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Basic Quantitative Methods Part 7-Quantitative Methods-Exam Paper, Exams of Quantitative Techniques

Dr. Bhim Rao Ambedkar UniversityQuantitative Techniques

This exam paper is for Quantitative Methods. This course is important because of general tests like GRE for further studies. This exam paper includes: Basic, Qualitative, Methods, Factorize, Expression, Equation, Payment, Semi-annual, Installment, Matrix, Algebra, Average, Feasible, Region

Typology: Exams

2011/2012

Uploaded on 09/04/2012

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QUANTITATIVE METHODS (MARKS 100)
Module A (3 hours)
Q.1 (a)
If
22
22
y
yxx , find the value of y. (03)
(b)
Factorize the expression 4224 416 yyxx . (03)
(c) On August 1, 2009 a supplier increased the price of a product by 25%. On August
15, 2009, he decreased the price by 16%. If the price of the product on August 15,
2009 is Rs. 63, what was the price on July 31, 2009. (02)
Q.2 (a) A line passes through the point (3, 5) and has same values of x-intercept and y-
intercept. Find the equation of the line. (03)
(b) A shopkeeper sold goods worth Rs. 3.0 million during 2008. If he is able to
increase his sale by 15% annually, determine the year in which he would achieve
annual sale of Rs. 25 million. (05)
Q.3 (a) A promissory note of Rs. 200,000 carries simple interest of 8% per annum. The
note is payable at the end of 2 years. The holder of the note got it discounted 6
months before the maturity date and received an amount of Rs. 221,797. Compute
the discount rate. (05)
(b) Shiraz acquired a new car worth Rs. 850,000 through a leasing company. He
made a down payment of Rs. 200,000 and has agreed to pay the remaining
amount in 10 equal semi-annual installments. The leasing company will charge
interest @ 19% per annum, over the lease term. You are required to find:
(i) Amount of semi-annual installment.
(ii) Total amount of interest that Shiraz will pay, over the term of the lease. (05)
Q.4 (a) The average cost function of a product is as follows:
x
xxxA 60
3003001.0)( 2
You are required to find the number of units at which the marginal cost will be
minimum. (06)
(b)
If x
xx
y)2)(1(
, show that:
x
x
xx
dx
dy
2
2
2
23 (04)
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Download Basic Quantitative Methods Part 7-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) If 2  ^2

(^2) 

y y

x x , find the value of y. (03)

(b) Factorize the expression 16 x^4  4 x^2 y^2  y^4. (03)

(c) On August 1, 2009 a supplier increased the price of a product by 25%. On August 15, 2009, he decreased the price by 16%. If the price of the product on August 15, 2009 is Rs. 63, what was the price on July 31, 2009. (02)

Q.2 (a) A line passes through the point (3, 5) and has same values of x-intercept and y- intercept. Find the equation of the line. (03)

(b) A shopkeeper sold goods worth Rs. 3.0 million during 2008. If he is able to increase his sale by 15% annually, determine the year in which he would achieve annual sale of Rs. 25 million. (05)

Q.3 (a) A promissory note of Rs. 200,000 carries simple interest of 8% per annum. The note is payable at the end of 2 years. The holder of the note got it discounted 6 months before the maturity date and received an amount of Rs. 221,797. Compute the discount rate. (05)

(b) Shiraz acquired a new car worth Rs. 850,000 through a leasing company. He made a down payment of Rs. 200,000 and has agreed to pay the remaining amount in 10 equal semi-annual installments. The leasing company will charge interest @ 19% per annum, over the lease term. You are required to find:

(i) Amount of semi-annual installment. (ii) Total amount of interest that Shiraz will pay, over the term of the lease. (05)

Q.4 (a) The average cost function of a product is as follows:

x

A x x x

You are required to find the number of units at which the marginal cost will be minimum. (06)

(b) If

x

x x

y

 , show that:

x

x

x x

dx

dy

2

Q.5 (a) Using matrix algebra, find the value of ‘a’, if |A| = 0 for the following set of equations:

4 x  3 y  z  5

x  2 y  z  4

ax  12 y  5 z  1 (03)

(b) A pharmaceutical company has developed a formula to prepare a herbal medicine. The medicine can be produced by using either product X or product Y or a combination of both. From each milligram (mg) of X it can extract one unit of iron and two units of calcium and from each mg of Y it can extract one unit of iron and one unit of calcium. Each tablet of the medicine is required to contain:  5 to 7 units of iron  8 to 10 units of calcium

The cost of X is Rs. 6 per mg whereas Y costs Rs. 4 per mg.

You are required to: (i) Construct the set of constraints and the objective function for cost minimization. (ii) Draw the graph and identify the feasible region, clearly indicating its boundaries. (iii) How many mg of each product should be used to produce the tablets at the lowest cost? (^) (11)

Q.6 (a) The following data represents the average monthly take-home salary of the employees of an organization:

Year 2005 2006 2007 2008 Pay (Rs.) 12,350 13,500 14,800 16, Price Index 110.1 122.3 137.6 160.

(i) Compute the real wages for each of the above years. (ii) Compute the amount of pay needed in 2008 to provide buying power equal to that enjoyed in 2006. (03)

(b) The following data relates to salaries of the employees of a reputed cement manufacturing company:

Salary (Rs in thousands)

Number of Employees

10 up to 20 120 20 up to 30 175 30 up to 40 100 40 up to 50 80 50 up to 60 44 60 up to 70 25 70 up to 80 17

(i) Draw a frequency polygon representing the above data. (ii) Assuming that the mean and standard deviation of salaries of another company is Rs. 36,544 and Rs. 8,982 respectively, determine which company’s salaries are more evenly distributed. (09)