Download Basic Quantitative Methods Part 2-Quantitative Methods-Exam Paper and more Exams Quantitative Techniques in PDF only on Docsity!
QUANTITATIVE METHODS (Marks 100)
Module A (3 hours)
Q.1 (a) Find the value of x, using the laws of logarithms:
32 x โ^2 =^32
(b) Factorize the given expression:
4 x^4 + 81 y^4
(c) Simplify the following to find the values of x:
xx x
xx
x
x
x
x
(d) The sum of 12 terms of an arithmetic progression is 234 and the last term is 36. Find the common difference and the first term. (04)
Q.2 (a) Excel Corporation has issued bonds having face value of Rs. 500 million. They carry annual interest @10% compounded semi-annually. The bonds are redeemable in 2ยฝ years. Interest as well as the face value will be paid on maturity. Find the amount that should be deposited each month into a sinking fund to be able to redeem all bonds on maturity, if the deposited amount earns interest @ 9% compounded monthly. (06)
(b) Compute effective rate of interest where nominal rate is 8% compounded quarterly. (02)
Q.3 (a) If y = 2 x^2 โ 6 x + 9 and x = 3 z + 5 , find dy/dz by applying chain rule. (04)
(b) The cost of producing x units of calculators is denoted by:
x
C x x
You are required to find: (i) the marginal cost function; (01) (ii) the total cost of 10 units; and (01) (iii) the cost of producing the 100 th^ unit of calculator. (01)
(c) The demand of a product at a price of Rs. 5 per unit is 80 units. When the price is increased to Rs. 12 per unit the demand is reduced to 45units. Determine the linear equation of the demand function in the form Q = f(p). (03)
Q.4 Solve the following system of equations by use of matrices:
2 x โ y + 2 z = 6 x โ 2 y + 3 z = 6 3 x โ 3 y โ z = โ6 (09)
Q.5 A manufacturer produces two products P and Q which must pass through the same processes in the departments A and B having weekly production capacities of 240 hours and 100 hours respectively. Product P needs 4 hours in department A and 2 hours in department B. Product Q requires 3 hours and 1 hour respectively, in department A and B. Profit yields for product P is Rs. 700 and for product Q is Rs. 500. The manufacturer wants to maximize the profit within the given sets of limitations.
You are required to: (a) Construct the objective function and all the constraints. (02) (b) Plot the above constraints graphically and identify the feasible region. (05) (c) Determine the combination of units which will give the maximum profit. (03)
Q.6 (a) The data relating to the length of 30 leaves measured correctly to the nearest centimeter is shown below:
Length (cm) 10 โ 14 15 โ 19 20 โ 24 25 โ 29 Frequency 3 8 12 7
Draw a histogram from the above data. (^) (04)
(b) The number of passengers carried by a boat during 25 trips is given below:
52 84 40 57 61 65 77 64 62 35 82 58 50 78 103 71 75 41 51 66 60 95 58 49 89
Construct a stem and leaf display with one digit leaves. (03)
(c) Sohrab & Company increased the wages of its workers by 20% during the year 2006, whereas, the consumer price index changed from 240 to 270. Compute the increase / decrease in real wages. (03)
Q.7 (a) Construct the scatter diagram for the following data:
x 9 2 12 7 16 5 8 y 12 18 11 16 9 16 14 (02)
(b) Determine the coefficient of correlation between x and y. (05) (c) Calculate the coefficient of determination. (01) (d) Interpret your results in (a), (b) and (c). (03)
Q.8 (a) A firm installed two machines U and V, on January 1, 2007. The probability that the machines will break down during the first year of operations is 0.2 and 0.1 for machines U and V respectively. Compute the probability that one of the two machines will break down during the year. (03)
