## 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

If, then the value ofis .

Derivative of a constant is zero.

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

______ is regarded as the best measure of central tendency.

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

______ correlation deals with qualitative characteristic.

Correlation coefficient is the ______ of two regression coefficient.

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

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

(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

(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) 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) 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) 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

(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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