The document provides information about the Business Mathematics course offered at Punjab College of Technical Education in Ludhiana. [1] It outlines the course topics which include matrix algebra, binomial theorem, functions, limits, and calculus among others. [2] The learning outcomes, textbooks, assignments, tests, and lecture schedule with topics are also detailed. [3] The document comprehensively outlines the structure and components of the Business Mathematics course.

1. PUNJAB COLLEGE OF TECHNICAL EDUCATION, LUDHIANA
COURSE BREAK UP 2010
Name of Instructor: Mr. Swapan Chanana Subject Name:BusinessMathematics
Ms.NidhiVerma, Ms. Prabhjot Arora Subject Code: BB102
Total No. of Lectures: 63
Course Information
• This mathematics course emphasizes the mathematics required in general
business processes. This course is designed to prepare students for the
mathematical and analytical application required in subsequent business and
economics courses.
• This course covers those topics which can be used in day to day business
transactions ,and covers the mathematical processes and techniques currently
used in the fields of business and finance.
Learning outcome
• Analysis of the Quantifiable data would help the students in interpreting better
results. It is of great help to Judge Company’s performance.
• Mathematics is an aid to decision making. For instance, Permutations &
Combinations helps us in selecting the best alternative out of many.
• It helps in deriving the relationship between two or more variables. Its practical
application comes when the company wants to know the key variables involved in
its success. For example, when we want to know whether the increase in profit is
because of increase in sales or decrease in cost, we can use the principles of
differentiation and maxima & minima. So, it is of great help in developing
relationship between the variables.
• They will be able to judge the growth of a company. A.P. & G.P. give an idea
about the consistency in profit growth of a company.
Course topics
• Linear & Quadratic Equations
• Matrix Algebra
• Permutations & Combinations
• Binomial Theorem
• Functions, Limits & Continuity
• Differential Calculus

2. • Arithmetic & Geometric Progressions
• Logarithms
• Set Theory
• Real Number System
• Logical Statements & Truth Tables
Textbooks
• Business Mathematics By DC Sancheti & VK Kapoor
• Spectrum Business Mathematics By Sharma & Sharma
Break up of Internal Assessment
BREAK UP WEIGHTAGE
MSE’s 15
Presentation 5
Assignments (3) 5
Tests (2) 10
CLASS TESTS (3) 5
TOTAL 40
Punctuality
• Assignments that are late will not be accepted and in case of an unavoidable
circumstances, prior submission of the assignment is acceptable
LECTUR TOPIC TEST ASSGN
E NO.
1,2 Chapter : Matrix Algebra
Concepts
- Introduction
- Order, representation, elements, diagonal
of a matrix, Types of Matrices
- Operations on matrices : addition,
subtraction, multiplication
3 Examples
- Ques on formation of matrices,
operations, etc.
4,5 Concepts
- Transpose
- Determinant

3. - Minors, Cofactors
- Adjoint
- Inverse
6 Examples
- Ques on dets, adj, etc.
7 Concepts
- Cramers Rule
- Special Cases
8 Concepts
- Matrix Inversion Method
- Special Cases
9.10 Concepts 1
- Elementary Transformations
- Gauss Elimination Method
- Gauss Jordan Elimination Method
11 Chapter: Binomial Theorem
Concepts
- Introduction : coefficients, terms, no of
terms
- Binomial Theorem
12 - Intro contd
Examples
- Simple ex. on binomial expansion
13,14 - Middle terms
- General term
15 - B. Thm with any Index
- Examples
16&17 - Applications of B. thm
18 Chapter : Set Theory
- Definition of a set
- Methods of describing a set
- Operations on sets
19 - Venn Diagrams (in brief)
- Laws of Operation : Demorgan’s Laws,
Distributive Laws, Associative Law
20 - Relations & Functions
21 Chapter: Functions, Limits & Continuity
Concepts
- Functions
- Mappings
22 - Types of Functions
- Limit of a function
23,24&25 Examples
- Methods of evaluating limit of a function
- Some important limits
- Continuity of a function

4. 26,27,28 Chapter: Differential Calculus
- Introduction
- Basic Formulae
- Sum Rule
- Product Rule
29,30.31 - Quotient Rule
- Problems
- Chain Rule
- Logarithmic Diff
32,33 - Diff by Substitution
- Implicit Diff
- Derivative of a function wrt another
function
34,35 Concepts
- Maxima & Minima
- Points of Inflexion
36,37 Chapter: Logarithms
- Introduction
- Laws of Operations
- Change of base
38,39 - Logarithm Tables
- Operations with Logarithms
40 - Compound Interest 2
41 Chapter: Logical Statements & Truth
Tables
- Introduction
- Logical Statements
- Truth tables
- Negation
42,43 - Tautologies & Fallacies Propositions
- Conditional Statements
- Biconditional Statements
44 Chapter : Arithmetic & Geometric
Progressions
- Introduction
- A.P., Sum of terms in A.P.
- Questions for practice
45,46 - Representation of terms in A.P.
- Arithmetic Mean
- Problems
47,48,49 - Geometric Progression
- Sum of a Series in G.P.
- Geometric Mean
50 Chapter : Permutations & Combinations
Concepts
- Introduction : perms, combs

5. - Factorial
- Fundamental Rules of Counting
51.52 Examples
- Questions on Counting principle
Concepts
- Permutations
- Per of n Different things
53 - Circular Permutations
- Perms of Things not all Different
Examples
- Ques on perms
54&55 Concepts 3
- Combinations
- Combs of things not all Different
- Problems
56 Chapter : Real Number System
- Number Systems, Natural Numbers
- Integers, Prime Numbers, Rational &
Irrational Numbers, Modulo
57,58 Chapter : Linear & Quadratic Equations
Concepts
- Introduction
- Degree of an equation: linear, quad,
cubic, etc.
- Solns to quad eqns : method of
factorization
- Simultaneous eqns
- Method of factorization
59,60 Examples
- Equations reducible to q.e.
- Irrational eqs
- Reciprocal Eqns
61,62 Concepts
- Nature of roots
- Symm expressions
- Formation of an eq
63 PROBLEMS & REVISION

6. PRESENTATION:
There will be one presentation for the subject. The students will be divided into
different groups. Each group consists of 2 members and will work upon a topic and
present it.
TOPICS:
1. Degree of an equation
2. Solution of a Quadratic Equation
3. Nature of roots of a Quadratic Equation
4. Formation of a Quadratic Equation
5. Operations on Matrices
6. Matrix Multiplication
7. Determinant of a Matrix
8. Inverse of a Matrix
9. Cramer’s Rule
10. Matrix Inversion Method
11. Gauss Elimination Method
12. Types of Matrices
13. Fundamental Principle of Counting
14. Difference between Permutations & Combinations
15. Binomial Theorem
16. Applications of Binomial Theorem
17. Functions
18. Limit of a function
19. Product Rule & Quotient Rule
20. Chain Rule & Parametric Differentiation
21. Logarithmic Diff & Derivative of Function of a Function
22. Maxima & Minima of a function
23. A.P. Series
24. G.P. Series
25. Basic Operations on Logs
26. Learning Log Tables
27. Compound Interest and Depreciation

7. ASSIGNMENTS
Assignment no.1
Topics: Matrix Algebra
2 3 10
1. Minor of 10 in the det 1 −1 2
1 1 2
2. Solve the equations x+y+z=7
x + 2y + 3z = 16
x + 3y + 4z = 22
by Gauss- Elimination method.
3. Solve the equations x – 2y + 3z = 4
2x + y – 3z = 5
-x + y + 2z = 3
by Cramer’s rule.
4. State Cramer’s rule.
5. Define Gauss Elimination Method.
6. Define the inverse of a square matrix.
1 3 3 
 
7. Find the inverse of the matrix 1 4 3
1 3 4 
 
8. Solve by matrix inversion method:
3x + y + 2z = 3
2x – 3y – z = -3
x – 2y + z = 4
9. Solve by Cramer’s rule:
x + 2y + z = 4
-x + y + z = 0
x – 3y + z = 2
10. Define a diagonal matrix and a unit matrix

8. Assignment no.2
Topics: Differential Calculus
Logarithms
dy
1. If y = a x , then find .
dx
2. If log 2 (log 3 (log 2 x)) = 1, find x.
−1
 1+ x − 1− x 
3. Differentiate with respect to x, the function y = tan   1+ x + 1− x 

 
1 1 1
4. If a x = b y = c z = d w , show that log a bcd = x  + +  .
 y z w
5. What is the function of log tables?
6. Find the maximum and minimum values of y = 8 x 3 − 9 x 2 + 6 .
dy
If y = ( x 3 + x 2 + x + 1) , find
−2
7. .
dx
8. Show that log a xy = log a x + log a y , (a ≠ 1).
1
.7136 × .08  3
9. Using logarithms, find the value of 
  .
 .0214 
Show that log a m = n log a m.
n
10.

9. Assignment no.3
Logical Statements&Truth Tables, A.P. & G.P and Permutations & Combinations
1. Simplify : ( p ∨ q) .
2. Prove that p → (q ∧ r ) = ( p → q) ∧ ( p → r ) .
3. How many numbers are there between 100 and 1000 such that every digit is either
2 or 3?
4. Construct the truth table for the statement ( p ∧ q ) ∨ (: r ) .
5. In how many ways, the letters of the word ‘RAM’ can be arranged?
6. Show that [( p ⇒ q ) ∧ ( q ⇒ r ) ⇒ ( p ⇒ r )] is a tautology.
7. How many different committees can be formed consisting of 4 men & 3 women out
of 7 men & 5 women?
8. Show that p ∧ ( p ∨ q ) = p , where p, q are logical statements.
9. What do you mean by permutations?
n
10. Find the value of Cn −3 .
11. Find the sum of the series 72 + 70 + 60 + …… + 40
th th
12. If a, b, c are the p , q and r terms of a G.P., then prove that
th
a q −r br − p c p −q = 1
13. Find the sum of 50 terms of the seqn. 7, 7.7, 7.77, 7.777,……..
14. If the m term of an A.P. is 1/n and n term is 1/m, then show that the mnth term
th th
is 1.

10. Practice Problems on Real Number System and Set Theory
1. Define complement of a set A ( A⊥ ).
2. Define Union & Intersection of two sets A and B.
3. Find the nth term of the series 1 + 3 + 5 + 7 + 9 + ……
4. If A ⊆ B, then show that B C ⊆ AC .
5. Prove that 2 is an irrational number.
Practice Problems on Linear & Quadratic Equations
1. Solve 3x + 1 − x − 1 = 2
2. Solve x 2 − 4 x − 6 − 2 x 2 − 8 x + 12 = 0
3. In a linear equation y = mx+c, what is meant by the terms m and c?
4. Solve 13 − 3 x + 3 = x
x−a x−b b a
5. Solve + = +
b a x−a x−b
6. Solve the equation 2 .3 = 100
x 2x
7. If α, β are the roots of the equation ax 2 + bx + c = 0 such that α, β are non zero,
1 1
α > β and then find the value of − .
α β
8. Solve the equation 12 + 9 ( x − 1)(3x + 2) = 3 x 2 − x
9. What is the difference between linear and quadratic equations?
10. Solve the following equation: 4 x 2 − 33 x + 8 = 0

11. Practice Problems on Binomial Theorem and Functions, Limits & Continuity
10
 1
1. Find the term independent of x in  x +  .
 x
2. If f(x) = k, then find f(1) ( here k is a constant).
1+ x −1
3. Evaluate lim .
x→0 x
4. Prove that the function f ( x) = x 2 + 4 x − 2 is continuous at x = 1.
5. What is Binomial Theorem? Explain its utility with suitable illustrations.
6. Prove that the coefficient of xn in (1+x)2n is twice the coefficient of xn in
(1+x)2n-1.
7
 3 x3 
7. Find the third term from the end in the expansion of  2 −  .
x 6 
8. A function f is defined as
 x2 − 4 x + 3 
 2 for x ≠ 1
 
f ( x) =  x + 2 x − 3 
− 1 for x = 1 
 2
 

Show that f(x) is differentiable at x=1 and find its value.
x 3 + 27
9. Evaluate lim .
x →−3 x + 3
x2 − 9
10. Prove that the function f ( x) = is discontinuous at x=3.
x−3