Foundation Course examination :: Business Mathematics and Statistics Fundamentals: December 2004

*C-4(BMS)* *Revised Syllabus*
Business Mathematics and Statistics Fundamentals
Time Allowed : 3 Hours	Full Marks : 100
The figures in the margin on the right side indicate full marks.
SECTION A(Arithmetic — 15 marks)
Answer Question No. 1 (compulsory — 5 marks) and any one (10 marks) from the rest.

(a)

The ratio of the present age of mother to her daughter is 5 : 3. Ten years hence the ratio would be 3 : 2. Find their present ages.

(b)

Find a mean proportional between 27 and 243.

(c)

If an examination 20% of the candidates failed in English, 30% in Mathematics and 10% in both. Find the percentage of those who passed in both subjects.

(a)

Monthly incomes of two persons are in the ratio 2 : 3 and their monthly expenditures are in the ratio 4 : 7. If each saves Rs. 50 a month, find their monthly incomes and expenditures.

(b)

The price of cooking gas is increased by 20%. Find by how much percent a man must reduce his consumption so that the expenditure on cooking gas may increase only by 8%.

(a)

If the difference between true discount and banker's discount on a sum due in 6 months at 4% per annum is Rs. 20, find the amount of the bill.

(b)

A sum of money becomes double in 20 years at simple interest. Find the number of years by which the sum will be tripple.

SECTION B(Algebra — 25 marks)

Answer Question No. 4 (compulsory — 5 marks) and any two (10x2=20 marks) from the rest.

Answer any five part of the following :

1x5

(a)

Find the modulus of

24 + 7i

4 + 3i

(b)

Simplify

X^a+b X^a-b X^m-2a

Xx^m-a

(c)

Show that log (1 + 2 + 3) = log 1 + log 2 + log 3.

(d)

Find the value of 3 √

−4

÷ 2 √

−9

(e)

Solve for P if 2^{p + 3} + 2^{P + 1 = 320.}

(f)

If 7p_r = 2520, find the value of r.

Please turn over

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C-4(BMS)
Revised syllabus

Marks

(a)

Given p² = 7p — 3 and q² = 7q — 3 where p is not equal to q. Form a quadratic

and

(b)

Solve for x: (√5)^4(x−1) 5 ^2x−3 + 20

(a)

logx

y² + z² + yz

log y

z² + x² + zx

log z

x² + y² + xy

, show that x^y−z z^x−y = 1.

(b)

An engine without any wagons can run 24 km/hr and its speed is diminished by a quantity varying as the square root of the number of wagons attached to it. With 4 wagons its speed becomes 20 km/hr. Find the maximum number of wagons with which the engine can move.

(a)

A question paper is divided into three groups A, B and C, each of which contains 3 questions, each of 25 marks. One examinee is required to answer 4 questions taking at least one from each group. In how many ways he can choose the questions to answer 100 marks?

(b)

In a survey of 100 students it was found that 60 read Economics, 70 read Mathematics, 50 read Statistics 27 read Mathematics and Statistics, 25 read Statistics and Economics and 35 read Mathematics and Economics and 4 read none. How many students read all three subjects?

SECTION C(Mensuration — 30 marks)

Answer Question No. 8 (compulsory — 10 marks) and any two (10x2=20 marks) from the rest.

Answer any five of the following :

(a)	Three cubes, whose edges are 6 cm, 8 cm and 10 cm respectively, are melted without any loss of metal into a single cube. Find the edge of the new cube.
(b)	The circumference of the base of a right circular cylinder is 44 cm and its height is 10 cm. Find the volume of the cylinder.
(c)	Find the equation of the circle whose centre is (—2, 3) and diameter is 8 units.
(d)	Find the equation of a straight line passing through (1, 2) and perpendicular to line 2x — 3y = 2.
(e)	Find the area of a triangle having sides 3 cm, 4 cm and 5 cm.
(f)	The point p divides the line joining the points M (4, 5) and (7, —1) internally in the ratio 1 : 2. Find the co-ordinates of P.

2x5

(g)

Find the eccentricity of the ellipse

x²

y²

= 1

(h)

Find the distance of the line x — 2y = 4 from the point (3, —5).

(a)

Find the number of tiles of area 200 sq. cm to cover the entire floor of a hall 16 m by 10 m.

(b)

How many solid right circular cylinder each of length 8 cm and diameter 6 cm can be made out of the material of a solid cone of height 36 cm and base of diameter 24 cm? Find the total surface area of each cylinder?

10.

(a)

Find the value of the constant m such that the three lines 2x — 3y + m = 0, 3x — 4y = 1 and 4x — 5y = 2 are concurrent.

(b)

Find the volume of the cone where radius of the base is 5 cm and slant height 13 cm.

11.

(a)

Find the equation of the circle having (0, 4) and (3, —1) as the extremities of its diameter. Also find the centre and radius.

(b)

Find the equation of parabola whose focus is (—1, 1) and equation of directrix is x + y + 1 = 0. Also find the length of the latus rectum and the equation of axis.

Please turn over

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C-4(BMS)
Revised Syllabus

SECTION D(Elementary Statistics — 30 marks)

Answer Question No. 12 (compulsory — 10 marks) and any two (10x2=20 marks) from the rest.

12.

Attempt any five of the following :

2x5

(a)

Find the geometric mean of 3, 6, 24, 48.

(b)

For a group of 10 items Σx = 65, Σx² = 295, mode = 6, Comment on skewness

(c)

For a sample mean = 112, variance = 1600; find its CV.

(d)

AM of two numbers is 25 and their HM is 9; find their GM.

(e)

The means of samples of sizes 50 and 75 are 60 and x respectively. If the mean of the combined group is 54, find x.

(f)

Find the median of the following frequency distribution:

Value (x) :	1	2	3	4
frequency (f) :	7	12	18	4

(g)

If each of 3, 48 and 96 occurs thrice, verify that geometric mean is greater than harmonic mean.

13.

(a)

The following table shows the total cost (in 100 rupees) and its component parts in two calendar years. Draw component bar charts showing total costs and their components.

	1990	1991
Direct material Direct labour Direct expenses Overheads	80 100 16 34	90 110 24 36
Total	230	260

(b)

Represent the following data by pie diagram :

Items		Wages		Materials		Taxes		Profits		Administration
Expenses (in Rs.)		125		110		180		65		20

14.

(a)

Find the mean deviation about mean of the following distribution:

Weight (in kg)
No of persons

45-50
10

50-55
20

55-60
40

60-65
20

65-70
10

(b)

Find the mean and standard deviation of the following distribution :

Score
Frequency

:
:

0-10
5

10-20
28

20-30
40

30-40
22

40-50
5

15.

(a)

An analysis of the monthly wages paid to the workers in two firms A and B belonging to the same industry give the following result:

			Firm A		Firm B
No. of wage earners Average monthly wages Standard deviation of wages	: : :		300 Rs. 500 Rs. 100		700 Rs. 400 Rs. 120

(i)	If in firm A average monthly wage of 100 workers is Rs. 450, what is average monthly wage of other workers?
(ii)	Which firm A or B has greater variability in individual wages?

(b)

In question 15(a), find the average monthly wage and standard deviation of the wages of all the workers in two firms A and B taken together.

__________

CWA/ICWA Foundation :: Business Mathematics and Statistics Fundamentals : December 2004