St. Joseph’s College of Commerce B.Com. 2014 I Sem Mathematics For Managers Question Paper PDF Download

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  1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – OCTOBER 2014

  1. COM – I SEMESTER

 MATHEMATICS FOR MANAGERS

Duration: 3 Hours                                                                                       Max. Marks: 100

SECTION – A

 

  1. Answer ALL the questions. Each carries 2 marks.                                       (10 x2 =20)

 

  1. Solve 8x2-10x+3=0 using formula method.
  2. In the two consecutive numbers, 1/4th of the smaller one exceeds the 1/5th of the larger one by 3. Find the numbers.
  3. Adarsh bought goods worth Rs. 20, 000. He was offered trade discount of 25% and further received a cash discount of 10%. Find the net price that he had to pay.
  4. Out of 60 students, 20 passed. Find the percentage of failure.
  5. What is Inverse proportion?
  6. If 3/5th of an estate is worth Rs.1, 800. Find the value of 2/3rd of it.
  7. y=1/x and y=(1/x4 )- ex + x. Then find dy/dx
  8. If f(x) = 2x+3. Find f(-3)+f(1)
  9. If the Total cost function is C= 2x2+x+10 and the quantity produced is 10 units. Find the variable cost and the fixed cost.
  10. The total cost of an article was Rs.24 and its selling price was marked at S. Later it was offered for sale at 90% of this selling price. The dealer still made a profit of 10% of his original cost. What was the marked price?
  11. An Indian merchant imports goods worth Rs.24, 990 pounds. If the exchange rate is GBP/INR: 100. How much is it worth in Indian rupees?

 

                                                SECTION – B

 

  1. Answer any FOUR Each carries 5 marks.                                  (4×5=20)
  2. a. Divide 5, 000 in the ratio given- A:B is 2:3 and B: C is 4:3
  3. 5 men each working 9 hours a day can finish a work in 30 days. How many men are required to finish 8 times the work in 25 days each working eight hours a day.

 

  1. a. The population of a village 2 years ago was 6250. Due to migration to cities for higher education etc.., it decreases every year at 4% p.a. Find the present population of the village.
  2. A machine depreciates in value each year at 10% of its value at the beginning of a year. If the machine is purchased at Rs.15, 000, find its value at the end of the 3rd year.
  3. If the banker’s gain on a bill is 1/9th of the banker’s discount. The rate of interest being 10% p.a. Find the unexpired period of the bill.
  4. Differentiate the following:
  5. y= 2ex + 2x + 2/x + 7 logx
  6. y= (2x2 – x) (3x2 + x-1)

 

  1. Define Learning curve. It is highly impractical to achieve a learning effect of 50%. Illustrate with learning curve table.
  2. a. Parents of Krishna want to send him to London after 7 years. He expects the cost of the trip will be Rs.5, 00, 000. How much should he save semi annually to have Rs. 5, 00, 000 after seven years, if the interest rate is 12% p.a.
  3. Bank of Baroda offers 12% p.a. interest on 12 months recurring deposit account. If I deposit Rs.1, 000 per month for 12 months, how much can I get at the end of 1 year assuming that each deposit is to be made at the beginning of the month?

 

SECTION – C

 

III)      Answer any THREE questions.    Each carries 15 marks.                    (3×15=45)

 

  1. a. Karan buys a two wheeler on loan. The loan amount is Rs.60, 000. He wants to clear the loan in 10 months. How much should he pay every month? Prepare the loan amortization schedule. Interest charged is 18 % p.a.
  2. A man invests Rs.5, 000 for 3 years at a certain rate of interest compounded annually. At the end of one year it amounts to Rs.5, 700.
  3. Calculate the rate of interest per annum.
  4. The interest accrued in the second year.

iii. The amount at the end of the third year.

(10 +5)

  1. a. The manufacturer’s total cost function is C= 500+25x+x2. Find the variable cost when 10 units are produced,  Average cost function, Marginal cost function, Marginal cost when 10 units are produced, and Actual cost of producing 11th unit.
  2. x= 32-4p-p2, when p=3. Find the elasticity of demand.

(10 + 5)

  1. a. If you deposit Rs.5, 000 today at 12% p.a. C.I. In how many years will the amount grow to Rs.1, 60, 000?
  2. Which is better Rs. 55, 000 now or Rs. 90, 000 after 3 years at 15% p.a. C.I.
  3. A loan of Rs. 1, 00, 000 is taken on which interest is payable at 10% p.a. C.I. However, the repayment is to start at the end of 3rd year from now. What should be the annual payment if the total loan and interest is to be repaid in 9 installments?

(5+5+5)

  1. a. A bill of Rs. 1, 700 was drawn on 3rd April 2000 and made payable 4 months after date. It was discounted on 15th April 2000 at 16 % p.a. What was the discounted value of the bill and how much has the banker gained on this transaction.
  2. A bill for Rs.2, 920 was drawn on September 11th for 3 months after date and was discounted at 16% p.a. for Rs. 2, 875. On what date was the bill discounted?

 

  1. a) Find the simple interest compound interest and their difference on Rs.5000 invested for 4 years at 8% Per Annum.
  2. b) An Investment, which requires an initial outlay of Rs.100000, Will yield an annuity of Rs.20000 for 12 years. If the discount rate is 14% per annum should we accept this investment proposal?
  3. c) Steve has an option of investing Rs. 1200 at 8% P.a for 2 years with the following alternatives
  4. Interest calculated annually.
  5. Interest calculated half yearly.
  • Interest calculated quarterly.
  1. Interest calculated monthly.

Which of the 4 above alternatives would you recommend Steve and why?

(5+5+5)

SECTION – D

  1. IV) Compulsory question. (15 marks)
  2. a. i)A company has been asked to bid for prospective contract for the supply of 90 engines. They have just completed an initial trial order for 30 engines involving a total of 6, 000 direct labour hours at Rs. 50/ hour. It is expected that there will be an 80% learning effect. Estimate labour cost for the new order.

ii). If material cost if Rs.5, 000 per engine, variable overheads is Rs.12 per direct labour hour, fixed overhead is Rs.5, 600. Profit expected is 12.5% over cost. Find the price per unit that can be quoted for the contract.

 

  1. b) Find Maximum profit if R= 30X-X2 and C=20+4X

(10+5)

 

                                

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