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Topic:- OR MPHIL S2N

1. Let the feasible region of a linear programming problem be given by a polyhedral set P = {X ∈ Rⁿ: AX = b, X ≥ 0, b ≥ 0} Then the problem has a bounded feasible region, if there exists ______ such that for every X ∈ P, we have ______

   [Question ID = 11062]

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   1. a positive constant M, |X| ≤ M
   2. a positive constant M, |X| = M
   3. a negative constant M, |X| = M
   4. a negative constant M, |X| ≥ M

   Correct Answer :-

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   • a positive constant M, |X| ≤ M

2. In R³, a polytope has ______ like shape.

   [Question ID = 11063]

   1. circle

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   2. triangle
   3. prism
   4. ellipse

   Correct Answer :-

   • prism

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3. The vertices of a bounded closed set may be ______

   [Question ID = 11064]

   1. finite
   2. infinite

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   3. indefinite
   4. countable

   Correct Answer :-

   • infinite

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4. The redundant constraint among the constraints x₁-x₂ + 2x₃ = 4, 2x₁ + x₂ - x₃ = 3, 5x₁ + x₂ = 10, x_j ≥ 0, j = 1,2,3 is

   [Question ID = 11065]

   1. x₁ - x₂ + 2x₃ = 4
   2. 2x₁ + x₂ - x₃ = 3
   3. 5x₁ + x₂ = 10

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5. The dual problem of the primal linear programming problem max z = 4x₁ - 3x₂ s.t. x₁ - x₂ ≤ 1, -x₁ + x₂ ≤ -2, x₁ ≥ 0, x₂ ≥ 0 has ______

   [Question ID = 11066]

   1. a feasible solution
   2. no feasible solution

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   3. a unique solution
   4. unbounded solution

   Correct Answer :-

   • no feasible solution

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6. Applications of assignment problem may include

   [Question ID = 11067]

   1. matching personnel to jobs
   2. assigning machines to tasks
   3. designing buses routes

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   4. all of these

   Correct Answer :-

   • all of these

7. The transportation method assumes that ______

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   [Question ID = 11068]

   1. the number of occupied cells in any solution must be equal to the number of rows plus the number of columns plus 1
   2. the number of dummy sources equals the number of dummy destinations
   3. there are no economies of scale if large quantities are shipped from one source to one destination
   4. none of these

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   Correct Answer :-

   • there are no economies of scale if large quantities are shipped from one source to one destination

8. In a balanced transportation problem with two sources and three destinations and availabilities 15 at each source and demand 10 at each destination, the dual variables in the optimal table corresponding to sources and destinations are 1, -2 and 1, 1, 1, respectively. Then the optimal objective value of the transportation problem is

   [Question ID = 11069]

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   1. 45
   2. 20
   3. 10
   4. 15

   Correct Answer :-

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   • 15

9. The linear programming problem max z = 2x₁ + 3x₂ s.t. x₁ + x₂ ≥ 4, x₁ - x₂ ≤ 2, x₁ ≥ 0, x₂ ≥ 0 has

   [Question ID = 11070]

   1. alternate optimal solution

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   2. unique optimal solution
   3. unbounded solution
   4. none of these

10. The stationary point of the function f(x) = 2 + 2x₁ + 3x₂ - x₁² - x₂², X = (x₁,x₂) ∈ R² is ______

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    [Question ID = 11071]

    1. local maximum
    2. local minimum
    3. neither a local maximum nor a local minimum
    4. none of these

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    Correct Answer :-

    • local maximum

11. The function f(x) = x₁² + (x₂-x₃)², X = (x₁,x₂,x₃) ∈ R³ is ______

    [Question ID = 11072]

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    1. positive definite
    2. negative definite
    3. positive semi-definite
    4. negative semi-definite

    Correct Answer :-

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    • positive semi-definite

12. The solution to the dual linear programming problem ______

    [Question ID = 11073]

    1. presents the marginal profits/costs of each additional unit of a resource

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    2. can always be derived by examining the z_j row of the primal problem's optimal simplex tableau
    3. is better than the solution to the primal problem
    4. all of these

    Correct Answer :-

    • presents the marginal profits/costs of each additional unit of a resource

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13. Which of the following is not a direct inventory?

    [Question ID = 11074]

    1. Work-in-process inventories
    2. Spare parts inventories

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    3. Waste inventories
    4. Fluctuation inventories

    Correct Answer :-

    • Fluctuation inventories

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14. Jessica Choi works in her bakery for 6 days a week for 49 weeks a year. Flour is delivered directly with a charge of Rs. for each delivery Jessica uses an average of 10 sacks of whole-grain flour a day, for which she pays Rs. 12 a sack. She estimates her inventory holding cost at 15 per cent a year, with spillage, storage, loss and insurance costing 6.75 per cent. What size pick delivery should Jessica use?

    [Question ID = 11075]

    1. 160 units
    2. 140 units
    3. 142 units

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    4. none of these

    Correct Answer :-

    • 140 units

15. ______ are of the nature, if they are not available, they will not stop the system from working nor they reduce the efficiency of the system.

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    [Question ID = 11076]

    1. Vital items
    2. Essential items
    3. Important items
    4. Desirable items

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    Correct Answer :-

    • Desirable items

16. The ordering cost is Rs. 10 per order for a certain type of commodity whose holding cost per unit is Rs. 2 per year. If the annual demand is 4,000 units and the replacement is instantaneous and no shortages are allowed then the EOQ is

    [Question ID = 11077]

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    1. 200 units
    2. 800 units
    3. 550 units
    4. 450 units

    Correct Answer :-

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    • 200 units

17. A producer has to supply 12,000 units of a product per year to his customer. The demand is fixed and known and shortages are not allowed. The inventory holding cost is Rs.0.20 per unit per month and the set up cost per run is Rs. 350. The optimum scheduling period is

    [Question ID = 11078]

    1. 1.87 month

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    2. 1.5 month
    3. 2 month
    4. 1 month

    Correct Answer :-

    • 1.87 month

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18. The common basic queuing models assume that arrival rate follows the ______ and that service times follow ______

    [Question ID = 11079]

    1. Poisson distribution, negative exponential distribution
    2. normal distribution, Poisson distribution

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    3. Poisson distribution, exponential distribution
    4. Beta distribution, normal distribution

    Correct Answer :-

    • Poisson distribution, negative exponential distribution

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19. A product manufacturing plant at a city distributes its products by trucks, loaded at the factory warehouse. It has its own fleet of trucks plus trucks of a private transport company. This transport company has complained that sometimes its trucks have to wait in line and thus the company loses money paid for a truck and driver of waiting truck. The company has asked the plant manager either to go in for a second warehouse or discount prices equivalent to the waiting time. The data available is: Average arrival rate of all trucks = 3 per hour, Average service rate = 4 per hour. The transport company has provided 40% of the total number of trucks. Assuming that these rates are random according to the Poisson distribution, the expected waiting time of company trucks per day is ______

    [Question ID = 11080]

    1. 7.2 hours per day
    2. 5 hours per day
    3. 3 hours per day

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    4. 7 hours per day

    Correct Answer :-

    • 7.2 hours per day

20. A company is analyzing the following list of service rates (customers/hour) for one of its servers as 5, 9, 4, 6, 5, 4, 8, 7. Then mean service time for this server

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    [Question ID = 11081]

    1. 0.22 minutes
    2. 10.71 minutes
    3. 11.33 minutes
    4. 4.5 minutes

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    Correct Answer :-

    • 10.71 minutes

21. Consider the case when several customers may collaborate and only one of them may stand in the queue. Such a customer behavior can be classified as ______

    [Question ID = 11082]

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    1. Balking
    2. Jockeying
    3. Collusion
    4. none of these

    Correct Answer :-

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    • Collusion

22. Assume that system failure rate (λ) = 0.005 failures per hour, rate of system down for preventive maintenance (λ_p) = 0.008 per hour, system repair rate (μ) = 0.009 repairs per hour, and rate of system preventive maintenance performance (μ_p) = 0.009 per hour. The system steady state availability is ______

    [Question ID = 11083]

    1. 41%

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    2. 40%
    3. 50%
    4. 51%

    Correct Answer :-

    • 41%

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23. A system was observed over a period of time and the following data is obtained: downtime per breakdown or failure (T_b = 0.1 month), downtime per inspection (T_i = 0.05 month), a constant associated with the system (c=3). The optimal number of inspections per month is

    [Question ID = 11084]

    1. 2
    2. 1

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    3. 1.5
    4. 0

    Correct Answer :-

    • 2

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24. The constant part of the bath-tub hazard rate called as the "useful period" begins just after the ______ and ends just before the ______

    [Question ID = 11085]

    1. infant mortality period, wear-out period
    2. debugging period, break-in period
    3. burn-in period, debugging period

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    4. break-in period, wear-out period

    Correct Answer :-

    • infant mortality period, wear-out period

25. Let the reliability of a system is defined by R(t) = e^-λt where λ = 0.0004 failures per hour. Then the Mean time to Failure (MTTF) is

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    [Question ID = 11086]

    1. 2500 hours
    2. 2400 hours
    3. 2300 hours

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26. The probability of Mr. X living 20 years more is 1/5 and that of Mr. Y is 1/7. Then the probability that at least one of them will survive 20 years hence is ______

    [Question ID = 11087]

    1. 12/35
    2. 1/35
    3. 11/35

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    4. 13/35

    Correct Answer :-

    • 11/35

27. For the given mid values 25, 34, 43, 52, 61, 70, the first class of the distribution is ______

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    [Question ID = 11088]

    1. 24.5-34.5
    2. 25-34
    3. 20-30
    4. 20.5-29.5

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    Correct Answer :-

    • 20.5-29.5

28. Which of the following example does not constitute an infinite population?

    [Question ID = 11089]

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    1. Population consisting of odd numbers
    2. Population of weights of newly born babies
    3. Population of heights of 15-year old children
    4. Population of heads and tails in tossing a coin successively

    Correct Answer :-

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    • Population of heights of 15-year old children

29. The mean produce of wheat of a sample of 100 fields is 200 lbs per acre with a standard deviation of 10 lbs. Another sample of 150 fields gives the mean of 220 lbs with a standard deviation of 12 lbs. The two samples have been taken from the same population whose standard deviation is 11 lbs. The test statistic z is ______

    [Question ID = 11090]

    1. -14.08

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    2. 14.08
    3. 14.52
    4. -14.52

    Correct Answer :-

    • -14.08

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30. The average score in an aptitude test administered at the national level is 80. To evaluate a state's education system, the average score of 100 of the state's students selected on random basis was 75. The state wants to know if there is a significant difference between the local scores and the national scores. In such a situation the null hypotheses may be stated as under:

    [Question ID = 11091]

    1. H₀: μ ≠ 75
    2. H₀: μ > 80

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    3. H₀: μ < 75
    4. H₀: μ = 80

    Correct Answer :-

    • H₀: μ = 80

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31. In a survey, 500 consumers were contacted states that 64 per cent of all consumers of a certain product were motivated by the product's advertising. Then the lower confidence limit for the proportion of consumers motivated by advertising in the population, given 0.95 (corr

    [Question ID = 11092]

    1. 52.24%
    2. 75.76%
    3. 50.42%

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    4. 45.21%

    Correct Answer :-

    • 52.24%

32. In a random selection of 64 of the 2400 intersections in a small city, the mean number of scooter accidents per year is 3.2 and the sample standard deviation is 0.8. Then the standard error of mean for this finite population is ______

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    [Question ID = 11093]

    1. 0.097
    2. 0.08
    3. 0.064
    4. 0.001

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    Correct Answer :-

    • 0.097

33. In case of bivariate population, Correlation can be studied through ______

    [Question ID = 11094]

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    1. coefficient of correlation
    2. coefficient of partial correlation
    3. cross tabulation
    4. none of these

    Correct Answer :-

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    • cross tabulation

34. Kurtosis is the measure of ______ of a curve.

    [Question ID = 11095]

    1. flat-toppedness

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    2. skewness
    3. symmetry
    4. non-symmetry

    Correct Answer :-

    • flat-toppedness

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35. If the marital status of individuals is recorded as a nominal data using numbers 1,2,3, or 4, then which of following operations are valid for marital status?

    [Question ID = 11096]

    1. 4 > 2 or 3 < 4
    2. 3-1 = 4-2

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    3. 4 ÷ 2
    4. none of these

    Correct Answer :-

    • none of these

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36. Consider a population of size N = 9000 divided into two strata of size 6000 and 3000, respectively. If we draw a sample of size n = 30, then the proportion of population included in these strata are

    [Question ID = 11097]

    1. 20 and 10
    2. 9 and 21
    3. 15 and 15

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    Correct Answer :-

    • 20 and 10

37. ______ are the random variations in the sample estimates around the true population parameters.

    [Question ID = 11098]

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    1. Sampling errors
    2. Sampling size
    3. Sampling biases
    4. Natural biases

    Correct Answer :-

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    • Sampling errors

38. ______ concerns with the question of how many items are to be observed and how the information and data gathered are to be analyzed.

    [Question ID = 11099]

    1. The statistical design

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    2. The observational design
    3. The operational design
    4. The sampling design

    Correct Answer :-

    • The statistical design

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39. ______ refers to consistency and authenticity in responses.

    [Question ID = 11100]

    1. Validity
    2. Objectivity

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    3. Reliability
    4. Generalization

    Correct Answer :-

    • Reliability

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40. Most of the survey types of research designs are ______

    [Question ID = 11101]

    1. one-time research
    2. simulation research
    3. interventional research

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    4. analytical research

    Correct Answer :-

    • one-time research

41. The ethical issues involved in formulating a research problem include ______

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    [Question ID = 11102]

    1. the study population may be adversely affected by some of the questions
    2. the study population may expected to be simply experimental 'guinea pigs'
    3. the study population may expected to share sensitive and private information
    4. all of these

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    Correct Answer :-

    • all of these

42. For any investigation, the selection of an appropriate ______ is crucial in enabling a researcher to arrive at valid findings, comparisons and conclusions.

    [Question ID = 11103]

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    1. research design
    2. research methodology
    3. research question
    4. none of these

    Correct Answer:-

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    • research design

43. Quantitative research focuses on ______

44. From the view point of application, the research can be broadly categorized as ______

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    [Question ID = 11105]

    1. pure and applied
    2. qualitative and quantitative
    3. descriptive and explanatory
    4. exploratory and correlational

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    Correct Answer :-

    • pure and applied

45. Which of the following is not a random sampling technique?

    [Question ID = 11106]

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    1. Purposive sampling
    2. Stratified sampling
    
    

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