Bachelor of Management Studies (B.M.S.) SEM II 2022 2023 Apr 2023 S BUSINESS MATHEMATICS Question Paper - Mumbai University | munotes

Questions asked in this paper

• Figures to the right indicate marks

1. Q1 A. Choose the correct alternative (Any 8) 8 marks
   • 1) The simple interest for 3 years at 9% p.a. for is %) The total money including principal and interest is called
   • 3) For the function f(x) = 7x + 9, the value of f(2) is 4} The point where there is “no profit no loss” is called
   • 6) Iftwo rows (or two columns) of determinant are same, then its value is
   • a) -l b) | c) Zero d) none of these The derivative of a derivative is called
   • 8) of "Co is
   • 9) Ifthe Total Cost Function C = D* + 2D — 20, then the average cost function is
   • 10) The relation between the operators E and A is
2. Q1 B. State whether the following statements are True or False (Any 7) (07) \
   • 1) The future value of an amount is always greater than its present value
   • 2) EMI stands for Equal Monthly Installments
   • 3) The relation between permutation and combination is "P, = x
   • 4) The adjoint of a matrix is obtained by taking transpose of the minor matrix
   • 5) The sum of two Identity matrices is an Identity matrix
   • 7) IfR is the Total Revenue Function then, its derivative is called Total Average Revenue
   • 8) In input-output analysis, the final demands of the consumers are known
   • 9) The forward differences are denoted by Operator E
   • 10) y = logx is called linear function
3. Q2 A Solve the following:
   • ii. If f(x) = kx — 3 and f(3) = 6, find the value of k. Hence find f(2) 3
4. Q2 B Find the amount at the end of one year of an annuity of payable at each quarter with the rate of interest 12% p.a 98 marks
5. Q2 C Answer the following:
   • i. How many different 5 digit numbers can be formed from the digits 1, 2, 3, 4, 5 and 6, none of the digit being repeated in any one of the numbers so formed? ii, Find the value of nif =91:4 (04) 3
6. Q2 D A principal amount to after 4 years and to 14040 after 7 years. Find the principal and the rate of interest / Q.3.A Solve the following: i find the matrix a? 24, (03) ii, that the matrix A = satisfies the equation A? — 44 + 3/ = 0. (04) 8 marks
7. Q3 B Solve the following using Cramer’s Rule. 8 marks
8. Q3 C For the following input-output model. Find the total outputs if final demand are increased by each. Also calculate labour requirements for this output. (08) Industry Consumption by Industry Final Total 30 marks
9. Q3 D Find the inverse of the matrix A =| 2 8 1] by adjoint 7 marks
10. Q4 A Find derivative of 8 marks
11. Q4 B Find maxima and minima for the function f(x) = x3 — 9x? + 24x +7 7 marks
12. Q4 C The Demand function is D = where D is the demand and p is the price of commodity. Find the elasticity of demand when the price is S
13. Q4 D The number of students with marks above 90% at the HSC Examination of M.K.V College for years is given below. Estimate the number of students with marks above 90% for.the year 2015. (08) / Q.5.A Food I contains 2, | and 3 units of vitamin A, B and C respectively. The same figures for Food II are 1, 2 and | respectively and for Food III are 2, 0 and 1 respectively. Find the amounts of Food I, II and III that can exactly satisfy the daily requirements of vitamins. The daily requirements of vitamin A, B and C are 9, 7 and 8 units respectively. If the cost per unit for Food I, II and III are 8, 6, and 4 respectively, then find the total cost for the same. (08) If f(x) = x3 — 2x? find the value of f(x) for x = 0,1,2,3,4, and 5. Prepare the forward difference table and verify that the third order differences are constant. (07)
14. Q5 C Write short notes on the following (Any 3) 15 marks
    • i. Annuity and Types of Annuity
    • ii. Types of Matrices
    • iii. of Economic Functions
    • iv. Assumptions of Input-Output Analysis
    • v. Newton’s Forward and Newton’s Backward Interpolation Formula

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