Download "Quantitative Techniques and Methods" Question Paper of B. Com. (Bachelor of Commerce) 4th Semester Hons. Previous Years for Students.

B. Com. - Bachelor of Commerce 4th Semester
Quantitative Techniques and Methods

Paper: BCM-406

Time Allowed: Three Hours]  [Maximum Marks: 80

Note: Attempt any FOUR.

SECTION-A

1. What do you mean by Quantitative Techniques? Discuss its important functions.

2. The mean and variance of a binomial distribution are 3 and 2 respectively. Find the probability that the variable takes values: (i) less than or equal to 2 and (ii) greater than or equal to 7.

3. Define and explain :

(i) Constraints

(ii) Optimum solution.

(iii) Feasible Region.

4. Interpolate the missing values from the following data:

5. Calculate coefficient of correlation between birth rate and death rate from the following data:

6. The lines of regression of Y on X and X on Y are respectively

Y = X +5 and 16X9Y = 94.

Find the variance of X if the variance of Y is 16.

SECTION-B

Note:- Attempt any TWO.

7. (a) Four persons are chosen at random from a group containing 3 men, 2 women and 4 children. Find the chance that exactly one of them will be children.

(b) Two balls are to be drawn one after another from an urn containing 6 white and 4 black balls. Determine the probability that both balls drawn are black if the ball selected on the first drawn is: (i) placed back into the urn, (ii) not placed back into the urn.

8. Using Poisson law of distribution, find a test for goodness of fit for the following data:

9. What is normal distribution? Discuss its properties. Bring out its importance in statistics.

10. Draw the graph of the following inequalities:

X + 2Y ≤ 8, 3X + Y ≤ 12, X + Y ≤5

and X 0 and Y ≥ 0.

Also indicate the common region.

SECTION-C

Note:- Attempt any TWO.

11. The following table shows the output and input related to a certain product. Interpolate the input for output at 42.

12. The following table gives the distribution of items and relatively defective items among them according to size groups:

13. Following information regarding X and Y variables is given :

Calculate:-

(i) Regression co-efficients,

(ii) The two regression equations, and

(iii) Coefficient of correlation.

14. Write notes on the following:-

 (a) Explain the usefulness of interpolation and extrapolation in business.

(b) Explain the properties of correlation coefficient.

(c) What is the relationship between correlation and regression coefficients?