1
ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – OCTOBER 2013
BBM – I SEMESTER
BUSINESS MATHEMATICS AND STATISTICS
Time : 3 HOURS Max. Marks : 100
SECTION – A
I) Answer ALL the questions. (10x 2 = 20)
1) Solve: (2x-7)(3x+1)=(2x-5)(3x-1).
2) Find the Simple interest on Rs. 17,000 for 3 months at 4% P.a.
3) Define Statistics.
4) Mention any 4 applications of statistics.
5) Arun can do a piece of work in 8 days, which Bala alone can do in 10 days. In
how many days both working together can do it?
6) Ramesh, Mohan and Chandra start a business jointly. Twice the investment of
Ramesh is equal to thrice the capital of Mohan and the capital of Mohan is four
times the capital of Chandra. Find the share of Mohan in an annual profit of
2,97,000.
7) A reduction of 20% in the price of sugar enables a man to purchase 4 kg more of
Rs. 280. What is the original rate and what is the reduced rate?
8) Solve x2-6x-72=0.
9) A company needs Rs. 10,00,000 at the end of 5 years from now. It would like to
set aside equal amount each year out of its profits. If the present market rate of
interest is 16%. How much of annual amount should be invested?
10) How is the value of r in Karl Pearson’s coefficient of correlation interpreted?
SECTION – B
II) Answer ANY FOUR of the following. (4×5=20)
11) Describe the characteristics of statistics.
12) Explain the limitations and scope of Statistics.
13) The following are heights in centimetres of 40 students. Form the frequency
distribution with appropriate class interval. 163.3, 155.0, 163.9, 163.9, 148.2, 151.5,
178.9, 155, 146.1, 145.2, 156.6, 159.9, 158.0, 153.4, 160.0, 149.3, 154.2, 164.7, 159.0,
160.8, 157.1, 176, 164.4, 170.0, 152.9, 169.3, 159.5, 162.4, 173.6, 154.8, 158.3, 172.5,
158.0, 154.0, 172.2, 148.0, 152.4, 156.6, 157.7, 165.3
2
14) Locate the Median and Quartiles from the following data.
Size of
shoes
Frequencie
s
4 20
4.5 36
5 44
5.5 50
6 80
6.5 30
7 30
7.5 16
8 14
15)A sum of Rs.8448 is divided between 2 persons A and B who are respectively 18 years
and 19 years old in such a way that their shares be invested at 6.25% per annum
compound interest. They shall receive equal amount on attaining the age of 21 years.
How should the sum be divided. How much will each receive when 21 years old?
16)Draw a histogram from the following and locate the mode. verify it by actual
calculations.
Class
Interval
Frequencies
0-10 14
10-20 23
20-30 35
30-40 20
40-50 8
50-60 5
SECTION -C
III) Answer ANY THREE of the following questions. (3×15=45)
17) a) Explain the functions of Statistics?
b) Describe the uses of Statistics?
18) a) Following are the runs scored by 2 batsmen in 10 innings. Find who is a
better scorer and who is more consistent.
Player1-101, 22, 0, 36, 82, 45,7,13, 65, 14
Player2- 97, 12, 40, 96, 13,8, 85 ,8, 56,16.
3
b) Draw Ogives from the following data and measure the median value. verify it by
actual calculations.
Mid point: 5 15 25 35 45.
Frequency: 5 11 21 16 10.
19) The life of 2 types of tyres in a sample survey is given below.
Life
(kms)
Number of
Tyres of Type
A
Number of
Tyres of
Type B
5000-10000 10 18
10000-15000 18 22
15000-20000 32 40
20000-25000 40 32
25000-30000 22 18
30000-35000 18 10
a) Which of the 2 makes has a higher average life?
b) If prices are same for both the types, which type would you prefer and why?
20) The competitors of a beauty contest were ranked by 3 judges as follows:
Judge A: 3 5 4 10 8 8 1 6 8 2
Judge B: 5.5 5.5 1 8.5 4 10 2 7 8.5 3
Judge c: 9 9 7 5 2 2 2 5 5 9
21) a) The following data relates to the ages of husbands and wives.
Age of the
Husband : 25 28 30 32 35 36 38 39 42 55
Age of wife: 20 26 29 30 25 18 26 35 35 46.
Obtain the two regression equations and determine the most likely age of
husband for the age of wife of 25 years.
b) Define and explain the different types of Annuity.
22) a) Compute the mean runs scored by a batsman from the following data.
Runs Scored: 10 20 30 40 50 60 70 80 90
Number of : 7 8 15 25 30 20 16 7 2.
Batsmen
4
b) Represent the following data in a suitable diagram
Newspaper Daily
Sales
Times of India 1432000
Deccan Herald 1431000
Indian Express 1327000
Asian Age 1119000
Hindustan times 894000
6.3) if the mean of a set of scores is 20, median is 22.Find the mode?
SECTION – D
IV) Compulsory question. (15 marks)
23) a) Compute the Karl Pearson’s coefficient of correlation between per capita
national income and per capita consumer expenditure from the data given
below. (8 marks)
Year
Per
capita
National
Income
Per capita
consumer
expenditure
1978 249 237
1979 251 238
1980 248 236
1981 252 240
1982 258 245
1983 269 255
1984 271 254
1985 272 252
1986 280 258
1987 275 251
b) LIC offers a special annuity scheme called the Jeevan Dhara scheme. One of
the options in this scheme is as follows. If a lump sum amount is paid now,
the LIC will pay an annuity of Rs.12000 commencing from the end of 1st year
till the person’s death. Assuming that LIC allows 9% P.a rate of interest and
the person’s life expectation is 15 years, how much should be deposited in
lump sum now. (7 marks)
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Latest Govt Job & Exam Updates: