Course: Business Mathematics (1429) Semester: Spring, 2012

Level: BA, B.Com, BBA Total Marks: 100

(Units 1–4)

Note: All questions carry equal marks.

Q.1 (a) In a game show, the contestant is shown 10 boxes, 3 of which contain prizes. If a contestant is allowed to select any three boxes then what is the probability that
i) The contestant wins all the three prizes.
ii) Only one selected box contains prize.

(b) Explain the rolling of a fair die and then flipping of a fair coin with the help of tree diagram.

Q.2 (a) How can we differentiate between continuous and discrete random variables. Explain with the help of examples.

(b) Let X be a random variable having normal distribution with mean 48 and standard deviation 10. Then find [IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image002.gif[/IMG].

Q.3 (a) Compute the mean, median, mode and standard deviation for the following discrete probability distribution.

Value of X

(b) Discuss any one continuous probability distribution.

Q.4 (a) Solve the quadratic equation.
[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image004.gif[/IMG] by two different methods.

(b) Find the solution set for the following inequality
[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image006.gif[/IMG]

Q.5 (a) The value of personal computer is decreasing linearly over time. Two points indicate its price at two different times:

After one year Price= Rs. 45,000

After two years Price= Rs. 40,000

(i) Determine a linear equation representing this information.
(ii) Predict when the computer will be worthless.

(Units 1–4) Total Marks: 100

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Note: All questions carry equal marks.

Q.1 (a) What is a matrix. Give examples.

(b) Find the determinant of the matrix A

[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image008.gif[/IMG]

Q.2 (a) Find the solution of the system of equations.

[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image010.gif[/IMG]
[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image012.gif[/IMG]
[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image014.gif[/IMG]
(b) Find [IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image016.gif[/IMG] if [IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image018.gif[/IMG]

Q.3 (a) Consider the function [IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image020.gif[/IMG]

Find its derivative also the points at which the slope of the function is zero.

(b) Let a satellite is moving in an orbit given by the equation [IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image022.gif[/IMG]. At what rate the position of the satellite y is changing with respect to x. When the satellite is at the point ([IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image024.gif[/IMG]

Q.4 (a) The table given below shows the nutritional and cost information for the meat (fish) and vegetable (spinach)

Per unit of fish
Per unit of spinach
Minimum requirement
Units of vitamins
Units of protein
Unit cost
Rs. 50
Rs. 20

Find a diet (i.e. units of vitamins and proteins) to meet the minimum nutritional requirement at minimum cost.

(b) Locate the critical points and determine their nature for the function

[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image026.gif[/IMG]

Q.5 (a) Sketch the graph of the curve given by

[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image028.gif[/IMG]

(b) The total cost of producing q units of a product is described by the function C=500,000+250q+0.002[IMG]file:///C:%5CUsers%5Crabeel%5CAppData%5CLocal%5CTemp%5Cmso htmlclip1%5C01%5Cclip_image030.gif[/IMG] where C is the total cost in dollars.

(i) How many units should be produced to minimize the average cost per unit.

(ii) What is the minimum average cost per unit.


Level: B.A/B.Com/BBA Course Code: 1429

Unit No.1 Probability Theory
Introduction, basic probability theory, definition, laws of probability, conditional probability, independent and dependent events, applications.

Unit No.2 Random Variables
Introduction, Random numbers and their generation, Application of random numbers, concepts of random variables and their construction, Discrete and continuous random variables.

Unit No.3 Equations
Solving fist degree equations, Quadratic equations, Solution of quadratic equations by different methods, inequalities, absolute value, Co-ordinate system

Unit No.4 Linear Equations
Characteristic of linear equations, Slope- intercept form, determining the equations, Applications.

Unit No.5 Matrices and Determinants
Matrices, Different kinds of Matrices, Addition, Subtraction and Multiplication of matrices, Determinants, Application of matrices and determinants.

Unit No.6 Inverse of Matrices
Expansion of determinants, different Properties of determinants, Cofactors and minors of elements of a matrix, Cramer’s rule, Solution of system of linear equations by use of matrices.

Unit No.7 Differentiation
Derivatives, Differentiation of explicit and implicit functions, maxima and minima, Applications of derivatives.

Unit No.8 Partial Derivatives
Partial Derivatives, maxima and minima for functions of multi-variables Applications of partial derivatives.

Unit No.9 Optimization
First derivative test. 2nd Derivative test, Curve sketching, Revenue, Cost and profit applications in business.

Recommended Book:-
1. Applied mathematics for Business, Economics and the Social Sciences. By Frank
S. Budnick. Mcgraw-Hill