Pokhara University || Mathematics-I Fall 2019 || BBA\BCIS

Very Short Answer Questions (10×2)

Attempt all the questions.

1. If U={4,5,6,7,8,9,10}, P== {6, 7, 8, 9} and Q = {5, 7, 9}, Find theelements of the set P’-Q’ .
2. A person has 5 post letters and there are 4 letterboxes in the locality. In how many ways can these letters be posted?
3. Rewrite the expression -11/10≤x≤-1/4 by using an absolute sign.
5. Find the domain and range of the function f(x)=x²-5.
6. Show that the vectors 2
7. Solve:
8. Find dy/dx from the function y=5^(x/5-7)
9. Find the magnitude of and the unit vector along.
10. Find the equation of the tangent to the curve f(x)=1/2x²+5x

Section “A”

Descriptive Answer Questions (10×6)

a) On a group of 200 students, 100 are interested in music, 70 are interested in photography and 40 like swimming, furthermore, 40 are interested in both music and photography, 30 are interested in both music and swimming and 10 are interested in all 3 activities. Using Venn-diagram find the number of students that are interested in

• Photography but not music and swimming
• Exactly one activity
• At least one activity

11.(b) Find the domain and range of the function f(x)= √(6-x-x²)

12.(a) If A= [1,3) and B=(2,5] find A∪B, A∩B and A-B.

12.(b) Prove that √2 is an irrational number.

13.(a) An epidemic is spreading through a large western region. Health estimates that the number of persons will be affected by the disease is a function of time since the disease was first detected. Specifically, the function n=f(t)=300t³-20t²

where n is the number of persons and 0≤t≤60 measured in days.

• How many persons are expected to have caught the diseases after 20 days?
• At what rate is the disease spreading at t=30?

13.(b) A monopolist has a demand curve q=400-20p and the cost curve C=5q+q²/50. What is the profit-maximizing level of output when the monopolist fixes its output? Also, find the maximum profit.

14.(a) Find dy/dx (any two)

• e^xy=xy
• y=3u²-6u+2, u=v²-1 and v=2x
• y=√((x-1)/(x+1))

15.(a) Show that:

15.(b) Solve the following system of equations by using Cramer’s rule or matrix method: x-2y+z=-4, 2x+y-z=5 and 3x+2y+4z=3

16.(a)Determine the value of the constant K so that the function

is continuous at x=1.

16.(b) If y= (t-2)/3t and t=√(x+1), find dy/dx.

17.(a) A student is required to answer 8 out of 12 questions which are divided into 2 groups each containing 6 questions, and that student is not permitted to attempt more than 5 from any group. In how many different ways can the students make up choices?

17.(b) In how many ways can the letters of the word MATHEMATICS be arranged?

Section “C”

                         Case Analysis

18. A tire manufacturer studying the effectiveness of television advertising and other promotions on sales of its A-brand tires attempted to fit data it had gathered to the equation a₀+a₁x+a₂x²+b₁y where S is sales in revenue in millions of dollars spent on other promotions and a₀, a₁, a₂, and b₁are constants. The data gathered in two different regions of the country where expenditures for other promotions were kept constant (at B₁ and B₂) resulted in the following quadratic equations relating to TV advertising and sales.

Region1: S₁=30+20x-0.4x²+B₁

Region2: S₂=20+36x-1.3x²+B₂

The company wants to know how to make the best use of its advertising dollars in the regions and whether the current location could be improved. Advise management about current advertising effectiveness, allocation of additional expenditures and reallocation for current advertising expenditures by answering the following questions.

1. In the analysis of sales and advertising marginal return to sales is usually used and it is given dS₁/dx for Region 1 and dS₂/dx for Region2
2. Find dS₁/dx and dS₂/dx
3. If $10 million is being spent on TV advertising in each region, what is the marginal return to sales in each region?
4. Which region would benefit more than additional advertising expenditure, if $10 million is currently being spent in each region?
5. If any additional money is made available for advertising, in which region should it be spent?
6. How could money already being spent be reallocated to produce more sales revenue?
7. Aakash construction, one of the leading construction companies in Pokhara is going to construct three types of apartments in Chiple Dhunga, Pokhara. Currently, the managers and engineers of the company are analyzing the cost and the selling strategies of the apartments. For the Apartment of type1, all the raw materials except the sand and concrete will be imported from India. For types 2 and 3, local Nepali raw materials will be used and also the Nepali buyers are that the imported things have better quality than the local things. The following table summarizes the requirements per unit of each type of Apartment.

If it is imported from India, Cement costs Rs. 1000 per sack, Brick costs Rs.25 per unit, and Iron costs Rs. 180 per kg and the labor costs Rs.100 per hour. It is not imported and all domestic products are used, then the cost of cement is Rs.750 per sack, bricks cost Rs.12 per unit, Iron costs Rs.110 per kg, Sand Rs.7000 per truck, concrete cost Rs.14000 per truck and the labor costs Rs.60 per hour. From the meeting of the board of directors, it is decided that they will construct 10 apartments 1, 12 apartments of type 2 and 8 apartments of type 3.

1. Perform matrix multiplication to calculate the cost of each type of apartment and the total cost of the entire project.
2. Perform a matrix multiplication to calculate the cost of each type of apartment of type 1,2 and 3.
3. If the total area of the apartment of type1 is 2800 sq. feet, type2 is 2500 sq. feet and type3 is 3400 sq. feet respectively and if we’re a buyer of the apartment, which apartment would you buy? Give logical reasons.
4. If you were a sales manager of the company, depending on the information given above and the result which you have calculated, describe how would you promote your product?