Business Statistics and Operation Research in Business Question Paper’ 2021 (Held in 2022)
Gauhati University B.Com 3rd Sem CBCS Pattern
4 (SEM-3/CBCS) HG 1/HG 2
2021 (Held in 2022)
COMMERCE (Honours Generic)Â
Answer the Questions from any one Option.
OPTION – A
Paper: COM-HG-3016
(Business Statistics)Â
Full Marks: 80
Time: Three hours
The figures in the margin indicate full marks for the questions.Â
Answer Questions Nos. 1, 2, 3 and any four from the rest.
1. (a) Select the correct answer: 1×4=4
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Sum of the squares of deviations of the given set of observations from their arithmetic means is
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Maximum.Â
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Minimum.Â
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Zero.Â
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None of the above.Â
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Standard deviation is dependent on the change ofÂ
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Origin.Â
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Scale.Â
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Origin and scale.Â
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None of the above.Â
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Seasonal variations areÂ
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Short-term variations.Â
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Long-term variations.Â
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Sudden variations.Â
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Cyclical variations.Â
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Coefficient of variations is calculated by the formulaÂ
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.
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.
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.Â
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.
(b) Fill in the blanks: 1×3=3
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An index number is a special type of _______.Â
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Correlation coefficient is _______ of two regression coefficients.Â
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If A and B are mutually exclusive events, _______.Â
(c) Write True or False: 1×2=2
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An average alone is sufficient to understand the basic characteristics of a frequency distribution.Â
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Mean of binomial distribution is always greater than variance.Â
(d) What do you mean by sample? 1
2. Answer the following questions: 2×5=10
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What is estimation?
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Write two properties of correlation coefficient.Â
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Two regression coefficients in a distribution are calculated as – 1.89 and – 0.52. Is it possible? Justify your answer.Â
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Find the E(X) for the following probability distribution of X:Â
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Define skewness.Â
3. Answer any four of the following questions: 5×4=20
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What is sample survey? Write the advantages and disadvantages of sample survey.Â
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Prove that the expectation of a random variable x is equal to the arithmetic mean.Â
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Discuss briefly various problems involved in the construction of index numbers.Â
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Given the two regression equations as follows: and . Find the correlation coefficient between x and y.Â
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State the additive law of probability and explain it with an example.Â
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What do you mean by correlation between two variables? Mention different types of correlation.Â
4. (a) A study of 100 companies gives the following information:Â
Calculate mean and standard deviation of the profit earned. 3+3=6
(b) Mention the desirable properties of a good measure of dispersion. 4
5. (a) Find the coefficient of correlation between X and Y from the following data: 6
(b) What is a regression line? What purpose does it serve? When are the two regression lines identical?  2+1+1=4
6. (a) What is a binomial probability distribution? Mention the properties of this distribution. 2+4=6
(b) In a business a person can make a profit of Rs. 2,00,000 with a probability of 0.4 or have a loss of Rs. 1,00,000 with a probability of 0.6. What is his expected profit? 4
7. (a) Write the probability density function of a normal distribution. Under what conditions a binomial distribution tends to a normal distribution? 3+2=5
(b) If 5% of electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs (1) 3 bulbs will be defective and (2) none will be defective. (Given) 5
8. (a) What is time series? Explain various components of time series. 6
(b) Calculate Fisher’s price index number from the data given below: 4
9. (a) What is estimator? Write the characteristics of a good estimator. 2+4=6
(b) Explain null hypothesis and alternative hypothesis. 4
10. (a) Write the definitions of arithmetic mean, median and mode. Mention one use of each of these three measures. 6
(b) Given below the mean, median and standard deviation of two distributions. Determine which distribution is more skewed. 4
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Mean = 22
Median = 24
Standard deviation = 10
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Mean = 22
Median = 25
Standard deviation = 12
11. (a) What is cost of living index number? Discuss the importance of cost of living index number. 5
(b) A can hit a target thrice in 5 shots, B twice in 5 shots and C thrice in 4 shots. They fire a volley. What is the probability that A and B can hit the target and C cannot hit? 5
OPTION – B
Paper: COM-HG-3026
(Operation Research in Business)Â
Full Marks: 80
Time: Three hours
The figures in the margin indicate full marks for the questions.Â
Answer Questions Nos. 1, 2, 3 and any four from the rest.
1. Answer the following as directed: 1×10=10
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What is network?
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What is event?
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What is PERT?
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What is CPM?
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The word inventory means _______.Â
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Write one benefit of controlling inventory.Â
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Write one limitation of EOQ.Â
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The set of feasible solutions to an LPP is a _______ set.Â
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What is adjacent activity?
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What is ABC analysis?
2. Answer the following in short: 2×5=10
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What is the difference between ABC analysis and VED analysis?
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What is graphical method?
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Define EOQ in inventory control.Â
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When do we replace an item?
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What is shortage cost?
3. Answer any four questions: 5×4=20
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Write the concept of linear programming.Â
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Solve graphically the linear programming problem (LPP):Â
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Explain the different types of replacement models.Â
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Discuss various costs involved in inventory models.Â
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Group the items given below into an ABC classification:Â
4. Answer any four questions: 10×4=40
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XYZ leather company manufactures two types of soccer balls A and B. Each type of ball requires work by both types of employees – semi-skilled and skilled. The semi-skilled employees employ machines in the manufacture of balls while the skilled employees hand-sew the balls. The available time (per week) for each type of employee and the time requirement for each type of balls is given below:Â
The cost of an hour of semi-skilled labour is Rs. 10 and that of an hour of skilled labour is Rs. 16. To meet weekly demand requirements at least 25 balls of type A and at least 20 balls of type B must be manufactured. Formulate this problem as an LPP model to minimise the cost of production.Â
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Solve by simplex method:Â
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(1) Construct a network diagram and find the EST and LST for the following data:Â
(2) Write the benefits of replacement problem.Â
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Explain briefly the replacement of items whose maintenance cost increases with time and the value of money also changes with time.Â
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Write short notes on:Â
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Nature and characteristic of O.R.Â
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The carrying cost or storage cost.Â
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What are the costs associated with inventory? Distinguish between deterministic and stochastic model in inventory theorem. 4+6=10
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Write an explanatory note on evolution of operation research.Â
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