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. 

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

Or

2. (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

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

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

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

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

Or

2. (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

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

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