Business Mathematics

Daffodil International University Faculty of Science & Information Technology Department of Information Technology & Management (ITM) Final Examination, Fall 2024 Course Code: MATH101, Course Title: Business Mathematics Section: A & Teacher: Prof. Dr. Bimal Chandra Das Time: 02:00 Hrs Marks: 40 • Answer ALL Questions [The figures in the right margin indicate the full marks and corresponding course outcomes. All portions of each question must be answered sequentially.] 1. a) The supply function for a product is p_s(q) = 10 - 0.25q where q is in million of tons and P_s(q) is in dollars per ton. Market equilibrium occurs at a demand to 50 million tons. Compute the producer's surplus. | 5 | CLO4 (3,5) 1. b) Evaluate ∫_1^2 (5/(5x^2 + 1)^(1/2) + 2e^(-3x) - 3) dx | 5 2. a) For an examination, a candidate has to select 7 subjects from 3 different groups A, B, and C. The group contain 4, 5, 6 subjects respectively. In how many different ways can a candidate make his selection if he has to select at least 2 subjects from each group? | 5 | CLO3 (6) 2. b) Solve the system of linear equations using Gauss-Elimination method 2x + y + 2z = 3 3x - y + 2z = 2 2x + 3y + 2z = 5 | 5 3. a) Find dy/dx if (i) y = x^(sin x) + e^(x^2) x^(-2/3) (ii) y = (log e^(2x)) / cos(sin x) + tan x cos x^2 + a | 2+3=5 | CLO4 (5) 3. b) The profit realized when x gallons of distilled water are produced and sold is P(x) = 20x - 0.005x^2. (i) Find the number of gallons that should be made to maximize profit. (ii) What is the maximum point and compute the maximum profit? | 5 4. a) What is the condition for multiplication of two matrices? Define symmetric matrix. If A = [1 -2 1; 2 3 1] and B = [3 1 1; 1 1 2; 0 2 3]; Is AB = BA true? Verify your comments. | 1+1+3=5 | CLO4 (1,5) 4. b) Find the derivative of f(x) = sin ax using first principal rule. | 5