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Quantitative Techniques

Section A: Objective Type & Short Questions (30 Marks)

Part One:

Multiple Choices:

1. The value of 3n+4 –  6.3n+1  is
2. 27.3n+1 b. 21.3n-1 c. 21.3n+1 d. 27.3n-1 e. 21.3-n-1
3. The value of x which satisfies the question x/2-x/4=x-9 is
4. 12 b. 14 c. 16 d. 18 e. 20
5. The sum of 5ax-7by+cz and ax+2by-cz is
6. 6ax+5by b. 6ax-5by c. 6ax+5by-2cz d. 6ax-5by-cz e. 6ax-5by+2cz.
7. The product of 3x-5 and 2x+7 is
8. 6×2-11x-35 b. 6×2-11x+35 c. 6×2+11x-35 d. 6×2 +10x-35 e. 6×2+11x+35
9. The 37th term in the series -2.8, 0, 2.8,…. Is
10. 98 b. 89 c. 87 d. 78 e. 68
11. The sum of the series 14, 64, 114, … to 20 terms is
12. 7890 b. 8970 c. 9780 d. 10820 e. 10920
13. The last term in the series 2, 4, 8, … to 9 terms is
14. 612 b. 512 c. 412 d. 312 e. 212
15. If an unbiased coin is tossed 3 times then the probability that at least one head occurs is
16. 0.875 b. 0.5 c. 0.375 d. 0.125 e. 0.1.
17. Again in continuation with the above question the probability that 3 heads result is
18. 0.100 b. 0.125 c. 0.250 d. 0.500 e. 0.875
19. The line y=5-10x cuts the y axis at_________ and has slope________
20. (0,10), -5 b. (0,-10), 5 c. (0,5), -10 d. (0,-5), 10 e. (0,5), 10
21. If y=F(x) is the equation of a line then the slope at (5,2) is given by
22. F‟(2) b. F‟(5) c. F(2) d. F(5) e. None of the above
23. Slope of the line passing through the points (4,4) and (5,5) is
24. 1 b. 9 c. 1/9 d. 20 e. 1/20
25. An „Ogive‟ is
26. A graph of ungrouped data b. A graph of grouped data c. A graph of cumulative frequencies d. A graph of ranges of fractiles e. A graph with rectangles as opposed to a line graph.
27. If p=3×4 + 9xy + y3 then ∂p/∂y is given by
28. 12×3+9x b. 12×3+9x+3y2 c. 9x+3y2 d. 9y+3y3 e. 12×3+9y+3y2
29. For a function f(x), f‟(x)=0 at x=a then „a‟ is a point of minima if
30. F(a)<0 b. F(a)=0 c. F‟‟(a)=0 d. F‟‟(a)< 0 e. F‟‟(a)>0
31. The function 2×2 + 3x +2 has a
32. Maximum value at x = – 3/4 b. Minimum value at x = – 2 c. Maximum value at x = -3/2 d. Minimum value at x = -3/4 e. The equation has no maxima and minima.
33. The probability of getting exactly 3 heads in four tosses of a fair coin is
34. 1/2 b. 1/4 c. 1/8 d. 1/10 e. 1/16
35. In multiple regression, the number of normal equations will be
36. Two b. Three c. One d. More than three e. More than or equal to three
37. The index of industrial production is an example of
38. Price index b. Value index c. Quality index d. Relative index e. Industrial production index
39. As the sample size is increased, the standard error of the mean would
40. Increase b. Decrease c. Remain unchanged d. May or may not increase e. The value of sample mean would be lot closer of population mean

Part Two:

1. What do you understand by „Infeasibility‟ of the solution?
2. Write about „Big – M‟ method for minimization.
3. Write about the „Classical Economic Order Quantity (EOQ) models.
4. Write a short note on „Interfering Float‟.

Section B: Practical Problems (40 marks)

1. A car retailer thinks that a 40,000 mile claim for tire life by the manufacturer is too high. She carefully records the mileage obtained from a sample of 64 such tires. The mean turns out to be 38,500 miles. The standard deviation of the life of all tires of this type has previously been calculated by the manufacturer to be 7,600 miles. Assuming that the mileage is normally distributed, determine the largest significance level at which we should accept the manufacturer’s mileage claim, that is, at which we would not conclude the mileage is significantly less than 40,000 miles.

1. Consider the following data:
 Output                                                                           Total Cost            (in lakhs of units)                                                          (in lakhs of rupees)                     5                                                                                              140 7                                                                                              155 9                                                                                              170 11                                                                                              180 14                                                                                              200 17                                                                                              230 20                                                                                              240 22                                                                                              260 24                                                                                              275 28                                                                                              310

Identify the fixed and variable cost components using the least squares method.

Section C: Applied Theory (30 marks)

1. In a recent survey, senior company executives in five metros has ranked two former finance ministers Mr. Manmohan Singh and Mr. P. Chindambaram as first and second and the present finance minister Mr. Yashwant Sinha in third position as regarding their popularity. In this, an example of sampling survey? Discuss about necessity of sampling and the different methods of sampling?

1. “Index numbers are an indispensable tool in day to day life. Comment. Also, explain with examples how index numbers provide a summary measurement of movements of a large number of economic variables. Is there a possibility that, their method of computation could give a distorted picture of reality?