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Wednesday, January 5, 2022




B. Com 4th Semester
Quantitative Techniques and Methods
Paper: BCM-406


Time Allowed: Three Hours] [Maximum Marks: 80




SECTION-A


Note: Attempt any four. 

1. Explain what do you understand by Quantitative techniques. Discuss its scope and limitations.


2. There are two series with 5000 lottery tickets in each. There is only one prize of Rs. 3000 and tickets are sold at Rs. 2 each. A person buys two tickets. What will be his expected gain if he buys:

(a) one ticket of each series, 

(b) two tickets of the same series?


3. A book contains 100 misprints distributed randomly throughout its 100 pages. What is the probability that a page observed at random contains at least two misprints? Assume Poisson Distribution.



4. Interpolate by the curve fitting method the quantity supplied for the price Rs. 5 and extrapolate for Rs. 7 

Price in Rs.                                   2  4  6

Quantity Supplied in ton            8  15  35



5. What are the advantages and limitations of Karl Pearson's coefficient correlation?



6. Compute the coefficient of multiple linear correlations of X3 on X2 and X1 from the given data.


X1 3 5 6 8 12 14 

X2 16 10 7 4 3 2 

X3 90 72 54 42 30 12



SECTION-B


7. Note: Attempt any two. 

&. Write short notes on


(i) Binomial distribution

(ii) Poisson distribution.



8. A certain factory manufacturing razor blades, there is a small balance 1/50 for any blade to be defective. The blades are placed packet, each containing 10 blades. Using the Poisson distribution, calculate the approximate number of packets containing not more a 2 defective blades in a consignment of 10,000 packets.


9. Discuss the various classes of problems for which solutions can obtained using linear programming techniques.


10. A manufacturer of toothpaste has three plants located in Amritsar,

Bhopal and Jalgaon. Major distribution warehouses are located at Noida, Kanpur, Raipur, Patna, and Thane. Sales requirements from each of the warehouses for the next year are given in the table below: 




SECTION-C


Note: Attempt any two. 

11. Given below are some concepts. Explain these using graph to illustrate each concept 

(a) Perfect positive linear correlation 

(b) Nonlinear correlation 

(c) Perfect negative correlation

(d) Spurious correlation.



12. Calculate the coefficient of correlation between age and sum assured from the data given below and comment on the value




13. Distinguish between simple linear regression and multiple linear regressions. Describe the steps involved in the process of multiple regression.

14. Ishwinder, owner of a business unit, is concerned about the sales behaviour of his product. He narrates that there are many factors that might help explain sales but believes that advertising and process are major determinants. He has collected the following data: 

Sales (unit sold)                 33 61 70 82 17 24 
Advertising                        (No. 3 6 10 139 6 of ads.) 
Prices (Rs)                         125 115 140 130 145 140 


(a) Calculate the regression equation to predict sales from advertising and price. 

(b) If advertising is 7 and the price is Rs 132, what sales would you predict?





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