Business Mathematics and Statistics Question Paper' 2021 (Held in 2022), Dibrugarh University B.Com 2nd Sem Non Hons

 2 SEM TDC BMS (CBCS) DSC CC 203 (BL)

2021 (Held in January/February, 2022)
COMMERCE (Discipline Specific Course)
(For Non-Honours)
Paper: CC-203 (Business Mathematics and Statistics)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions. 

PART – A

(Business Mathematics)

(Marks: 32)

1. Write True or False: 1x3=3

  1. If, then the value ofis .

  2. Derivative of a constant is zero. 

  3. Simple interest on Rs. 500 at 4% p.a. for 30 months is Rs. 50.

2. If , and , find matrixsuch that.       3

3. If, then find. 6

Or

If, then prove that

4. Find the value of. 3

5. Find, if. 6

Or

If, then prove that

6. Distinguish between nominal rate of interest and effective rate of interest with suitable example. 5

7. Compound interest on a sum for 2 years is Rs. 920.25. Simple interest on the sum for the same time is Rs. 900. Find the sum and rate of interest. 6

Or

Find the nominal rate of interest percent p.a. interest payable half-yearly which is equivalent to the effective rate of 4% p.a. 

PART – B

(Business Statistics)

8. Fill up the gaps: 1x5=5

  1. ______ is regarded as the best measure of central tendency. 

  2. For a symmetrical distribution, values of mean, median and mode are ______. 

  3. ______ correlation deals with qualitative characteristic. 

  4. Correlation coefficient is the ______ of two regression coefficient. 

  5. The index number for the base year is taken as ______. 

9. Answer either (a) or (b): 

  1. (1) In a moderately asymmetrical distribution, mode and mean are 32.1 and 35.4 respectively. Find the median. 

(2) Which measure of variation is regarded as the best and why? 3+5

(3) Calculate the standard deviation for the following data: 6

Wages (in Rs.)

No. of man

0 and above

20 and above 

40 and above 

60 and above 

80 and above 

100 and above 

50

45

34

16

6

0

Or

  1. (1) Prove that for any two positive numbers, . 3

(2) State the characteristics of a good measure of variation. 5

(3) The mean and standard deviation of 100 observations are 50 and 5, and that of another 150 observations are 40 and 6 respectively. Find the combined standard deviation of this 250 observations. 6

10. Answer either (a) or (b):

  1. (1) What are the properties of the two regression coefficient? 3

(2) Prove that Karl Pearson’s coefficient of correlation is independent of change of origin and scale of measurement. 5

(3) Calculate the coefficient of correlation from the following data: 6

Or

  1. (1) Distinguish between Karl Pearson and Spearman correlation coefficient. 3

(2) Calculate the coefficient of rank correlation from the data given below: 5

X:

48

33

40

9

16

65

24

18

44

20

Y:

13

10

24

6

15

4

20

9

10

19


(3) Derive the regression equation of X on Y from the following data: 6

X:

35

42

20

50

72

64

Y:

40

48

24

60

84

68


11. Answer either (a) or (b): 

  1. (1) If the annual trend equation of a time series be(origin = 1990, t unit = 1 year), find the trend line equation with 1995 as origin. 3

(2) What are the uses of index number? 5

(3) Using Fisher’s formula calculate quantity index number from the data given below: 7

Item

2017

2019


Price (in Rs.)

Quantity

Price (in Rs.)

Quantity

A

B

C

D

E

5

3

4

11

7

50

100

60

30

40

10

4

6

14

10

56

120

60

24

36


Or

  1. (1) What do you understand by secular trend? What are the factors responsible for trend in a time series?     3

(2) Estimate trend values by using 4-yearly moving average for the following data: 5

Year

Profit

2011

2012

2013

2014

2015

2016

2017

2018

60

46

53

54

48

48

42

51


(3) Using the method of least square, calculate the trend values for the data given below: 7

Year: 

2001

2002

2003

2004

2005

2006

Sales: 

60

72

75

65

80

85

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