two unknowns .....................................................................2.6
2.1.4 Method of Solution ..........................................................................................................................2.6
2.1.5 Method of Solving Simultaneous Linear Equation with three variables ................................2.7
2.1.6 Problems Leading to Simultaneous Equations .........................................................................2.12
2.1.7 Quadratic Equation .......................................................................................................................2.14
2.1.8 How to Construct a Quadratic Equation....................................................................................2.15
2.1.9 Nature of the Roots........................................................................................................................2.16
2.1.10 Problems on Quadratic Equation ................................................................................................2.23
2.1.11 Solution of Cubic Equation ..........................................................................................................2.25
Unit-II: Matrices
2.2.1 Introduction ...................................................................................................................................2.35
2.2.2 Types of Matrices ..........................................................................................................................2.36
2.2.3 Algebra of Matrices ......................................................................................................................2.38
2.2.4 Determinant of Matrices ...............................................................................................................2.46
2.2.5 Matrix Inverse ...............................................................................................................................2.49
2.2.6 Solution of linear equations by Crammer’s method ................................................................2.53
Chapter – 3: Linear Inequalities
3.1 Overview ...........................................................................................................................................3.1
3.2 Linear Inequalities in one variable and the Solution space .......................................................3.2
Additional Question Bank ............................................................................................................3.22
Chapter – 4: Time Value of Money
4.1 Introduction ......................................................................................................................................4.2
4.2 Why is Interest Paid? .......................................................................................................................4.2
4.3 Definition of Interest and some other Related Terms ................................................................4.3
4.4 Simple Interest and Compound Interest ......................................................................................4.3
4.5 Effective Rate of Interest ...............................................................................................................4.17
4.6 Annuity ...........................................................................................................................................4.21
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4.7 Future Value ...................................................................................................................................4.23
4.8 Present Value ..................................................................................................................................4.27
4.9 Sinking Fund ..................................................................................................................................4.33
4.10 Applications ...................................................................................................................................4.34
4.11 Perpetuity....................................................................................................................................... 4.36
4.12 Net Present value ..........................................................................................................................4.37
4.13 Nominal and Real Rate of Return ..............................................................................................4.39
4.14 Compound Annual Growth Rate (CAGR) ...............................................................................4.40
Additional Question Bank ............................................................................................................4.45
Chapter – 5: Basic Concepts of Permutations and Combinations
5.1 Introduction ......................................................................................................................................5.2
5.2 The Factorial .....................................................................................................................................5.2
5.3 Permutations ....................................................................................................................................5.3
5.4 Results ...............................................................................................................................................5.4
5.5 Circular Permutations .....................................................................................................................5.9
5.6 Permutation with Restrictions .....................................................................................................5.10
5.7 Combinations .................................................................................................................................5.15
5.8 Standard Results ............................................................................................................................5.21
Additional Question Bank ............................................................................................................5.31
Chapter – 6: Sequence and Series - Arithmetic and Geometric Progressions
6.1 Sequence ............................................................................................................................................6.2
6.2 Series ..................................................................................................................................................6.3
6.3 Arithmetic Progression (A.P.) ........................................................................................................6.3
6.4 Geometric Progression (G.P.) .........................................................................................................6.9
6.5 Geometric Mean .............................................................................................................................6.11
Additional Question Bank ............................................................................................................6.20
Chapter – 7: Sets, Functions and Relations
7.1 Sets .....................................................................................................................................................7.2
7.2 Friend Diagrams ............................................... .................................................. ............................... 7.5
7.3 Product Sets ......................................................................................................................................7.8
7.4 Relations and Functions ..................................................................................................................7.9
7.5 Domain & Range of a Function .....................................................................................................7.9
7.6 Various Types of Function ...........................................................................................................7.10
Additional Question Bank ............................................................................................................7.23
Chapter – 8: Basic Concepts of Differential and Integral Calculus
(A) DifferentialCalculus
8.A.1 Introduction ......................................................................................................................................8.2
8.A.2 Derivative or Differential Coefficient ...........................................................................................8.2
8.A.3 Some Standard Results (Formulas) ...............................................................................................8.5
8.A.4 Derivative of a Function of Function ............................................................................................8.8
8.A.5 Implicit Functions ............................................................................................................................8.8
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8.A.6 Parametric Equation ........................................................................................................................8.9
8.A.7 Logarithmic Differentiation ...........................................................................................................8.9
8.A.8 Some More Examples ....................................................................................................................8.10
8.A.9 Basic Idea about Higher Order Differentiation .........................................................................8.12
8.A.10 Geometric Interpretation of the Derivative ...............................................................................8.13
Applications of Differential calculus .........................................................................................8.14
(B) Integral Calculus
8.B.1 Integration Calculus ......................................................................................................................8.24
8.B.2 Basic Formulas ...............................................................................................................................8.24
8.B.3 Method of Substitution (change of variable) .............................................................................8.27
8.B.4 Integration By Parts .......................................................................................................................8.28
8.B.5 Method of Partial Fraction............................................................................................................8.30
8.B.6 Definite Integration .......................................................................................................................8.32
8.B.7 Important Properties .....................................................................................................................8.33
Additional Question Bank ............................................................................................................8.43
PART – B : LOGICAL REASONING
Chapter – 9: Number Series, Coding and Decoding and Odd Man Out
9.1 Number Series .................................................................................................................................9.1
9.2 Coding and Decoding ....................................................................................................................9.2
9.3 Oddman out ....................................................................................................................................9.4
Exercise .............................................................................................................................................9.5
Chapter – 10: Direction Tests
10.1 Introduction ...................................................................................................................................10.1
Exercise ...........................................................................................................................................10.5
Chapter – 11: Seating Arrangements
11.1 Introduction ...................................................................................................................................11.1
Exercise ............................................................................................................................................11.9
Chapter – 12: Blood Relations
12.1 Introduction ....................................................................................................................................12.1
Exercise ............................................................................................................................................12.6
Chapter – 13: Syllogism
13.1 Introduction .................................................................................................................................. 13.1
Exercise ..........................................................................................................................................13.18
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PART – C : STATISTICS
Chapter – 14: Statistical Description of Data
14.1 Introduction of Statistics ...............................................................................................................14.2
14.2 Collection of Data ..........................................................................................................................14.3
14.3 Presentation of Data ......................................................................................................................14.6
14.4 Frequency Distribution ...............................................................................................................14.14
14.5 Graphical representation of Frequency Distribution .............................................................14.19
Additional Question Bank ..........................................................................................................14.37
Chapter – 15: Measures of Central Tendency and Dispersion
Unit 1: Measures of Central Tendency
15.1.1 Definition of Central Tendency ...................................................................................................15.2
15.1.2 Criteria for an ideal measure of Central Tendency ..................................................................15.2
15.1.3 Arithmetic Mean ............................................................................................................................15.2
15.1.4 Median – Partition Values ............................................................................................................15.7
15.1.5 Mode ..............................................................................................................................................15.14
15.1.6 Geometric Mean and Harmonic Mean .....................................................................................15.15
Exercise ..........................................................................................................................................15.24
Unit 2: Dispersion
15.2.1 Definition of Dispersion..............................................................................................................15.30
15.2.2 Range .............................................................................................................................................15.31
15.2.3 Mean Deviation ............................................................................................................................15.33
15.2.4 Standard Deviation ......................................................................................................................15.38
15.2.5 Quartile Deviation .......................................................................................................................15.47
Exercise ..........................................................................................................................................15.55
Additional Question Bank ..........................................................................................................15.61
Chapter – 16 : Probability
16.1 Introduction ....................................................................................................................................16.2
16.2 Random Experiment .....................................................................................................................16.2
16.3 Classical Definition of Probability ...............................................................................................16.3
16.4 Statistical Definition of Probability .............................................................................................16.8
16.5 Operations on Events: Set Theoretic Approach to Probability .............................................16.10
16.6 Axiomatic or Modern Definition of Probability ......................................................................16.13
16.7 Addition Theorems .....................................................................................................................16.14
16.8 Conditional Probability and Compound Theorem of Probability .......................................16.17
16.9 Random Variable- Probability Distribution.............................................................................16.26
16.10 Expected Value of a Random Variable .....................................................................................16.28
Additional Question Bank ..........................................................................................................16.52
Chapter – 17: Theoretical Distributions
17.1 Introduction ....................................................................................................................................17.1
17.2 Binomial Distribution ....................................................................................................................17.2
17.3 Fish Distribution ............................................... .................................................. 17.10 ...................
17.4 Normal Distribution or Gaussian Distribution .......................................................................17.19
Additional Question Bank ..........................................................................................................17.48
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Chapter – 18: Correlation And Regression
18.1 Introduction ....................................................................................................................................18.2
18.2 Bivariate Data .................................................................................................................................18.2
18.3 Correlation Analysis ......................................................................................................................18.5
18.4 Measures of Correlation ...............................................................................................................18.6
18.5 Regression Analysis ....................................................................................................................18.25
18.6 Properties of Regression Lines ...................................................................................................18.34
18.7 Review of Correlation and Regression Analysis .....................................................................18.37
Additional Question Bank ..........................................................................................................18.51
CHAPTER – 19: Index numbers and Time Series
Unit – I: Index Numbers
19.1.1 Introduction ....................................................................................................................................19.2
19.1.2 Issues Involved...............................................................................................................................19.2
19.1.3 Construction of Index Number ...................................................................................................19.3
19.1.4 Usefulness of Index Numbers ....................................................................................................19.10
19.1.5 Deflating Time Series using Index Numbers ...........................................................................19.10
19.1.6 Shifting and Splicing of Index Numbers ..................................................................................19.11
19.1.7 Test of Adequacy .........................................................................................................................19.12
Additional Question Bank ..........................................................................................................19.21
Unit – II: Time Series
19.2.1 Introduction .................................................................................................................................19.39
19.2.2 Models of Time Series ................................................................................................................19.40
19.2.3 Measurement of Secular Trend .................................................................................................19.41
Summary .......................................................................................................................................19.51
