(Department of Mathematics and Statistics)

WARNING

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

Level: BA, B.Com, BBATotal Marks: 100

ASSIGNMENT No. 1

(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 [pic].

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

|Value of X |20 |30 |40 |50 |60 | |Frequency |8 |12 |10 |12 |8 |

(b)Discuss any one continuous probability distribution.

Q.4 (a)Solve the quadratic equation.

[pic] by two different methods.

(b)Find the solution set for the following inequality

[pic]

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

After one yearPrice= Rs. 45,000

After two yearsPrice= Rs. 40,000

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

ASSIGNMENT No. 2

(Units 1–4)Total Marks: 100

Note: All questions carry equal marks.

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

(b)Find the determinant of the matrix A

[pic]

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

[pic]

[pic]

[pic]

(b)Find [pic] if [pic]

Q.3(a)Consider the function [pic]

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 [pic]. At what rate the position of the satellite y is changing with respect to x. When the satellite is at the point ([pic]

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 |5 |1 |13 | |Units of protein |10 |3 |16 | |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

[pic]

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

[pic]

(b) The total cost of producing q units of a product is described by the function C=500,000+250q+0.002[pic] 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.

BUSINESS MATHEMATICS

Level: B.A/B.Com/BBACourse Code: 1429

Unit No.1Probability Theory

Introduction, basic probability theory, definition, laws...